Abstract

In longitudinal observational studies, Marginal structural models (MSMs) estimated via Inverse Probability of Treatment Weighting (IPTW) are a class of causal models to analyse the effect of an exposure on (survival) outcomes, while accounting for time-dependent confounders. Despite less robust than G-estimation or doubly robust methods, IPTW-based MSMs have largely been adopted in the applied literature, especially in epidemiology and medicine, due to its simplicity in both implementation and interpretation. IPTW-based MSMs require the correct specification of the exposure model conditional on patient characteristics and special attention to the identifiability assumptions of consistency, no unmeasured confounding, and positivity. This work focuses on the latter, which is crucial for valid causal inference but is often overlooked compared to confounding bias.
Positivity holds if, for any combination of covariates occurring among individuals in the population, there is a non-zero (i.e., positive) probability of receiving every level of exposure. In the context of binary treatment (exposure vs unexposure; treatment vs control), positivity violations can arise from subjects having zero probability of being exposed/unexposed (strict violations) or near-zero probabilities due to sampling variability (near violations). While existing research lacks systematic simulations for realistic longitudinal survival settings incorporating both exposure-affected confounding and positivity violations, this study aims to fill that gap.
Building on prior algorithms for simulating longitudinal survival data from MSMs with binary exposures, this work extends simulations to include strict and near violations of positivity. The advantage of extending existing algorithms is threefold: (i) non-collapsibility of models and replication of complex confounding dynamics have been overcome; (ii) by controlling exposure-confounder path and avoiding misspecification of the weighting model, the effect due to positivity violations is separated from other sources of bias; (iii) original algorithms can be used as benchmarks for cases where the positivity assumption is valid. Various simulation scenarios are explored by varying (i) the size of the confounder interval in which positivity violations arise, (ii) the sample size, (iii) the weight truncation (WT) strategy, or (iv) the subject's propensity to follow the protocol violation rule. Estimands of interest include MSM regression coefficients and counterfactual survival probabilities for the always treated versus never treated regimens.
Results suggested that even minor strict violations of the positivity assumption can have significant implications for the performance, compromising estimator stability and increase variability, regardless of sample sizes or WT strategies. Near violations were found to be less problematic than strict violations. Near violations are less detrimental, especially under appropriate WT. However, while adopting a WT strategy can be appealing in terms of reducing variability, it should be approached cautiously due to the potential risk of increasing the bias.
In summary, this is the first study investigating how positivity violations impact the IPTW-based causal estimates from MSMs in a survival framework with longitudinal binary treatment and time-dependent confounding. It underscores the importance of diligently assessing positivity compliance to ensure robust and reliable causal inference in longitudinal survival studies.