Structural accelerated failure time models for survival analysis in studies with time-varying treatments

Abstract

In the absence of unmeasured confounding factors and model misspecification, standard methods for estimating the causal effect of time-varying treatments on survival are biased when (i) there exists a time-dependent risk factor for survival that also predicts subsequent treatment and (ii) past treatment history predicts subsequent risk factor level. In contrast, structural models provide consistent estimates of causal effects when unmeasured confounding and model misspecification are absent. The parameters of nested structural models are estimated by g-estimation and those of marginal structural models by inverse probability weighting. We describe a nested structural accelerated failure time model and use it to estimate the total causal effect of highly active antiretroviral therapy (HAART) on the time to AIDS or death among human immunodeficiency virus (HIV)-infected participants of the Multicenter AIDS Cohort and Women's Interagency HIV Studies. The Appendix describes g-estimation and methods to deal with censoring. Comparing the regime 'always treated' to 'never treated,' the AIDS-free survival time ratio was 2.5 (95% confidence interval [CI]: 1.7, 3.3). Our finding of a strongly beneficial effect is consistent with results from randomized trials and from a previous analysis of the same data using a marginal structural Cox model. In contrast, a previous analysis using a standard (non-structural) model did not find an effect of treatment on survival.