Machine perfusion distribution across clinical phenotypes in kidney transplantation: A national cohort study using unsupervised clustering

Abstract

BACKGROUND

Unsupervised machine learning identifies clinically meaningful subgroups across biomedical domains, yet remains underutilised in transplantation. Existing machine perfusion (MP) machine learning research relies on small cohorts with supervised models of variable performance, rarely investigating multivariate phenotypes integrating donor-recipient characteristics. Unsupervised methods can uncover latent phenotypes in high-dimensional data, revealing favourable-outcome groups and high-risk profiles overlooked by current scoring systems. Applying these methods to United Kingdom MP data may yield novel insights from the underexplored National Health Service Blood and Transplant (NHSBT) dataset. We hypothesised that MP cases occupy preferential positions within data-derived clinical phenotypes from unsupervised clustering, and these phenotypes retain structural stability and outcome stratification in the MP subgroup.

AIM

To evaluate whether MP cases are non-randomly distributed across unsupervised clinical clusters and whether MP status modifies cluster structure or outcome stratification.

METHODS

We analysed the standard NHSBT kidney dataset comprising all United Kingdom adult kidney transplants from 2014 to 2024. The full cohort had 15904 cases and a machine-perfused subgroup of 544. Dimensionality reduction was conducted using a mixed-type principal component analysis embedding approach (FAMD-like) to generate a shared latent space for all features. Gaussian mixture model was fitted to the full cohort to define latent phenotypes, and then transferred to the MP subgroup. We performed descriptive post hoc characterisation of the cluster and assessed graft and patient survival outcomes.

RESULTS

Six distinct clinical phenotypes were identified with moderate-to-good stability. MP cases showed non-random distribution, with notable enrichment in cluster 6 (40% of MP patients) and differential perfusion-type associations (hypothermic MP: Clusters 3, 5, 6; normothermic MP: Clusters 1, 4). When applied to the MP subgroup, cluster definitions remained stable, though with modestly reduced assignment confidence (mean entropy 0.815 vs 0.783), indicating MP cases are embedded within the general population structure. Clusters retained outcome stratification in the MP subgroup, though outcome patterns diverged in specific phenotypes: Cluster 2 showed concentrated early graft failures (all within 2.07 years), while cluster 4 had lower patient survival despite stability in the full cohort. These findings suggest MP status may interact with underlying clinical phenotypes to modify outcome trajectories.

CONCLUSION

MP cases showed non-random cluster distribution and perfusion-type associations. Cluster structure remained stable with retained outcome stratification in the MP subgroup, though outcome patterns differed in specific phenotypes.

Key Words: Kidney transplant; Hypothermic machine perfusion; Normothermic machine perfusion; Machine learning; Clustering; Phenotype

Core Tip: Using unsupervised clustering, we identified latent clinical phenotypes that demonstrated a non-random distribution of machine perfusion (MP) across the population. MP cases were notably concentrated within specific clusters, while the overall cluster structure remained mostly stable when focusing solely on MP recipients. This indicates that MP is integrated within the wider phenotypic landscape rather than creating distinct subgroups. Importantly, these phenotypes continued to hold outcome patterns within the MP cohort, although some varied among certain clusters. These findings suggest that MP interacts with the underlying profiles of recipients and donors, potentially altering outcome trajectories depending on the specific phenotype.

INTRODUCTION

Machine learning is increasingly used to identify clinically meaningful subgroups across biomedical domains, yet its application in transplantation remains limited[1-4]. Existing work on machine perfusion (MP) as an organ preservation, assessment and reconditioning modality relies mainly on small or moderate cohorts, employs supervised prediction models with variable performance, and rarely investigates multivariate perfusion features[5-11]. Although prior studies show that perfusion metrics can inform risk stratification, they do not derive clinically interpretable phenotypes integrating donor and recipient information[5]. Unsupervised methods offer the ability to uncover latent phenotypes in high-dimensional data without predefined labels, revealing groups associated with favourable outcomes as well as hidden high-risk profiles overlooked by current scoring systems[12,13]. Although a few clustering studies are starting to emerge in transplantation, they are not aimed at MP cases[14-20]. Applying these methods to United Kingdom MP data may yield novel insights from the underexplored National Health Service Blood and Transplant (NHSBT) dataset. To our knowledge, this is the first study to evaluate whether MP cases occupy preferential positions within data-derived clinical phenotypes from unsupervised clustering, and whether these phenotypes continue to differentiate patients with distinct outcome trajectories within the MP subgroup.

MATERIALS AND METHODS

Data source and study population

This study analysed the standard kidney dataset from the high-dimensional NHSBT database, which includes information on all kidney transplant events in the United Kingdom. We focused on adults aged 18 to 70 who received a kidney-only transplant from donation after brain and circulatory death (donation after brain death and donation after cardiac death) during the period from 2014 to 2024. Cases with missing or unreported preservation modality were excluded. The resulting analytical cohort comprised 15904 kidney transplants, of which 544 involved MP and formed the MP subgroup. Data access was granted after de-identification and the necessary ethical approvals by the NHSBT through the national research pathway.

In this retrospective observational study, we adopted a two-stage analytical strategy to interrogate the relationship between MP status and the underlying phenotypic structure of the full cohort (n = 15904). First, we applied dimensionality reduction and unsupervised clustering to the full cohort to derive latent groups based on mixed-type clinical, demographic, and transplant-related features from donors and recipients, independent of outcome information. We then transferred this learned clustering framework to a clinically defined MP subgroup (n = 544) to examine how these individuals are situated within the broader population-derived structure. Specifically, we investigated whether patients with MP preferentially localise to particular clusters or are diffusely distributed, and whether restricting the analysis to the MP subgroup alters the stability, composition, or clinical relevance of these clusters, including their association with survival outcomes.

Variable selection and data preprocessing

Categorical and numerical features were appropriately cleaned and formatted. Some features were engineered for better modelling while keeping clinical significance (e.g. deprivation group by quartiles)[21-23]. Afterwards, the percentage of missing data within them was calculated. Initially, for the full cohort, all the features with > 10% of missing data were going to be discarded, but after careful inspection, it was expanded to > 20% since key features [e.g. body mass index (BMI) 22.6% for the MP subgroup and 20% for the full cohort] would be lost. Considering that the tradeoff of a wider missingness percentage was acceptable, taking into account the clinical value and impact on graft outcomes according to the broad available evidence and expert opinion[14-20]. The same features were preserved for the MP subgroup, even if they had a higher missing percentage, to maintain the logic of the study design. Only two features had > 20% (deprivation group 31.2% and recipient BMI 22.6%) (Table 1).

Table 1 Features selected for modelling and their missingness percentage before imputation.

Features	Missing data full cohort (n = 15904) (%)	Missing data MP subgroup (n = 544) (%)
Recipient BMI	19.98	22.61
Serum creatinine (umol/L) 12-month post-transplant	19.54	13.42
Serum creatinine (umol/L) 3-month post-transplant	15.79	13.79
Recipient deprivation group	16.17	31.25
Predniscolone/predniscone immunosuppression 3 months post-transplant	16.10	13.24
Type of dialysis at transplant	15.17	16.36
Donor allergy	12.09	10.85
Initial graft function	8.53	9.93
Donor cause of death	5.29	4.60
Recipient positive CMV status	4.89	5.33
Donor family history of diabetes	4.52	4.41
Recipient ethnicity	4.44	4.04
Donor positive EBV status	4.21	2.76
Donor creatinine at retrieval	3.41	5.88
Donor ethnicity	3.40	2.21
Donor history of drug abuse	2.50	3.68
Donor history of cardiac disease	2.18	4.23
Donor history of UTI	1.88	2.57
Donor hypertension	1.62	2.02
Donor positive toxo status	1.37	1.10
Perfusate used	1.08	0.74
Donor history of diabetes	0.91	1.29
Perfusion quality	0.74	2.94
Donor positive CMV status	0.59	1.10
Graft status	0.57	0
Follow-up time	0.55	0
Donor BMI	0.53	0.37
Donor smoker	0.52	0.55
Dialysis status at registration	0.35	0.18
Cold ischemia time	0.22	0.37
Allocation matchability score	0.18	0
Waiting list time	0.17	0.18
Dialysis status at transplant	0.13	0
Kidney used by local centre	0.10	0
Donor ABO blood group	0.04	0
Recipient sex	0.04	0.18
Highly sensitised status flag	0.03	0
Donor homozygous at DR locus	0.01	0
Donor homozygous at B locus	0.01	0
Donor homozygous at A locus	0.01	0
HLA mismatch group	0.01	0
Recipient homozygous at B locus	0.01	0
Recipient homozygous at DR locus	0.01	0
Recipient homozygous at A locus	0.01	0
Number of mismatches at DR locus	0.01	0
Number of mismatches at A locus	0.01	0
Number of mismatches at B locus	0.01	0
Recipient age	0	0
Donor sex	0	0
Donor type	0	0
Recipient diabetes	0	0
Donor age	0	0
Recipient ABO blood group	0	0
Donor organ	0	0
Transplant year	0	0
Machine perfusion type	0	0

BMI: Body mass index; UTI: Urinary tract infection; HLA: Human leukocyte antigen; EBV: Epstein-Barr virus; CMV: Cytomegalovirus.

Variables were scaled to have the same units, redundant features were removed, multiple categories were mapped into bigger groups for better within-feature balance, very low variance binary features were removed, skewdness was checked, and values were capped at 1% and 99% percentiles for extreme outliers. Missing values were then imputed with the multivariable imputation by chained equation method[24].

Dimensionality reduction

A mixed-type principal component analysis (PCA) embedding approach was employed[25,26]. Numeric features were scaled, and categorical features were one-hot encoded on the full cohort. A block-weighting scheme was applied to the preprocessed data matrices. Each one-hot encoded block, corresponding to a single original categorical variable, was scaled by the inverse square root of the number of unique categories within that variable. This weighting mechanism ensured that each original variable contributed equally to the latent space, approximating the balance constraints of mixed-data factor methods (FAMD-like approach)[27,28]. PCA was then applied to the preprocessed full cohort to derive 10 latent components (d = 1-10). The MP subset was transformed using the same preprocessor and PCA model without re-fitting. These d components were appended to both groups so they shared the same latent space.

The number of retained components was not selected only based on variance, as this criterion is not necessarily aligned with clustering objectives[28-30]. Instead, dimensionality was treated as a tuning parameter and jointly optimised with the number of gaussian mixture model (GMM) mixture components.

We performed a grid search over the number of latent dimensions (d = 3-10) and mixture components (K = 3-10). For each (d, K) combination, a GMM was fitted to the mixed-type PCA embedding, and clustering robustness was assessed using bootstrap resampling (10 replicates). Stability was quantified as the mean adjusted rand index (ARI) between the reference clustering and clustering obtained from bootstrap samples[31-33]. For each candidate model, we additionally computed the Bayesian information criterion (BIC), the average maximum posterior membership probability, and the minimum cluster proportion. Models with very small clusters (< 5% of the sample), low assignment confidence, or substantially inferior BIC were excluded. Among the remaining candidates, the final model was selected based on high clustering stability, competitive BIC, and parsimony[34].

This multi-criteria approach was chosen to balance fit quality, robustness, and interpretability, acknowledging that no single metric is sufficient for unsupervised model selection in mixed-data settings.

Clustering

We then applied an unsupervised clustering approach using GMM to identify and categorise clinical phenotypes latent in the full cohort. It was selected for its ability to model cluster-specific covariance structure and provide probabilistic assignments[34-36]. The full covariance structure was tested, and k number of clusters selected based on the grid search mentioned above using ARI, BIC, the average maximum posterior membership probability, and the minimum cluster proportion. Convergence was assessed using a tolerance of 1 × 10^-3 with a maximum of 100 iterations; the model converged after 6 iterations, well within the specified criteria. Hard cluster labels were derived as the argmax of the posterior probability vector for each patient, and maximum posterior probability (MPP) and Shannon entropy of the full posterior distribution were computed per patient to characterise membership confidence[34]. The random state used was 0 to ensure reproducibility in both the full cohort and the transfer analyses to the MP subgroup.

The GMM was fitted exclusively on the full cohort and used to predict posterior probabilities and assign cluster labels for subset patients, with no re-fitting in the MP subgroup. Cluster labels and posterior probabilities for patients in the MP subgroup were obtained by applying the fitted model directly to their FAMD-reduced coordinates. This transfer design was done to test whether MP patients occupy similar positions within the cluster structure derived from the full cohort, and whether that structure is preserved or modified within this clinically defined subgroup.

Stability analyses

Cluster stability was assessed in the full cohort via consensus clustering across 100 iterations with 80% subsampling. For each run, co-clustering of sample pairs was recorded, producing a consensus matrix representing the fraction of times each pair clustered together. From this matrix, we computed the proportion of ambiguous clustering (PAC), cluster-level stability, and sample-level stability. High PAC or low stability scores indicate clusters or samples with inconsistent assignments across resampled runs[37-39]. Membership uncertainty was quantified per patient using MPP and Shannon entropy of the full posterior distribution[34]. For the MP subgroup, consensus clustering was not performed because cluster labels were derived by transferring the full-dataset GMM rather than by independent model fitting; repeating the consensus procedure on the subset would not reflect the transfer design and would instead evaluate an independent clustering exercise of the same fixed predictions on a small sample (n = 544). Every iteration would produce identical labels because no refitting of the GMM occurred. Membership uncertainty in the subset was therefore characterised using the posterior probability distributions from the transferred model: MPP and Shannon entropy of the full posterior vector were computed per patient, overall and stratified by cluster, and compared to the equivalent metrics from the full dataset[34].

