Table I.

Simulation 1: k = 1.2: ‘MSE’ is mean squared error for unadjusted estimate, RE (relative efficiency) is the ratio of unadjusted MSE to MSE of remaining estimators’ and ‘Rej’ is the proportion of rejected tests at 0.05 level with the coverage probability of a 95 per cent confidence interval in parenthesis. Three methods for selecting Q(A, W), ‘Correct’ is correctly specified, ‘Mis-spec’ is mis-specified, ‘DSA’ is data-adaptive selection based on DSA algorithm. ‘Adjusted’ method for the OR results based on the conditional logistic regression model.

	n = 250	n = 500	n = 1000
Risk difference
Unadjusted MSE	3.8e−03	1.9e−03	9.5e−04
Correct RE	10.46	13.70	13.67
Mis-spec RE	2.14	2.19	2.18
DSA RE	11.72	13.31	13.49
Unadjusted Rej	0.07 (0.94)	0.08 (0.95)	0.10 (0.95)
Correct Rej	0.26 (0.90)	0.42 (0.94)	0.67 (0.95)
Mis-spec Rej	0.08 (0.94)	0.10 (0.95)	0.16 (0.95)
DSA Rej	0.26 (0.90)	0.43 (0.93)	0.67 (0.94)
Relative risk
Unadjusted MSE	3.6e−02	1.7e−02	8.2e−03
Correct RE	9.70	13.97	13.70
Mis-spec RE	2.22	2.27	2.25
DSA RE	12.50	13.59	13.53
Unadjusted Rej	0.05 (0.95)	0.07 (0.95)	0.10 (0.95)
Correct Rej	0.25 (0.90)	0.41 (0.94)	0.67 (0.95)
Mis-spec Rej	0.03 (0.95)	0.05 (0.96)	0.10 (0.96)
DSA Rej	0.19 (0.91)	0.37 (0.94)	0.64 (0.96)
Odds ratio
Unadjusted MSE	1.0e−01	4.6e−02	2.2e−02
Adjusted RE	0.46	0.51	0.48
Correct RE	2.83	14.60	14.04
Mis-spec RE	2.24	2.28	2.21
DSA RE	13.46	14.19	13.86
Unadjusted Rej	0.06 (0.95)	0.08 (0.95)	0.10 (0.95)
Adjusted Rej	0.05 (0.97)	0.07 (0.96)	0.11 (0.96)
Correct Rej	0.26 (0.90)	0.42 (0.94)	0.67 (0.95)
Mis-spec Rej	0.08 (0.94)	0.10 (0.95)	0.15 (0.95)
DSA Rej	0.26 (0.90)	0.43 (0.93)	0.67 (0.95)