9 9 2 1 P. C. AUSTIN Table IV. Coverage and width of empirical 95 per cent conﬁdence intervals and estimation of sampling variances of treatment effects – 0.29 treatment effect, strong treatment-selection model. Coverage of 95 per cent conﬁdence intervals True risk difference Independent Paired Lengths of 95 per cent conﬁdence intervals Independent Paired Ratio of length of independent CI to paired CI Ratio of mean estimated variance of treatment effect to variance of empirical sampling distribution Independent Paired Independent normal covariates 0 0.979 0.958 −0.02 0.980 0.956 −0.05 0.976 0.951 −0.1 0.975 0.950 −0.15 0.979 0.957 Correlated normal covariates 0 0.979 0.944 −0.02 0.982 0.945 −0.05 0.981 0.952 −0.1 0.968 0.928 −0.15 0.947 0.897 Mixture covariate scenario 1 0 0.970 0.946 −0.02 0.976 0.947 −0.05 0.971 0.942 −0.1 0.969 0.945 −0.15 0.964 0.940 Mixture covariate scenario 2 0 0.966 −0.02 0.970 −0.05 0.969 −0.1 0.968 −0.15 0.968 0.949 0.951 0.944 0.951 0.946 Independent Bernoulli covariates 0 0.959 0.946 −0.02 0.964 0.948 −0.05 0.966 0.948 −0.1 0.965 0.951 −0.15 0.966 0.956 0.181 0.181 0.181 0.180 0.179 0.188 0.189 0.191 0.193 0.193 0.180 0.180 0.179 0.178 0.176 0.176 0.176 0.175 0.172 0.169 0.172 0.172 0.170 0.167 0.163 0.157 0.157 0.157 0.157 0.156 0.157 0.158 0.160 0.162 0.163 0.158 0.158 0.158 0.157 0.156 0.161 0.160 0.159 0.157 0.155 0.161 0.160 0.159 0.156 0.153 1.153 1.153 1.153 1.146 1.147 1.197 1.196 1.194 1.191 1.184 1.139 1.139 1.133 1.134 1.128 1.093 1.100 1.101 1.096 1.090 1.068 1.075 1.069 1.071 1.065 1.391 1.391 1.370 1.356 1.398 1.470 1.478 1.508 1.470 1.334 1.251 1.288 1.240 1.268 1.218 1.205 1.206 1.207 1.223 1.191 1.137 1.117 1.150 1.128 1.121 1.044 1.044 1.032 1.026 1.066 1.027 1.034 1.057 1.039 0.954 0.966 0.995 0.961 0.987 0.956 1.003 1.004 1.005 1.021 1.003 0.989 0.973 1.004 0.990 0.992 treatment effects [5]. The results of our series of Monte Carlo simulations suggest than when outcomes are dichotomous and the risk difference (or the absolute risk reduction) is used as the measure of treatment effect, then statistical methods of inference that account for the matched nature of the propensity-score matched sample are preferable to methods for the analysis of independent samples. The use of methods for independent samples will result in conservative conﬁdence intervals – that is, conﬁdence intervals whose coverage rates exceed the advertised rate. Furthermore, the estimated conﬁdence intervals will tend to be wider, with an associated loss in precision, when methods for independent samples are used compared with when methods for matched samples are used. However, one should note that the estimated risk difference does not depend on whether one assumes that methods for matched samples or methods for independent samples should be used. The current study complements prior published research. An earlier study found that in many settings, methods for paired samples tended to result in improved inference compared with when methods for independent samples were used for the analysis of propensity-score matched samples [15]. In the prior study, empirical coverage rates of conﬁdence intervals and variance estimation was studied for differences in means, rate ratios and relative risks. Furthermore, empirical type I error rates were studied for these three measures of effects as well as for odds ratios and hazard ratios. This prior study did not examine inferences about risk differences. The recent description of a data-generating process for simulating data in which treatment induces a speciﬁed absolute risk reduction [12] permitted the examination of inferences for risk differences that was conducted in the current study. It is important to examine the effect of different methods of analysis on inference when estimating risk differences or absolute risk reductions. Binary outcomes are common in healthcare research [8]. Copyright © 2011 John Wiley & Sons, Ltd. Statist. Med. 2011, 30 1292--1301