Post-hoc analyses

Post-hoc characterisation was performed separately for the full cohort and the MP subgroup. Baseline characteristics were summarised for each cluster using mean ± SD for continuous variables and count (proportion) for categorical variables. Cluster phenotypes were profiled using the standardized mean difference (SMD) for each feature, calculated by comparing each cluster against the remainder of the dataset. All comparisons were treated as descriptive, given that the same data were used for both cluster derivation and characterisation. Inferential testing on clustering variables was not performed, as this would inflate type I error. Effect sizes (SMD) were used as the primary measure of between-cluster differences[40,41].

SMD profiles were visualised using heatmaps for all features. Cross-dataset phenotypic alignment between the full cohort and MP subgroup clusters was assessed by computing Pearson correlation coefficients and Mean Absolute Differences between matched SMD profiles[40,41]. Optimal cluster correspondence between datasets was determined using the Hungarian algorithm to maximise phenotypic similarity[42]. Cluster proportion in each dataset was also compared descriptively.

Outcomes

Outcome analyses were performed independently of the clustering pipeline; cluster labels were fully determined prior to any outcome extraction, and outcome data played no role in model fitting or cluster derivation.

Two post-transplant outcomes were evaluated separately. The primary outcome was graft survival, defined as time from the transplant operation to graft failure. Graft failure was recorded as a discrete event in the dataset; patients who died with a functioning graft or were lost to follow-up were censored at their last recorded contact date, yielding a death-censored graft failure endpoint. The secondary outcome was patient survival, defined as time from transplant to death from any cause; patients alive at last contact were censored at that date. Both outcomes were measured from day 0 (day of transplant operation) to a maximum of 5 years of follow-up.

Survival functions were estimated using the Kaplan-Meier method, and differences across clusters were compared using the log-rank test, applied separately in the full cohort and the MP subgroup. 95% confidence intervals were also calculated.

Software and instrumentation

We performed all analyses in Python 3.13.3 with JupyterLab, and a comprehensive suite of libraries including scikit-learn 1.6.1 for the models, and others such as pandas 2.2.2, numpy 2.0.2, matplotlib 3.10.0, seaborn 0.13.2, pingouin latest compatible version, prince 0.12, lifelines 0.30.3, scipy 1.16.3, autograd-gamma: 0.5.0, formulaic 1.2.1, interface-meta: 1.3.0.

RESULTS

The final sample for the full cohort included 15904 patients, and the MP subgroup included 544. Baseline characteristics for the full cohort and the MP subgroup, overall and stratified by cluster, are presented in Tables 2 and 3. Continuous variables were described using means and standard deviations, while categorical variables were summarised with counts and percentages. Comparisons across clusters were performed to provide descriptive context rather than formal inference.

Table 2 Full cohort descriptive baseline characteristics, n (%).

Characteristic	All (n = 15904)	Cluster 1 (n = 2797)	Cluster 2 (n = 2826)	Cluster 3 (n = 2370)	Cluster 4 (n = 1854)	Cluster 5 (n = 2402)	Cluster 6 (n = 3655)
Recipient age	53.6 (13.3)	47.6 (13.6)	61.4 (9.7)	49.2 (13.4)	55.8 (12.0)	45.7 (12.2)	59.3 (10.3)
Recipient BMI	27.4 (4.8)	27.2 (5.0)	28.8 (4.5)	27.3 (4.9)	27.6 (4.6)	26.0 (4.7)	27.6 (4.5)
Recipient sex
Female	5888 (37.0)	1106 (39.5)	663 (23.5)	856 (36.1)	742 (40.0)	1249 (52.0)	1272 (34.8)
Male	10010 (62.9)	1690 (60.4)	2163 (76.5)	1514 (63.9)	1112 (60.0)	1149 (47.8)	2382 (65.2)
Recipient ABO blood group
A	6220 (39.1)	1121 (40.1)	1095 (38.7)	991 (41.8)	651 (35.1)	902 (37.6)	1460 (39.9)
AB	816 (5.1)	179 (6.4)	159 (5.6)	93 (3.9)	90 (4.9)	139 (5.8)	156 (4.3)
B	2071 (13.0)	346 (12.4)	346 (12.2)	227 (9.6)	351 (18.9)	341 (14.2)	460 (12.6)
O	6797 (42.7)	1151 (41.2)	1226 (43.4)	1059 (44.7)	762 (41.1)	1020 (42.5)	1579 (43.2)
Recipient ethnicity
Asian	3026 (19.0)	484 (17.3)	435 (15.4)	238 (10.0)	525 (28.3)	628 (26.1)	716 (19.6)
Black	1684 (10.6)	315 (11.3)	303 (10.7)	128 (5.4)	309 (16.7)	263 (10.9)	366 (10.0)
White	10488 (65.9)	1859 (66.5)	1963 (69.5)	1938 (81.8)	887 (47.8)	1408 (58.6)	2433 (66.6)
Recipient diabetes	2205 (13.9)	267 (9.5)	683 (24.2)	217 (9.2)	337 (18.2)	140 (5.8)	561 (15.3)
Recipient positive CMV status	8478 (53.3)	1417 (50.7)	1476 (52.2)	1034 (43.6)	1198 (64.6)	1308 (54.5)	2045 (56.0)
Dialysis status at registration
Hemo	7790 (49.0)	1467 (52.4)	1633 (57.8)	888 (37.5)	992 (53.5)	1075 (44.8)	1735 (47.5)
Not	5514 (34.7)	840 (30.0)	711 (25.2)	1132 (47.8)	535 (28.9)	940 (39.1)	1356 (37.1)
Peritoneal	2545 (16.0)	477 (17.1)	476 (16.8)	342 (14.4)	318 (17.2)	380 (15.8)	552 (15.1)
Dialysis at transplant	13412 (84.3)	2430 (86.9)	2518 (89.1)	1735 (73.2)	1620 (87.4)	2024 (84.3)	3085 (84.4)
Type of dialysis at transplant
Hemo	10218 (64.2)	1851 (66.2)	1964 (69.5)	1228 (51.8)	1254 (67.6)	1530 (63.7)	2391 (65.4)
Not	79 (0.5)	35 (1.3)	13 (0.5)	8 (0.3)	7 (0.4)	2 (0.1)	14 (0.4)
Peritoneal	3195 (20.1)	579 (20.7)	555 (19.6)	507 (21.4)	366 (19.7)	494 (20.6)	694 (19.0)
Donor organ
Left kidney	7476 (47.0)	1197 (42.8)	1396 (49.4)	1067 (45.0)	928 (50.1)	978 (40.7)	1910 (52.3)
Right kidney	8428 (53.0)	1600 (57.2)	1430 (50.6)	1303 (55.0)	926 (49.9)	1424 (59.3)	1745 (47.7)
Highly sensitised status flag	1041 (6.5)	140 (5.0)	69 (2.4)	143 (6.0)	259 (14.0)	247 (10.3)	183 (5.0)
Waiting list time	2.6 (1.9)	2.9 (2.0)	2.9 (1.8)	1.6 (1.4)	2.8 (2.2)	2.6 (2.1)	2.6 (1.8)
Recipient deprivation group
Quartile 1 most deprived	3288 (20.7)	448 (16.0)	688 (24.3)	557 (23.5)	320 (17.3)	386 (16.1)	889 (24.3)
Quartile 2 second most deprived	3303 (20.8)	536 (19.2)	613 (21.7)	533 (22.5)	363 (19.6)	437 (18.2)	821 (22.5)
Quartile 3 second least deprived	3365 (21.2)	657 (23.5)	593 (21.0)	399 (16.8)	427 (23.0)	555 (23.1)	734 (20.1)
Quartile 4 least deprived	3377 (21.2)	661 (23.6)	498 (17.6)	423 (17.8)	467 (25.2)	639 (26.6)	689 (18.9)
Donor age	52.6 (14.0)	44.1 (12.3)	62.1 (9.0)	52.4 (12.6)	51.0 (14.0)	41.0 (12.6)	60.3 (9.7)
Donor BMI	27.4 (5.4)	26.3 (5.1)	28.8 (5.7)	27.4 (5.3)	27.0 (5.3)	26.0 (4.9)	28.2 (5.4)
Donor sex
Female	6983 (43.9)	1086 (38.8)	1313 (46.5)	1162 (49.0)	744 (40.1)	908 (37.8)	1770 (48.4)
Male	8921 (56.1)	1711 (61.2)	1513 (53.5)	1208 (51.0)	1110 (59.9)	1494 (62.2)	1885 (51.6)
Donor ABO blood group
A	6430 (40.4)	1166 (41.7)	1153 (40.8)	1026 (43.3)	644 (34.7)	937 (39.0)	1504 (41.1)
AB	523 (3.3)	118 (4.2)	96 (3.4)	41 (1.7)	58 (3.1)	99 (4.1)	111 (3.0)
B	1609 (10.1)	276 (9.9)	285 (10.1)	146 (6.2)	261 (14.1)	265 (11.0)	376 (10.3)
O	7335 (46.1)	1234 (44.1)	1291 (45.7)	1157 (48.8)	888 (47.9)	1101 (45.8)	1664 (45.5)
Donor ethnicity
