[Paper Review] A Semi-parametric Promotion Time Cure Model with Support Vector Machine

Suvra Pal, Wisdom Aselisewine|arXiv (Cornell University)|Apr 24, 2023

Gene expression and cancer classificationBiochemistry, Genetics and Molecular Biology3 citations

TL;DR

This paper proposes a novel semi-parametric promotion time cure model that integrates support vector machines (SVM) into the incidence component to capture non-linear relationships between covariates and cure probability, while retaining the Cox proportional hazards structure for the latency part. The method uses an EM algorithm with sequential minimal optimization and Platt scaling for parameter estimation, and simulation results show superior performance in bias, mean squared error, and classification accuracy compared to logistic regression and spline-based models.

ABSTRACT

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.

Motivation & Objective

• To address the limitation of existing cure models in capturing non-linear effects of covariates on the incidence (cure) probability.
• To develop a flexible yet interpretable cure model by replacing the linear incidence component with a support vector machine.
• To improve estimation accuracy and predictive performance in survival data with a cured subgroup.
• To provide a first integration of SVM into the promotion time cure model framework.
• To enable better classification of cured vs. non-cured subjects when the true boundary is non-linear.

Proposed method

• Proposes a semi-parametric promotion time cure model (PCM) where the incidence part is modeled using a support vector machine (SVM) to capture complex, non-linear relationships between covariates and cure probability.
• Retains the standard Cox proportional hazards structure for the latency part (time-to-event for susceptible subjects), ensuring interpretability of survival effects.
• Develops an expectation-maximization (EM) algorithm for parameter estimation, with the E-step using Platt scaling to estimate posterior probabilities of cure.
• Employs sequential minimal optimization (SMO) to efficiently solve the SVM subproblem within the EM framework.
• Uses a Poisson distribution for the unobserved number of competing risks, with the mean parameterized via the SVM to model the incidence of susceptibility.
• Applies the method to real data from a leukemia bone marrow transplant study to demonstrate practical utility.

Experimental results

Research questions

• RQ1 Can an SVM-based incidence model improve the estimation accuracy of cure probabilities compared to traditional logistic regression in cure rate models?
• RQ2 Does the integration of SVM into the promotion time cure model enhance classification accuracy for cured versus non-cured subjects, especially when the true decision boundary is non-linear?
• RQ3 How does the proposed PCM-SVM model perform in comparison to spline-based and neural network-based cure models in terms of bias, mean squared error, and predictive accuracy?
• RQ4 Can the proposed model maintain good performance under high-dimensional covariates or complex covariate structures involving interactions and correlations?
• RQ5 Does the model’s ability to capture non-linear effects also improve the estimation of survival probabilities in the latency part?

Key findings

• The proposed PCM-SVM model significantly outperforms the PCM-Logit model in terms of bias and mean squared error for estimating uncured probabilities, particularly when the true boundary between cured and non-cured subjects is non-linear.
• The PCM-SVM achieves higher classification accuracy and better predictive performance than PCM-Logit, especially in scenarios with non-linear decision boundaries.
• In a high-dimensional simulation setting with 10 covariates including interactions and correlations, the PCM-SVM outperformed both the PCM-Spline and PCM-Neural Network models in estimating non-cured and overall survival probabilities.
• The model’s ability to capture complex, non-linear relationships enhances the accuracy of the latency part estimates, indicating a holistic improvement across both incidence and latency components.
• The use of SMO and Platt scaling within the EM algorithm enables efficient and stable parameter estimation, supporting practical implementation.
• The model demonstrates strong empirical performance on real leukemia data, confirming its applicability in clinical survival analysis.