Likelihood-Based Inference for Semi-Parametric Transformation Cure Models with Interval Censored Data

A simple yet effective way of modeling survival data with cure fraction is by considering Box-Cox transformation cure model (BCTM) that unifies mixture and promotion time cure models. In this article, we numerically study the statistical properties of the BCTM when applied to interval censored data. Time-to-events associated with susceptible subjects are modeled through proportional hazards structure that allows for non-homogeneity across subjects, where the baseline hazard function is estimated by distribution-free piecewise linear function with varied degrees of non-parametricity. Due to missing cured statuses for right censored subjects, maximum likelihood estimates of model parameters are obtained by developing an expectation-maximization (EM) algorithm. Under the EM framework, the conditional expectation of the complete data log-likelihood function is maximized by considering all parameters (including the Box-Cox transformation parameter $\alpha$) simultaneously, in contrast to conventional profile-likelihood technique of estimating $\alpha$. The robustness and accuracy of the model and estimation method are established through a detailed simulation study under various parameter settings, and an analysis of real-life data obtained from a smoking cessation study.Comment: 20 page

Joint frailty model for recurrent events and a terminal event in the presence of cure fraction

The observations of repeated or recurrent events occur in many longitudinal studies. Furthermore, sometimes there may exist a terminal event such as death, which is strongly correlated with recurrent events. In many situations, a fraction of subjects who will never experience the event of interest during a long follow-up period is considered to be cured. In this article, we proposed a joint frailty model in the presence of cure fraction. The dependency is modeled by shared frailty that is contained in both the recurrent andterminal events hazard functions. It allows to estimate two separate sets of parameters on the recurrent, death, and cure model. We applied the maximum likelihood method under a piecewise constant hazard function for model fitting. The proposed model is evaluated by simulation studies and an application to a breast cancer data is provided

Comparison of Parametric Survival Extrapolation Approaches Incorporating General Population Mortality for Adequate Health Technology Assessment of New Oncology Drugs

Objectives: Survival extrapolation of trial outcomes is required for health economic evaluation. Generally, all-cause mortality (ACM) is modeled using standard parametric distributions, often without distinguishing disease-specific/excess mortality and general population background mortality (GPM). Recent National Institute for Health and Care Excellence guidance (Technical Support Document 21) recommends adding GPM hazards to disease-specific/excess mortality hazards in the log-likelihood function ("internal additive hazards"). This article compares alternative extrapolation approaches with and without GPM adjustment. Methods: Survival extrapolations using the internal additive hazards approach (1) are compared to no GPM adjustment (2), applying GPM hazards once ACM hazards drop below GPM hazards (3), adding GPM hazards to ACM hazards (4), and pro-portional hazards for ACM versus GPM hazards (5). The fit, face validity, mean predicted life-years, and corresponding uncertainty measures are assessed for the active versus control arms of immature and mature (30-and 75-month follow-up) multiple myeloma data and mature (64-month follow-up) breast cancer data. Results: The 5 approaches yielded considerably different outcomes. Incremental mean predicted life-years vary most in the immature multiple myeloma data set. The lognormal distribution (best statistical fit for approaches 1-4) produces survival increments of 3.5 (95% credible interval: 1.4-5.3), 8.5 (3.1-13.0), 3.5 (1.3-5.4), 2.9 (1.1-4.5), and 1.6 (0.4-2.8) years for approaches 1 to 5, respectively. Approach 1 had the highest face validity for all data sets. Uncertainty over parametric distributions was comparable for GPM-adjusted approaches 1, 3, and 4, and much larger for approach 2. Conclusion: This study highlights the importance of GPM adjustment, and particularly of incorporating GPM hazards in the log-likelihood function of standard parametric distributions

A Vertical Mixture Cure Model for Credit Risk Analysis

Credit risk assessment is one of the most important tasks of banks and other financial institutions. There are three main reasons of credit termination: maturity, early repayment and default. Credits that mature can be considered as not susceptible to early termination, whereas early repayments can be treated as competing risk to default. Most credits end on time (mature) or are repaid early, default happens only for a few percentage of credits. Modelling probability of default requires taking into account the probability of early repayment and maturity. We propose the use of a vertical mixture cure model with a cured fraction to analyse the probability of default. Empirical research was conducted on the sample of 5,000 consumer credit accounts of a Polish financial institution. Credits were observed 24 months since origination. The vertical mixture cure model was estimated with characteristics of borrowers as predictors. The discrimination ability of the model through 24 months of the credit life span was compared with a mixture model that has been earlier proposed in the literature