Asian	457 (2.9)	79 (2.8)	96 (3.4)	44 (1.9)	59 (3.2)	68 (2.8)	111 (3.0)
Black	199 (1.3)	37 (1.3)	32 (1.1)	28 (1.2)	29 (1.6)	34 (1.4)	39 (1.1)
White	14707 (92.5)	2545 (91.0)	2597 (91.9)	2259 (95.3)	1688 (91.0)	2193 (91.3)	3425 (93.7)
Donor positive CMV status	7699 (48.4)	1198 (42.8)	1468 (51.9)	1157 (48.8)	837 (45.1)	1084 (45.1)	1955 (53.5)
Donor positive EBV status	14349 (90.2)	2561 (91.6)	2624 (92.9)	2131 (89.9)	1676 (90.4)	2073 (86.3)	3284 (89.8)
Donor positive toxoplasmosis status	2505 (15.8)	326 (11.7)	522 (18.5)	375 (15.8)	279 (15.0)	328 (13.7)	675 (18.5)
Donor cardiac disease	1966 (12.4)	132 (4.7)	719 (25.4)	229 (9.7)	170 (9.2)	79 (3.3)	637 (17.4)
Donor diabetes	1262 (7.9)	85 (3.0)	432 (15.3)	168 (7.1)	130 (7.0)	67 (2.8)	380 (10.4)
Donor family history of diabetes	4889 (30.7)	998 (35.7)	801 (28.3)	703 (29.7)	617 (33.3)	833 (34.7)	937 (25.6)
Donor history of drug abuse	3073 (19.3)	1380 (49.3)	236 (8.4)	163 (6.9)	609 (32.8)	586 (24.4)	99 (2.7)
Donor hypertension	4738 (29.8)	253 (9.0)	1596 (56.5)	663 (28.0)	461 (24.9)	153 (6.4)	1612 (44.1)
Donor smoker	9722 (61.1)	2143 (76.6)	1704 (60.3)	1205 (50.8)	1323 (71.4)	1548 (64.4)	1799 (49.2)
Donor history of UTI	896 (5.6)	142 (5.1)	186 (6.6)	119 (5.0)	102 (5.5)	111 (4.6)	236 (6.5)
Donor allergy	5382 (33.8)	1097 (39.2)	1295 (45.8)	622 (26.2)	739 (39.9)	517 (21.5)	1112 (30.4)
Donor creatinine at retrieval	0.3 (0.5)	0.3 (0.5)	0.2 (0.4)	0.3 (0.5)	0.3 (0.5)	0.4 (0.5)	0.3 (0.4)
Donor type
DBD	8900 (56.0)	1772 (63.4)	1349 (47.7)	1649 (69.6)	932 (50.3)	1520 (63.3)	1678 (45.9)
DCD	7004 (44.0)	1025 (36.6)	1477 (52.3)	721 (30.4)	922 (49.7)	882 (36.7)	1977 (54.1)
Donor cause of death
Neurological	13832 (87.0)	2439 (87.2)	2534 (89.7)	2073 (87.5)	1617 (87.2)	1935 (80.6)	3234 (88.5)
Other	1231 (7.7)	172 (6.1)	117 (4.1)	199 (8.4)	133 (7.2)	343 (14.3)	267 (7.3)
Cold ischemia time	13.8 (4.8)	14.0 (5.0)	14.1 (4.7)	13.2 (4.6)	14.3 (4.9)	13.7 (4.9)	13.7 (4.8)
Perfusate used
HTK	979 (6.2)	324 (11.6)	381 (13.5)	11 (0.5)	253 (13.6)	2 (0.1)	8 (0.2)
Marshalls	2536 (15.9)	265 (9.5)	489 (17.3)	352 (14.9)	244 (13.2)	305 (12.7)	881 (24.1)
Wisconsin	12217 (76.8)	2180 (77.9)	1915 (67.8)	1984 (83.7)	1326 (71.5)	2074 (86.3)	2738 (74.9)
Perfusion quality
Fair	1031 (6.5)	128 (4.6)	223 (7.9)	142 (6.0)	141 (7.6)	129 (5.4)	268 (7.3)
Good	14139 (88.9)	2583 (92.3)	2461 (87.1)	2128 (89.8)	1628 (87.8)	2177 (90.6)	3162 (86.5)
Poor	616 (3.9)	77 (2.8)	126 (4.5)	78 (3.3)	75 (4.0)	78 (3.2)	182 (5.0)
Machine perfusion type
HMP	359 (2.3)	13 (0.5)	27 (1.0)	72 (3.0)	13 (0.7)	71 (3.0)	163 (4.5)
NMP	185 (1.2)	27 (1.0)	31 (1.1)	20 (0.8)	26 (1.4)	29 (1.2)	52 (1.4)
SCS	15360 (96.6)	2757 (98.6)	2768 (97.9)	2278 (96.1)	1815 (97.9)	2302 (95.8)	3440 (94.1)
Donor homozygous at A locus	2501 (15.7)	419 (15.0)	419 (14.8)	635 (26.8)	218 (11.8)	320 (13.3)	490 (13.4)
Donor homozygous at B locus	1366 (8.6)	250 (8.9)	239 (8.5)	407 (17.2)	41 (2.2)	177 (7.4)	252 (6.9)
Donor homozygous at DR locus	1850 (11.6)	272 (9.7)	286 (10.1)	548 (23.1)	69 (3.7)	289 (12.0)	386 (10.6)
Recipient homozygous at A locus	2781 (17.5)	397 (14.2)	396 (14.0)	235 (9.9)	443 (23.9)	586 (24.4)	724 (19.8)
Recipient homozygous at B locus	1793 (11.3)	166 (5.9)	167 (5.9)	87 (3.7)	476 (25.7)	440 (18.3)	457 (12.5)
Recipient homozygous at DR locus	2502 (15.7)	167 (6.0)	184 (6.5)	109 (4.6)	633 (34.1)	650 (27.1)	759 (20.8)
Number of mismatches at A locus
One	7784 (48.9)	1474 (52.7)	1498 (53.0)	955 (40.3)	864 (46.6)	1162 (48.4)	1831 (50.1)
Two	5598 (35.2)	937 (33.5)	966 (34.2)	321 (13.5)	835 (45.0)	1051 (43.8)	1488 (40.7)
Zero	2521 (15.9)	386 (13.8)	362 (12.8)	1094 (46.2)	155 (8.4)	188 (7.8)	336 (9.2)
Number of mismatches at B locus
One	10801 (67.9)	2032 (72.6)	2040 (72.2)	1338 (56.5)	501 (27.0)	2015 (83.9)	2875 (78.7)
Two	2824 (17.8)	211 (7.5)	389 (13.8)	0 (0.0)	1331 (71.8)	286 (11.9)	607 (16.6)
Zero	2278 (14.3)	554 (19.8)	397 (14.0)	1032 (43.5)	22 (1.2)	100 (4.2)	173 (4.7)
Number of mismatches at DR locus
One	8205 (51.6)	1553 (55.5)	1804 (63.8)	38 (1.6)	844 (45.5)	1346 (56.0)	2620 (71.7)
Two	1276 (8.0)	15 (0.5)	111 (3.9)	0 (0.0)	986 (53.2)	45 (1.9)	119 (3.3)
Zero	6422 (40.4)	1229 (43.9)	911 (32.2)	2332 (98.4)	24 (1.3)	1010 (42.0)	916 (25.1)
HLA mismatch group
(0 DR and 2B) OR (1 DR and 1/0 B)	8319 (52.3)	1706 (61.0)	1911 (67.6)	38 (1.6)	289 (15.6)	1499 (62.4)	2876 (78.7)
(1 DR and 2 B) OR (2 DR)	2207 (13.9)	43 (1.5)	233 (8.2)	0 (0.0)	1565 (84.4)	98 (4.1)	268 (7.3)
0 DR and 1/0 B	4494 (28.3)	1011 (36.1)	662 (23.4)	1506 (63.5)	0 (0.0)	804 (33.5)	511 (14.0)
0 Mismatches	883 (5.6)	37 (1.3)	20 (0.7)	826 (34.9)	0 (0.0)	0 (0.0)	0 (0.0)
Initial graft function
DGF	3352 (21.1)	466 (16.7)	855 (30.3)	370 (15.6)	420 (22.7)	345 (14.4)	896 (24.5)
Immediate	10826 (68.1)	1968 (70.4)	1571 (55.6)	1774 (74.9)	1187 (64.0)	1858 (77.4)	2468 (67.5)
PNF	369 (2.3)	69 (2.5)	134 (4.7)	20 (0.8)	50 (2.7)	17 (0.7)	79 (2.2)
Predniscolone/predniscone immunosuppression 3 months post-transplant
No	3843 (24.2)	553 (19.8)	605 (21.4)	674 (28.4)	354 (19.1)	610 (25.4)	1047 (28.6)
Yes	9500 (59.7)	1703 (60.9)	1605 (56.8)	1453 (61.3)	1081 (58.3)	1531 (63.7)	2127 (58.2)
Graft status
Died functioning	1861 (11.7)	146 (5.2)	362 (12.8)	245 (10.3)	193 (10.4)	175 (7.3)	740 (20.2)
Died unknown function	45 (0.3)	3 (0.1)	16 (0.6)	3 (0.1)	6 (0.3)	5 (0.2)	12 (0.3)
Failed	2030 (12.8)	214 (7.7)	543 (19.2)	309 (13.0)	181 (9.8)	211 (8.8)	572 (15.6)
Functioning	11878 (74.7)	2419 (86.5)	1879 (66.5)	1804 (76.1)	1456 (78.5)	2002 (83.3)	2318 (63.4)
Allocation matchability score	6.5 (2.8)	4.9 (2.7)	4.7 (2.7)	5.6 (2.5)	8.3 (2.1)	8.2 (1.8)	7.7 (2.1)
Serum creatinine (umol/L) at 3 months post-transplant	152.3 (63.4)	128.3 (40.2)	209.8 (80.7)	150.1 (54.4)	141.5 (54.7)	110.4 (30.6)	163.0 (55.5)
Serum creatinine (umol/L) at 12 months post-transplant	143.6 (58.8)	121.9 (39.9)	195.5 (75.9)	144.8 (53.7)	134.2 (51.8)	107.2 (30.8)	155.6 (53.0)
Follow-up time	4.2 (2.9)	2.5 (1.7)	2.0 (1.6)	6.1 (2.6)	2.4 (1.9)	6.6 (2.4)	5.3 (2.6)
Transplant year
2014	1484 (9.3)	9 (0.3)	34 (1.2)	420 (17.7)	21 (1.1)	462 (19.2)	538 (14.7)
2015	1475 (9.3)	17 (0.6)	49 (1.7)	389 (16.4)	32 (1.7)	421 (17.5)	567 (15.5)
2016	1630 (10.2)	35 (1.3)	88 (3.1)	446 (18.8)	47 (2.5)	403 (16.8)	611 (16.7)
2017	1785 (11.2)	85 (3.0)	145 (5.1)	445 (18.8)	54 (2.9)	421 (17.5)	635 (17.4)
2018	1920 (12.1)	225 (8.0)	249 (8.8)	318 (13.4)	114 (6.1)	390 (16.2)	624 (17.1)
2019	1870 (11.8)	355 (12.7)	329 (11.6)	213 (9.0)	312 (16.8)	198 (8.2)	463 (12.7)
2020	1462 (9.2)	501 (17.9)	354 (12.5)	65 (2.7)	339 (18.3)	71 (3.0)	132 (3.6)
2021	1577 (9.9)	594 (21.2)	548 (19.4)	43 (1.8)	308 (16.6)	23 (1.0)	61 (1.7)
2022	1420 (8.9)	548 (19.6)	531 (18.8)	22 (0.9)	288 (15.5)	11 (0.5)	20 (0.5)
2023	745 (4.7)	290 (10.4)	309 (10.9)	8 (0.3)	133 (7.2)	1 (0.0)	4 (0.1)
2024	536 (3.4)	138 (4.9)	190 (6.7)	1 (0.0)	206 (11.1)	1 (0.0)	0 (0.0)
Kidney used by local centre
No	12057 (75.8)	2472 (88.4)	2420 (85.6)	1764 (74.4)	1579 (85.2)	1644 (68.4)	2178 (59.6)
Yes	3831 (24.1)	324 (11.6)	403 (14.3)	604 (25.5)	275 (14.8)	755 (31.4)	1470 (40.2)

