Conditional separable effects

Causal inference with recurrent and competing events

Many research questions concern treatment effects on outcomes that can recur several times in the same individual. For example, medical researchers are interested in treatment effects on hospitalizations in heart failure patients and sports injuries in athletes. Competing events, such as death, complicate causal inference in studies of recurrent events because once a competing event occurs, an individual cannot have more recurrent events. Several statistical estimands have been studied in recurrent event settings, with and without competing events. However, the causal interpretations of these estimands, and the conditions that are required to identify these estimands from observed data, have yet to be formalized. Here we use a formal framework for causal inference to formulate several causal estimands in recurrent event settings, with and without competing events. When competing events exist, we clarify when commonly used classical statistical estimands can be interpreted as causal quantities from the causal mediation literature, such as (controlled) direct effects and total effects. Furthermore, we show that recent results on interventionist mediation estimands allow us to define new causal estimands with recurrent and competing events that may be of particular clinical relevance in many subject matter settings. We use causal directed acyclic graphs and single world intervention graphs to illustrate how to reason about identification conditions for the various causal estimands based on subject matter knowledge. Furthermore, using results on counting processes, we show that our causal estimands and their identification conditions, which are articulated in discrete time, converge to classical continuous time counterparts in the limit of fine discretizations of time. We propose estimators and establish their consistency for the various identifying functionals. Finally, we use the proposed estimators to compute the effect of blood pressure lowering treatment on the recurrence of acute kidney injury using data from the Systolic Blood Pressure Intervention Trial.

Effect Measure Modification by Covariates in Mediation: Extending Regression-based Causal Mediation Analysis

Existing methods for regression-based mediation analysis assume that the exposure-mediator effect, exposure-outcome effect, and mediator-outcome effect are constant across levels of the baseline characteristics of patients. However, investigators often have insight into how these underlying effects may be modified by baseline characteristics and are interested in how the resulting mediation effects, such as the natural direct effect (NDE), the natural indirect effect. (NIE), and the proportion mediated, are modified by these baseline characteristics. Motivated by an empirical example of anti-interleukin-1 therapy's benefit on incident anemia reduction and its mediation by an early change in an inflammatory biomarker, we extended the closed-form regression-based causal mediation analysis with effect measure modification (EMM). Using a simulated numerical example, we demonstrated that naive analysis without considering EMM can give biased estimates of NDE and NIE and visually illustrated how baseline characteristics affect the presence and magnitude of EMM of NDE and NIE. We then applied the extended method to the empirical example informed by pathophysiologic insights into potential EMM by age, diabetes, and baseline inflammation. We found that the proportion modified through the early post-treatment inflammatory biomarker was greater for younger, nondiabetic patients with lower baseline level of inflammation, suggesting differential usefulness of the early post-treatment inflammatory biomarker in monitoring patients depending on baseline characteristics. To facilitate the adoption of EMM considerations in causal mediation analysis by the wider clinical and epidemiologic research communities, we developed a free- and open-source R package, regmedint.

Translating questions to estimands in randomized clinical trials with intercurrent events

Intercurrent (post‐treatment) events occur frequently in randomized trials, and investigators often express interest in treatment effects that suitably take account of these events. Contrasts that naively condition on intercurrent events do not have a straight‐forward causal interpretation, and the practical relevance of other commonly used approaches is debated. In this work, we discuss how to formulate and choose an estimand, beyond the marginal intention‐to‐treat effect, from the point of view of a decision maker and drug developer. In particular, we argue that careful articulation of a practically useful research question should either reflect decision making at this point in time or future drug development. Indeed, a substantially interesting estimand is simply a formalization of the (plain English) description of a research question. A common feature of estimands that are practically useful is that they correspond to possibly hypothetical but well‐defined interventions in identifiable (sub)populations. To illustrate our points, we consider five examples that were recently used to motivate consideration of principal stratum estimands in clinical trials. In all of these examples, we propose alternative causal estimands, such as conditional effects, sequential regime effects, and separable effects, that correspond to explicit research questions of substantial interest.