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.

Leaching kinetics of low-grade copper ore containing calcium-magnesium carbonate in ammonia-ammonium sulfate solution with persulfate

The leaching kinetics of copper from low-grade copper ore was investigated in ammonia-ammonium sulfate solution with sodium persulfate. The effect parameters of stirring speed, temperature, particle size, concentrations of ammonia, ammonium sulfate and sodium persulfate were determined. The results show that the leaching rate is nearly independent of agitation above 300 r/min and increases with the increase of temperature, concentrations of ammonia, ammonium sulfate and sodium persulfate. The EDS analysis and phase quantitative analysis of the residues indicate that bornite can be dissolved by persulfate oxidization. The leaching kinetics with activation energy of 22.91 kJ/mol was analyzed by using a new shrinking core model （SCM） in which both the interfacial transfer and diffusion across the product layer affect the leaching rate. A semi-empirical rate equation was obtained to describe the leaching process and the empirical reaction orders with respect to the concentrations of ammonia, ammonium sulfate and sodium persulfate are 0.5, 1.2 and 0.5, respectively.

Regression Analysis of Doubly Censored Data with a Cured Subgroup under a Class of Promotion Time Cure Models

In some situations,the failure time of interest is defined as the gap time between two related events and the observations on both event times can suffer either right or interval censoring.Such data are usually referred to as doubly censored data and frequently encountered in many clinical and observational studies.Additionally,there may also exist a cured subgroup in the whole population,which means that not every individual under study will experience the failure time of interest eventually.In this paper,we consider regression analysis of doubly censored data with a cured subgroup under a wide class of flexible transformation cure models.Specifically,we consider marginal likelihood estimation and develop a two-step approach by combining the multiple imputation and a new expectation-maximization(EM)algorithm for its implementation.The resulting estimators are shown to be consistent and asymptotically normal.The finite sample performance of the proposed method is investigated through simulation studies.The proposed method is also applied to a real dataset arising from an AIDS cohort study for illustration.

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.

A novel nonparametric mixture model for the detection pattern of COVID-19 on Diamond Princess cruise

The outbreak of COVID-19 on the Diamond Princess cruise ship has attracted much attention.Motivated by the PCR testing data on the Diamond Princess,we propose a novel cure mixture nonparametric model to investigate the detection pattern.It combines a logistic regression for the probability of susceptible subjects with a nonparametric distribution for the detection of infected individuals.Maximum likelihood estimators are proposed.The resulting estimators are shown to be consistent and asymptotically normal.Simulation studies demonstrate that the proposed approach is appropriate for practical use.Finally,we apply the proposed method to PCR testing data on the Diamond Princess to show its practical utility.

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.

Joint modeling of longitudinal proportional measurements and survival time with a cure fraction

In cancer clinical trials and other medical studies, both longitudinal measurements and data on a time to an event(survival time) are often collected from the same patients. Joint analyses of these data would improve the efficiency of the statistical inferences. We propose a new joint model for the longitudinal proportional measurements which are restricted in a finite interval and survival times with a potential cure fraction. A penalized joint likelihood is derived based on the Laplace approximation and a semiparametric procedure based on this likelihood is developed to estimate the parameters in the joint model. A simulation study is performed to evaluate the statistical properties of the proposed procedures. The proposed model is applied to data from a clinical trial on early breast cancer.