Despite modern effective HIV treatment, hepatitis C virus (HCV) co-infection is associated with a high risk of progression to end-stage liver disease (ESLD) which has emerged as the primary cause of death in this population. Clinical interest lies in determining the impact of clearance of HCV on risk for ESLD. In this case study, we examine whether HCV clearance affects risk of ESLD using data from the multicenter Canadian Co-infection Cohort Study. Complications in this survival analysis arise from the time-dependent nature of the data, the presence of baseline confounders, loss to follow-up, and confounders that change over time, all of which can obscure the causal effect of interest. Additional challenges included non-censoring variable missingness and event sparsity.
In order to efficiently estimate the ESLD-free survival probabilities under a specific history of HCV clearance, we demonstrate the double-robust and semiparametric efficient method of Targeted Maximum Likelihood Estimation (TMLE). Marginal structural models (MSM) can be used to model the effect of viral clearance (expressed as a hazard ratio) on ESLD-free survival and we demonstrate a way to estimate the parameters of a logistic model for the hazard function with TMLE. We show the theoretical derivation of the efficient influence curves for the parameters of two different MSMs and how they can be used to produce variance approximations for parameter estimates. Finally, the data analysis evaluating the impact of HCV on ESLD was undertaken using multiple imputations to account for the non-monotone missing data.