Cure Fraction Models Research Articles

Equivalence tests under the non mixture and mixture cure fraction models

In this article, we propose equivalence tests for the difference of two survival functions in the presence of cure fraction. We consider both the non mixture cure model (NMCM) and mixture cure model (MCM). We first demonstrate that the existing tests can be used to test equivalence of two improper survival functions under the class of log transformation (LT) and Box-Cox transformation (BCT) NMCM. For the MCM, a logistic regression model is assumed for the probability of being uncured and the class of LT or BCT models are used to describe the distribution of event time for the uncured subjects. Under the MCM, we consider testing separately the null hypothesis of identical cure rate and that of equivalence of two survival functions of the uncured subjects. We also develop a Wald statistic for simultaneously testing whether or not both the maximal difference between cure rates and that between two short-term survival functions fall within some equivalence margins. Simulation results indicate that the proposed tests have a satisfactory size and an adequate power in finite sample.

Analysis of Copula Frailty defective models in presence of Cure Fraction

Introduction: Analyzing long term survivors such as diabetic patients can't be done using the usual survival models. One approach to analyze it is using defective distribution that doesn't force a pre-assumption of cure fraction to the model. To study more than one random variable interacting together, multivariate distributions may be used. However, most of multivariate distributions have complicated forms, which make the computations difficult. Besides, it may be hard to find a multivariate distribution that fits the data properly, especially in health care field. To get over this problem, one can use copula approach. In literature, to the best of our knowledge, only one paper handled copula defective models and didn't consider the effect of covariates. In this paper, we take into consideration not only existed covariates but also unobserved ones by including frailty term. Methods: Two new models are introduced. The first model, used Gumbel copula to take the dependence into consideration together with the observed covariates. The second one take into consideration not only the dependence but also the unobserved covariates by integrating frailty term in to the model. Results: A diabetic retinopathy data is analyzed. The two models indicated the existence of long-term survivals through negative parameters without the need of pre-assuming the existence of it. Including frailty term to the model helped in capturing more dependence between the variables. We compared the results using goodness of fit methods, and the results suggested that the model with frailty term is the best to be used. Conclusion: The two introduced models correctly detected the existence of cure fraction with less estimated parameters than that in mixture cure fraction models. Also, it has the advantage of not pre-assuming the existence of cure fraction to the model. comparing both models, the model with frailty term fitted the data better.

Marginal logistic regression with a cure fraction in a cluster design: An application in dental traumatology

Logistic regression model is the first option to deal with binary outcomes in cross-sectional health studies. However, some conditions, such as the presence of a cure fraction, characterized when an unknown portion of the population is no longer at risk of developing the event of interest, can lead to the non-adequacy of the model. Therefore, the presence of a cure fraction requires an extension in the standard form of the logistic regression model or the use of an alternative one. The present work aims to identify risk factors for the presence of External Inflammatory Root Resorption (EIRR) using a real application. The data set consisted in replanted permanent teeth referred to treatment at the Dental Trauma Clinic of the School of Dentistry from the Federal University of Minas Gerais (DTC-SD-UFMG) after emergency care at the Metropolitan Hospital Odilon Beherns in Belo Horizonte, Brazil. A logistic regression type model is considered to study the association between clinical and radiographic factors and the presence/absence of EIRR, measured radiographically at the first patient appointment at DTC-SD-UFMG. Considering that EIRR is only expected in those cases where the root canal become infected following pulp necrosis, those teeth whose pulp healing is favorable are not at risk of developing EIRR. However, pulpal status usually can only be defined in the long term, such that information is not available at the time of data collection, characterizing the presence of a latent cure fraction. Moreover, in the present sample some patients contributed with more than one replanted tooth, forming clusters of correlated measurements. In the present work we followed the methodology proposed by Hall & Zhang (2004) in which they used an adaption of the EM (expectation-maximization) algorithm, called ES (Expectation-Solution) algorithm combined with GEE (Generalized Estimation Equations) to accommodate the cluster (individual) multivariate response in a logistic cure fraction model.

Gamma-Gompertz mixture model with cure fraction to analyze data on Anglo-Nubian goats with positive EPG

The exposure of small ruminants to gastrointestinal endoparasites is one of the main factors limiting their production, by compromising the herd’s performance because of delayed growth and mortality, among other factors. But with advancements in the treatments, an increase in the life expectancy this ruminants under-going new treatments is expected. In this paper, we present a study experimental goat herd belonging to the Agrarian Sciences Center of Federal University of Piaui (UFPI) diagnosed with positive EPG. The objective of this study was to use the approach of cure fraction models. The proposed modeling is based on the gamma-Gompertz mixture model with cure fraction model in which the frailty variable assumes the Gamma distribution and the basis risk function is Gompertz. The model proposed was suitable for this type of analysis, because besides enabling quantifying the heterogeneity not observed due to hard-to-measure factors, it was possible to identify evidence of long-term survival for some subgroups of animals while in others the survival curve approached zero with increase of useful life.

