Parametric inference for the average hazard approach in time-to-event analysis with sparse risk sets

Abstract

The average hazard (AH) is a recently proposed model-free summary of an event-time distribution. Over a prespecified window $[0,τ]$, it equals the cumulative incidence probability at $τ$ divided by the restricted mean survival time at $τ$ and can be interpreted as a person-time incidence rate that does not depend on the censoring distribution. The difference and ratio of AHs from two groups, DAH and RAH, are between-group contrasts on absolute and relative scales without requiring proportional hazards. Existing nonparametric inference for AH and its contrasts is based on the Kaplan--Meier estimator of the survival function, and can become unreliable when risk sets become sparse or exhausted near $τ$, as may occur in stratified analyses. As a practical remedy, we investigate parametric AH inference using Weibull and generalized gamma models. We use maximum-likelihood estimators and corresponding confidence intervals for group-specific AHs, DAH and RAH in both unstratified and stratified analyses. Simulations show that under correct model specification, little bias and near-nominal coverage can be achieved in settings where nonparametric inference is inadequately supported by observed data. We illustrate the method using a randomized trial comparing neratinib plus capecitabine with lapatinib plus capecitabine in metastatic breast cancer. Parametric inference provides a practical complement to nonparametric AH analysis when sparse or exhausted risk sets make inference at clinically relevant truncation times less reliable.