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A simulation study of finite‐sample properties of marginal structural Cox proportional hazards models

Motivated by a previously published study of HIV treatment, we simulated data subject to time‐varying confounding affected by prior treatment to examine some finite‐sample properties of marginal structural Cox proportional hazards models. We compared (a) unadjusted, (b) regression‐adjusted, (c) unstabilized, and (d) stabilized marginal structural (inverse probability‐of‐treatment [IPT] weighted) model estimators of effect in terms of bias, standard error, root mean squared error (MSE), and 95% confidence limit coverage over a range of research scenarios, including relatively small sample sizes and 10 study assessments. In the base‐case scenario resembling the motivating example, where the true hazard ratio was 0.5, both IPT‐weighted analyses were unbiased, whereas crude and adjusted analyses showed substantial bias towards and across the null. Stabilized IPT‐weighted analyses remained unbiased across a range of scenarios, including relatively small sample size; however, the standard error was generally smaller in crude and adjusted models. In many cases, unstabilized weighted analysis showed a substantial increase in standard error compared with other approaches. Root MSE was smallest in the IPT‐weighted analyses for the base‐case scenario. In situations where time‐varying confounding affected by prior treatment was absent, IPT‐weighted analyses were less precise and therefore had greater root MSE compared with adjusted analyses. The 95% confidence limit coverage was close to nominal for all stabilized IPT‐weighted but poor in crude, adjusted, and unstabilized IPT‐weighted analysis. Under realistic scenarios, marginal structural Cox proportional hazards models performed according to expectations based on large‐sample theory and provided accurate estimates of the hazard ratio. Copyright © 2012 John Wiley & Sons, Ltd.