Goodness-of-fit test for the parametric proportional hazard regression model with interval-censored data

ABSTRACT

Interval-censored data are common in medical research. Fully parametric models provide simple and efficient inference for the estimation of survival functions using interval-censored observations. Inference based on a parametric regression model requires the complete specification of the probability density function, and therefore, correctly specifying the model is crucial, while the regression diagnostic is a very important step. However, regression diagnostic methods for use with the interval-censored data have not been completely developed. Here, we developed a model-checking procedure based on the cumulative martingale residuals for the interval-censored observations. We employed the conditional expectation of residuals for the diagnostics, because the data showing the exact failure time cannot be obtained for the interval-censoring analyses, and developed the formal resampling-based supremum-type test and graphical model-checking techniques. A simulation study demonstrated an excellent performance of the proposed method during the detection of a misspecified functional form of covariates in the finite sample. Furthermore, we used this method for the analysis of the medical checkup data obtained in Japan.

KEYWORDS:

• Goodness-of-fit test
• covariate functional form
• interval-censoring
• Cox–Snell residual
• martingale residual

Acknowledgement

We would like to thank Professor Takashi Yanagawa and Mr. Yoshihiro Hidaka, who are the professor emeritus and the graduate of Kurume University in Japan, for offering us the dataset used in Section 4, which is available on https://www.kindaikagaku.co.jp/support.htm, and helpful advices throughout our study. We would also like to thank our colleague from AIP, Ph.D. Masao Ueki, for comments that greatly improved the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partly supported by RIKEN Center for Advanced Intelligence Project (AIP), and the second author's research was partly supported by Grant-in-Aid for Challenging Exploratory Research from the Ministry of Education, Science, Sports and Technology of Japan (#16K12403).

Notes on contributors

Rieko Sakurai

Rieko Sakurai is a doctoral candidate at Kurume University Graduate School of Medicine in Japan. Ms Sakurai conducted research on statistical methodology and application for analysis of cohort data. She currently joins RIKEN Center for Advanced Intelligence Project in Japan, and engages in the research of methodologies for analyzing the large cohort data containing genetic and family data which are correlated complicatedly with each other.

Satoshi Hattori

Satoshi Hattori is a Professor of Osaka University Graduate School of Medicine, Department of Integrated Medicine, Biomedical Statistics in Japan. Mr Hattori received the Ph.D. degree of clinical statistics from Kitazato University in Japan, in 2003. He was a fellow of Kurume University in 2005, where he was an Associate Professor and a Professor from 2005 to 2008 and from 2008 to 2017, respectively. Between 2014 and 2015, he was a visiting fellow of the University of Washington, Department of Biostatistics. Mr Hattori has been engaged in the development of medical statistical methodology and its applied research. For a methodological research, he has been conducting research on survival time analysis, time series analysis, observational research with propensity score, meta-analysis method of biomarker research, and so on. Currently, he engages in the research for sensitivity analysis on published bias in multivariate meta-analysis and the regional cohort study on the various indicators and the onset of diabetes by individuals within the blood sugar fluctuation monitoring.