Penalized likelihood estimation of the proportional hazards model for survival data with interval censoring

Ma Jun (), Couturier Dominique-Laurent, Heritier Stephane and Marschner Ian C.
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Ma Jun: Department of Mathematics and Statistics, Macquarie University, Sydney, Australia
Couturier Dominique-Laurent: Cancer Research UK – Cambridge Institute, University of Cambridge, Cambridge, Cambridgeshire, UK
Heritier Stephane: School of Public Health and Preventive Medicine, Monash University, Melbourne, Australia
Marschner Ian C.: NHMRC Clinical Trials Centre, University of Sydney, Camperdown, Australia

The International Journal of Biostatistics, 2022, vol. 18, issue 2, 553-575

Abstract: This paper considers the problem of semi-parametric proportional hazards model fitting where observed survival times contain event times and also interval, left and right censoring times. Although this is not a new topic, many existing methods suffer from poor computational performance. In this paper, we adopt a more versatile penalized likelihood method to estimate the baseline hazard and the regression coefficients simultaneously. The baseline hazard is approximated using basis functions such as M-splines. A penalty is introduced to regularize the baseline hazard estimate and also to ease dependence of the estimates on the knots of the basis functions. We propose a Newton–MI (multiplicative iterative) algorithm to fit this model. We also present novel asymptotic properties of our estimates, allowing for the possibility that some parameters of the approximate baseline hazard may lie on the parameter space boundary. Comparisons of our method against other similar approaches are made through an intensive simulation study. Results demonstrate that our method is very stable and encounters virtually no numerical issues. A real data application involving melanoma recurrence is presented and an R package ‘survivalMPL’ implementing the method is available on R CRAN.

Keywords: asymptotic properties; automated smoothing; constrained optimization; interval censoring; semi-parametric proportional hazard model (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1515/ijb-2020-0104

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