Choosing inclusion criteria that minimize the time and cost of clinical trials

Table 1 Expected values of enumeration data in a model trial

	Experimental group	Control group
Number of successes (responses)	α (nπ1 + mπ2)	(1 - α) (nπ3 + mπ4)
Total	α (n + m)	(1 - α) (n + m)

Table 2 Raw data from a reconstructed study of cancer treatment

Class	Old	Male	Smoke	Receptor	Exp	Exp	Control	Control	x	x%
					NR count	R count	NR count	R count
1	1	1	1	1	0	0	0	0	-0.072	47
2	1	1	1	0	5	1	4	2	-0.619	0
3	1	1	0	1	0	0	0	0	0.211	71
4	1	1	0	0	6	1	4	2	-0.336	24
5	1	0	1	1	0	0	1	0	0.113	63
6	1	0	1	0	9	1	6	3	-0.434	16
7	1	0	0	1	1	3	2	2	0.396	87
8	1	0	0	0	9	1	7	3	-0.151	40
9	0	1	1	1	0	0	0	0	0.078	60
10	0	1	1	0	4	0	3	1	-0.468	13
11	0	1	0	1	0	1	1	0	0.362	84
12	0	1	0	0	4	0	3	2	-0.185	37
13	0	0	1	1	0	0	0	0	0.263	76
14	0	0	1	0	6	1	5	2	-0.283	29
15	0	0	0	1	3	6	4	4	0.547	100
16	0	0	0	0	4	1	5	3	0	53
pNR	0.588	0.373	0.471	0.078
pR	0.438	0.188	0.188	0.625
Coef- ficients	a1	a2	a3	a4
	-0.151	-0.185	-0.283	0.547

Table 3 Analysis of data sorted by x-value

x (%)	Sorted experimental data and ROC curve						Sorted control data and regression analysis
	NRcount	R count	p (NR|x)	p (R|x)	ffp	ftp	NR count	R count	pc|xc≥x	u	y= pc (q + u)
0	5	1	0.098	0.063	1.000	1.000	4	2	0.348	1	0.457
13	4	0	0.078	0	0.902	0.938	3	1	0.349	0.962	0.446
16	9	1	0.176	0.063	0.824	0.938	6	3	0.356	0.878	0.424
24	6	1	0.118	0.063	0.647	0.875	4	2	0.360	0.739	0.379
29	6	1	0.118	0.063	0.529	0.813	5	2	0.364	0.652	0.351
37	4	0	0.078	0	0.412	0.750	3	2	0.378	0.549	0.326
40	9	1	0.176	0.063	0.333	0.750	7	3	0.375	0.444	0.284
47	0	0	0	0	0.157	0.688	0	0	0.409	0.228	0.222
53	4	1	0.078	0.063	0.157	0.688	5	3	0.409	0.228	0.222
60	0	0	0	0	0.078	0.625	0	0	0.429	0.125	0.188
63	0	0	0	0	0.078	0.625	1	0	0.429	0.125	0.188
71	0	0	0	0	0.078	0.625	0	0	0.462	0.125	0.203
76	0	0	0	0	0.078	0.625	0	0	0.462	0.125	0.203
84	0	1	0	0.063	0.078	0.625	1	0	0.462	0.125	0.203
87	1	3	0.02	0.188	0.078	0.563	2	2	0.500	0.139	0.227
100	3	6	0.059	0.375	0.059	0.375	4	4	0.500	0.157	0.235