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. 2013 Sep 30;33(5):721–737. doi: 10.1002/sim.5991

Table 2.

Estimated risk differences, log risk ratios and log odds ratios from n = 5,000 simulated datasets, with sample sizes per arm (n) of 50, 100 and 500. The mean treatment effect estimate (Est), the empirical variance across simulations (Emp Var), the mean of the variance estimates (Est Var) and the coverage of the 95% confidence interval (95% Cov) calculated from that variance estimate are shown.

Adjustment Method n per arm Risk difference (True value = 0.07) Log risk ratio (True value = 0.31) Log odds ratio (True value = 0.4)
Est Emp Est 95% Est Emp Est 95% Est Emp Est 95%
Var Var Cov Var Var Cov Var Var Cov
Unadjusted
50 0.07 0.007 0.007 94.8 0.33 0.169 0.169 96.8 0.42 0.333 0.263 95.8
100 0.07 0.003 0.003 95.1 0.32 0.080 0.079 95.2 0.40 0.126 0.125 95.4
500 0.07 0.001 0.001 94.4 0.31 0.015 0.015 95.2 0.40 0.024 0.024 94.8
Adjusting for X1 only
Covariate adjustment 50 0.06 0.007 0.006 93.3 0.32 0.172 0.168 96.2 0.43 0.341 0.270 95.7
100 0.07 0.003 0.003 94.9 0.32 0.081 0.079 95.0 0.41 0.128 0.127 95.4
500 0.07 0.001 0.001 94.5 0.31 0.015 0.015 95.0 0.40 0.025 0.024 94.7
IPTW 50 0.07 0.007 0.007 94.6 0.33 0.171 0.166 96.4 0.42 0.333 0.259 95.5
(i) 0.007 94.7 0.169 96.6 0.263 95.7
(ii) 0.007 94.3 0.168 96.2 0.300 96.7
100 0.07 0.003 0.003 95.1 0.32 0.080 0.078 95.0 0.40 0.126 0.124 95.3
(i) 0.003 95.1 0.079 95.2 0.125 95.4
(ii) 0.003 95.0 0.078 95.2 0.145 96.7
500 0.07 0.001 0.001 94.5 0.31 0.015 0.015 95.1 0.40 0.024 0.024 94.6
(i) 0.001 94.6 0.015 95.1 0.024 94.7
(ii) 0.001 94.4 0.015 95.0 0.028 96.4
Adjusting for X1,X2 and X3
Covariate adjustment 50 0.06 0.007 0.006 90.7 0.31 0.182 0.167 95.0 0.43 0.316 0.284 95.0
100 0.06 0.003 0.003 94.1 0.30 0.751 0.078 95.3 0.41 0.132 0.130 95.3
500 0.07 0.001 0.001 94.9 0.31 0.015 0.015 95.4 0.41 0.024 0.024 95.2
IPTW 50 0.07 0.007 0.007 94.0 0.32 0.182 0.167 95.2 0.42 0.293 0.257 94.4
(i) 0.007 94.4 0.174 95.6 0.269 95.1
(ii) 0.007 94.1 0.172 95.2 0.306 96.1
100 0.07 0.003 0.003 94.9 0.32 0.081 0.078 95.7 0.40 0.126 0.124 95.2
(i) 0.003 95.4 0.080 96.0 0.127 95.4
(ii) 0.003 94.9 0.079 95.8 0.146 96.9
500 0.07 0.001 0.001 94.9 0.31 0.015 0.015 95.3 0.40 0.024 0.024 95.3
(i) 0.001 95.0 0.015 95.4 0.024 95.4
(ii) 0.001 95.0 0.015 95.3 0.028 96.8
Adjusting for X4 only
Covariate adjustment 50 0.06 0.007 0.007 94.1 0.33 0.176 0.169 96.2 0.43 0.280 0.269 95.7
100 0.07 0.003 0.003 94.4 0.31 0.081 0.079 95.2 0.41 0.128 0.126 95.2
500 0.07 0.001 0.001 95.2 0.31 0.015 0.015 95.2 0.40 0.024 0.024 95.8
IPTW 50 0.07 0.007 0.007 95.2 0.33 0.178 0.168 96.0 0.42 0.273 0.260 95.6
(i) 0.007 95.3 0.170 96.2 0.263 95.7
(ii) 0.007 94.7 0.168 95.3 0.300 96.6
100 0.07 0.003 0.003 94.7 0.32 0.081 0.079 95.2 0.40 0.127 0.124 95.1
(i) 0.003 94.7 0.079 95.2 0.125 95.2
(ii) 0.003 94.7 0.079 95.2 0.145 96.7
500 0.07 0.001 0.001 95.2 0.31 0.015 0.015 95.1 0.40 0.024 0.024 95.8
(i) 0.001 95.2 0.015 95.2 0.024 95.8
(ii) 0.001 95.3 0.015 95.1 0.028 97.0

(i) = Est Var is the incorrect robust estimate (Inline graphic); (ii) = Est Var is the ‘plug-in’ variance estimator.IPTW, inverse probability-of-treatment weighting.