Propensity score matching with time-dependent covariates.

In observational studies with a time-dependent treatment and time-dependent covariates, it is desirable to balance the distribution of the covariates at every time point. A time-dependent propensity score based on the Cox proportional hazards model is proposed and used in risk set matching. Matching on this propensity score is shown to achieve a balanced distribution of the covariates in both treated and control groups. Optimal matching with various designs is conducted and compared in a study of a surgical treatment, cystoscopy and hydrodistention, given in response to a chronic bladder disease, interstitial cystitis. Simulation studies also suggest that the statistical analysis after matching outperforms the analysis without matching in terms of both point and interval estimations.