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

Bayesian Estimations of Exponential Distribution Based on Interval-Censored Data with a Cure Fraction

Censored data are considered to be of the interval type where the upper and lower bounds of an event’s failure time cannot be directly observed but only determined between interval inspection times. The analyses of interval-censored data have attracted attention because they are common in the fields of reliability and medicine. A proportion of patients enrolled in clinical trials can sometimes be cured. In some instances, their symptoms mostly disappear without any recurrence of the disease. In this study, the proportion of such patients who are cured is estimated. Furthermore, the Bayesian approach under the gamma prior and maximum likelihood estimation (MLE) is used to estimate the cure fraction depending on the bounded cumulative hazard (BCH) model based on interval-censored data with an exponential distribution. The Bayesian approach uses three loss functions: squared error, linear exponential, and general entropy. These functions are compared with the MLE and used between estimators. Moreover, they are obtained using the mean squared error, which locates the best option to estimate the parameter of an exponential distribution. The results show that the BCH model and lambda parameter of the exponential distribution based on the interval-censored data can be best estimated using the Bayesian gamma prior with a positive loss function of the linear exponential.

Nadarajah-Haghighi Model for Survival Data With Long Term Survivors in the Presence of Right Censored Data

In this paper, a new long term survival model called Nadarajah-Haghighi model for survival data with long term survivors was proposed. The model is used in fitting data where the population of interest is a mixture of individuals that are susceptible to the event of interest and individuals that are not susceptible to the event of interest. The statistical properties of the proposed model including quantile function, moments, mean and variance were provided. Maximum likelihood estimation procedure was used to estimate the parameters of the model assuming right censoring. Furthermore, Bayesian method of estimation was also employed in estimating the parameters of the model assuming right censoring. Simulations study was performed in order to ascertain the performances of the MLE estimators. Random samples of different sample sizes were generated from the model with some arbitrary values for the parameters for 5%, 1:3% and 1:5% cure fraction values. Bias, standard error and mean square error were used as discrimination criteria. Additionally, we compared the performance of the proposed model with some competing models. The results of the applications indicates that the proposed model is more efficient than the models compared with. Finally, we fitted some models considering type of treatment as a covariate. It was observed that the covariate have effect on the shape parameter of the proposed model.

Secondarily estimated cure fraction and five-year recurrence-free conditional survival probabilities among patients undergoing surgical resection for hepatocellular carcinoma presenting with minor gross vascular invasion

Background Surgical resection (SR) has been selectively applied in hepatocellular carcinoma (HCC) presenting with minor gross vascular invasion (mGVI) which is defined when tumor invasion is confined to second-order portal branches or segmental branches of hepatic vein. However, little data of long-term outcomes are available for supporting the role of SR as a potentially curable therapeutic option for HCC presenting with mGVI. This study is aimed to estimate a statistical cure fraction and the improvement of recurrence-free conditional survival (RFCS) over time among patients undergoing SR for HCC presenting with mGVI. Methods The literature search was conducted focusing on previous studies that investigated the long-term survival rates of patients after SR for HCC presenting with mGVI. The reference cohort was extracted from a study including patients undergoing SR for HCC without vascular invasion. A non-mixture cure model was adopted to estimate the statistical cure fraction. The 5-year RFCS probabilities were also calculated. Results Three retrospective studies were secondarily analyzed. The probability of being statistically cured after SR for HCC presenting with mGVI was 7.3% (95% confidence interval, 4.4%–11.2%) in the mGVI group, lower than that of the reference cohort (hazard ratio, 1.81; 95% confidence interval, 1.59–2.05). The estimated 5-year RFCS probabilities improved with each additional year of survival. Moreover, 1 year after SR, the 5-year RFCS probabilities of patients with HCC presenting with mGVI was essentially the same as that of the reference cohort. Conclusions This study shows that a cure can be expected in around seven percent of patients undergoing SR for HCC presenting with mGVI. Furthermore, recurrence-free survival expectancy improves dramatically over time among those patients who do not have recurrence. Overall, these findings suggest that SR should be considered as a potentially curable treatment for patients with HCC presenting with mGVI.

Classical and Bayesian inference approaches for the exponentiated discrete Weibull model with censored data and a cure fraction

In this paper, we introduce maximum likelihood and Bayesian parameter estimation for the exponentiated discrete Weibull (EDW) distribution in presence of randomly right censored data. We also consider the inclusion of a cure fraction in the model. The performance of the maximum likelihood estimation approach is assessed by conducting an extensive simulation study with different sample sizes and different values for the parameters of the EDW distribution. The usefuness of the proposed model is illustrated with two examples considering real data sets.

A new perspective on the BO06 trial in osteosarcoma: short- and long-term prognostic value of histologic response and intensified chemotherapy

Purpose. Despite evidence of cured patients, previous osteosarcoma studies have not taken it into consideration. We aim to better understand the prognostic value of histologic response and chemotherapy intensification on cure fraction and progression-free survival (PFS) for the uncured patients. Methods. A logistic model is assumed for the effect of histologic response and intensified chemotherapy on the cure status, while a Cox regression model is estimated only for the uncured patients on PFS. The mixture cure model is used to simultaneously study these two effects. Results. Histologic response is a strong prognostic factor for the cure status (OR: 3.00 [1.75-5.17]), but it has no clear effect on PFS for the uncured patients (HR: 0.78 [0.53-1.16]). The cure fractions are 55% [46%-63%] and 29% [22%-35%] among GR and patients with poor histologic response (PR) respectively. The intensified regimen was associated with higher cure fraction among PR (OR: 1.90 [0.93-3.89]), with no evidence of effect for GR (OR: 0.78 [0.38-1.59]). Conclusions. Accounting for cured patients is valuable in distinguishing the covariate effects on cure and PFS for the uncured patients. Estimating cure chances based on these prognostic factors is relevant for counseling patients and can also affect treatment decisions.

Mediation analysis for mixture Cox proportional hazards cure models

Mediation analysis aims to decompose a total effect into specific pathways and investigate the underlying causal mechanism. Although existing methods have been developed to conduct mediation analysis in the context of survival models, none of these methods accommodates the existence of a substantial proportion of subjects who never experience the event of interest, even if the follow-up is sufficiently long. In this study, we consider mediation analysis for the mixture of Cox proportional hazards cure models that cope with the cure fraction problem. Path-specific effects on restricted mean survival time and survival probability are assessed by introducing a partially latent group indicator and applying the mediation formula approach in a three-stage mediation framework. A Bayesian approach with P-splines for approximating the baseline hazard function is developed to conduct analysis. The satisfactory performance of the proposed method is verified through simulation studies. An application of the Alzheimer’s disease (AD) neuroimaging initiative dataset investigates the causal effects of APOE-[Formula: see text] allele on AD progression.

Statistical methods for estimating cure fraction of COVID-19 patients in India

Human race is under the COVID-19 pandemic menace since beginning of the year 2020. Even though the disease is easily transmissible, a massive fraction of the affected people is recovering. Most of the recovered patients will not experience death due to COVID-19, even if they observed for a long period. They can be treated as long term survivors in the context of lifetime data analysis. In this article, we present statistical methods to estimate the proportion of long term survivors (cure fraction) of the COVID-19 patient population in India. The proportional hazards mixture cure model is used to estimate the cure fraction and the effect of the covariates gender and age, on lifetime. We can see that the cure fraction of the COVID-19 patients in India is more than 90%, which is indeed an optimistic information.