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.
Acknowledgments
The authors wish to thank the referees and the associate editor for their thoughtful comments and suggestions which helped improve the quality of this paper. Heritier’s research was partially supported by a Centre of Research Excellence grant from the National Health and Medical Research Council, ID# 1171422, to the Australian Trials Methodology Research Network (AusTriM).
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: None declared.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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Supplementary Material
The online version of this article offers supplementary material (https://doi.org/10.1515/ijb-2020-0104).
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