BMI: Body mass index; UTI: Urinary tract infection; DBD: Donation after brain death; DCD: Donation after cardiac death; HTK: Histidine-tryptophan-ketoglutarate solution; HMP: Hypothermic machine perfusion; CMV: Cytomegalovirus; NMP: Normothermic machine perfusion; EBV: Epstein-Barr virus; HLA: Human leukocyte antigen; DGF: Delayed graft function; PNF: Primary non-function.

Table 3 Machine perfusion subgroup descriptive baseline characteristics, n (%).

Characteristic	All (n = 544)	Cluster 1 (n = 41)	Cluster 2 (n = 59)	Cluster 3 (n = 93)	Cluster 4 (n = 36)	Cluster 5 (n = 97)	Cluster 6 (n = 218)
Recipient age	55.9 (12.1)	49.5 (12.0)	62.9 (9.5)	52.9 (12.4)	53.2 (12.2)	48.9 (12.7)	60.2 (9.5)
Recipient BMI	27.7 (5.0)	26.3 (4.7)	29.1 (4.7)	28.1 (4.5)	28.2 (6.3)	26.5 (4.9)	28.0 (5.0)
Recipient sex
Female	183 (33.6)	12 (29.3)	10 (16.9)	33 (35.5)	17 (47.2)	42 (43.3)	69 (31.7)
Male	360 (66.2)	29 (70.7)	49 (83.1)	60 (64.5)	19 (52.8)	55 (56.7)	148 (67.9)
Recipient ABO blood group
A	214 (39.3)	17 (41.5)	29 (49.2)	38 (40.9)	15 (41.7)	37 (38.1)	78 (35.8)
AB	21 (3.9)	3 (7.3)	1 (1.7)	4 (4.3)	1 (2.8)	5 (5.2)	7 (3.2)
B	69 (12.7)	4 (9.8)	7 (11.9)	4 (4.3)	6 (16.7)	11 (11.3)	37 (17.0)
O	240 (44.1)	17 (41.5)	22 (37.3)	47 (50.5)	14 (38.9)	44 (45.4)	96 (44.0)
Recipient ethnicity
Asian	68 (12.5)	5 (12.2)	7 (11.9)	6 (6.5)	10 (27.8)	14 (14.4)	26 (11.9)
Black	34 (6.2)	5 (12.2)	6 (10.2)	1 (1.1)	5 (13.9)	5 (5.2)	12 (5.5)
White	420 (77.2)	28 (68.3)	44 (74.6)	85 (91.4)	16 (44.4)	74 (76.3)	173 (79.4)
Recipient diabetes	74 (13.6)	4 (9.8)	12 (20.3)	6 (6.5)	6 (16.7)	4 (4.1)	42 (19.3)
Recipient positive CMV serostatus	260 (47.8)	17 (41.5)	28 (47.5)	33 (35.5)	24 (66.7)	52 (53.6)	106 (48.6)
Dialysis status at registration
Hemodialysis	251 (46.1)	20 (48.8)	36 (61.0)	37 (39.8)	27 (75.0)	31 (32.0)	100 (45.9)
Not	211 (38.8)	12 (29.3)	20 (33.9)	43 (46.2)	7 (19.4)	45 (46.4)	84 (38.5)
Peritoneal	81 (14.9)	9 (22.0)	3 (5.1)	12 (12.9)	2 (5.6)	21 (21.6)	34 (15.6)
Dialysis at transplant	454 (83.5)	36 (87.8)	53 (89.8)	75 (80.6)	34 (94.4)	81 (83.5)	175 (80.3)
Type of dialysis at transplant
Hemodialysis	345 (63.4)	25 (61.0)	43 (72.9)	56 (60.2)	31 (86.1)	60 (61.9)	130 (59.6)
Not	1 (0.2)	1 (2.4)	0 (0.0)	0 (0.0)	0 (0.0)	0 (0.0)	0 (0.0)
Peritoneal	109 (20.0)	11 (26.8)	10 (16.9)	19 (20.4)	3 (8.3)	21 (21.6)	45 (20.6)
Donor organ
Left kidney	293 (53.9)	20 (48.8)	30 (50.8)	50 (53.8)	15 (41.7)	44 (45.4)	134 (61.5)
Right kidney	251 (46.1)	21 (51.2)	29 (49.2)	43 (46.2)	21 (58.3)	53 (54.6)	84 (38.5)
Highly sensitised status flag	26 (4.8)	2 (4.9)	1 (1.7)	4 (4.3)	4 (11.1)	10 (10.3)	5 (2.3)
Waiting list time	2.0 (1.5)	2.6 (1.7)	2.6 (1.8)	1.6 (1.2)	2.4 (1.6)	2.0 (1.6)	1.9 (1.3)
Recipient deprivation group
Quartile 1 most deprived	105 (19.3)	11 (26.8)	11 (18.6)	16 (17.2)	6 (16.7)	18 (18.6)	43 (19.7)
Quartile 2 second most deprived	82 (15.1)	4 (9.8)	15 (25.4)	10 (10.8)	6 (16.7)	9 (9.3)	38 (17.4)
Quartile 3 second least deprived	99 (18.2)	8 (19.5)	7 (11.9)	14 (15.1)	11 (30.6)	19 (19.6)	40 (18.3)
Quartile 4 least deprived	88 (16.2)	10 (24.4)	6 (10.2)	14 (15.1)	6 (16.7)	21 (21.6)	31 (14.2)
Donor age	54.7 (13.0)	46.1 (11.9)	60.2 (8.5)	54.9 (12.4)	51.9 (13.9)	41.9 (12.2)	61.0 (8.7)
Donor BMI	27.0 (5.3)	24.9 (4.3)	28.5 (5.9)	26.9 (5.2)	26.4 (4.9)	25.3 (4.3)	27.8 (5.6)
Donor sex
Female	224 (41.2)	11 (26.8)	23 (39.0)	47 (50.5)	15 (41.7)	24 (24.7)	104 (47.7)
Male	320 (58.8)	30 (73.2)	36 (61.0)	46 (49.5)	21 (58.3)	73 (75.3)	114 (52.3)
Donor ABO blood group
A	221 (40.6)	18 (43.9)	29 (49.2)	39 (41.9)	14 (38.9)	40 (41.2)	81 (37.2)
AB	12 (2.2)	2 (4.9)	1 (1.7)	2 (2.2)	1 (2.8)	2 (2.1)	4 (1.8)
B	58 (10.7)	4 (9.8)	7 (11.9)	3 (3.2)	6 (16.7)	8 (8.2)	30 (13.8)
O	253 (46.5)	17 (41.5)	22 (37.3)	49 (52.7)	15 (41.7)	47 (48.5)	103 (47.2)
Donor ethnicity
Asian	2 (0.4)	0 (0.0)	1 (1.7)	0 (0.0)	0 (0.0)	0 (0.0)	1 (0.5)
Black	1 (0.2)	1 (2.4)	0 (0.0)	0 (0.0)	0 (0.0)	0 (0.0)	0 (0.0)
White	529 (97.2)	36 (87.8)	57 (96.6)	93 (100.0)	36 (100.0)	95 (97.9)	212 (97.2)
Donor positive CMV status	250 (46.0)	16 (39.0)	25 (42.4)	37 (39.8)	19 (52.8)	44 (45.4)	109 (50.0)
Donor positive EBV status	483 (88.8)	33 (80.5)	54 (91.5)	82 (88.2)	32 (88.9)	86 (88.7)	196 (89.9)
Donor positive toxoplasmosis status	98 (18.0)	8 (19.5)	9 (15.3)	18 (19.4)	4 (11.1)	13 (13.4)	46 (21.1)
Donor cardiac disease	64 (11.8)	5 (12.2)	18 (30.5)	7 (7.5)	4 (11.1)	4 (4.1)	26 (11.9)
Donor diabetes	28 (5.1)	0 (0.0)	10 (16.9)	2 (2.2)	2 (5.6)	3 (3.1)	11 (5.0)
Donor family history of diabetes	151 (27.8)	10 (24.4)	23 (39.0)	20 (21.5)	10 (27.8)	27 (27.8)	61 (28.0)
Donor history of drug abuse	74 (13.6)	20 (48.8)	4 (6.8)	3 (3.2)	13 (36.1)	26 (26.8)	8 (3.7)
Donor hypertension	148 (27.2)	2 (4.9)	36 (61.0)	15 (16.1)	8 (22.2)	5 (5.2)	82 (37.6)
Donor smoker	306 (56.2)	29 (70.7)	39 (66.1)	50 (53.8)	26 (72.2)	68 (70.1)	94 (43.1)
Donor history of UTI	37 (6.8)	3 (7.3)	7 (11.9)	4 (4.3)	4 (11.1)	3 (3.1)	16 (7.3)
Donor allergy	162 (29.8)	16 (39.0)	29 (49.2)	26 (28.0)	18 (50.0)	15 (15.5)	58 (26.6)
Donor creatinine at retrieval	0.3 (0.5)	0.3 (0.5)	0.1 (0.4)	0.3 (0.4)	0.2 (0.4)	0.4 (0.5)	0.3 (0.5)
Donor type
DBD	33 (6.1)	3 (7.3)	3 (5.1)	6 (6.5)	5 (13.9)	5 (5.2)	11 (5.0)
DCD	511 (93.9)	38 (92.7)	56 (94.9)	87 (93.5)	31 (86.1)	92 (94.8)	207 (95.0)
Donor cause of death
Neurological	470 (86.4)	35 (85.4)	57 (96.6)	73 (78.5)	32 (88.9)	84 (86.6)	189 (86.7)
Other	49 (9.0)	1 (2.4)	0 (0.0)	15 (16.1)	2 (5.6)	11 (11.3)	20 (9.2)
Cold ischemia time	13.4 (4.7)	13.7 (4.7)	15.2 (4.6)	12.2 (4.3)	16.2 (4.7)	12.9 (4.6)	13.1 (4.7)
Perfusate used
HTK	10 (1.8)	1 (2.4)	2 (3.4)	2 (2.2)	3 (8.3)	1 (1.0)	1 (0.5)
Marshalls	112 (20.6)	3 (7.3)	14 (23.7)	21 (22.6)	2 (5.6)	15 (15.5)	57 (26.1)
Wisconsin	418 (76.8)	37 (90.2)	42 (71.2)	69 (74.2)	31 (86.1)	81 (83.5)	158 (72.5)
Perfusion quality
Fair	63 (11.6)	1 (2.4)	8 (13.6)	13 (14.0)	3 (8.3)	16 (16.5)	22 (10.1)
Good	424 (77.9)	36 (87.8)	44 (74.6)	70 (75.3)	31 (86.1)	72 (74.2)	171 (78.4)
Poor	41 (7.5)	4 (9.8)	7 (11.9)	7 (7.5)	2 (5.6)	5 (5.2)	16 (7.3)
Machine perfusion type
HMP	359 (66.0)	13 (31.7)	29 (49.2)	73 (78.5)	12 (33.3)	71 (73.2)	161 (73.9)
NMP	185 (34.0)	28 (68.3)	30 (50.8)	20 (21.5)	24 (66.7)	26 (26.8)	57 (26.1)
Donor homozygous at A locus	104 (19.1)	8 (19.5)	14 (23.7)	21 (22.6)	4 (11.1)	17 (17.5)	40 (18.3)
Donor homozygous at B locus	54 (9.9)	4 (9.8)	5 (8.5)	12 (12.9)	0 (0.0)	15 (15.5)	18 (8.3)
Donor homozygous at DR locus	88 (16.2)	5 (12.2)	7 (11.9)	34 (36.6)	1 (2.8)	17 (17.5)	24 (11.0)
Recipient homozygous at A locus	103 (18.9)	8 (19.5)	8 (13.6)	6 (6.5)	8 (22.2)	23 (23.7)	50 (22.9)
Recipient homozygous at B locus	67 (12.3)	2 (4.9)	6 (10.2)	5 (5.4)	9 (25.0)	14 (14.4)	31 (14.2)
Recipient homozygous at DR locus	94 (17.3)	1 (2.4)	3 (5.1)	6 (6.5)	13 (36.1)	23 (23.7)	48 (22.0)
Number of mismatches at A locus
One	306 (56.2)	25 (61.0)	31 (52.5)	61 (65.6)	20 (55.6)	52 (53.6)	117 (53.7)
Two	156 (28.7)	7 (17.1)	19 (32.2)	8 (8.6)	13 (36.1)	35 (36.1)	74 (33.9)
Zero	82 (15.1)	9 (22.0)	9 (15.3)	24 (25.8)	3 (8.3)	10 (10.3)	27 (12.4)
Number of mismatches at B locus
One	388 (71.3)	28 (68.3)	39 (66.1)	69 (74.2)	12 (33.3)	81 (83.5)	159 (72.9)
Two	97 (17.8)	3 (7.3)	13 (22.0)	0 (0.0)	24 (66.7)	13 (13.4)	44 (20.2)
Zero	59 (10.8)	10 (24.4)	7 (11.9)	24 (25.8)	0 (0.0)	3 (3.1)	15 (6.9)
Number of mismatches at DR locus
One	309 (56.8)	31 (75.6)	42 (71.2)	1 (1.1)	22 (61.1)	60 (61.9)	153 (70.2)
Two	37 (6.8)	0 (0.0)	3 (5.1)	0 (0.0)	14 (38.9)	4 (4.1)	16 (7.3)
Zero	198 (36.4)	10 (24.4)	14 (23.7)	92 (98.9)	0 (0.0)	33 (34.0)	49 (22.5)
HLA mismatch group
(0 DR and 2B) OR (1 DR and 1/0 B)	301 (55.3)	32 (78.0)	43 (72.9)	1 (1.1)	10 (27.8)	62 (63.9)	153 (70.2)
(1 DR and 2 B) OR (2 DR)	78 (14.3)	1 (2.4)	9 (15.3)	0 (0.0)	26 (72.2)	8 (8.2)	34 (15.6)
0 DR and 1/0 B	149 (27.4)	8 (19.5)	7 (11.9)	76 (81.7)	0 (0.0)	27 (27.8)	31 (14.2)
0 mismatches	16 (2.9)	0 (0.0)	0 (0.0)	16 (17.2)	0 (0.0)	0 (0.0)	0 (0.0)
Initial graft function
DGF	108 (19.9)	5 (12.2)	18 (30.5)	16 (17.2)	9 (25.0)	16 (16.5)	44 (20.2)
Immediate	370 (68.0)	31 (75.6)	29 (49.2)	66 (71.0)	25 (69.4)	73 (75.3)	146 (67.0)
PNF	12 (2.2)	2 (4.9)	3 (5.1)	0 (0.0)	0 (0.0)	0 (0.0)	7 (3.2)
Predniscolone/predniscone immunosuppression 3 months post-transplant
No	150 (27.6)	9 (22.0)	8 (13.6)	30 (32.3)	11 (30.6)	27 (27.8)	65 (29.8)
Yes	322 (59.2)	24 (58.5)	35 (59.3)	53 (57.0)	19 (52.8)	62 (63.9)	129 (59.2)
Graft status
Died functioning	89 (16.4)	2 (4.9)	9 (15.3)	11 (11.8)	5 (13.9)	7 (7.2)	55 (25.2)
Died unknown function	1 (0.2)	0 (0.0)	0 (0.0)	0 (0.0)	0 (0.0)	1 (1.0)	0 (0.0)
Failed	80 (14.7)	5 (12.2)	16 (27.1)	10 (10.8)	4 (11.1)	7 (7.2)	38 (17.4)
Functioning	374 (68.8)	34 (82.9)	34 (57.6)	72 (77.4)	27 (75.0)	82 (84.5)	125 (57.3)
Allocation matchability score	6.8 (2.4)	5.0 (2.4)	4.9 (2.4)	6.0 (2.4)	8.5 (1.7)	7.9 (1.9)	7.3 (2.1)
Serum creatinine (umol/L) 3-month post-transplant	154.8 (61.0)	133.6 (37.9)	219.8 (87.2)	155.1 (53.2)	132.5 (44.0)	114.6 (44.5)	164.8 (53.3)
Serum creatinine (umol/L) 12-month post-transplant	146.6 (57.2)	126.0 (36.3)	199.3 (89.6)	145.5 (56.3)	135.8 (45.1)	111.2 (39.0)	157.9 (49.1)
Follow-up time	5.5 (3.1)	3.3 (1.8)	2.1 (1.7)	6.8 (2.8)	2.4 (1.6)	7.5 (2.4)	5.9 (2.9)
Transplant year
2014	125 (23.0)	0 (0.0)	4 (6.8)	29 (31.2)	1 (2.8)	31 (32.0)	60 (27.5)
2015	80 (14.7)	0 (0.0)	3 (5.1)	19 (20.4)	0 (0.0)	21 (21.6)	37 (17.0)
2016	89 (16.4)	3 (7.3)	8 (13.6)	19 (20.4)	1 (2.8)	12 (12.4)	46 (21.1)
2017	45 (8.3)	0 (0.0)	1 (1.7)	7 (7.5)	2 (5.6)	15 (15.5)	20 (9.2)
2018	49 (9.0)	5 (12.2)	3 (5.1)	10 (10.8)	4 (11.1)	11 (11.3)	16 (7.3)
2019	49 (9.0)	9 (22.0)	6 (10.2)	6 (6.5)	4 (11.1)	5 (5.2)	19 (8.7)
2020	46 (8.5)	7 (17.1)	15 (25.4)	1 (1.1)	9 (25.0)	1 (1.0)	13 (6.0)
2021	44 (8.1)	13 (31.7)	14 (23.7)	1 (1.1)	8 (22.2)	1 (1.0)	7 (3.2)
2022	4 (0.7)	3 (7.3)	0 (0.0)	0 (0.0)	1 (2.8)	0 (0.0)	0 (0.0)
2023	2 (0.4)	1 (2.4)	1 (1.7)	0 (0.0)	0 (0.0)	0 (0.0)	0 (0.0)
2024	11 (2.0)	0 (0.0)	4 (6.8)	1 (1.1)	6 (16.7)	0 (0.0)	0 (0.0)
Kidney used by local centre
No	232 (42.6)	28 (68.3)	44 (74.6)	35 (37.6)	25 (69.4)	30 (30.9)	70 (32.1)
Yes	312 (57.4)	13 (31.7)	15 (25.4)	58 (62.4)	11 (30.6)	67 (69.1)	148 (67.9)

BMI: Body mass index; UTI: Urinary tract infection; DBD: Donation after brain death; CMV: Cytomegalovirus; DCD: Donation after cardiac death; HTK: Histidine-tryptophan-ketoglutarate solution; EBV: Epstein-Barr virus; HMP: Hypothermic machine perfusion; NMP: Normothermic machine perfusion; HLA: Human leukocyte antigen; DGF: Delayed graft function; PNF: Primary non-function.

A mixed-data dimensionality reduction approach was applied to the full cohort using a FAMD-like PCA. Ten latent components were retained for evaluation (d = 10). A grid search evaluated combinations of the number of retained latent dimensions (d = 3-10) and the number of mixture components (K = 3-10) in the full cohort. Models were assessed using bootstrap stability (mean ARI), BIC, average MPP, and minimum cluster proportion. Pathological solutions were excluded. Of 64 candidate models, 7 met validity criteria. The model with K = 6 clusters and d = 3 components demonstrated the most favourable balance of fit and stability: Mean ARI: 0.7836, BIC: 177937.9, average MPP: 0.6959, minimum cluster proportion: 11.7%. Models with fewer clusters showed lower stability or less distinct separation, while higher-K models exhibited reduced stability and smaller cluster sizes.

