# The Challenge of Time‐to‐Event Analysis for Multiple Events: A Guided Tour From Time‐to‐First‐Event to Recurrent Time‐to‐Event Analysis

## TL;DR

The paper explains how to analyze multiple events in clinical trials using advanced statistical methods to better understand treatment effects.

## Contribution

It introduces a stepwise approach to extend time-to-first-event models to complex multistate models with non-Markov properties.

## Key findings

- Partly conditional transition rates can replace hazards in non-Markov models under random censoring.
- Simulation studies show the impact of random censoring and sensitivity of Markov tests.
- New summary measurements like state occupation probability help interpret treatment effects.

## Abstract

Clinical trials often compare a treatment to a control group concerning multiple possible combined time‐to‐event endpoints like hospital‐free survival. Thereby, the first endpoint may occur more than once (“recurrent”), whereas the second endpoint is absorbing. Inclusion of all observed events in the analysis can increase the power and provide a more complete picture of the disease but it needs more sophisticated methodology. We give a stepwise guidance on how to extend the simple time‐to‐first event model to complex multistate methodology, where multiple events are incorporated. We thereby consider non‐ and semiparametric methods and show how they are related. Special attention is given to the prerequisites of the models, for example, the Markov property, and their interpretation. Due to novel results in non‐Markov models, the summary measurements: state occupation probability, mean number of hospitalizations, and average length of stay allow an easy interpretation of a treatment effect in non‐Markov models if the censoring is random. Partly conditional transition rates can be estimated instead of hazards. We investigate the difference between partly conditional transition rates and hazards and the impact of the random censoring condition in a simulation study. Furthermore, the simulation study considers the sensitivity of a Markov test. Different estimators are introduced, and their use is explained based on data from the randomized controlled Interdisciplinary Network Heart Failure trial, which investigated the effects of a nurse‐coordinated disease management program. The aim is to give an overview of existing methods, present the assumptions, and elaborate on the differences in interpretation.