Estimation method of the semiparametric mixture cure gamma frailty model

A Weibull mixture cure frailty model for high-dimensional covariates

A novel mixture cure frailty model is introduced for handling censored survival data. Mixture cure models are preferable when the existence of a cured fraction among patients can be assumed. However, such models are heavily underexplored: frailty structures within cure models remain largely undeveloped, and furthermore, most existing methods do not work for high-dimensional datasets, when the number of predictors is significantly larger than the number of observations. In this study, we introduce a novel extension of the Weibull mixture cure model that incorporates a frailty component, employed to model an underlying latent population heterogeneity with respect to the outcome risk. Additionally, high-dimensional covariates are integrated into both the cure rate and survival part of the model, providing a comprehensive approach to employ the model in the context of high-dimensional omics data. We also perform variable selection via an adaptive elastic-net penalization, and propose a novel approach to inference using the expectation-maximization (EM) algorithm. Extensive simulation studies are conducted across various scenarios to demonstrate the performance of the model, and results indicate that our proposed method outperforms competitor models. We apply the novel approach to analyze RNAseq gene expression data from bulk breast cancer patients included in The Cancer Genome Atlas (TCGA) database. A set of prognostic biomarkers is then derived from selected genes, and subsequently validated via both functional enrichment analysis and comparison to the existing biological literature. Finally, a prognostic risk score index based on the identified biomarkers is proposed and validated by exploring the patients' survival.

Long-term Dagum-power variance function frailty regression model: Application in health studies

Survival models with cure fractions, known as long-term survival models, are widely used in epidemiology to account for both immune and susceptible patients regarding a failure event. In such studies, it is also necessary to estimate unobservable heterogeneity caused by unmeasured prognostic factors. Moreover, the hazard function may exhibit a non-monotonic shape, specifically, an unimodal hazard function. In this article, we propose a long-term survival model based on a defective version of the Dagum distribution, incorporating a power variance function frailty term to account for unobservable heterogeneity. This model accommodates survival data with cure fractions and non-monotonic hazard functions. The distribution is reparameterized in terms of the cure fraction, with covariates linked via a logit link, allowing for direct interpretation of covariate effects on the cure fraction-an uncommon feature in defective approaches. We present maximum likelihood estimation for model parameters, assess performance through Monte Carlo simulations, and illustrate the model's applicability using two health-related datasets: severe COVID-19 in pregnant and postpartum women and patients with malignant skin neoplasms.

The estimation of long and short term survival time and associated factors of HIV patients using mixture cure rate models

BACKGROUND

HIV is one of the deadliest epidemics and one of the most critical global public health issues. Some are susceptible to die among people living with HIV and some survive longer. The aim of the present study is to use mixture cure models to estimate factors affecting short- and long-term survival of HIV patients.

METHODS

The total sample size was 2170 HIV-infected people referred to the disease counseling centers in Kermanshah Province, in the west of Iran, from 1998 to 2019. A Semiparametric PH mixture cure model and a mixture cure frailty model were fitted to the data. Also, a comparison between these two models was performed.

RESULTS

Based on the results of the mixture cure frailty model, antiretroviral therapy, tuberculosis infection, history of imprisonment, and mode of HIV transmission influenced short-term survival time (p-value < 0.05). On the other hand, prison history, antiretroviral therapy, mode of HIV transmission, age, marital status, gender, and education were significantly associated with long-term survival (p-value < 0.05). The concordance criteria (K-index) value for the mixture cure frailty model was 0.65 whereas for the semiparametric PH mixture cure model was 0.62.

CONCLUSION

This study showed that the frailty mixture cure models is more suitable in the situation where the studied population consisted of two groups, susceptible and non-susceptible to the event of death. The people with a prison history, who received ART treatment, and contracted HIV through injection drug users survive longer. Health professionals should pay more attention to these findings in HIV prevention and treatment.

An Accelerated Failure Time Cure Model with Shifted Gamma Frailty and Its Application to Epidemiological Research

Survival analysis is a set of methods for statistical inference concerning the time until the occurrence of an event. One of the main objectives of survival analysis is to evaluate the effects of different covariates on event time. Although the proportional hazards model is widely used in survival analysis, it assumes that the ratio of the hazard functions is constant over time. This assumption is likely to be violated in practice, leading to erroneous inferences and inappropriate conclusions. The accelerated failure time model is an alternative to the proportional hazards model that does not require such a strong assumption. Moreover, it is sometimes plausible to consider the existence of cured patients or long-term survivors. The survival regression models in such contexts are referred to as cure models. In this study, we consider the accelerated failure time cure model with frailty for uncured patients. Frailty is a latent random variable representing patients’ characteristics that cannot be described by observed covariates. This enables us to flexibly account for individual heterogeneities. Our proposed model assumes a shifted gamma distribution for frailty to represent uncured patients’ heterogeneities. We construct an estimation algorithm for the proposed model, and evaluate its performance via numerical simulations. Furthermore, as an application of the proposed model, we use a real dataset, Specific Health Checkups, concerning the onset of hypertension. Results from a model comparison suggest that the proposed model is superior to existing alternatives.