Analysis of survival data with cure fraction and variable selection: A pseudo-observations approach.

In biomedical studies, survival data with a cure fraction (the proportion of subjects cured of disease) are commonly encountered. The mixture cure and bounded cumulative hazard models are two main types of cure fraction models when analyzing survival data with long-term survivors. In this article, in the framework of the Cox proportional hazards mixture cure model and bounded cumulative hazard model, we propose several estimators utilizing pseudo-observations to assess the effects of covariates on the cure rate and the risk of having the event of interest for survival data with a cure fraction. A variable selection procedure is also presented based on the pseudo-observations using penalized generalized estimating equations for proportional hazards mixture cure and bounded cumulative hazard models. Extensive simulation studies are conducted to examine the proposed methods. The proposed technique is demonstrated through applications to a melanoma study and a dental data set with high-dimensional covariates.

Modified score function for monotone likelihood in the semiparametric mixture cure model.

The cure fraction models are intended to analyze lifetime data from populations where some individuals are immune to the event under study, and allow a joint estimation of the distribution related to the cured and susceptible subjects, as opposed to the usual approach ignoring the cure rate. In situations involving small sample sizes with many censored times, the detection of nonfinite coefficients may arise via maximum likelihood. This phenomenon is commonly known as monotone likelihood (ML), occurring in the Cox and logistic regression models when many categorical and unbalanced covariates are present. An existing solution to prevent the issue is based on the Firth correction, originally developed to reduce the estimation bias. The method ensures finite estimates by penalizing the likelihood function. In the context of mixture cure models, the ML issue is rarely discussed in the literature; therefore, this topic can be seen as the first contribution of our paper. The second major contribution, not well addressed elsewhere, is the study of the ML issue in cure mixture modeling under the flexibility of a semiparametric framework to handle the baseline hazard. We derive the modified score function based on the Firth approach and explore finite sample size properties of the estimators via a Monte Carlo scheme. The simulation results indicate that the performance of coefficients related to the binary covariates are strongly affected to the imbalance degree. A real illustration, in the melanoma dataset, is discussed using a relatively novel data set collected in a Brazilian universityhospital.

Exponentiated Weibull Models Applied to Medical Data in Presence of Right-censoring, Cure Fraction and Covariates

Cure fraction models have been widely used to analyze survival data in which a proportion of the individuals isnot susceptible to the event of interest. This article considers frequentist and Bayesian methods to estimate the unknown model parameters of the exponentiated Weibull (EW) distribution considering right-censored survival data with a cure fraction and covariates. The EW distribution is as an extension to the Weibull distribution by considering an additional shape parameter to the model. We consider four types of cure fraction models: the mixture cure fraction (MCF), the nonmixture cure fraction (NMCF), the complementary promotion time cure (CPTC), and the cure rate proportional odds (CRPO) models. Bayesian inferences are obtained by using MCMC (Markov Chain Monte Carlo) methods. A simulation study was conducted to examine the performance of the maximum likelihood estimators for different sample sizes. Two real datasets were considered to illustrate the applicability of the proposed model. The EW distribution and its sub-models have the flexibility to accommodate different shapes for the hazard function and should be an attractive choice for survival data analysis when a cure fraction is present.

The Extrapolation Performance of Survival Models for Data With a Cure Fraction: A Simulation Study

ObjectivesCurative treatments can result in complex hazard functions. The use of standard survival models may result in poor extrapolations. Several models for data which may have a cure fraction are available, but comparisons of their extrapolation performance are lacking. A simulation study was performed to assess the performance of models with and without a cure fraction when fit to data with a cure fraction. MethodsData were simulated from a Weibull cure model, with 9 scenarios corresponding to different lengths of follow-up and sample sizes. Cure and noncure versions of standard parametric, Royston-Parmar, and dynamic survival models were considered along with noncure fractional polynomial and generalized additive models. The mean-squared error and bias in estimates of the hazard function were estimated. ResultsWith the shortest follow-up, none of the cure models provided good extrapolations. Performance improved with increasing follow-up, except for the misspecified standard parametric cure model (lognormal). The performance of the flexible cure models was similar to that of the correctly specified cure model. Accurate estimates of the cured fraction were not necessary for accurate hazard estimates. Models without a cure fraction provided markedly worse extrapolations. ConclusionsFor curative treatments, failure to model the cured fraction can lead to very poor extrapolations. Cure models provide improved extrapolations, but with immature data there may be insufficient evidence to choose between cure and noncure models, emphasizing the importance of clinical knowledge for model choice. Dynamic cure fraction models were robust to model misspecification, but standard parametric cure models were not.

