A New Approach to Modeling the Cure Rate in the Presence of Interval Censored Data.

We consider interval censored data with a cured subgroup that arises from longitudinal followup studies with a heterogeneous population where a certain proportion of subjects is not susceptible to the event of interest. We propose a two component mixture cure model, where the first component describing the probability of cure is modeled by a support vector machine-based approach and the second component describing the survival distribution of the uncured group is modeled by a proportional hazard structure. Our proposed model provides flexibility in capturing complex effects of covariates on the probability of cure unlike the traditional models that rely on modeling the cure probability using a generalized linear model with a known link function. For the estimation of model parameters, we develop an expectation maximization-based estimation algorithm. We conduct simulation studies and show that our proposed model performs better in capturing complex effects of covariates on the cure probability when compared to the traditional logit link-based two component mixture cure model. This results in more accurate (smaller bias) and precise (smaller mean square error) estimates of the cure probabilities, which in-turn improves the predictive accuracy of the latent cured status. We further show that our model's ability to capture complex covariate effects also improves the estimation results corresponding to the survival distribution of the uncured. Finally, we apply the proposed model and estimation procedure to an interval censored data on smoking cessation.

A support vector machine-based cure rate model for interval censored data.

The mixture cure rate model is the most commonly used cure rate model in the literature. In the context of mixture cure rate model, the standard approach to model the effect of covariates on the cured or uncured probability is to use a logistic function. This readily implies that the boundary classifying the cured and uncured subjects is linear. In this article, we propose a new mixture cure rate model based on interval censored data that uses the support vector machine to model the effect of covariates on the uncured or the cured probability (i.e. on the incidence part of the model). Our proposed model inherits the features of the support vector machine and provides flexibility to capture classification boundaries that are nonlinear and more complex. The latency part is modeled by a proportional hazards structure with an unspecified baseline hazard function. We develop an estimation procedure based on the expectation maximization algorithm to estimate the cured/uncured probability and the latency model parameters. Our simulation study results show that the proposed model performs better in capturing complex classification boundaries when compared to both logistic regression-based and spline regression-based mixture cure rate models. We also show that our model's ability to capture complex classification boundaries improve the estimation results corresponding to the latency part of the model. For illustrative purpose, we present our analysis by applying the proposed methodology to the NASA's Hypobaric Decompression Sickness Database.

On the integration of decision trees with mixture cure model.

The mixture cure model is widely used to analyze survival data in the presence of a cured subgroup. Standard logistic regression-based approaches to model the incidence may lead to poor predictive accuracy of cure, specifically when the covariate effect is non-linear. Supervised machine learning techniques can be used as a better classifier than the logistic regression due to their ability to capture non-linear patterns in the data. However, the problem of interpret-ability hangs in the balance due to the trade-off between interpret-ability and predictive accuracy. We propose a new mixture cure model where the incidence part is modeled using a decision tree-based classifier and the proportional hazards structure for the latency part is preserved. The proposed model is very easy to interpret, closely mimics the human decision-making process, and provides flexibility to gauge both linear and non-linear covariate effects. For the estimation of model parameters, we develop an expectation maximization algorithm. A detailed simulation study shows that the proposed model outperforms the logistic regression-based and spline regression-based mixture cure models, both in terms of model fitting and evaluating predictive accuracy. An illustrative example with data from a leukemia study is presented to further support our conclusion.