# Causal Inference for First Non‐Fatal Events With the Competing Risk of Death: A Principal Stratification Approach

## TL;DR

This paper introduces a new statistical method to estimate the direct effect of treatments on nonfatal events in clinical trials, accounting for the competing risk of death.

## Contribution

The novel contribution is the development of a principal stratification framework to estimate direct treatment effects on nonfatal events in the presence of death.

## Key findings

- The proposed model estimates the principal stratum hazard ratio, which reflects the direct treatment effect on nonfatal events.
- Simulation studies confirm the reliability of the new estimators.
- The method is illustrated using a heart failure clinical trial.

## Abstract

In clinical trials involving both mortality and morbidity, an active treatment can influence the observed risk of the first nonfatal event either directly, through its effect on the underlying nonfatal event process, or indirectly, through its effect on the death process, or both. Discerning the direct effect of treatment on the underlying first nonfatal event process holds clinical interest. However, with the competing risk of death, the Cox proportional hazards model that treats death as non‐informative censoring and evaluates treatment effects on time to the first nonfatal event provides an estimate of the cause‐specific hazard ratio, which may not correspond to the direct effect. To obtain the direct effect on the underlying first nonfatal event process, within the principal stratification framework, we define the principal stratum hazard and introduce the proportional principal stratum hazards model. This model estimates the principal stratum hazard ratio, which reflects the direct effect on the underlying first nonfatal event process in the presence of death and simplifies to the hazard ratio in the absence of death. The principal stratum membership is identified probabilistically using the shared frailty model, which assumes independence between the first nonfatal event process and the potential death processes, conditional on per‐subject random frailty. Simulation studies are conducted to verify the reliability of our estimators. We illustrate the method using the Carvedilol Prospective Randomized Cumulative Survival trial, which involves heart‐failure events.