A likelihood-based approach for cure regression models
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A likelihood-based approach for cure regression models Kevin Burke1
· Valentin Patilea2
Received: 26 August 2019 / Accepted: 27 October 2020 © Sociedad de Estadística e Investigación Operativa 2020
Abstract We propose a new likelihood-based approach for estimation, inference and variable selection for parametric cure regression models in time-to-event analysis under random right-censoring. In this context, it often happens that some subjects are “cured”, i.e., they will never experience the event of interest. Then, the sample of censored observations is an unlabeled mixture of cured and “susceptible” subjects. Using inverse probability censoring weighting (IPCW), we propose a likelihood-based estimation procedure for the cure regression model without making assumptions about the distribution of survival times for the susceptible subjects. The IPCW approach does require a preliminary estimate of the censoring distribution, for which general parametric, semi- or nonparametric approaches can be used. The incorporation of a penalty term in our estimation procedure is straightforward; in particular, we propose 1 -type penalties for variable selection. Our theoretical results are derived under mild assumptions. Simulation experiments and real data analysis illustrate the effectiveness of the new approach. Keywords Binary regression · Iid representation · Inverse probability censoring weighting · Penalized likelihood Mathematics Subject Classification 62N01 · 62N02 · 62J07
Both authors acknowledge the support of the Irish Research Council and the French Ministry of Foreign Affairs through the Ulysses scheme. V. Patilea acknowledges support from the research program New Challenges for New Data of Fondation du Risque/ILB and LCL. Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11749020-00738-8) contains supplementary material, which is available to authorized users.
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Kevin Burke [email protected]
1
Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland
2
CREST, Ensai, Bruz, France
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K. Burke , V. Patilea
1 Introduction Standard survival models assume that all individuals experience the event of interest eventually (see Kalbfleisch and Prentice 2002). However, this assumption is not always tenable since, for example, some diseases might only activate when specific biological and/or lifestyle traits are present, or immunity may result from successful curative treatment (or a combination of both treatment and pre-treatment attributes); individuals who will never experience the event are referred to as cured or non-susceptible. In practice, the binary “cure status”, B ∈ {0, 1} (where B = 1 ⇔ “the individual is cured”), typically cannot be measured directly, and, so, survival studies are required. Let T ∈ (0, ∞] denote the survival time, and note in particular that, in contrast to standard survival models, the support includes T = ∞ corresponding to cured individuals. Thus, B = 1(T = ∞) ∼ Bernoulli(π ) where π is the cure probability. F
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