Adjusting for time-varying confounding in the subdistribution analysis of a competing risk.

Despite decades of research in the medical literature, assessment of the attributable mortality due to nosocomial infections in the intensive care unit (ICU) remains controversial, with different studies describing effect estimates ranging from being neutral to extremely risk increasing. Interpretation of study results is further hindered by inappropriate adjustment (a) for censoring of the survival time by discharge from the ICU, and (b) for time-dependent confounders on the causal path from infection to mortality. In previous work (Vansteelandt et al. Biostatistics 10:46-59), we have accommodated this through inverse probability of treatment and censoring weighting. Because censoring due to discharge from the ICU is so intimately connected with a patient's health condition, the ensuing inverse weighting analyses suffer from influential weights and rely heavily on the assumption that one has measured all common risk factors of ICU discharge and mortality. In this paper, we consider ICU discharge as a competing risk in the sense that we aim to infer the risk of 'ICU mortality' over time that would be observed if nosocomial infections could be prevented for the entire study population. For this purpose we develop marginal structural subdistribution hazard models with accompanying estimation methods. In contrast to subdistribution hazard models with time-varying covariates, the proposed approach (a) can accommodate high-dimensional confounders, (b) avoids regression adjustment for post-infection measurements and thereby so-called collider-stratification bias, and (c) results in a well-defined model for the cumulative incidence function. The methods are used to quantify the causal effect of nosocomial pneumonia on ICU mortality using data from the National Surveillance Study of Nosocomial Infections in ICU's (Belgium).