Penalized maximum likelihood for cure regression models
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We propose a new likelihood approach for estimation, inference and variable selection for parametric cure regression models in time-to-event analysis under random right-censoring. In such a context, it often happens that some subjects under study are "cured", meaning that they do not experience the event of interest. Then, sample of the censored observations is an unlabeled mixture of cured and "susceptible" subjects. Using inverse probability censoring weighting (IPCW), we propose a binary outcome regression likelihood for the probability of being cured given the covariate vector. Meanwhile the conditional law of the susceptible subjects is allowed to be very general. The IPCW requires a preliminary fit for the conditional law of the censoring, for which general parametric, semi- or non-parametric approaches could be used. The incorporation of a penalty term in our approach is straightforward; we propose L1-type penalties for variable selection. Our theoretical results are derived under mild technical assumptions. Simulation experiments and real data analysis illustrate the effectiveness of the new approach.
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