A comparison of mixture cure fraction models to traditional parametric survival models in estimation of the cost-effectiveness of nivolumab for relapsed small cell lung cancer

Background In August 2018, the US FDA granted accelerated approval for nivolumab in small cell lung cancer (SCLC) that has progressed after platinum-based chemotherapy and at least one other line of therapy. The objective of this study was to evaluate the cost-effectiveness of nivolumab vs. usual care as third-line (3 L) therapy for patients with recurrent SCLC (rSCLC) from the health payer perspective. Given the potential for a meaningful fraction of treated patients to achieve long-term response to nivolumab, we also assessed the impact of using mixture cure modeling (MCM) vs. parametric survival modeling on survival estimates and cost-effectiveness from the US Medicare payer perspective. Methods We created a partitioned survival decision model to assess the cost-effectiveness of 3 L nivolumab vs. usual care in rSCLC, based on observed US treatment patterns. Using this approach, we assessed the impact of extrapolating long-term survival from the CheckMate 032 trial, using both MCM and standard parametric curve fits. Nivolumab survival, resource use, and Grade 3/4 adverse event rates were derived from CheckMate 032. Usual care survival, resource use, and costs were derived from an analysis of patients receiving 3 L treatment for rSCLC in the SEER-Medicare registry. We applied 2020 Wholesale Acquisition Cost for drugs and 2020 CMS reimbursement for procedures. Utilities were derived from the literature. We estimated life years (LY), quality-adjusted life years (QALYs), and costs over a lifetime horizon. Results MCM and parametric survival model extrapolations resulted in 0.43 versus 0.38 more LYs, 0.34 versus 0.30 more QALYs, and $69,308 versus $61,336 more expenditure for nivolumab vs. usual care, respectively. The costs per QALY gained using mixture cure versus parametric survival modeling were $204,386 and $207,431, respectively. Conclusions Mixture cure modeling was equivalent compared to parametric modeling in estimating the cost-effectiveness of nivolumab-based therapy due to the small fraction of patients achieving a long-term response with nivolumab (12.9%).

On Containment Plan Amid COVID-19 in Red Zone Districts of India: Using Clinical Life Table and Cure Fraction Model

Background and Objective: Ministry of Health and Family Welfare, Government of India took many measures to arrest the spread of COVID-19 disease. This research is intended to shed light on number of confirmed cases with respect to population density of the affected districts, to study the proportion of positives among total sample tested, to construct clinical life table of general population w.r.t. number of daily positive cases and to estimate the long-term survivors among general population. Materials and Methods: Simple scatter plot has been used to see relation between population density and number of cases in different districts of India, cluster analysis technique is used for making cluster of Districts having similar features. Clinical life table is prepared for general population of affected Districts, and mixture & non-mixture cure fraction models used to estimate the proportion of long-term survivors (disease free survival) of general population. Result: Median daily proportion of positives are found to be below 0.05. In 79 identified hot spot Districts average population is very high (36.29 lakhs) with population density of 3404 per square kilometre. Even among those Districts there are huge inter cluster differences w.r.t. number of cases and population density. Clinical life table is constructed for general population of 429 affected Districts, increasing pattern in hazard is found even though study period is small. Long term survivors of disease is simulated and found to be 99.812%. Conclusion: Government ought to make cluster of Districts among red zone Districts, clustering should be based on number of cases and population density. Different containment strategy may be prepared for each cluster of Districts.

Firth adjusted score function for monotone likelihood in the mixture cure fraction model.

Models for situations where some individuals are long-term survivors, immune or non-susceptible to the event of interest, are extensively studied in biomedical research. Fitting a regression can be problematic in situations involving small sample sizes with high censoring rate, since the maximum likelihood estimates of some coefficients may be infinity. This phenomenon is called monotone likelihood, and it occurs in the presence of many categorical covariates, especially when one covariate level is not associated with any failure (in survival analysis) or when a categorical covariate perfectly predicts a binary response (in the logistic regression). A well known solution is an adaptation of the Firth method, originally created to reduce the estimation bias. The method provides a finite estimate by penalizing the likelihood function. Bias correction in the mixture cure model is a topic rarely discussed in the literature and it configures a central contribution of this work. In order to handle this point in such context, we propose to derive the adjusted score function based on the Firth method. An extensive Monte Carlo simulation study indicates good inference performance for the penalized maximum likelihood estimates. The analysis is illustrated through a real application involving patients with melanoma assisted at the Hospital das Clínicas/UFMG in Brazil. This is a relatively novel data set affected by the monotone likelihood issue and containing cured individuals.

