How to impute study-specific standard deviations in meta-analyses of skewed continuous endpoints?

Table 5 Absolute differences between standardized estimates, θstand_ijk, calculated by means of one of the four methods (conservative SD, less conservative SD, mean SD and interquartile range), and the reference

Distributionscenario	Dataset	Conservative SD	Less Conservative SD	Mean SD	IQR
Normal	15	-0.310	1.274	0.149	0.110
Normal	30	0.029	-1.483	-0.109	-0.081
Normal	50	-0.434	-0.946	-0.599	-0.444
Normal	100	0.340	0.095	0.243	0.180
Normal	500	-0.336	-0.357	-0.353	-0.261
Normal	1000	0.754	0.989	0.860	0.638
No. of times of beginning first in the ranking1		2	1	0	3
Standard normal	15	-0.335	1.072	0.062	0.046
Standard normal	30	-0.101	-1.710	-0.290	-0.215
Standard normal	50	-0.535	-1.013	-0.690	-0.511
Standard normal	100	0.502	0.281	0.416	0.308
Standard normal	500	-0.306	-0.314	-0.317	-0.235
Standard Normal	1000	0.814	1.054	0.923	0.684
No. of times of beginning first in the ranking1		1	1	0	4
Gamma	15	-0.283	0.054	-0.119	-0.088
Gamma	30	1.441	2.229	1.846	1.368
Gamma	50	1.795	2.929	2.218	1.644
Gamma	100	4.915	8.193	6.070	4.500
Gamma	500	24.081	35.799	28.753	21.314
Gamma	1000	49.089	71.072	58.012	43.002
No. of times of beginning first in the ranking1		0	1	0	5
Exponential	15	-0.150	-0.163	-0.157	-0.116
Exponential	30	1.880	2.958	2.301	1.706
Exponential	50	2.948	4.975	3.707	2.748
Exponential	100	10.213	19.490	13.493	10.002
Exponential	500	39.546	74.955	51.913	38.481
Exponential	1000	80.605	157.083	106.593	79.016
No. of times of beginning first in the ranking1		0	0	0	6
Bimodal	15	1.142	4.114	1.751	1.298
Bimodal	30	0.079	0.356	0.096	0.071
Bimodal	50	0.545	3.051	1.110	0.823
Bimodal	100	2.405	6.849	3.650	2.706
Bimodal	500	19.156	41.495	26.212	19.431
Bimodal	1000	38.825	81.301	52.527	38.938
No. of times of beginning first in the ranking1		5	0	0	1
ICU stay	15	0.076	-2.816	2.667	1.977
ICU stay	30	-3.011	-6.341	-4.201	-3.114
ICU stay	50	-1.361	-3.162	-2.163	-1.603
ICU stay	100	-0.58	-2.205	1.393	1.032
ICU stay	500	-6.218	-21.788	-6.462	-4.790
ICU stay	1000	3.162	-5.020	6.801	5.042
No. of times of beginning first in the ranking1		5	0	0	1
Hospital stay	15	1.437	8.948	2.777	2.058
Hospital stay	30	2.603	-1.088	2.595	1.924
Hospital stay	50	0.297	-0.839	-0.055	-0.041
Hospital stay	100	-4.674	-13.063	-6.734	-4.992
Hospital stay	500	-29.239	-55.703	-37.170	-27.554
Hospital stay	1000	-52.720	-85.673	-63.453	-47.038
No. of times of beginning first in the ranking1		2	1	0	3
1st quartile		0.337	1.023	0.368	0.273
Median		1.399	2.944	2.190	1.624
3rd quartile		4.855	12.034	6.666	4.942
Total number of times of beginning first in the ranking1		15	4	0	23

¹The ranking procedure was based on differences in absolute value. Number of times that each standardized estimate ranked as for first, for each simulated distribution. Median (interquartile range) of overall standardized estimate distributions. IQR: Interquartile range.