Modelling the Survival of Western Honey Bee Apis mellifera and the African Stingless Bee Meliponula ferruginea Using Semiparametric Marginal Proportional Hazards Mixture Cure Model

Classical survival analysis assumes all subjects will experience the event of interest, but in some cases, a portion of the population may never encounter the event. These survival methods further assume independent survival times, which is not valid for honey bees, which live in nests. The study introduces a semi-parametric marginal proportional hazards mixture cure (PHMC) model with exchangeable correlation structure, using generalized estimating equations for survival data analysis. The model was tested on clustered right-censored bees survival data with a cured fraction, where two bee species were subjected to different entomopathogens to test the effect of the entomopathogens on the survival of the bee species. The Expectation-Solution algorithm is used to estimate the parameters. The study notes a weak positive association between cure statuses (ρ1=0.0007) and survival times for uncured bees (ρ2=0.0890), emphasizing their importance. The odds of being uncured for A. mellifera is higher than the odds for species M. ferruginea. The bee species, A. mellifera are more susceptible to entomopathogens icipe 7, icipe 20, and icipe 69. The Cox-Snell residuals show that the proposed semiparametric PH model generally fits the data well as compared to model that assume independent correlation structure. Thus, the semi parametric marginal proportional hazards mixture cure is parsimonious model for correlated bees survival data.

Transformation Models for Survival Data Analysis with Applications

When the event of interest never occurs for a proportion of subjects during the study period, survival models with a cure fraction are more appropriate in analyzing this type of data. Considering the non-linear relationship between response variable and covariates, we propose a class of generalized transformation models motivated by Zeng et al. [1] transformed proportional time cure model, in which fractional polynomials are used instead of the simple linear combination of the covariates. Statistical properties of the proposed models are investigated, including identifiability of the parameters, asymptotic consistency, and asymptotic normality of the estimated regression coefficients. A simulation study is carried out to examine the performance of the power selection procedure. The generalized transformation cure rate models are applied to the First National Health and Nutrition Examination Survey Epidemiologic Follow-up Study (NHANES1) for the purpose of examining the relationship between survival time of patients and several risk factors.

Semiparametric estimation for accelerated failure time mixture cure model allowing non-curable competing risk

The mixture cure model is the most popular model used to analyse the major event with a potential cure fraction.But in the real world there may exist a potential risk from other non-curable competing events.In this paper,we study the accelerated failure time model with mixture cure model via kernel-based nonparametric maximum likelihood estimation allowing non-curable competing risk.An EM algorithm is developed to calculate the estimates for both the regression parameters and the unknown error densities,in which a kernel-smoothed conditional profile likelihood is maximised in the M-step,and the resulting estimates are consistent.Its performance is demonstrated through comprehensive simulation studies.Finally,the proposed method is applied to the colorectal clinical trial data.

The Proportional Mean Residual Life Regression Model with Cure Fraction and Auxiliary Covariate

As biological studies become more expensive to conduct,it is a frequently encountered question that how to take advantage of the available auxiliary covariate information when the exposure variable is not measured.In this paper,we propose an induced cure rate mean residual life time regression model to accommodate the survival data with cure fraction and auxiliary covariate,in which the exposure variable is only assessed in a validation set,but a corresponding continuous auxiliary covariate is ascertained for all subjects in the study cohort.Simulation studies elucidate the practical performance of the proposed method under finite samples.As an illustration,we apply the proposed method to a heart disease data from the Study of Left Ventricular Dysfunction.