Estimation of premium cost for HIV/AIDS patients under ART

The primary aim of this paper is to bring an insurance plan for HIV/AIDS patients. Recent studies based on antiretroviral therapy (ART) and highly active antiretroviral therapy (HAART) suggests long term survival of HIV/AIDS patients. Use of cure fraction model has revealed that a considerable proportion of patients are long term survivors out of the diseased cohort (Grover et al. 2019). The survival time is defined under the purview of CD4 cell counts which are considered to be the disease marker for HIV/AIDS patients. Many patients suffer financially along with risk of death. Here, we introduce an insurance plan which involves low risk for insurers and affordable premium for patients. The premium is calculated, using the survival estimates from Kaplan–Meier survival curve, on the basis of a deterministic model.

PBI33 HOW NOVEL IS ICER METHODS GUIDANCE ON HIGH-IMPACT, SINGLE, AND SHORT-TERM THERAPIES?

Innovative cell and gene therapies are often single-administration treatments with high-upfront costs but the potential for long-term health gains and possibly cure. Given the uncertainty in outcomes at launch and the unrecoverable high costs, the US Institute for Clinical and Economic Review (ICER) recently developed novel methods for assessing these treatments. We reviewed these methods and recent health technology assessments (HTAs) by the UK National Institute for Health and Care Excellence (NICE) and the Scottish Medicines Consortium (SMC) of tisagenlecleucel and voretigene neparvovec, to examine whether ICER’s new methods are already considered in HTAs in the UK. The adapted ICER methods require cure-fraction modeling, discounting of outcomes and costs at the standard 3%, and a threshold analysis of the duration of the beneficial effect. A cost-effectiveness threshold of $150,000 per quality-adjusted life-year (QALY) gained is used to guide evaluation of long-term value for money. ICER will also consider benefits beyond QALYs, including the value of treatment choice and potential benefit or disadvantage of option value. In the HTAs of tisagenlecleucel and voretigene neparvovec, NICE considered cure-fraction models and reduction of the discount rate to 1.5%, and acknowledged value beyond health benefits, such as patients retaining independence and research advancing the broader field of gene therapy. SMC accepted additional value in the single administration, and reduced patient and carer burden. Both NICE and SMC applied higher cost-effectiveness thresholds for ultra-rare diseases. While higher cost-effectiveness thresholds and cure-fraction models are already considered in HTAs for costly, single, or short-term therapies in the UK, ICER’s consideration of the value of treatment choice and option value is a novel approach. ICER plans to implement the adapted methods in January 2020. A review of future ICER assessments will indicate whether the new methodology provides a better way to demonstrate the value of potentially curative treatments.

Bayesian cure fraction models with measurement error in the scale mixture of normal distribution.

Cure fraction models have been widely used to model time-to-event data when part of the individuals survives long-term after disease and are considered cured. Most cure fraction models neglect the measurement error that some covariates may experience which leads to poor estimates for the cure fraction. We introduce a Bayesian promotion time cure model that accounts for both mismeasured covariates and atypical measurement errors. This is attained by assuming a scale mixture of the normal distribution to describe the uncertainty about the measurement error. Extending previous works, we also assume that the measurement error variance is unknown and should be estimated. Three classes of prior distributions are assumed to model the uncertainty about the measurement error variance. Simulation studies are performed evaluating the proposed model in different scenarios and comparing it to the standard promotion time cure fraction model. Results show that the proposed models are competitive ones. The proposed model is fitted to analyze a dataset from a melanoma clinical trial assuming that the Breslow depth is mismeasured.

Evaluation of prognostic factors affecting long and short term survival rates of Hodgkin's lymphoma patients using the cure fraction models

Evaluation of prognostic factors affecting long and short term survival rates of Hodgkin's lymphoma patients using the cure fraction models

Mixture and nonmixture cure fraction models assuming discrete lifetimes: Application to a pelvic sarcoma dataset.