A semiparametric mixture model approach for regression analysis of partly interval-censored data with a cured subgroup

Failure time data with a cured subgroup are frequently confronted in various scientific fields and many methods have been proposed for their analysis under right or interval censoring. However, a cure model approach does not seem to exist in the analysis of partly interval-censored data, which consist of both exactly observed and interval-censored observations on the failure time of interest. In this article, we propose a two-component mixture cure model approach for analyzing such type of data. We employ a logistic model to describe the cured probability and a proportional hazards model to model the latent failure time distribution for uncured subjects. We consider maximum likelihood estimation and develop a new expectation-maximization algorithm for its implementation. The asymptotic properties of the resulting estimators are established and the finite sample performance of the proposed method is examined through simulation studies. An application to a set of real data on childhood mortality in Nigeria is provided.

Bayesian mixture cure rate frailty models with an application to gastric cancer data

Mixture cure rate models are commonly used to analyze lifetime data with long-term survivors. On the other hand, frailty models also lead to accurate estimation of coefficients by controlling the heterogeneity in survival data. Gamma frailty models are the most common models of frailty. Usually, the gamma distribution is used in the frailty random variable models. However, for survival data which are suitable for populations with a cure rate, it may be better to use a discrete distribution for the frailty random variable than a continuous distribution. Therefore, we proposed two models in this study. In the first model, continuous gamma as the distribution is used, and in the second model, discrete hyper-Poisson distribution is applied for the frailty random variable. Also, Bayesian inference with Weibull distribution and generalized modified Weibull distribution as the baseline distribution were used in the two proposed models, respectively. In this study, we used data of patients with gastric cancer to show the application of these models in real data analysis. The parameters and regression coefficients were estimated using the Metropolis with Gibbs sampling algorithm, so that this algorithm is one of the crucial techniques in Markov chain Monte Carlo simulation. A simulation study was also used to evaluate the performance of the Bayesian estimates to confirm the proposed models. Based on the results of the Bayesian inference, it was found that the model with generalized modified Weibull and hyper-Poisson distributions is a suitable model in practical study and also this model fits better than the model with Weibull and Gamma distributions.

Long-Term Disease-Free Survival of Non-Metastatic Breast Cancer Patients in Iran: A Survival Model with Competing Risks Taking Cure Fraction and Frailty into Account

Introduction: Survival modeling is a very important tool to detect risk factors and provide a basis for health care planning. However, cancer data may have properties leading to distorted results with routine methods. Therefore, this study aimed to cover specific factors (competing risk, cure fraction and heterogeneity) with a real dataset of Iranian breast cancer patients using a competing risk-cure-frailty model. Materials and methods: For this historical cohort study, information for 550 Iranian breast cancer patients who underwent surgery for tumor removal from 2001 to 2007 and were followed up to March 2017, was analyzed using R 3.2 software. Results: In contrast to T-stage and N-stage, hormone receptor status did not have any significant effect on the cure fraction (long-term disease-free survival). However, T-stage, N-stage and hormone receptor status all had a significant effect on short-term disease-free survival so that the hazard of loco-regional relapse or distant metastasis in cases positive for a hormone receptor was only 0.3 times that for their negative hormone receptor counterparts. The likelihood of locoregional relapse in the first quartile of follow up was nearly twice that of other quartiles. The least cumulative incidence of time to locoregional relapse was for cases with a positive hormone receptor, low N stage and low T stage. The effect of frailty term was significant in this study and a model with frailty appeared more appropriate than a model without, based on the Akaike information criterion (AIC); values for the frailty model and one without the frailty parameter were 1370.39 and 1381.46, respectively. Conclusions: The data from this study indicate ae necessity to consider competing risk, cure fraction and heterogeneity in survival modeling. The competing risk-cure-frailty model can cover complex situations with survival data.

The analysis--hierarchical models: past, present and future

This paper discusses statistical modelling for data with a hierarchical structure, and distinguishes in this context between three different meanings of the term hierarchical model: to account for clustering, to investigate variability and separate predictive equations at different hierarchical levels (multi-level analysis), and in a Bayesian framework to involve multiple layers of data or prior information. Within each of these areas, the paper reviews both past developments and the present state, and offers indications of future directions. In a worked example, previously reported data on piglet lameness are reanalyzed with multi-level methodology for survival analysis, leading to new insights into the data structure and predictor effects. In our view, hierarchical models of all three types discussed have much to offer for data analysis in veterinary epidemiology and other disciplines.

Cure frailty models for survival data: Application to recurrences for breast cancer and to hospital readmissions for colorectal cancer

Owing to the natural evolution of a disease, several events often arise after a first treatment for the same subject. For example, patients with a primary invasive breast cancer and treated with breast conserving surgery may experience breast cancer recurrences, metastases or death. A certain proportion of subjects in the population who are not expected to experience the events of interest are considered to be ‘cured’ or non-susceptible. To model correlated failure time data incorporating a surviving fraction, we compare several forms of cure rate frailty models. In the first model already proposed non-susceptible patients are those who are not expected to experience the event of interest over a sufficiently long period of time. The other proposed models account for the possibility of cure after each event. We illustrate the cure frailty models with two data sets. First to analyse time-dependent prognostic factors associated with breast cancer recurrences, metastases, new primary malignancy and death. Second to analyse successive rehospitalizations of patients diagnosed with colorectal cancer. Estimates were obtained by maximization of likelihood using SAS proc NLMIXED for a piecewise constant hazards model. As opposed to the simple frailty model, the proposed methods demonstrate great potential in modelling multivariate survival data with long-term survivors (‘cured’ individuals).