Z-residual diagnostic tool for assessing covariate functional form in shared frailty models

Tingxuan Wu, Longhai Li and Cindy Feng

Journal of Applied Statistics, 2025, vol. 52, issue 1, 28-58

Abstract: Survival analysis often involves modeling hazard functions while considering frailty to account for unobserved cluster-level factors in clustered survival data. Shared frailty models have gained popularity for this purpose, but assessing covariate functional form in these models presents unique challenges. Martingale and deviance residuals are commonly used for visually assessing covariate functional form against continuous covariates. Nevertheless, their subjective nature and lack of a reference distribution make it challenging to derive numerical statistical tests from these residuals. To address these limitations, we propose ‘Z-residuals’, a novel diagnostic tool designed for shared frailty models, leveraging the concept of randomized survival probability and introducing both graphical and numerical tests. To implement this approach, we develop an R package to compute Z-residuals for shared frailty models. Through extensive simulation studies, we demonstrate the high power of our derived numerical test for assessing the functional form of covariates. To validate the effectiveness of our method, we apply it to a real data application concerning the modelling of survival time for acute myeloid leukemia patients. Our Z-residual diagnosis results reveal the inadequacy of log-transformation of the covariate, highlighting the limitations of other diagnostic methods for effectively assessing covariate functional form in shared frailty models.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/02664763.2024.2355551 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:japsta:v:52:y:2025:i:1:p:28-58

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/CJAS20

DOI: 10.1080/02664763.2024.2355551

Access Statistics for this article

Journal of Applied Statistics is currently edited by Robert Aykroyd

More articles in Journal of Applied Statistics from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().