Abstract: A common objective of biomedical cohort studies is assessing the effect of a time-varying treatment or exposure on a survival time. In the presence of time-varying confounders, marginal structural models fit using inverse probability weighting can be employed to obtain a consistent and asymptotically normal estimator of the causal effect of a time-varying treatment. This article considers estimation of parameters in the semiparametric marginal structural Cox model (MSCM) from a case-cohort study. Case-cohort sampling entails assembling covariate histories only for cases and a random subcohort, which can be cost effective, particularly in large cohort studies with low outcome rates. Following Cole et al. (2012), we consider estimating the causal hazard ratio from a MSCM by maximizing a weighted-pseudo-partial-likelihood. The estimator is shown to be consistent and asymptotically normal under certain regularity conditions. Finite sample performance of the proposed estimator is evaluated in a simulation study. In the corresponding supplementary document, computation of the estimator using standard survival analysis software is presented.

Key words and phrases: Case-cohort study, causal inference, Cox model, marginal structural model, survival analysis.