# Comparative effectiveness research with average hazard for censored time-to-event outcomes: simulation study and application to observational data

## TL;DR

This paper introduces a new way to compare treatment effects using average hazard in observational studies, showing it's reliable even with partial model errors.

## Contribution

The study evaluates and validates average hazard as a robust alternative to hazard ratios for comparative effectiveness research with censored survival data.

## Key findings

- All six confounding adjustment methods performed well in estimating average hazards.
- Augmented inverse probability of treatment weighting (AIPTW) showed robustness under partial model misspecification.
- Average hazard analysis is a feasible and reliable alternative to traditional hazard ratios for survival outcomes.

## Abstract

The average hazard is a summary measure of event time distributions with a given time window, \documentclass[12pt]{minimal}
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\begin{document}$$[0,\tau ],$$\end{document} and allows intuitive interpretation as an average person-time incidence rate over the time window. This metric is calculated as the ratio of the cumulative incidence probability at \documentclass[12pt]{minimal}
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\begin{document}$$\tau$$\end{document} to the restricted mean survival time at \documentclass[12pt]{minimal}
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\begin{document}$$\tau$$\end{document} and can be estimated through non-parametric methods and thus robust. While previously proposed for randomized trials, its use in comparative effectiveness research remains underexplored.

We evaluate inference procedures for the difference and ratio of average hazards from two comparative groups, using six common confounding adjustment methods for survival functions, including direct standardization, inverse probability of treatment weighting (IPTW), propensity score matching, empirical likelihood, and augmented IPTW (AIPTW). Extensive simulation studies under varying model specification are conducted to assess bias, variance, coverage probability, and width of confidence interval. We apply the method to data from the preference cohort in the CANVAS study.

All adjustment methods achieved satisfactory performance; AIPTW was notably robust under partial model misspecification.

Using difference in average hazards and ratio of average hazards as estimands, when combined with common confounding adjustment methods, is feasible and reliable for comparative effectiveness research. The average hazard-based analysis provides a practical alternative to the traditional hazard ratio approach for quantifying the magnitude of the intervention effect on survival outcomes.

The online version contains supplementary material available at 10.1186/s12874-025-02741-9.