Additionally, in the full cohort, the first three components (d = 3) explained 20.5%, 17.2%, and 13.8% of the total variance, respectively, corresponding to a cumulative variance of 51.5%. These components also captured the majority of the structured variability and were therefore selected for downstream clustering. The same transformation was applied to the MP subgroup to ensure both datasets were embedded in a common latent space.

A GMM with six components (K = 6) and full covariance structure was fitted to the first three latent components of the full cohort. Cluster membership probabilities and hard assignments were derived for all individuals, and the model was subsequently applied, without retraining, to the MP subgroup. Resulting clusters for both groups can be visualised in Figure 1 and Table 4.

Figure 1 Resulting clusters in the full cohort and the machine perfusion subgroup. A and B: 3D visualisation of clustering results from weighted principal component analysis for mixed-type data followed by gaussian mixture model in the full cohort (A) and machine perfusion subgroup (B). Points represent individuals projected onto the first three principal components (PC1–PC3), with colours indicating gaussian mixture model-derived cluster membership. MP: Machine perfusion.

Table 4 Resulting clusters phenotype summary.

Cluster	Core phenotype	Immunologic profile	Outcomes	Allocation/time	MP type	Key modifiers	Transplant centre
1	Young, donor low cardiovascular comorbidity, donor behavioural risk	Low risk (fewer DR/B mismatches)	Intermediate graft survival. Patient survival↑	Low matchability score; recent years	NMP		No local
2	Older, comorbid males	Intermediate risk (DRMM = 1 enriched)	Graft and patient survival↓. Immediate graft function↓	Low matchability score	HMP/NMP	Donor quality↓, ↑(MP subgroup)	No local
3	Immunologically favourable; shorter waiting time, predominantly white recipients	Very low/near-perfect matching (DRMM = 0 dominant)	Graft and patient survival↑	Low matchability score; earlier years	HMP	Shorter CIT (MP subgroup); less dialysis at transplant	Local
4	Immunologically unfavourable, diverse recipient ethnicity, donor risk factors	High risk (DRMM = 2, BMM = 2 enriched)	Graft and patient survival↑ in full cohort	High matchability score; later years	NMP	Longer CIT (MP subgroup); hemodialysis at transplant (MP subgroup)
5	Young, females, donor low cardiovascular comorbidity	Intermediate risk	Graft and patient survival↑	High matchability score; earlier years	HMP	Less dialysis at transplant	Local
6	Older, donor hypertension with no behavioural risk	Intermediate risk	Intermediate graft and patient survival	High matchability score	HMP		Local

B: B locus; BMM: Number of mismatches at B locus; DR: DR locus; DRMM: Number of mismatches at DR locus; HMP: Hypothermic machine perfusion; NMP: Normothermic machine perfusion; CIT: Cold ischemia time.

Cluster sample counts and distributions in both groups can be found in Figure 2. There was a bigger proportion of patients in clusters 1, 2, and 4 in the full cohort compared to the MP subgroup, while there was a slightly higher proportion for clusters 3 and 5 in the MP compared to the full cohort. For both groups, cluster 6 had the biggest proportion of patients compared to the rest of the clusters, with the difference being higher in the MP subgroup.

Figure 2 Cluster samples distribution comparison between the full cohort (n = 15904) and the machine perfusion subgroup (n = 544). The machine perfusion (MP) subgroup shows notable enrichment in cluster 6 (40.0% vs 22.9% in full cohort) and cluster 5 (17.8% vs 15.1%), with corresponding under-representation in clusters 1 (7.5% vs 17.5%) and 4 (6.6% vs 11.6%). Cluster distribution in the full cohort: Cluster 1 n = 2797 (17.5%), cluster 2 n = 2826 (17.7%), cluster 3 n = 2370 (14.9%), cluster 4 n = 1854 (11.6%), cluster 5 n = 2402 (15.1%), cluster 6 n = 3655 (22.9%); In the MP subgroup: Cluster 1 n = 41 (7.5%), cluster 2 n = 59 (10.8%), cluster 3 n = 93 (17.0%), cluster 4 n = 36 (6.6%), cluster 5 n = 97 (17.8%), cluster 6 n = 218 (40.0%). MP: Machine perfusion.

Stability analysis comparison

For the full cohort (n = 15904), the PAC score was 0.146, indicating good stability. Cluster-wise stability scores ranged from 0.912 (cluster 3) to 0.827 (cluster 5). Mean sample-level stability was 0.869 (SD 0.104) (Figure 3). Mean MPP across all patients was 0.696 (SD 0.184; median 0.699), with clusters 3 and 4 showing the highest membership confidence (mean posteriors 0.726 and 0.757, respectively) and clusters 5 and 6 showing the lowest (0.666 and 0.663). Entropy was correspondingly lowest in clusters 3 and 4 (0.664 and 0.644) and highest in cluster 6 (0.904) (Figure 4).

Figure 3 Full cohort cluster stability consensus matrix. Consensus clustering matrix for the full cohort based on 100 iterations with 80% subsampling. Each cell represents the proportion of times a pair of samples was assigned to the same cluster across resampled runs. Samples are ordered by cluster membership, with blocks along the diagonal indicating stable clusters. Higher values (yellow) reflect more consistent co-clustering, whereas diffuse or intermediate values indicate instability (dark purple). Clusters are ordered from left to right (first on the left cluster 1, last on the right cluster 6).

Figure 4 Cluster membership uncertainty assessed by maximum posterior probability and Shannon entropy in the full cohort. A: Boxplots showing the distribution of maximum posterior probability for each of the six patient clusters identified by gaussian mixture model. Maximum posterior probability represents each patient’s confidence of assignment to their designated cluster, with values closer to 1 indicating higher certainty. Box boundaries represent the 25^th and 75^th percentiles, horizontal lines indicate medians, and whiskers extend to 1.5 × the interquartile range; B: Boxplots showing the distribution of Shannon entropy of the full posterior distribution for each cluster. Entropy quantifies assignment uncertainty, with lower values indicating more confident cluster membership. Cluster 4 demonstrates the highest membership confidence (median max probability = 0.80, median entropy = 0.63), while clusters 5 and 6 show greater uncertainty (median max probabilities = 0.66 for both, median entropies = 0.84 and 0.90, respectively).

Membership confidence was assessed in the MP subgroup (n = 544) using the posterior probability distributions from the transferred GMM. Overall, the mean MPP was 0.679 (SD 0.178; median 0.680), with the interquartile range spanning 0.517 to 0.845, indicating meaningful spread in assignment confidence across subgroup patients. Cluster 4 showed the highest membership confidence (mean 0.723, median 0.743), followed by cluster 2 (mean 0.702, median 0.699). Clusters 3, 5, and 6 showed moderate confidence (mean 0.672, 0.675, and 0.685 respectively), while cluster 1 showed the lowest confidence of all six clusters (mean 0.607, median 0.556). Mean entropy followed the inverse pattern: Lowest in cluster 4 (0.726) and highest in cluster 1 (1.046), where an elevated entropy approaching 1.05 indicates that probability mass was distributed broadly across multiple clusters for many patients in this group rather than concentrated on a single assignment. Cluster 6 also showed elevated entropy (0.904), consistent with its behaviour in the full cohort. Taken together, the posterior uncertainty profile of the MP subgroup reflects a model that characterises most clusters with moderate-to-good confidence, with cluster 1 representing the group of greatest ambiguity under the transferred model (Figure 5).

Figure 5 Cluster membership uncertainty assessed by maximum posterior probability and Shannon entropy in the machine perfusion subgroup. A: Boxplots showing the distribution of maximum posterior probability for each of the six patient clusters identified by gaussian mixture model. Maximum posterior probability represents each patient’s confidence of assignment to their designated cluster, with values closer to 1 indicating higher certainty. Box boundaries represent the 25^th and 75^th percentiles, horizontal lines indicate medians, and whiskers extend to 1.5 × the interquartile range; B: Boxplots showing the distribution of Shannon entropy of the full posterior distribution for each cluster. Entropy quantifies assignment uncertainty, with lower values indicating more confident cluster membership. Cluster 4 demonstrates the highest membership confidence also in the machine perfusion subgroup (median max probability = 0.74, median entropy = 0.72), while cluster 1 shows greater uncertainty (median max probability = 0.55, median entropy = 1.11). MP: Machine perfusion.

Membership confidence in the MP subgroup was compared to the full cohort using mean and median MPP and mean entropy per cluster (Table 5). Overall, the transferred model showed modestly lower confidence in the MP subgroup (mean MPP 0.679 vs 0.696; mean entropy 0.815 vs 0.783). At the cluster level, confidence remained highest for cluster 4 in both groups (mean posterior 0.757 full, 0.723 subgroup) and was largely preserved for cluster 2 (mean posterior Δ -0.013). Clusters 5 and 6, which showed the lowest confidence in the full cohort, demonstrated a slight improvement in mean MPP in the MP subgroup. Cluster 1 showed the largest degradation: Mean posterior fell from 0.678 to 0.607 and median posterior from 0.685 to 0.556, with entropy rising from 0.839 to 1.046.

Table 5 Clusters’ stability comparison (full cohort vs machine perfusion subgroup).

Cluster	Mean MPP (full cohort)	Median MPP (full cohort)	Mean entropy (full cohort)	Mean MPP (MP subgroup)	Median MPP (MP subgroup)	Mean entropy (MP subgroup)
1	0.678	0.685	0.839	0.607	0.555	1.046
2	0.715	0.723	0.724	0.701	0.699	0.765
3	0.726	0.723	0.664	0.671	0.646	0.759
4	0.756	0.802	0.644	0.723	0.743	0.725
5	0.666	0.658	0.828	0.674	0.689	0.796
6	0.663	0.666	0.903	0.685	0.689	0.831

MPP: Maximum posterior probability; MP: Machine perfusion.

Clinical characteristics of each kidney transplant cluster

Cluster phenotypes were characterised by their most distinguishing features, defined as those with the highest absolute SMD values when comparing each cluster against the remainder of the dataset (Tables 6 and 7). Summary of the clusters phenotypes characteristics are found in Table 4. For the full cohort, cluster 1 was characterised by younger donors and recipients (SMD -0.77 and SMD -0.53), with donor low cardiovascular comorbidity burden and no hypertension (SMD +0.59), despite a higher prevalence of behavioural risk factors (smoking SMD +0.39 and drug abuse SMD +0.81). Immunologically, this cluster reflects a low-risk profile, characterised by fewer high-risk mismatches [e.g., human leukocyte antigen (HLA) mismatch group: (1 DR and 2 B) OR (2 DR) SMD -0.64; number of mismatches at DR locus (DRMM) = 2 SMD -0.50] and enrichment of more favourable compatibility patterns, despite lower allocation matchability scores (SMD -0.82). Clinically, patients had lower serum creatinine at 3 and 12 months posttransplant (SMD -0.55 and -0.55, respectively) and a higher proportion of functioning grafts (SMD +0.33). However, follow-up duration is substantially shorter because transplants were predominantly recent (e.g. 2022 SMD +0.37), limiting assessment of long-term outcomes.

Table 6 Full cohort features standardized mean differences by cluster.

