Marginal Structural Models to Estimate the Causal Effect of Zidovudine on the Survival of HIV-Positive Men

TLDR

Standard methods for survival analysis, such as the time‑dependent Cox model, may produce biased effect estimates when time‑dependent confounders are affected by prior treatment, whereas marginal structural models use inverse‑probability‑of‑treatment weighting to appropriately adjust for such confounding. The study describes a marginal structural Cox proportional hazards model to estimate the causal effect of zidovudine on survival of HIV‑positive men in the Multicenter AIDS Cohort Study and compares this approach with previously proposed causal methods. The marginal structural Cox model applies inverse‑probability‑of‑treatment weighting, accounting for CD4 lymphocyte count as a time‑dependent confounder affected by prior zidovudine treatment. Crude analysis showed a mortality rate ratio of 3.6, which reduced to 2.3 after baseline adjustment, and further to 0.7 when time‑dependent confounding was controlled using the marginal structural model.

Abstract

Standard methods for survival analysis, such as the time-dependent Cox model, may produce biased effect estimates when there exist time-dependent confounders that are themselves affected by previous treatment or exposure. Marginal structural models are a new class of causal models the parameters of which are estimated through inverse-probability-of-treatment weighting; these models allow for appropriate adjustment for confounding. We describe the marginal structural Cox proportional hazards model and use it to estimate the causal effect of zidovudine on the survival of human immunodeficiency virus-positive men participating in the Multicenter AIDS Cohort Study. In this study, CD4 lymphocyte count is both a time-dependent confounder of the causal effect of zidovudine on survival and is affected by past zidovudine treatment. The crude mortality rate ratio (95% confidence interval) for zidovudine was 3.6 (3.0–4.3), which reflects the presence of confounding. After controlling for baseline CD4 count and other baseline covariates using standard methods, the mortality rate ratio decreased to 2.3 (1.9–2.8). Using a marginal structural Cox model to control further for time-dependent confounding due to CD4 count and other time-dependent covariates, the mortality rate ratio was 0.7 (95% conservative confidence interval = 0.6–1.0). We compare marginal structural models with previously proposed causal methods.