Inference for One-Shot Devices with Dependent k-Out-of-M Structured Components under Gamma Frailty

A device that performs its intended function only once is referred to as a one-shot device. Actual lifetimes of such kind of devices under test cannot be observed, and they are either left-censored or right-censored. In addition, one-shot devices often consist of multiple components that could cause the failure of the device. The components are coupled together in the manufacturing process or assembly, resulting in the failure modes possessing latent heterogeneity and dependence. In this paper, we develop an efficient expectation–maximization algorithm for determining the maximum likelihood estimates of model parameters, on the basis of one-shot device test data with multiple failure modes under a constant-stress accelerated life-test, with the dependent components having exponential lifetime distributions under gamma frailty that facilitates an easily understandable interpretation. The maximum likelihood estimate and confidence intervals for the mean lifetime of k-out-of-M structured one-shot device under normal operating conditions are also discussed. The performance of the proposed inferential methods is finally evaluated through Monte Carlo simulations. Three examples including Class-H failure modes data, mice data from ED01 experiment, and simulated data with four failure modes are used to illustrate the proposed inferential methods.

Generalized Lindley Shared Frailty Based on Reversed Hazard Rate

Due to the unavailability of complete data in various circumstances in biological, epidemiological, and medical studies, the analysis of censored data is very common among practitioners. But the analysis of bivariate censored data is not a regular mechanism because it is not necessary to always have independent data. Observed and unobserved covariates affect the variables under study. So, heterogeneity is present in the data. Ignoring observed and unobserved covariates may have objectionable consequences. But it is not easy to find that whether there is any effect of the unobserved covariate or not. Shared frailty models are the viable choice to counter such scenarios. However, due to certain restrictions such as the identifiability condition and the requirement that their Laplace transform exists, finding a frailty distribution can be difficult. As a result, in this paper, we introduce a new frailty distribution generalized Lindley (GL) for reversed hazard rate (RHR) setup that outperforms the gamma frailty distribution. So, our main motive is to establish a new frailty distribution under the RHR setup. By assuming exponential Gumbel (EG) and generalized inverted exponential (GIE) baseline distributions, we propose a new class of shared frailty models based on RHR. We estimate the parameters in these frailty models and use the Bayesian paradigm of the Markov Chain Monte Carlo (MCMC) technique. Model selection criteria have been performed for the comparison of models. We analyze Australian twin data and suggest a better model.

Evaluation of the Factors Affecting the Cure Rate of Cervical Intra-Epithelial Neoplasia Recurrence Using Defective Models

Background: Treatment of cervical intraepithelial neoplasia is very important since if it remains untreated, it may progress to cervical cancer. It is usually treated with excisional surgery. This study aimed to find the factors affecting the cure rate of cervical intraepithelial neoplasia recurrence after surgery using defective models. Study design: A retrospective cohort study. Methods: Excisional surgery was performed on 307 patients with high-grade cervical intraepithelial neoplasia, from 2009 to 2017. The patients were followed up until recurrence based on histopathology report. Hematologic factors were measured before surgery. The cure rates were estimated using defective models with a Gamma frailty term and the results were compared. Results: Neutrophil-to-lymphocyte ratio (NLR) (P<0.001) and excised mass size (P<0.001) had significant impacts on cure rates, and their cut-off values were 1.9 (P<0.001) and 15 mm2 (P<0.001), respectively. Patients with lower neutrophil-to-lymphocyte ratios and larger excised tissues had higher cure rates. Defective 3-parameter Gompertz distribution with gamma frailty term had the best fit to the data, and its estimated cure rates were 98% among patients with an excised mass size of >15 mm2 and NLR of <1.9, 84% among patients with an excised mass size of >15 mm2 and NLR of >1.9, 79% among patients with an excised mass size of <15 mm2 and NLR of <1.9, and 30% among patients with an excised mass size of <15 mm2 and NLR of >1.9. Conclusion: Cervical intraepithelial neoplasia must be identified and treated before its progress. Excision of more tissues during excisional surgery, especially when the NLR of the patient is high, can help to prevent cervical intraepithelial neoplasia recurrence.

The XGTDL family of survival distributions

Non-PH parametric survival modelling is developed within the framework of the multiple logistic function. The family considered comprises three basic models: (a) a PH model, (b) an accelerated life model and (c) a model which is non-proportional hazards and non-accelerated life. The last model, the generalised time-dependent logistic model was described first by the author in 1996 and this model gives its name to the entire family. The family is generalised by means of a Gamma frailty extension which is shown to accommodate crossing hazards data. A further generalisation is the inclusion of a dispersion model. These extensions lead naturally to the concept of a multi-parameter regression model described by Burke and MacKenzie in which the scale and shape parameters are modelled simultaneously as functions of covariates. Where possible, we include the MPR extension in the XGTDL family. Following a simulation study, the new models are used to analyse two sets survival data and the methods are discussed.

Frailty Models for Predicting Eruption Time and Sequence of Permanent Dentition in Sri Lankan Children

The main goal of this study is to create a suitable model to predict the tooth eruption pattern of Sri Lankan children. Also, we identify the relationship between variables associated with eruption sequence, compare the eruption sequence between sexes, compare the eruption sequences between upper and lower jaws, identifying common polymorphisms of tooth eruption sequences of children and determine the frequencies of occurrence of emergence polymorphisms for different tooth pairs. This analysis was performed using the data of the extent of tooth eruption of all 28 teeth at 10 different time points in each year. Welch two-sample t-test was used to identify the relationship between variables associated with eruption sequence. Frailty models and Cox-Proportional Hazard models developed for each tooth type separately and the model selection procedures Akaike information criterion (AIC), Bayesian information criterion (BIC) and Root Mean Square Error (RMSE) values are measured for each model. Since Gamma Frailty models have the smallest AIC and BIC for seven types of tooth which divide according to the eruption stage of the each tooth, we choose Gamma Frailty models as the best predictor for the tooth eruption. There is a significant difference between the eruption pattern of gender and jaw associated with time. However, no significant difference between sides associated with the eruption sequence was observed.