title: A simulation study of finite-sample properties of marginal structural Cox proportional hazards models.
abstract: 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.
authors.affiliation: Department of Obstetrics and Gynecology and Duke Global Health Institute, Duke University, Durham, NC, USA. daniel.westreich@duke.edu
authors.forename: Daniel
authors.initials: D
authors.lastname: Westreich
authors.forename: Stephen R
authors.initials: SR
authors.lastname: Cole
authors.forename: Enrique F
authors.initials: EF
authors.lastname: Schisterman
authors.forename: Robert W
authors.initials: RW
authors.lastname: Platt
mesh_terms: D023241:Antiretroviral Therapy, Highly Active / Q000706:statistics & numerical data*; D015982:Bias; D016010:Binomial Distribution; D003198:Computer Simulation; D016001:Confidence Intervals; D015986:Confounding Factors, Epidemiologic; D005260:Female; D015658:HIV Infections / Q000188:drug therapy* / Q000401:mortality; D006801:Humans; D008297:Male; D009010:Monte Carlo Method; D015337:Multicenter Studies as Topic; D016016:Proportional Hazards Models; D011446:Prospective Studies; D018401:Sample Size; D013997:Time Factors; D016896:Treatment Outcome; D014481:United States