In longitudinal analyses of observational data, the hazard ratio (HR) averaged over the duration of the study's follow-up is often reported for estimating the effect of drug exposure on clinical outcomes. However, the HR may change according to how the treatment effects cumulate over time (Hernan, 2010). Xiao et al. (Xiao et al., 2014) proposed a flexible marginal structural model for estimating the cumulative effect of a time-dependent treatment on the hazard. The model extended the flexible Weighted Cumulative Exposure (WCE) Cox model (Sylvestre and Abrahamowicz, 2009) by addressing the issue of time-dependent covariates that also act as confounders and mediators of the effects and treatments. Our goal was to evaluate the performances of the marginal flexible WCE model in various plausible situations of cohort data analyses.

In a simulation study, we considered different models of time-varying effect of treatment, used the marginal WCE model to estimate parameters and we compared the estimated curve of time-varying HR with the true curve. We generated data in the context of a cohort of patients chronically infected with hepatitis C virus (HCV). During the follow-up, patients may receive HCV antiviral treatment and the propensity of being treated was related to the fibrosis stage according to the French recommendations on treatment of hepatitis C. The fibrosis stage was a proxy of liver disease severity, affected by treatment, and acted as a time-dependent confounder. We explored different scenarios of time-varying effect of treatment on clinical outcomes (constant, cumulative linear, non-linear effect) in different situations of time-dependent confounding (absent, present) and according to whether observed values of the time-dependent confounder were used to estimate the model. We applied the marginal WCE model to estimate the time-varying effect of Direct Acting Antivirals agents on hepatocellular carcinoma, using data from the ANRS CO22 HEPATHER cohort study.

The Fig. 1 presents preliminary simulation results for different scenarios of time-varying effects of treatment on clinical outcomes using the WCE model. Simulations are ongoing.

The WCE yielded an estimated curve that was the same as the true curve when the risk change was constant with harmful effects.