Characteristic	Cluster 1 (n = 2797)	Cluster 2 (n = 2826)	Cluster 3 (n = 2370)	Cluster 4 (n = 1854)	Cluster 5 (n = 2402)	Cluster 6 (n = 3655)
Recipient age	-0.53127	0.890174	-0.37819	0.263441	-0.74394	0.652855
Recipient BMI	-0.05273	0.36501	-0.0351	0.050277	-0.36817	0.051705
Recipient sex
Female	0.046416	-0.37198	-0.0387	0.057848	0.354276	-0.07143
Male	-0.04642	0.371976	0.038704	-0.05785	-0.35428	0.07143
Recipient ABO blood group
A	0.029565	-0.00315	0.072027	-0.09341	-0.03266	0.026294
AB	0.065362	0.025794	-0.06948	-0.01586	0.034174	-0.04917
B	-0.03387	-0.03848	-0.13933	0.186659	0.030704	-0.02611
O	-0.03678	0.017429	0.048903	-0.03802	-0.00484	0.013025
Recipient ethnicity
Asian	-0.06851	-0.13465	-0.33311	0.28277	0.195452	-0.00306
Black	0.016715	-0.00709	-0.24634	0.227795	0.001301	-0.03807
White	0.047113	0.119418	0.451491	-0.41774	-0.17413	0.028319
Recipient diabetes	-0.15378	0.332122	-0.16925	0.148745	-0.3113	0.056299
Recipient positive CMV status	-0.076	-0.037	-0.2564	0.270441	0.030052	0.075713
Dialysis status at registration
Hemodialysis	0.086843	0.213382	-0.28001	0.112707	-0.10092	-0.03491
Not	-0.11826	-0.25069	0.325769	-0.14902	0.111091	0.060756
Peritoneal	0.032607	0.024453	-0.05462	0.035873	-0.00844	-0.03204
Dialysis at transplant	0.097919	0.171868	-0.33548	0.107925	-0.00066	0.004394
Type of dialysis at transplant
Hemodialysis	-0.01072	0.059037	-0.13685	0.044986	0.001169	0.047248
Not	0.108832	-0.00796	-0.0172	-0.02224	-0.09087	-0.01846
Peritoneal	-0.01332	-0.05813	0.140569	-0.04158	0.011823	-0.04447
Donor organ
Left kidney	-0.09442	0.06469	-0.0406	0.080451	-0.14511	0.133529
Right kidney	0.094421	-0.06469	0.0406	-0.08045	0.145105	-0.13353
Highly sensitised status flag	-0.1051	-0.25405	-0.05252	0.278585	0.137113	-0.10495
Waiting list time	0.205676	0.184614	-0.68461	0.155021	0.029542	0.033337
Recipient deprivation group
Quartile 1 most deprived	-0.13673	0.125214	0.135129	-0.11206	-0.14645	0.114791
Quartile 2 second most deprived	-0.0373	0.028104	0.089469	-0.04483	-0.08356	0.043987
Quartile 3 second least deprived	0.086139	-0.01602	-0.12754	0.046672	0.05857	-0.05414
Quartile 4 least deprived	0.078204	-0.14132	-0.10361	0.102159	0.15673	-0.10738
Donor age	-0.77397	1.151346	0.059862	-0.07552	-1.07416	0.922674
Donor BMI	-0.22905	0.335247	0.015342	-0.0657	-0.29796	0.217399
Donor sex
Female	-0.11263	0.072835	0.134812	-0.08067	-0.13794	0.120255
Male	0.112627	-0.07283	-0.13481	0.080672	0.137942	-0.12026
Donor ABO blood group
A	0.039102	0.016699	0.077042	-0.13229	-0.02753	0.024879
AB	0.060752	0.008323	-0.11541	-0.00955	0.054528	-0.01621
B	-0.01511	-0.00672	-0.17588	0.143325	0.030238	0.001161
O	-0.05233	-0.01535	0.059672	0.039371	-0.01204	-0.01951
Donor ethnicity
Asian	0.000514	0.038364	-0.0821	0.024941	0.0001	0.010053
Black	0.00643	-0.01655	-0.01361	0.030552	0.015678	-0.02584
White	-0.00408	-0.02369	0.075358	-0.03827	-0.00908	0.005607
Donor positive CMV status	-0.12041	0.098053	0.021299	-0.06591	-0.06611	0.132632
Donor positive EBV status	0.029951	0.081959	0.001328	0.019402	-0.13784	0.02228
Donor positive toxoplasmosis status	-0.13706	0.095696	0.010196	-0.01706	-0.06299	0.098
Donor cardiac disease	-0.29989	0.452731	-0.07382	-0.09806	-0.3734	0.210295
Donor diabetes	-0.23863	0.303632	-0.02393	-0.02724	-0.25273	0.120616
Donor family history of diabetes	0.117106	-0.06168	-0.04535	0.05733	0.078348	-0.15243
Donor history of drug abuse	0.81861	-0.42472	-0.48799	0.339628	0.105875	-0.68139
Donor hypertension	-0.59749	0.75056	-0.00457	-0.09059	-0.70759	0.419629
Donor smoker	0.386329	-0.04618	-0.28052	0.233903	0.062836	-0.32145
Donor history of UTI	-0.02595	0.051784	-0.0268	-0.00334	-0.05092	0.049397
Donor allergy	0.182199	0.349431	-0.23512	0.17585	-0.37885	-0.12589
Donor creatinine at retrieval	0.111216	-0.20679	-0.04272	0.058724	0.126459	-0.05897
Donor type
DBD	0.163396	-0.21653	0.322543	-0.15502	0.161577	-0.26117
DCD	-0.1634	0.216534	-0.32254	0.155025	-0.16158	0.261166
Donor cause of death
Neurological	0.079257	0.188412	-0.01799	0.032678	-0.25947	0.031494
Other	-0.07926	-0.18841	0.017991	-0.03268	0.259472	-0.03149
Cold ischemia time	0.034621	0.064709	-0.1487	0.110151	-0.03088	-0.03307
Perfusate used
HTK	0.215541	0.290157	-0.37809	0.297393	-0.41002	-0.3985
Marshalls	-0.20981	0.069047	-0.01459	-0.0697	-0.08986	0.273508
Wisconsin	0.024312	-0.25256	0.202352	-0.14489	0.288148	-0.0685
Perfusion quality
Fair	-0.09903	0.066815	-0.02273	0.053659	-0.05518	0.043223
Good	0.124324	-0.07958	0.038627	-0.05322	0.067024	-0.081
Poor	-0.0704	0.039988	-0.03226	0.015022	-0.03558	0.071809
Machine perfusion type
HMP	-0.16465	-0.10792	0.072853	-0.13631	0.066932	0.165752
NMP	-0.02219	-0.00674	-0.03713	0.026516	0.005664	0.028618
SCS	0.139758	0.087785	-0.0411	0.083732	-0.05858	-0.15598
Donor homozygous at A locus	-0.02882	-0.03397	0.331391	-0.14094	-0.08519	-0.08234
Donor homozygous at B locus	0.018333	-0.00219	0.324462	-0.32254	-0.05012	-0.07189
Donor homozygous at DR locus	-0.07049	-0.05484	0.384054	-0.34321	0.018206	-0.03753
Recipient homozygous at A locus	-0.11426	-0.12039	-0.26716	0.185844	0.20061	0.06497
Recipient homozygous at B locus	-0.24938	-0.25056	-0.36106	0.442481	0.216542	0.018343
Recipient homozygous at DR locus	-0.3925	-0.3688	-0.4553	0.514814	0.316519	0.132615
Number of mismatches at A locus
One	0.100524	0.107959	-0.19918	-0.046	-0.00287	0.037924
Two	-0.04103	-0.02375	-0.61386	0.245613	0.214416	0.138909
Zero	-0.08528	-0.11969	0.865188	-0.28684	-0.30846	-0.25372
Number of mismatches at B locus
One	0.194076	0.181726	-0.21583	-1.02907	0.522414	0.361438
Two	-0.43557	-0.20574	-0.80177	1.61737	-0.26989	-0.11265
Zero	0.168862	-0.01822	0.860889	-0.57823	-0.41804	-0.39044
Number of mismatches at DR locus
One	0.156213	0.362725	-1.58327	-0.08453	0.169242	0.572884
Two	-0.49823	-0.29474	-0.53587	1.400915	-0.41166	-0.3312
Zero	0.083765	-0.20624	2.088466	-1.29858	0.038214	-0.39782
HLA mismatch group
(0 DR and 2B) OR (1 DR and 1/0 B)	0.320803	0.492691	-1.5359	-0.88766	0.35718	0.817322
(1 DR and 2 B) OR (2 DR)	-0.64264	-0.32933	-0.73181	2.732471	-0.5118	-0.36669
0 DR and 1/0 B	0.200285	-0.13652	0.942319	-1.01767	0.132115	-0.42344
0 Mismatches	-0.29107	-0.33901	1.013344	-0.3991	-0.3991	-0.3991
Initial graft function
DGF	-0.11953	0.293189	-0.1664	0.075526	-0.21589	0.094297
Immediate	0.107333	-0.35624	0.207118	-0.087	0.260541	-0.08576
PNF	0.019437	0.177065	-0.13987	0.038363	-0.15666	-0.01597
Predniscolone/predniscone immunosuppression 3 months post-transplant
No	-0.10243	-0.02439	0.089443	-0.0981	0.005436	0.123103
Yes	0.102431	0.024386	-0.08944	0.098099	-0.00544	-0.1231
Graft status
Died functioning	-0.25092	0.067352	-0.02856	-0.02329	-0.15542	0.314832
Died unknown function	-0.04474	0.055994	-0.039	0.010615	-0.01671	0.011187
Failed	-0.18583	0.234386	0.023866	-0.09706	-0.13882	0.114523
Functioning	0.330622	-0.24579	0.006453	0.089744	0.222438	-0.33668
Allocation matchability score	-0.82615	-0.91113	-0.48134	0.939133	0.94143	0.608976
Serum creatinine (umol/L) at 3 months post-transplant	-0.55205	1.076702	-0.00929	-0.20292	-1.05008	0.27868
Serum creatinine (umol/L) at 12 months post-transplant	-0.54517	1.001822	0.035808	-0.20997	-0.97139	0.28784
Follow-up time	-1.02083	-1.36537	1.02637	-1.03852	1.304328	0.609898
Transplant year
2014	-0.46973	-0.40766	0.318161	-0.41243	0.36776	0.215761
2015	-0.44461	-0.3679	0.280245	-0.36841	0.317711	0.249368
2016	-0.43155	-0.31821	0.318755	-0.35172	0.25152	0.249478
2017	-0.35466	-0.2451	0.278868	-0.36176	0.238236	0.233183
2018	-0.14226	-0.11021	0.065559	-0.22613	0.162749	0.19049
2019	0.031142	-0.00751	-0.11104	0.1739	-0.14187	0.03025
2020	0.29756	0.11046	-0.33259	0.309795	-0.32021	-0.2833
2021	0.37828	0.319815	-0.4093	0.228833	-0.46416	-0.41834
2022	0.368105	0.342109	-0.43481	0.233157	-0.46783	-0.46145
2023	0.262064	0.285086	-0.3182	0.121005	-0.34658	-0.33995
2024	0.066904	0.161389	-0.30486	0.355243	-0.30492	-0.30949
Kidney used by local centre
No	0.358659	0.266388	-0.07062	0.248008	-0.23235	-0.46553
Yes	-0.35866	-0.26639	0.070616	-0.24801	0.232346	0.465532

BMI: Body mass index; UTI: Urinary tract infection; DBD: Donation after brain death; DCD: Donation after cardiac death; HTK: Histidine-tryptophan-ketoglutarate solution; HMP: Hypothermic machine perfusion; NMP: Normothermic machine perfusion; HLA: Human leukocyte antigen; DGF: Delayed graft function; PNF: Primary non-function.

Table 7 Machine perfusion subgroup features standardized mean differences by cluster.

