On a reparameterization of a flexible family of cure models

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.

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

On the integration of decision trees with mixture cure model

Aselisewine,

Pal

2023

“…While the objective of this study was to develop an efficient estimation algorithm for the destructive negative binomial cure rate model under interval censoring and perform a detailed analysis of its performance, a valuable future work will be to generalize this application to families of cure rate models; see Koutras and Milienos 49 and Milienos. 50 Considering a generalized family of lifetime distributions, for instance, the generalized gamma distribution, would allow us to perform model discrimination for the lifetime distribution under a fully parametric setup; see Wang and Pal. 51 Exploring the performance of the proposed SEM algorithm under semiparametric or nonparametric modeling for the lifetimes of susceptibles will provide greater insight as to the versatility of this estimation method.…”

Section: Discussionmentioning

confidence: 99%

On the estimation of interval censored destructive negative binomial cure model

Treszoks,

Pal

2023

In this article, a competitive risk survival model is considered in which the initial number of risks, assumed to follow a negative binomial distribution, is subject to a destructive mechanism. Assuming the population of interest to have a cure component, the form of the data as interval‐censored, and considering both the number of initial risks and risks remaining active after destruction to be missing data, we develop two distinct estimation algorithms for this model. Making use of the conditional distributions of the missing data, we develop an expectation maximization (EM) algorithm, in which the conditional expected complete log‐likelihood function is decomposed into simpler functions which are then maximized independently. A variation of the EM algorithm, called the stochastic EM (SEM) algorithm, is also developed with the goal of avoiding the calculation of complicated expectations and improving performance at parameter recovery. A Monte Carlo simulation study is carried out to evaluate the performance of both estimation methods through calculated bias, root mean square error, and coverage probability of the asymptotic confidence interval. We demonstrate the proposed SEM algorithm as the preferred estimation method through simulation and further illustrate the advantage of the SEM algorithm, as well as the use of a destructive model, with data from a children's mortality study.

“…34 Milienos proposed a new reparametrization of a family of transformation cure models where the case of zero cured proportion is not at the boundary of the parameter space. 35…”

Section: Box-cox Transformation Cure Rate Modelmentioning

confidence: 99%

“…Wang and Pal proposed a wider class of generalized gamma BCT cure model and addressed model selection and model discrimination 34 . Milienos proposed a new reparametrization of a family of transformation cure models where the case of zero cured proportion is not at the boundary of the parameter space 35 …”

Section: Box‐cox Transformation Cure Rate Modelmentioning

confidence: 99%

On the parameter estimation of Box‐Cox transformation cure model

Pal

Roy

2023

We propose an improved estimation method for the Box‐Cox transformation (BCT) cure rate model parameters. Specifically, we propose a generic maximum likelihood estimation algorithm through a non‐linear conjugate gradient (NCG) method with an efficient line search technique. We then apply the proposed NCG algorithm to BCT cure model. Through a detailed simulation study, we compare the model fitting results of the NCG algorithm with those obtained by the existing expectation maximization (EM) algorithm. First, we show that our proposed NCG algorithm allows simultaneous maximization of all model parameters unlike the EM algorithm when the likelihood surface is flat with respect to the BCT index parameter. Then, we show that the NCG algorithm results in smaller bias and noticeably smaller root mean square error of the estimates of the model parameters that are associated with the cure rate. This results in more accurate and precise inference on the cure rate. In addition, we show that when the sample size is large the NCG algorithm, which only needs the computation of the gradient and not the Hessian, takes less CPU time to produce the estimates. These advantages of the NCG algorithm allows us to conclude that the NCG method should be the preferred estimation method over the already existing EM algorithm in the context of BCT cure model. Finally, we apply the NCG algorithm to analyze a well‐known melanoma data and show that it results in a better fit when compared to the EM algorithm.