Discussion of Identification, Estimation and Approximation of Risk under Interventions that Depend on the Natural Value of Treatment Using Observational Data, by Jessica Young, Miguel Hernán, and James Robins

Impact of discretization of the timeline for longitudinal causal inference methods

In longitudinal settings, causal inference methods usually rely on a discretization of the patient timeline that may not reflect the underlying data generation process. This article investigates the estimation of causal parameters under discretized data. It presents the implicit assumptions practitioners make but do not acknowledge when discretizing data to assess longitudinal causal parameters. We illustrate that differences in point estimates under different discretizations are due to the data coarsening resulting in both a modified definition of the parameter of interest and loss of information about time-dependent confounders. We further investigate several tools to advise analysts in selecting a timeline discretization for use with pooled longitudinal targeted maximum likelihood estimation for the estimation of the parameters of a marginal structural model. We use a simulation study to empirically evaluate bias at different discretizations and assess the use of the cross-validated variance as a measure of data support to select a discretization under a chosen data coarsening mechanism. We then apply our approach to a study on the relative effect of alternative asthma treatments during pregnancy on pregnancy duration. The results of the simulation study illustrate how coarsening changes the target parameter of interest as well as how it may create bias due to a lack of appropriate control for time-dependent confounders. We also observe evidence that the cross-validated variance acts well as a measure of support in the data, by being minimized at finer discretizations as the sample size increases.

Double robust and efficient estimation of a prognostic model for events in the presence of dependent censoring

In longitudinal data arising from observational or experimental studies, dependent subject drop-out is a common occurrence. If the goal is estimation of the parameters of a marginal complete-data model for the outcome, biased inference will result from fitting the model of interest with only uncensored subjects. For example, investigators are interested in estimating a prognostic model for clinical events in HIV-positive patients, under the counterfactual scenario in which everyone remained on ART (when in reality, only a subset had). Inverse probability of censoring weighting (IPCW) is a popular method that relies on correct estimation of the probability of censoring to produce consistent estimation, but is an inefficient estimator in its standard form. We introduce sequentially augmented regression (SAR), an adaptation of the Bang and Robins (2005. Doubly robust estimation in missing data and causal inference models. Biometrics 61, 962-972.) method to estimate a complete-data prediction model, adjusting for longitudinal missing at random censoring. In addition, we propose a closely related non-parametric approach using targeted maximum likelihood estimation (TMLE; van der Laan and Rubin, 2006. Targeted maximum likelihood learning. The International Journal of Biostatistics 2 (1), Article 11). We compare IPCW, SAR, and TMLE (implemented parametrically and with Super Learner) through simulation and the above-mentioned case study.