On a Class of Transmuted Distributions to Model Survival Data with a Cure Fraction

Modelling time to event data, when there is always a proportion of the individuals, commonly referred to as immunes who do not experience the event of interest, is of importance in many biomedical studies. Improper distributions are used to model these situations and they are generally referred to as cure rate models. In the literature, two main families of cure rate models have been proposed, namely the mixture cure models and promotion time cure models. Here we propose a new model by extending the mixture model via a generating function by considering a shifted Bernoulli distribution. This gives rise to a new class of popular distributions called the transmuted class of distributions to model survival data with a cure fraction. The properties of the proposed model are investigated and parameters estimated. The Bayesian approach to the estimation of parameters is also adopted. The complexity of the likelihood function is handled through the Metropolis-Hasting algorithm. The proposed method is illustrated with few examples using different baseline distributions. A real life data set is also analysed. AMS subject classifications: 62N02, 62F15

Cure Models with Exponentiated Weibull Exponential Distribution for the Analysis of Melanoma Patients

In the survival data analysis, commonly, it is presumed that all study subjects will eventually have the event of concern. Nonetheless, it tends to be unequivocally expected that a fraction of these subjects will never expose to the event of interest. The cure rate models are usually used to model this type of data. In this paper, we introduced a maximum likelihood estimates analysis for the four-parameter exponentiated Weibull exponential (EWE) distribution in the existence of cured subjects, censored observations, and predictors. Aiming to include the fraction of unsusceptible (cured) individuals in the analysis, a mixture cure model, and two non-mixture cure models—bounded cumulative hazard model, and geometric non-mixture model with EWE distribution—are proposed. The mixture cure model provides a better fit to real data from a Melanoma clinical trial compared to the other two non-mixture cure models.

Long-term frailty modeling using a non-proportional hazards model: Application with a melanoma dataset

The semiparametric Cox regression model is often fitted in the modeling of survival data. One of its main advantages is the ease of interpretation, as long as the hazards rates for two individuals do not vary over time. In practice the proportionality assumption of the hazards may not be true in some situations. In addition, in several survival data is common a proportion of units not susceptible to the event of interest, even if, accompanied by a sufficiently large time, which is so-called immune, “cured,” or not susceptible to the event of interest. In this context, several cure rate models are available to deal with in the long term. Here, we consider the generalized time-dependent logistic (GTDL) model with a power variance function (PVF) frailty term introduced in the hazard function to control for unobservable heterogeneity in patient populations. It allows for non-proportional hazards, as well as survival data with long-term survivors. Parameter estimation was performed using the maximum likelihood method, and Monte Carlo simulation was conducted to evaluate the performance of the models. Its practice relevance is illustrated in a real medical dataset from a population-based study of incident cases of melanoma diagnosed in the state of São Paulo, Brazil.

On the use of the modified power series family of distributions in a cure rate model context

In this paper, we propose a generalization of the power series cure rate model for the number of competing causes related to the occurrence of the event of interest. The model includes distributions not yet used in the cure rate models context, such as the Borel, Haight and Restricted Generalized Poisson distributions. The model is conveniently parameterized in terms of the cure rate. Maximum likelihood estimation based on the Expectation Maximization algorithm is discussed. A simulation study designed to assess some properties of the estimators is carried out, showing the good performance of the proposed estimation procedure in finite samples. Finally, an application to a bone marrow transplant data set is presented.

Semi-Parametric Cure Rate Proportional Odds Models with Spatial Frailties for Interval-Censored Data

In this work, we proposed the semi-parametric cure rate models with independent and dependent spatial frailties. These models extend the proportional odds cure models and allow for spatial correlations by including spatial frailty for the interval censored data setting. Moreover, since these cure models are obtained by considering the occurrence of an event of interest is caused by the presence of any nonobserved risks, we also study the complementary cure model, that is, the cure models are obtained by assuming the occurrence of an event of interest is caused when all of the nonobserved risks are activated. The MCMC method is used in a Bayesian approach for inferential purposes. We conduct an influence diagnostic through the diagnostic measures in order to detect possible influential or extreme observations that can cause distortions on the results of the analysis. Finally, the proposed models are applied to the analysis of a real data set.

D-Measure: A Bayesian Model Selection Criterion for Survival Data

An authentic way for assessing the goodness of a model is to estimate its predictive capability. In this paper, we propose the D-measure, which measures the goodness of a model by comparing how close its predictions are from the observed data based on the survival function. The proposed D-measure can be used for all kinds of survival data in the presence of censoring. It can also be used to compare cure rate models, even in the presence of random effects or frailties. The advantages of the D-measure are verified via simulation, in which it is compared to the deviance information criterion, which is a widely used Bayesian model comparison criterion. The D-measure is illustrated in two real data sets.