Abstract: Marginal structural mean (MSM) models for longitudinal data can be used to characterize the causal effect of a time-varying treatment on the mean of an outcome of interest. Several recent applications of MSM models have demonstrated their utility for quantifying the causal effect of new antiviral therapies and treatment regimens in HIV and AIDS. In this paper we describe marginal structural models for quantiles in which potential outcomes distributions corresponding to different treatment histories differ by quantile-specific location shifts. The formulation of marginal structural quantile (MSQ) models is similar in spirit to quantile regression models, and indeed the MSQ model can be estimated using weighted quantile regression routines under certain circumstances. In this paper we describe the formulation of MSQ models for longitudinal data, list the assumptions under which the models can be identified and estimated, and use the methodology to estimate the causal effect of combination antiviral regimens on both CD4 count and HIV viral load using data from an observational cohort study.
Key words and phrases: Causal inference, counterfactuals, highly active antiretroviral therapy, HIV/AIDS, inversely probability weighting, left censoring, longitudinal cohort study, potential outcomes, quantile regressive, selection bias, viral load, weighted estimating equations.