Characteristic	Cluster 1 (n = 41)	Cluster 2 (n = 59)	Cluster 3 (n = 93)	Cluster 4 (n = 36)	Cluster 5 (n = 97)	Cluster 6 (n = 218)
Recipient age	-0.52238	0.935377	-0.17692	-0.14135	-0.5752	0.624424
Recipient BMI	-0.33675	0.341342	0.100018	0.104799	-0.29737	0.077307
Recipient sex
Female	-0.12192	-0.47267	0.037357	0.329161	0.231682	-0.05627
Male	0.121923	0.472666	-0.03736	-0.32916	-0.23168	0.05627
Recipient ABO blood group
A	0.00696	0.193519	-0.00775	0.011911	-0.07437	-0.13309
AB	0.173135	-0.16482	0.013513	-0.08419	0.062414	-0.0548
B	-0.07912	0.001768	-0.32229	0.169568	-0.01784	0.17967
O	-0.03561	-0.13813	0.183969	-0.09859	0.058822	0.026817
Recipient ethnicity
Asian	-0.07204	-0.10315	-0.33003	0.507309	-0.00709	-0.10166
Black	0.177035	0.076748	-0.40214	0.282133	-0.15149	-0.13602
White	-0.06636	0.031694	0.534651	-0.65321	0.100554	0.173304
Recipient diabetes	-0.11318	0.251095	-0.25194	0.133863	-0.36278	0.217526
Recipient positive CMV status	-0.16999	-0.02122	-0.31585	0.471722	0.070829	-0.01996
Dialysis status at registration
Hemodialysis	-0.04066	0.256224	-0.24872	0.630677	-0.46044	-0.11067
Not	-0.16484	-0.04565	0.272456	-0.43957	0.263876	0.070191
Peritoneal	0.261768	-0.34949	-0.02704	-0.32742	0.252628	0.060744
Dialysis at transplant	0.060974	0.136638	-0.17833	0.330709	-0.08688	-0.18986
Type of dialysis at transplant
Hemodialysis	-0.26222	0.116985	-0.06999	0.45709	-0.08642	-0.08056
Not	0.235702	-0.10426	-0.10426	-0.10426	-0.10426	-0.10426
Peritoneal	0.203308	-0.1042	0.083027	-0.4446	0.099488	0.093619
Donor organ
Left kidney	-0.03682	0.012793	0.082894	-0.20909	-0.11916	0.271376
Right kidney	0.036822	-0.01279	-0.08289	0.209092	0.119164	-0.27138
Highly sensitised status flag	-0.04705	-0.24711	-0.07932	0.239504	0.207115	-0.20468
Waiting list time	0.293259	0.292544	-0.51323	0.140545	-0.11534	-0.19133
Recipient deprivation group
Quartile 1 most deprived	0.144294	0.009881	0.047681	-0.19907	-0.02608	0.012131
Quartile 2 second most deprived	-0.29413	0.468065	-0.08528	-0.02003	-0.2488	0.103914
Quartile 3 second least deprived	-0.06986	-0.25307	-0.02343	0.291574	0.042275	-0.0128
Quartile 4 least deprived	0.171772	-0.25815	0.053363	-0.09517	0.199419	-0.10384
Donor age	-0.68036	0.878226	0.228306	-0.07469	-1.10569	0.959388
Donor BMI	-0.43307	0.415931	0.055243	-0.05396	-0.33119	0.259145
Donor sex
Female	-0.29708	0.014101	0.296941	0.079911	-0.35442	0.227365
Male	0.297078	-0.0141	-0.29694	-0.07991	0.354417	-0.22736
Donor ABO blood group
A	0.045051	0.172103	-0.00267	-0.07713	-0.01967	-0.11994
AB	0.151565	-0.07105	-0.03261	0.015795	-0.03985	-0.05891
B	-0.03287	0.048817	-0.33718	0.218087	-0.09518	0.118041
O	-0.08087	-0.18356	0.190299	-0.07592	0.087987	0.05895
Donor ethnicity
Asian	-0.09388	0.172408	-0.09388	-0.09388	-0.09388	0.019577
Black	0.235702	-0.10426	-0.10426	-0.10426	-0.10426	-0.10426
White	-0.18284	-0.10107	0.140638	0.140638	0.140638	0.050717
Donor positive CMV status	-0.15319	-0.07133	-0.12388	0.179753	0.047903	0.118171
Donor positive EBV status	-0.09206	0.003988	-0.01369	0.12261	0.002437	-0.0115
Donor positive toxoplasmosis status	0.085221	-0.05017	0.100121	-0.19446	-0.10309	0.136286
Donor cardiac disease	-0.02698	0.549406	-0.207	-0.07812	-0.37416	-0.01591
Donor diabetes	-0.37831	0.475118	-0.20372	0.007774	-0.13606	-0.02641
Donor family history of diabetes	-0.06424	0.279421	-0.16018	-0.023	-0.03486	-0.0104
Donor history of drug abuse	0.834764	-0.49937	-0.67434	0.437373	0.154552	-0.65409
Donor hypertension	-0.67428	1.019971	-0.23869	-0.06014	-0.66262	0.343796
Donor smoker	0.18875	0.098478	-0.23545	0.284012	0.191422	-0.50291
Donor history of UTI	-0.01377	0.183746	-0.15672	0.14669	-0.2279	-0.00165
Donor allergy	0.153133	0.428873	-0.21322	0.413296	-0.60394	-0.24876
Donor creatinine at retrieval	0.125502	-0.42356	-0.02563	-0.096	0.351898	0.014002
Donor type
DBD	0.007415	-0.10228	-0.03346	0.273614	-0.09862	-0.10432
DCD	-0.00741	0.102277	0.033465	-0.27361	0.098615	0.10432
Donor cause of death
Neurological	0.26055	0.454746	-0.35274	0.090477	-0.15611	-0.07575
Other	-0.26055	-0.45475	0.352744	-0.09048	0.156112	0.075749
Cold ischemia time	-0.04488	0.342452	-0.45242	0.597162	-0.26049	-0.19252
Perfusate used
HTK	-0.03971	0.03199	-0.06026	0.294468	-0.16003	-0.21855
Marshalls	-0.34773	0.217686	0.179445	-0.42416	-0.04817	0.282263
Wisconsin	0.338959	-0.21966	-0.14738	0.191593	0.106176	-0.19929
Perfusion quality
Fair	-0.39856	0.091242	0.122445	-0.11029	0.215936	-0.02153
Good	0.225004	-0.18566	-0.09372	0.166457	-0.10417	0.027697
Poor	0.074921	0.158416	-0.00977	-0.11489	-0.12394	-0.01525
Machine perfusion type
HMP	-0.62818	-0.18049	0.573901	-0.58306	0.42157	0.439779
NMP	0.62818	0.180493	-0.5739	0.583062	-0.42157	-0.43978
Donor homozygous at A locus	0.021713	0.146149	0.112907	-0.25555	-0.0396	-0.01395
Donor homozygous at B locus	0.02525	-0.02818	0.14671	-0.49644	0.237927	-0.03754
Donor homozygous at DR locus	-0.10806	-0.12001	0.626996	-0.51105	0.071818	-0.15142
Recipient homozygous at A locus	0.044589	-0.14692	-0.41768	0.125595	0.168964	0.146465
Recipient homozygous at B locus	-0.3114	-0.08202	-0.28739	0.408741	0.074077	0.066697
Recipient homozygous at DR locus	-0.54784	-0.41639	-0.35489	0.589812	0.238174	0.188202
Number of mismatches at A locus
One	0.097199	-0.10749	0.212251	-0.03473	-0.08176	-0.08028
Two	-0.29478	0.128613	-0.58751	0.229485	0.228751	0.173743
Zero	0.19625	-0.01389	0.309202	-0.26653	-0.18904	-0.1127
Number of mismatches at B locus
One	0.048535	-0.00741	0.204379	-0.86645	0.476811	0.170374
Two	-0.48232	0.012601	-0.83654	1.326824	-0.2564	-0.04173
Zero	0.40401	-0.00523	0.446308	-0.5802	-0.39206	-0.2065
Number of mismatches at DR locus
One	0.483892	0.361597	-1.98063	0.104253	0.122609	0.334855
Two	-0.4994	-0.18924	-0.4994	0.968966	-0.23929	-0.08191
Zero	-0.25134	-0.26978	2.62874	-1.17182	0.002459	-0.30515
HLA mismatch group
(0 DR and 2B) OR (1 DR and 1/0 B)	0.673474	0.521873	-1.75727	-0.62392	0.28404	0.447561
(1 DR and 2 B) OR (2 DR)	-0.63189	-0.11729	-0.7675	1.718072	-0.36943	-0.1061
0 DR and 1/0 B	-0.18083	-0.42722	1.80884	-0.94859	0.05366	-0.34678
0 Mismatches	-0.26696	-0.26696	0.644658	-0.26696	-0.26696	-0.26696
Initial graft function
DGF	-0.29227	0.364925	-0.0898	0.109398	-0.13641	-0.00691
Immediate	0.191538	-0.4476	0.15867	-0.0392	0.205079	-0.02326
PNF	0.181014	0.220671	-0.24713	-0.24713	-0.24713	0.07753
Predniscolone/predniscone immunosuppression 3 months post-transplant
No	-0.08321	-0.32889	0.146769	0.159979	-0.00221	0.079611
Yes	0.083214	0.328894	-0.14677	-0.15998	0.002211	-0.07961
Graft status
Died functioning	-0.33468	0.076472	-0.04423	0.029598	-0.22774	0.38821
Died unknown function	-0.06428	-0.06428	-0.06428	-0.06428	0.144338	-0.06428
Failed	-0.07421	0.396202	-0.12747	-0.11402	-0.26933	0.103673
Functioning	0.299809	-0.38451	0.136365	0.068689	0.35079	-0.39189
Allocation matchability score	-0.89236	-0.89449	-0.31801	1.168311	0.775282	0.397993
Serum creatinine (umol/L) at 3 months post-transplant	-0.49329	1.139701	0.037743	-0.50205	-0.92856	0.25578
Serum creatinine (umol/L) at 12 months post-transplant	-0.5095	0.901736	-0.009	-0.24362	-0.87226	0.279751
Follow-up time	-0.81744	-1.51375	1.030244	-1.33825	1.48027	0.590485
Transplant year
2014	-0.70809	-0.36308	0.425425	-0.55108	0.447064	0.3227
2015	-0.54249	-0.24363	0.335796	-0.54249	0.373961	0.224117
2016	-0.21921	0.022467	0.247963	-0.43858	-0.02	0.268664
2017	-0.41371	-0.2814	0.045193	-0.0506	0.359465	0.11809
2018	0.099585	-0.20458	0.044465	0.058397	0.067217	-0.09786
2019	0.387393	-0.0166	-0.17485	0.02006	-0.23666	-0.07566
2020	0.153595	0.41158	-0.52733	0.399002	-0.53008	-0.26831
2021	0.546193	0.314455	-0.56336	0.269375	-0.56604	-0.4434
2022	0.353089	-0.20301	-0.20301	0.091326	-0.20301	-0.20301
2023	0.180164	0.11638	-0.12913	-0.12913	-0.12913	-0.12913
2024	-0.32116	0.146404	-0.21728	0.54339	-0.32116	-0.32116
Kidney used by local centre
No	0.400771	0.574001	-0.35512	0.431431	-0.53165	-0.49953
Yes	-0.40077	-0.574	0.355118	-0.43143	0.531653	0.499525

BMI: Body mass index; UTI: Urinary tract infection; DBD: Donation after brain death; CMV: Cytomegalovirus; EBV: Epstein-Barr virus; DCD: Donation after cardiac death; HTK: Histidine-tryptophan-ketoglutarate solution; HMP: Hypothermic machine perfusion; NMP: Normothermic machine perfusion; HLA: Human leukocyte antigen; DGF: Delayed graft function; PNF: Primary non-function.

Within the MP subgroup, cluster 1 demonstrated a consistent phenotypic pattern compared to the full cohort. Immunologically, the profile remained low-risk but was more clearly defined, with enrichment of intermediate DR mismatch (DRMM = 1 SMD +0.48) and lower number of B-locus mismatches (BMM) (e.g., BMM = 0 SMD +0.40; BMM = 2 SMD -0.48), alongside underrepresentation of high-risk HLA group (SMD -0.63). In this context, the cluster had higher normothermic MP (NMP) prevalence (NMP SMD +0.63), and there was a higher prevalence of organ not used by local centre (SMD +0.57).

In contrast to cluster 1, cluster 2 had older donor and recipient male patients (SMD +1.15 and SMD +0.89) with a higher burden of cardiovascular and metabolic comorbidities, such as donor hypertension (SMD +0.75), cardiovascular disease (SMD +0.45), recipient diabetes (SMD +0.33), and high BMI for both (SMD +0.36 and SMD +0.33). Immunologically, the profile reflects intermediate risk, with enrichment of moderate mismatch patterns (e.g., DRMM = 1 SMD +0.36) and reduced representation of fully matched transplants (HLA mismatch group: 0 mismatches SMD -0.34). This cluster had higher serum creatinine at 3 and 12 months posttransplant (SMD +1.08 and +1.00, respectively) and reduced prevalence of immediate graft function (SMD -0.36).

Within the MP subgroup, the pattern remained consistent, with additional signals suggesting greater donor and recipient complexity. Donors were more frequently of neurological cause of death (SMD +0.45) and exhibited lower pre-transplant donor renal creatinine (SMD -0.42). There was a higher prevalence of organ not used by local centre (SMD +0.57). Allocation matchability scores remained lower (SMD -0.89). Immunologically, the intermediate-risk profile persisted.

Cluster 3 in the full cohort was predominantly defined by a highly favorable immunologic profile, with strong enrichment of zero mismatches across loci (DRMM = 0 SMD + 2.08; number of A-locus mismatches = 0 SMD +0.86; BMM = 0 SMD +0.86) and fully matched HLA groups (0 mismatches SMD +1.01; 0 DR and 1/0 B SMD +0.94), alongside marked underrepresentation of intermediate and high-risk mismatch categories. This cluster also exhibited longer follow-up (SMD +1.02) and shorter waiting time (SMD -0.68), with lower allocation matchability scores (SMD -0.48). Demographically, recipients were more frequently White (SMD +0.45), with lower representation of Asian recipients (SMD -0.33), less likely to be on dialysis at transplant (SMD +0.33), and donors had no history of drug abuse (SMD +0.48).

Within the MP subgroup, the phenotype was preserved and remained strongly immunologically driven, with even greater enrichment of zero DRMM mismatches (DRMM = 0 SMD +2.62) and further depletion of higher mismatch categories (e.g., DRMM = 1 SMD -1.98). This cluster was preferentially associated with hypothermic MP (HMP) (SMD +0.57) and shorter cold ischemic time (SMD -0.45). Additionally, it showed a temporal shift toward earlier transplant years (e.g., 2014 SMD +0.42; 2021 SMD -0.56), alongside persistently shorter waiting time (SMD -0.51).

In comparison to cluster 3, cluster 4 was defined by a markedly high-risk immunologic profile, with strong enrichment of severe mismatch patterns (e.g., high-risk HLA group SMD +2.73; BMM = 2 SMD +1.61; DRMM = 2 SMD +1.40) and depletion of favourable matching (e.g., DRMM = 0 SMD -1.29; 0 DR and 1/0 B SMD -1.01). Recipient homozygosity was also more frequent (e.g., Recipient homozygous at DR locus SMD +0.51). This cluster exhibited shorter follow-up (SMD -1.03), higher allocation matchability scores (SMD +0.93), and a lower prevalence of White recipients (SMD -0.41). Transplants were more frequently from later years (e.g., 2024 SMD +0.35 vs 2014 SMD -0.41).

The high-risk immunologic phenotype was preserved for cluster 4 in the MP subgroup. Additional features included a higher prevalence of Asian recipients (SMD +0.50), increased recipient Cytomegalovirus seropositivity (SMD +0.47), and greater use of haemodialysis both at registration and transplant (SMD +0.63 and +0.45). This cluster was preferentially associated with NMP (SMD +0.58) and longer cold ischemic time (SMD +0.59), alongside lower serum creatinine at 3 months post-transplant (SMD -0.50). A temporal shift toward later years persisted (e.g., 2024 SMD +0.54 vs 2014 SMD -0.55).

Cluster 5 in the full cohort was primarily characterised by a younger donor–recipient profile (SMD -1.07 and SMD -0.74) with low cardiovascular comorbidity, including absence of donor hypertension (SMD +0.70) and cardiovascular disease (SMD +0.37). Recipients were more frequently female (SMD +0.35). Clinically, this cluster had lower serum creatinine at 3- and 12-month prevalence (SMD -1.05 and -0.97, respectively), alongside longer follow-up (SMD +1.30). Allocation matchability scores were more prevalent (SMD +0.94). Immunologically, the profile was intermediate, with enrichment of moderate mismatch patterns (e.g., BMM = 1 SMD +0.52) and reduced representation of both high-risk (e.g., SMD -0.51) and fully matched transplants (SMD -0.39). Transplants were more frequent in earlier years (e.g., 2014 SMD +0.36 vs 2022 SMD -0.46).

Accordingly, in the MP subgroup the phenotype remained consistent, driven by younger donors and recipients and low comorbidity, with additional signals including higher prevalence of organ used by local centre (SMD +0.53) and reduced dialysis at registration (SMD -0.46). Lower serum creatinine persisted for 3 and 12 months posttransplant (SMD -0.92 and -0.87) and longer follow-up (SMD +1.48), alongside higher allocation matchability scores (SMD +0.77) and earlier transplant years. Immunologic differentiation was less pronounced, remaining in an intermediate range (e.g., BMM = 1 SMD +0.47), while the cluster showed a relative association with HMP (SMD +0.42).

Lastly, cluster 6 in the full cohort had older donors and recipients (SMD +0.92 and SMD +0.65, respectively) with a higher prevalence of donor hypertension (SMD +0.41) but absence of behavioural risk factors, including drug abuse (SMD +0.68) and smoking (SMD +0.32). Immunologically, the profile is intermediate, with enrichment of moderate mismatch patterns (e.g., DRMM = 1 SMD +0.57; intermediate HLA group SMD +0.81) and reduced representation of both fully matched and high-risk transplants. This cluster showed longer follow-up (SMD +0.60) and higher allocation matchability scores (SMD +0.60). Graft outcomes were characterised by a lower proportion of functioning grafts (SMD -0.33) alongside a higher proportion of death with a functioning graft (SMD +0.31).