Mathematical modelling of Portuguese hydroelectric energy system

Hydropower is one of the most traditional renewable energy source and a major contributor for renewable energy production inmany countries. In Portugal it was the only renewable energy source for many years but nowadays wind presents similar production levels and for example in 2015 wind was the main source producing 45.5 % of the total renewable energy. However hydro energy will continue to be important in the renewable energy production and in this work ranking of nine models for hydro energy production with various numbers of parameters was done using adjusted R-squared and corrected Akaike information criterion (AICc).info:eu-repo/semantics/publishedVersio

Genome-wide association studies investigating a histological variant and time-to-metastasis of colorectal cancer

Colorectal cancer is a common and complex disease with significant impact on patients and their families. Despite the extensive research conducted on this disease, there is still significant variability in tumor characteristics and disease outcomes. The unknown variability may be explained, in part, by germline genetic variations. This dissertation aimed to identify genetic polymorphisms associated with colorectal cancer tumor histology as well as with the long-term risk and/or timing of metastasis in colorectal cancer using appropriate study designs and statistical methods. As a result of these comprehensive analyses, we identified a set of polymorphisms that significantly increase the discriminatory accuracy of a model for distinguishing between mucinous and non-mucinous colorectal tumors. In addition, we identified ten polymorphisms significantly associated with time-to-metastasis of colorectal cancer after adjusting for significant baseline characteristics. Once replicated, these results could assist in better understanding the complex biological mechanisms behind colorectal tumor histology and distant metastasis

Mixture Cure Survival Analysis Model for Cardiovascular Disease in Sulaimani, Iraq

Cardiovascular disease(CVDs) is one of the leading causes of death world- wide. Iraq ranks 20th in the age adjusted Death Rate due to CDVs. In recent years, the treatment of many diseases, especially heart disease, has significantly improved, so the number of patients who do not experience the desired outcome, including death, has increased. In statistical analysis of this type of diseases, cure models are used instead of the usual survival models. In this paper, a sample include 919 patients referred to Sulaimani Hospital with heart disease (including 365 female and 554 male) were followed up for a maximum of 650 days, during the years 2020 to 2022. Of these, 162 people, or 17.6%, have died. Since the Maller-Zhou test was significant (P < 0.01) and considering the cured fraction in this population, the mixture cure model with some statistical distributions was fitted to the data. Based on the re- sults and comparing AIC and BIC, it was observed that the healed model combined with Weibull distribution for survival time and Poisson distribu- tion for the number of deaths with the AIC=1972.54 , BIC=2092.985 was the best model

Comparison of survival analysis approaches to modelling credit risks

A Dissertation submitted in partial fulfillment of the requirements for the Master of Science in Mathematical Finance (MSc.MF) at Strathmore UniversityCredit risk is a critical area in finance and has drawn considerable research attention. As such, survival analysis has widely been used in credit risk, in particular, to model debt's time to default mechanisms. In this study, we revisit different survival analysis approaches as applied in credit risk defaulters' data and assess their performance in light of the Kenyan context. In practice, inconsistency in the validity of credit risk models used by many companies when predicting and analysis of loan default is a common phenomenon that occurs unexpectedly. Loan defaults often cause major loses to creditors' and can be of great benefit if quantified correctly in advance by using correct models. Here, we address the unbiasedness, analysis, and comparison of survival analysis approaches, particularly, the models of credit risk. We carry out data analysis using the Cox proportional hazard model and its extensions as well as the mixture cure and non-cure model. We then compare the results systematically by investigating the most efficient awl preferable model that produces best estimates in the Kenyan real data, sets. Results show the Cox Proportional Hazard (Cox PH) model is more efficient in the analysis of Kenyan real data set compared to the frailty, the mixture cure, and non-cure model