• The Korean Journal of Applied Statistics
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• v.36 no.5
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• pp.415-445
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• 2023

Oftentimes, the time dependent treatment covariate and the time dependent confounders exist in observation studies. It is an important problem to correctly adjust for the time dependent confounders in the propensity score analysis. Recently, In the survival data, Hade et al. (2020) used a propensity score matching method to correctly estimate the treatment delay effect when the time dependent confounder affects time to the treatment time, where the treatment delay effects is defined to the delay in treatment reception. In this paper, we proposed the Cox model based marginal structural model (Cox-MSM) framework to estimate the treatment delay effect and conducted extensive simulation studies to compare our proposed Cox-MSM with the propensity score matching method proposed by Hade et al. (2020). Our simulation results showed that the Cox-MSM leads to more exact estimate for the treatment delay effect compared with two sequential matching schemes based on propensity scores. Example from study in treatment discontinuation in conjunction with simulated data illustrates the practical advantages of the proposed Cox-MSM.