The phenotype was well preserved in the MP subgroup, with similar age, comorbidity, and intermediate immunologic patterns. The cluster showed a relative association with HMP (SMD +0.44), while maintaining longer follow-up (SMD +0.59), and higher allocation matchability scores (SMD +0.40). There was a higher prevalence of organ used by the local centre (SMD +0.49). The graft outcome pattern was consistent, with fewer functioning grafts (SMD -0.39) and a higher proportion of death with a functioning graft (SMD +0.39). Figure 6 has the SMD profiling heatmaps.

Figure 6 Standardized mean difference heatmaps for cluster characterization. Heatmaps displaying the top 30 clinical features with the largest absolute standardized mean difference (SMD) across clusters for the full cohort (n = 15904) and the machine perfusion subgroup (n = 544). Features include demographic, clinical, and transplant-related variables from both donors and recipients, ranked from top to bottom by maximum absolute SMD across all clusters. Each cell represents the SMD of a given feature in one cluster compared to all other clusters combined. The color scale ranges from blue (negative SMD, feature value lower than average) through white (SMD approximately 0) to orange (positive SMD, feature value higher than average). Columns represent the six patient clusters; rows represent individual features. SMD values ≥ 0.3 or ≤ -0.3 are generally considered clinically meaningful differences. A: The full cohort; B: The machine perfusion subgroup. SMD: Standardized mean difference; HLA: Human leukocyte antigen; MP: Machine perfusion.

Optimal cluster matching via the Hungarian algorithm confirmed robust phenotypic alignment between datasets. Matched clusters exhibited high Pearson correlations and low mean absolute differences (Table 8), consistent with the cluster-wise scatter plots (Figure 7). Data completeness was comparable across clusters, with no evidence of systematic differences in missingness.

Figure 7 Cross-dataset Standardized mean difference profile agreement between matched clusters. Scatter plots comparing standardized mean difference (SMD) profiles between corresponding clusters in the full cohort (X-axis) and machine perfusion subgroup (Y-axis) for cluster 1, cluster 2, cluster luster 3, cluster luster 4, cluster luster 5, and cluster luster 6 each point represents a single clinical feature’s SMD value in the matched cluster pair. Optimal cluster correspondence between datasets was determined using the Hungarian algorithm to maximize phenotypic similarity based on SMD profiles. The orange dashed line (Y = X) represents perfect agreement. Points closer to this line indicate consistent feature effect sizes across datasets, while deviations suggest differential phenotypic patterns. Phenotypic alignment was quantified using Pearson correlation coefficients and mean absolute differences between matched SMD profiles. A: Cluster 1; B: Cluster 2; C: Cluster 3; D: Cluster 4; E: Cluster 5; F: Cluster 6. MP: Machine perfusion; SMD: Standardized mean difference.

Table 8 Cross-Dataset cluster alignment metrics.

Full cohort cluster	MP subgroup cluster	Pearson r	Mean absolute SMD difference
1	1	0.843	0.130
2	2	0.895	0.128
3	3	0.902	0.152
4	4	0.865	0.164
5	5	0.895	0.117
6	6	0.867	0.101

SMD: Standardized mean difference; MP: Machine perfusion.

Posttransplant outcomes of each kidney transplant cluster

Kaplan-Meier analysis revealed significant differences in both outcomes across clusters in the full cohort and the clinical subset. In the full cohort, survival curves diverged markedly for graft survival (log-rank χ² = 810.7, P < 0.001) and patient survival (log-rank χ² = 1103.6, P < 0.001). In the clinical subset, statistically significant differences were also observed for graft survival (log-rank χ² = 41.7, P < 0.001) and patient survival (log-rank χ² = 57.4, P < 0.001), despite the substantially smaller sample size (n = 544). Kaplan-Meier curves for each outcome, stratified by cluster, are shown in Figures 8 and 9.

Figure 8 Graft survival Kaplan-Meier curves for the full cohort (n = 15904) and the machine perfusion subgroup (n = 544). Time zero represents the date of transplantation, with patients followed for up to 5 years. The y-axis shows overall survival probability. Numbers at risk are displayed below each panel. Survival differences between clusters were evaluated using the log-rank test; P values are displayed. Cluster 2 exhibited the steepest graft survival decline in both datasets. The machine perfusion subgroup showed the highest graft failure rate, with all events occurring within the first 2.07 years post-transplant. A: The full cohort; B: The machine perfusion subgroup. MP: Machine perfusion.

Figure 9 Patient survival Kaplan-Meier curves for the full cohort (n = 15904) and the machine perfusion subgroup (n = 544). Time zero represents the date of transplantation, with patients followed for up to 5 years. The y-axis shows overall survival probability. Numbers at risk are displayed below each panel. Survival differences between clusters were evaluated using the log-rank test; P values are displayed. Cluster 4 showed a marked decrease in 5-year patient survival in the machine perfusion subgroup compared with the full cohort (57% vs 78%), making it the worst-performing cluster in this population. A: The full cohort; B: The machine perfusion subgroup. MP: Machine perfusion.

In the full cohort, clusters 5 and 3 had the highest estimated 5-year patient survival probabilities (95.2% with a 95%CI: 94.2%-96.0% and 92.1%CI: 90.9%-93.2%, respectively), followed by clusters 1 and 6 (86.5%CI: 84.1%-88.6% and 82.4%CI: 81.1%-83.7%), cluster 4 (75.9%CI: 72.2%-79.1%), and cluster 2 (64.2%CI: 60.5%-67.6%). Graft survival in the full cohort followed a similar ranking, with clusters 5 and 3 again performing best (93.7%CI: 92.6%-94.6% and 91.2%CI: 89.9%-92.4%), clusters 6 and 1 in an intermediate position (86.9%CI: 85.7%-88.1% and 86.5%CI: 83.9%-88.7%), cluster 4 at 84.2%CI: 81.2%-86.7%, and cluster 2 showing the steepest progressive decline across the 5-year follow-up (64.4%CI: 60.6%-68.0%).

In the MP subgroup, the pattern for patient survival was largely preserved for clusters 5, 3, 1, and 6, which showed modest improvements compared to the full cohort (e.g. cluster 5: 95.2% vs 96.8%). Cluster 2 behaved similarly to the full cohort. Cluster 4 showed a marked decrease in 5-year patient survival in the subgroup compared with the full cohort (55.3% vs 75.9%), although estimates for the smaller MP clusters should be interpreted in the context of wider uncertainty.

For graft survival in the MP subgroup, clusters 5 and 3 continued to show the highest estimated survival probabilities with values closely mirroring the full cohort (94.7%CI: 87.6%-97.7% and 90.9%CI: 82.6%-95.4%). Clusters 6 and 1 remained in an intermediate position, with cluster 6 showing a slight improvement over cluster 1 within the subgroup. Cluster 4 showed a larger decline in the subgroup than in the other clusters relative to the full cohort (80.9%CI: 54.6%-92.8%). Cluster 2 exhibited the steepest graft survival decline in both datasets. The MP subgroup showed the highest graft failure rate, with all events occurring within the first 2.07 years post-transplant.

DISCUSSION

We applied unsupervised clustering, mixed-type PCA and GMM to identify clinical transplantation phenotypes and examine MP distribution across them. Transferring the GMM to the MP subgroup provided a within-sample face-validity assessment of whether learned latent structure is preserved under conditional restrictions, not independent validation. Models showed moderate-to-good cluster stability; the transferred model had modestly lower confidence in the MP subgroup (mean max posterior 0.679 vs 0.696; mean entropy 0.815 vs 0.783), consistent with application to a more constrained clinical subgroup[42,43].

Clusters with higher observed survival

Clusters 3 and 5 were consistently associated with better outcomes across both endpoints and groups. Cluster 3 presented a favourable immunological profile, shorter waiting times, less dialysis at transplant, and shorter cold ischemia time, though with less recipient ethnicity diversity (predominantly white patients) and lower allocation matchability scores. Cluster 5 had intermediate immunological risk but younger patients, low-comorbidity donors, less dialysis at transplant, and greater association with female recipients. Both showed higher prevalence of local organ use and HMP in the MP subgroup. Despite cluster 3’s superior immunological profile, cluster 5 showed slightly better observed outcomes. cluster 5 had the lowest stability in the full dataset but improved in the MP subgroup, suggesting greater phenotypic homogeneity in that context.

Clusters with intermediate survival patterns

Clusters 1 and 6 showed similar outcomes despite contrasting phenotypes. Cluster 1: Younger patients, low donor cardiovascular comorbidity but high behavioural risk, low allocation matchability, NMP preference, and lower local organ prevalence. Cluster 6: Older patients with hypertension, lower behavioural risk, higher allocation matchability, HMP preference, and higher local organ prevalence. Cluster 6 contained the largest proportion of patients (40% in the MP subgroup) but showed lower assignment confidence, indicating a phenotype with less sharply defined boundaries and greater overlap with neighbouring clusters. Cluster 1 exhibited substantial confidence degradation in the MP subgroup (mean posterior 0.678→0.607; entropy 0.839→1.046), indicating ambiguous cluster membership for many MP patients. Although post-hoc phenotype characterisation remained broadly consistent, findings from these lower-confidence clusters warrant cautious interpretation.

Cluster with lower observed survival

Cluster 2 was consistently associated with the poorest survival outcomes. In the MP subgroup, graft failure was concentrated early (16/59 patients, 27%; all within 2.07 years; median 0.28 years), with 6 failures occurred on the day of transplantation, a pattern potentially consistent with primary non-function (PNF), although PNF was not a predefined study endpoint and this observation should be regarded as hypothesis-generating. Beyond 2.07 years, no further failures occurred (18 patients at-risk at year 3). This early loss pattern differed from the full cohort, where failures occurred throughout follow-up (5-year survival 67%), suggesting MP patients in this cluster may experience different graft loss timing. The phenotype included older, highly comorbid males with intermediate immunological risk, lower organ quality, and similar HMP/NMP distribution. Stability remained good across groups (mean posterior Δ -0.013).

Context-dependent cluster

Cluster 4 showed divergent outcome patterns between groups. Stable in the full cohort but associated with poorer patient survival in the MP subgroup. This phenotype had the least favourable immunological profile, higher donor risk, longer cold ischemia time, more hemodialysis at transplant, and NMP association in the MP subgroup. Higher allocation matchability scores likely reflect prioritisation for immunological complexity while addressing demographic disparities. This cluster showed the highest stability across both groups (mean posterior 0.757 vs 0.723).

Limitations

This study has some limitations. First, full cohort findings may not extend to institutions with different transplant practices, organ allocation systems, or patient and donor characteristics. Also, the MP subgroup represents a specific clinical subset, and cluster behaviour may differ under alternative subgroup definitions (e.g., expanded criteria donors). Survival associations reflect United Kingdom care standards and follow-up practices, limiting applicability to populations with different post-transplant protocols or censoring patterns.

Second, cluster characterisation involved post-hoc descriptive analysis of defining cluster features, precluding unbiased inferential testing. Observed associations between clusters and clinical features are descriptive summaries, not independent statistical tests. Transfer of the GMM to the MP subgroup provided face-validity assessment of structural preservation under conditional restrictions, not independent validation, as this subgroup was included in model training. External validation in an independent cohort represents an appropriate next step. Additionally, several MP clusters contained relatively small numbers of patients, resulting in few individuals remaining at risk near the end of the 5-year follow-up period. Consequently, late Kaplan-Meier survival estimates for these clusters are associated with greater uncertainty and should be interpreted cautiously.

Third, registry data introduce systematic biases: The MP subgroup (n = 544) likely underestimates actual MP utilization due to incomplete capture in national registry data, reflecting documentation gaps rather than true practice patterns. Additional biases include selection bias from documented cases only, coding variability across centres, retrospective temporal confounding, and imputation uncertainty from the handling of missing data. These factors may influence both cluster membership and outcome associations. Consequently, observed outcome differences across clusters should be interpreted as descriptive characteristics of the identified phenotypes rather than evidence of causal relationships.

Fourth, unsupervised learning carries inherent methodological limitations. Latent representations were derived from mixed-type weighted PCA with GMM clustering in latent space. Although formal tests indicated deviation from multivariate normality, GMM served as a flexible parametric approximation rather than a strict generative model. Our proposed model selection methodology favoured robust, interpretable solutions, suggesting observed structure is not method-dependent. However, subjectivity in selecting the number of components and clusters remains, and no ground truth exists to validate phenotype definitions.

CONCLUSION

MP cases showed non-random distribution across data-derived clusters, with notable enrichment in cluster 6 (40% of MP patients), and preferential associations with specific perfusion strategies (HMP in clusters 3, 5, 6; NMP in clusters 1, 4). When restricted to the MP subgroup, cluster definitions remained largely stable and interpretable, though with modestly reduced assignment confidence, suggesting MP cases are embedded within the general population structure rather than representing fundamentally distinct phenotypes. Clusters retained outcome stratification within the MP subgroup, though outcome patterns diverged from the full cohort in specific clusters, particularly cluster 2, where graft failures concentrated early (all within 2.07 years), and cluster 4, which showed poorer patient survival despite stability in the full cohort. These findings suggest MP status interacts with underlying clinical phenotypes, potentially modifying outcome trajectories within certain risk profiles, though the observational design precludes causal inference regarding these associations.

ACKNOWLEDGEMENTS

The data reported in this study were derived from the United Kingdom Transplant Registry held by NHS Blood and Transplant and acquired via the National Research Pathway. We are thankful for their collaboration and support.