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.
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BibTeX
@misc{qian2026parametric,
title = {{Parametric inference for the average hazard approach in time-to-event analysis with sparse risk sets}},
author = {Zihan Qian and Lu Tian and Hajime Uno},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41935},
eprint = {2610.41935},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41935},
}
RIS
TY - UNPB
TI - Parametric inference for the average hazard approach in time-to-event analysis with sparse risk sets
AU - Zihan Qian
AU - Lu Tian
AU - Hajime Uno
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41935
UR - https://arxiv.org/abs/2610.41935
AB - 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.
ER -