Likelihood inference for the destructive exponentially weighted Poisson cure rate model with Weibull lifetime and an application to melanoma data

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.

A time-dependent survival analysis for early prognosis of chronic wounds by monitoring wound alkalinity

The objective is to determine whether monitoring wound alkalinity between visits may help prognosticate chronic wound healing. The alkalinity of 167 wounds during the first 3 visits was assessed using disposable DETEC® pH. Wounds grouped by frequency of alkaline results were compared by % wound size reduction during each visit and 120-day healing probability. The Cox proportional hazards model for time-dependent variables was used to generate non-healing probability curves, where variables are binary (alkaline/non-alkaline, infection/no infection), categorical (wound type), and continuous (wound area); the response is time to complete wound healing; and the event of interest is complete wound healing in 120 days. Results show that wounds with frequent alkaline results have significantly smaller % size reduction per visit. Logistic regression shows an increase in 120-day healing probability with fewer alkaline results. Survival analysis shows that the instantaneous healing rate of non-alkaline or non-alkaline transitioning wounds is 1.785, 2.925, and 5.908 times that of alkaline or alkaline-transitioning wounds for 1, 2, and 3 alkalinity measurements, respectively. Furthermore, the concordance statistic of each survival model shows that goodness of fit increases with more alkalinity measurements. Overall, frequent wound alkalinity assessments may serve as a novel way to prognosticate wound healing outcomes.

On the parameter estimation of Box-Cox transformation cure model

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.

A two-way flexible generalized gamma transformation cure rate model

We propose a two-way flexible cure rate model. The first flexibility is provided by considering a family of Box-Cox transformation cure models that include the commonly used cure models as special cases. The second flexibility is provided by proposing the wider class of generalized gamma distributions to model the associated lifetime. The advantage of this two-way flexibility is that it allows us to carry out tests of hypotheses to select an adequate cure model (within the family of Box-Cox transformation cure models) and a suitable lifetime distribution (within the wider class of generalized gamma distributions) that jointly provides the best fit to a given data. First, we study the maximum likelihood estimation of the generalized gamma Box-Cox transformation (GGBCT) model parameters. Then, we use the flexibility of our proposed model to carry out power studies to demonstrate the power of likelihood ratio test in rejecting mis-specified models. Furthermore, we study the bias and efficiency of the estimators of the cure rates under model mis-specification. Our findings strongly suggest the importance of selecting a correct lifetime distribution and a correct cure rate model, which can be achieved through the proposed two-way flexible model. Finally, we illustrate the applicability of our proposed model using a data from a breast cancer study and show that our model provides a better fit than the existing semiparametric Box-Cox transformation cure model with piecewise exponential approximation to the lifetime distribution.

A New Non-Linear Conjugate Gradient Algorithm for Destructive Cure Rate Model and a Simulation Study: Illustration with Negative Binomial Competing Risks

In this paper, we propose a new estimation methodology based on a projected non-linear conjugate gradient (PNCG) algorithm with an efficient line search technique. We develop a general PNCG algorithm for a survival model incorporating a proportion cure under a competing risks setup, where the initial number of competing risks are exposed to elimination after an initial treatment (known as destruction). In the literature, expectation maximization (EM) algorithm has been widely used for such a model to estimate the model parameters. Through an extensive Monte Carlo simulation study, we compare the performance of our proposed PNCG with that of the EM algorithm and show the advantages of our proposed method. Through simulation, we also show the advantages of our proposed methodology over other optimization algorithms (including other conjugate gradient type methods) readily available as R software packages. To show these, we assume the initial number of competing risks to follow a negative binomial distribution although our general algorithm allows one to work with any competing risks distribution. Finally, we apply our proposed algorithm to analyze a well-known melanoma data.

A simplified stochastic EM algorithm for cure rate model with negative binomial competing risks: An application to breast cancer data

In this article, a long-term survival model under competing risks is considered. The unobserved number of competing risks is assumed to follow a negative binomial distribution that can capture both over- and under-dispersion. Considering the latent competing risks as missing data, a variation of the well-known expectation maximization (EM) algorithm, called the stochastic EM algorithm (SEM), is developed. It is shown that the SEM algorithm avoids calculation of complicated expectations, which is a major advantage of the SEM algorithm over the EM algorithm. The proposed procedure also allows the objective function to be split into two simpler functions, one corresponding to the parameters associated with the cure rate and the other corresponding to the parameters associated with the progression times. The advantage of this approach is that each simple function, with lower parameter dimension, can be maximized independently. An extensive Monte Carlo simulation study is carried out to compare the performances of the SEM and EM algorithms. Finally, a breast cancer survival data is analyzed and it is shown that the SEM algorithm performs better than the EM algorithm.