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

Abstract

Young, Hernán, and Robins consider the mean outcome under a dynamic intervention that may rely on the natural value of treatment. They first identify this value with a statistical target parameter, and then show that this statistical target parameter can also be identified with a causal parameter which gives the mean outcome under a stochastic intervention. The authors then describe estimation strategies for these quantities. Here we augment the authors’ insightful discussion by sharing our experiences in situations where two causal questions lead to the same statistical estimand, or the newer problem that arises in the study of data adaptive parameters, where two statistical estimands can lead to the same estimation problem. Given a statistical estimation problem, we encourage others to always use a robust estimation framework where the data generating distribution truly belongs to the statistical model. We close with a discussion of a framework which has these properties.

Impact of discretization of the timeline for longitudinal causal inference methods

“…It is possible that the variance of the LTMLE—estimated using the efficient influence function on the selected dataset—is underestimated due to the selection of the timeline. One solution may be to use sample splitting to select a discretization and obtain estimates on separate data splits 48 …”

The Causal Effects of Religious Service Attendance on Prosocial Behaviours in New Zealand: A National Longitudinal Study

“…Initially, TMLE models the relationship between treatments, covariates, and outcomes. In our implementation, we employ machine learning algorithms for this step, allowing us to flexibly model complex, high-dimensional covariate spaces without imposing restrictive model assumptions (Laan et al 2014;Van Der Laan andRose 2011, 2018). The outcome of this step is a set of initial estimates for these relationships.…”

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