Performance of the marginal structural cox model for estimating individual and joined effects of treatments given in combination

Clovis Lusivika-Nzinga, Hana Selinger-Leneman, Sophie Grabar, Dominique Costagliola, Fabrice Carrat

The Marginal Structural Cox Model (Cox-MSM), an alternative approach to handle time-dependent confounder, was introduced for survival analysis and applied to estimate the joint causal effect of two time-dependent nonrandomized treatments on survival among HIV-positive subjects. Nevertheless, Cox-MSM performance in the case of multiple treatments has not been fully explored under different degree of time-dependent confounding for treatments or in case of interaction between treatments. We aimed to evaluate and compare the performance of the marginal structural Cox model (Cox-MSM) to the standard Cox model in estimating the treatment effect in the case of multiple treatments under different scenarios of time-dependent confounding and when an interaction between treatment effects is present. We specified a Cox-MSM with two treatments including an interaction term for situations where an adverse event might be caused by two treatments taken simultaneously but not by each treatment taken alone. We simulated longitudinal data with two treatments and a time-dependent confounder affected by one or the two treatments. To fit the Cox-MSM, we used the inverse probability weighting method. We illustrated the method to evaluate the specific effect of protease inhibitors combined (or not) to other antiretroviral medications on the anal cancer risk in HIV-infected individuals, with CD4 cell count as time-dependent confounder. Overall, Cox-MSM performed better than the standard Cox model. Furthermore, we showed that estimates were unbiased when an interaction term was included in the model. Cox-MSM may be used for accurately estimating causal individual and joined treatment effects from a combination therapy in presence of time-dependent confounding provided that an interaction term is estimated.