A Semi-parametric Promotion Time Cure Model with Support Vector Machine
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The promotion time cure rate model (PCM) is an extensively studied model for the analysis of time-to-event data in the presence of a cured subgroup. There are several strategies proposed in the literature to model the latency part of PCM. However, there aren't many strategies proposed to investigate the effects of covariates on the incidence part of PCM. In this regard, most existing studies assume the boundary separating the cured and non-cured subjects with respect to the covariates to be linear. As such, they can only capture simple effects of the covariates on the cured/non-cured probability. In this manuscript, we propose a new promotion time cure model that uses the support vector machine (SVM) to model the incidence part. The proposed model inherits the features of the SVM and provides flexibility in capturing non-linearity in the data. To the best of our knowledge, this is the first work that integrates the SVM with PCM model. For the estimation of model parameters, we develop an expectation maximization algorithm where we make use of the sequential minimal optimization technique together with the Platt scaling method to obtain the posterior probabilities of cured/uncured. A detailed simulation study shows that the proposed model outperforms the existing logistic regression-based PCM model as well as the spline regression-based PCM model, which is also known to capture non linearity in the data. This is true in terms of bias and mean square error of different quantities of interest, and also in terms of predictive and classification accuracies of cure. Finally, we illustrate the applicability and superiority of our model using the data from a study on leukemia patients who went through bone marrow transplantation.
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