Propensity score analysis for time-dependent exposure

Propensity score analysis (PSA) is widely used in medical literature to account for confounders. Conventionally, the propensity score (PS) is calculated by a binary logistic regression model using time-fixed covariates. In the presence of time-varying treatment or exposure, the conventional method may cause bias because subjects with early and late exposure are treated as the same. In effect, subjects who are treated latter can be different from those who are treated early. Thus, the conventional PSA must be modified to address this bias. In this paper, we illustrate how to perform analysis in the presence of time-dependent exposure. We conduct a simulation study with a known treatment effect. In the simulation study, we find the PSA method that directly adjust PS estimated by either a binary logistic regression model or a Cox regression model using time-fixed covariates still introduce significant bias. On the other hand, the time-dependent PS matching can help to achieve a result approaching the true effect. After time-dependent PS matching, the matched cohort can be analyzed with conventional Cox regression model or conditional logistic regression (CLR) model with time strata. The performance is comparable to the correctly specified Cox regression model with time-varying covariates (i.e., adjusting the exposure in a multivariable model as a time-varying covariate). We further develop a function called TDPSM() for time-dependent PS matching and it is applied to a real world dataset.