Different cure fraction models have been used in the analysis of lifetime data in presence of curedpatients. This paper considers mixture and nonmixture models based on discrete Weibull distribution to model recurrent eventdata in presence of a cure fraction. The novelty of this study is the use of a discrete lifetime distribution in place ofusual existing continuous lifetime distributions for lifetime data in presence of cured fraction, censored data, andcovariates. In the verification of the fit of the proposed model it is proposed the use of randomized quantile residuals. Anextensive simulation study is considered to evaluate the properties of the estimates of the parameters related to the proposedmodel. As an illustration of the proposed methodology, it is considered an application considering a medical dataset related tolifetimes in a retrospective cohort study conducted by Puchner etal. (2017) that consists of 147 consecutive cases withsurgical treatment of a sarcoma of the pelvis between the years of 1980 and2012.

A flexible bimodal model with long-term survivors and different regression structures

The cure fraction models are useful to model lifetime data with long-term survivors. In this paper, we introduce a flexible cure rate survival model where the model parameters are related to covariates in different regression structures. The regression model allows to model jointly the location, scale and shape effects. The maximum likelihood method is employed to estimate the model parameters. We provide Monte Carlo simulation experiments to verify the performance of the maximum likelihood estimates for different sample sizes and cure rate percentages. Furthermore, some diagnostic measures to assess departures from model assumptions as well as to detect outlying observations are also considered. Finally, applications to real data are presented to show the usefulness of the new cure rate model.

Cure Fraction Model for the Estimation of Long-term Survivors of HIV/AIDS Patients under Antiretroviral Therapy

Cure Fraction Model for the Estimation of Long-term Survivors of HIV/AIDS Patients under Antiretroviral Therapy

Application of a Mixture Cure Fraction Model Based on the Generalized Modified Weibull Distribution for Analyzing Survival of Patients with Breast Cancer

Background: Rapid progression in medical and health sciences have caused survival studies, where some patients have long-term survival, especially for chronic diseases such as breast cancer. Cure models can be applicable to analyze such data. Objectives: The aim of this study was to determine the risk factors associated with breast cancer, using mixture cure fraction model. Methods: We studied data for 438 patients, who were referred to cancer research center in Shahid Beheshti University of Medical Sciences. The patients were visited and treated during 1992 to 2012 and followed-up until October 2014. The data were analyzed by mixture cure fraction model based on GMW (generalized modified Weibull) distribution and inferences were obtained with Bayesian approach, using standard MCMC (Markov Chain Monte Carlo) methods. All analyses were performed, using SPSS v20 and OpenBUGS software. The significant level was considered at 0.05. Results: During the follow-up period, 75 (17.12%) deaths occurred by breast cancer and the one-year overall survival rate was 98%. Covariates such as numbers of metastatic lymph nodes and histologic grade were statistically significant. Also, the cure fraction estimation was obtained 58%. Conclusions: When some patients have a long-term survival, cure models can be an interesting model to study survival and these models estimate parameters better than the traditional models such as cox model. In this paper, the mixture cure fraction model based on GMW was fitted for analysing survival times in patients with breast cancer.

Factors Affecting Long-Survival of Patients with Esophageal Cancer Using Non-Mixture Cure Fraction Model

Objective:Esophageal cancer (EC) is one of the gastrointestinal malignancies with a very high morbidity and mortality rate due to poor prognosis. This study aims to assess the effects of risk factors on survival and cure fraction of patients with EC in a population of Iranian patients using a non-mixture cure fraction model.Methods:This retrospective cohort study was conducted on 127 patients with EC who were diagnosed during 2009-2010 and were followed up for 5 years in East-Azarbaijan, Iran. Stepwise selection and non-mixture cure fraction model were used to find the risk factors of EC survival patients.Results:The mean (±standard deviation) diagnosis age of the EC was 66.92(±11.95). One, three and five-year survival probabilities were 0.44 (95% confidence interval (CI): 0.36-0.54), 0.2 (95% CI: 0.14-0.28) and 0.13 (95% CI: 0.08-0.2) respectively. Female sex (Estimate=-0.99; 95% confidence interval (CI): -1.41,-0.58; p-value<0.001), low level socioeconomic status (Estimate=0.39; 95%CI: 0.12,0.66; p-value=0.043), the group who did not do esophagectomy surgery (Estimate=0.58; 95%CI: 0.17,0.99; p-value=0.005) and unmarried group (Estimate=0.58; 95%CI: 0.11-1.05; p-value=0.015) were found as the significant predictor of survival and cure fraction of the EC patients. Population cure rate was 0.11 (95%CI: 0.07-0.19) and Cure fraction was estimated 5.11 percent.Conclusion:This study found gender, socioeconomic status, Esophagectomy surgery and marital status as the potential risk factors for survival and cure fraction of Iranian EC patients. Moreover, non- mixture cure fraction provides more accurate and more reliable insight into long-term advantages of EC therapy compared to standard classic survival analysis alternatives.