Analysis of lifetime data from epidemiological studies or destructive testing often involves current status censoring, wherein individuals are examined only once and their event status is recorded only at that specific time point. In practice, some of these individuals may never experience the event of interest, leading to current status data with a cured fraction. Cure models are used to estimate the proportion of non-susceptible individuals, the distribution of susceptible ones, and covariate effects. Motivated from a biological interpretation of cancer metastasis, promotion time cure model is a popular alternative to the mixture cure rate model for analysing such data. The current study is the first to put forth a Bayesian inference procedure for analysing current status data with a cure fraction, resorting to a promotion time cure model. An adaptive Metropolis-Hastings algorithm is utilised for posterior computation. Simulation studies prove our approach's efficiency, while analyses of lung tumor and breast cancer data illustrate its practical utility. This approach has the potential to improve clinical cure rates through the incorporation of prior knowledge regarding the disease dynamics and therapeutic options.

Current status censoring or case I interval censoring takes place when subjects in a study are observed just once to check if a particular event has occurred. If the event is recurring, the data are classified as current count data; if non-recurring, they are classified as current status data. Several instances of dependence of these recurring and non-recurring events are observable in epidemiology and pathology. Estimation of the degree of this dependence and identification of major risk factors for the events are the major objectives of such studies. The current study proposes a Bayesian method for the joint modelling of such related events, employing a shared frailty-based semiparametric regression model. Computational implementation makes use of an adaptive Metropolis-Hastings algorithm. Methods for model selection and divergence-based Bayesian influence diagnostics are proposed. Comprehensive simulation studies are put into use to show the effectiveness of the method proposed and fracture-osteoporosis survey data are worked through to highlight its application.

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Measures of income inequality are used for modelling and analysis of income data. In this paper, we present various income inequality measures in the quantile set up. We also introduce quantile version of well known dullness property. The interrelationships among these measures are investigated. The monotonic behaviour of income inequality measures are discussed. We also develop new quantile functions useful for income analysis. Various applications of the measures are discussed.

Panel count data refers to the information collected in studies focusing on recurrent events, where subjects are observed only at specific time points. If these study subjects are exposed to recurrent events of several types, we obtain panel count data with multiple modes of recurrence. In this article, we present a novel method based on generalized estimating equations for the regression analysis of panel count data exposed to multiple modes of recurrence. A cause specific proportional mean model is developed to analyze the effect of covariates on the underlying counting process due to multiple modes of recurrence. We conduct a detailed investigation on the joint estimation of baseline cumulative mean functions and regression parameters. Simulation studies are carried out to evaluate the finite sample performance of the proposed estimators. The procedures are applied to two real data sets, to demonstrate the practical utility.

Panel count data refer to the data arising from studies concerning recurrent events where study subjects are observed only at distinct time points. If these study subjects are exposed to recurrent events of several types, we obtain panel count data with multiple modes of recurrence. In the present paper, we propose a nonparametric test for comparing cause specific rate functions of panel count data with more than one mode of recurrence. The test can also be employed to assess whether the competing modes of recurrence are affecting the recurrence times identically. We carry out simulation studies to evaluate the performance of the test statistic in a finite sample setup. The proposed test is illustrated using two real life panel count data sets, one arising from a medical follow up study on skin cancer chemo prevention trial and the other on a warranty database for a fleet of automobiles.

The current status censoring takes place in survival analysis when the exact event times are not known, but each individual is monitored once for their survival status. The current status data often arise in medical research, from situations that involve multiple causes of failure. Examining current status competing risks data, commonly encountered in epidemiological studies and clinical trials, is more advantageous with Bayesian methods compared to conventional approaches. They excel in integrating prior knowledge with the observed data and delivering accurate results even with small samples. Inspired by these advantages, the present study is pioneering in introducing a Bayesian framework for both modelling and analysis of current status competing risks data together with covariates. By means of the proportional hazards model, estimation procedures for the regression parameters and cumulative incidence functions are established assuming appropriate prior distributions. The posterior computation is performed using an adaptive Metropolis–Hastings algorithm. Methods for comparing and validating models have been devised. An assessment of the finite sample characteristics of the estimators is conducted through simulation studies. Through the application of this Bayesian approach to prostate cancer clinical trial data, its practical efficacy is demonstrated.

In this work, we present two defective regression models for the analysis of interval-censored competing risk data in the presence of cured individuals, viz., defective Gompertz and defective inverse Gaussian regression models. The proposed models enable us to estimate the cure fraction directly from the model. Simultaneously, we estimate the regression parameters corresponding to each cause of failure using the method of maximum likelihood. The finite sample behaviour of the proposed models is evaluated through Monte Carlo simulation studies. We illustrate the practical applicability of the models using a real-life data set on HIV patients.

In this article, we propose non-parametric estimators for mean inactivity time function for complete and censored data. The asymptotic properties of the estimators are established using suitable regularity conditions. Monte Carlo simulation studies are used to study the efficiency of the estimators. Three real data sets are used to demonstrate the usefulness of the estimation procedure.

In this article, we introduce the concept of proportional odds relevation transform. Various reliability properties and some results based on information measures are provided. Important stochastic orders and aging concepts are discussed. Quantile-based definition and its importance are presented. A new lifetime distribution called proportional odds relevated exponential is introduced and discussed its applications with two real datasets.

Repeated occurrences of events can be categorized into two main groups based on their monitoring patterns: recurrent event data and panel count data. Sometimes, individuals within a study are either continuously monitored or assessed at discrete time intervals. This research paper focuses on addressing the regression problem in the analysis of mixed-type data, which combines both recurrent event and panel count data structures. A family of semiparametric transformation models is proposed to capture the influence of covariates on the mean function while considering multiple failure modes. Estimators for the regression parameters are developed. The estimators’ asymptotic properties are studied, and their performance is assessed through comprehensive simulation studies. A real data set is utilized to demonstrate the applicability of the proposed techniques.

Recurrent event data are common in survival and reliability studies, where a subject experiences the same type of event repeatedly. There are situations, in which the event of interest can be observed only if they belong to a window of observational range, leading to double censoring of recurrent event times. In this paper, we study recurrent event data subject to double censoring. We propose a proportional mean model for the analysis of doubly censored recurrent event data based on the mean function of the underlying recurrent event process. The estimators of the regression parameters and the baseline mean function are derived and their asymptotic properties are studied. A Monte Carlo simulation study is conducted to assess the finite sample behavior of the proposed estimators. Finally, the procedures are illustrated using two real-life data sets, one from a bladder cancer study and the other from a study on chronic granulomatous disease.

Recurrent event data and panel count data are common in survival studies. There are situations in which some of the study individuals may be followed continuously during the study period, while the others may only be assessed at a series of discrete time periods. As a result, a data structure that combines recurring event and panel count data for a single study arises. This article describes the regression problem for analyzing such mixed type recurrent event data based on the mean function of the underlying recurrent event process with multiple failure modes. We introduce a proportional cause-specific mean model for multiple causes of failure. The estimators of the regression parameters and the baseline cause-specific mean function are derived, and their asymptotic properties are studied. The finite sample behaviour of the suggested estimators is evaluated using simulation studies. Finally, a real data is used to illustrate the proposed techniques.

In this paper, we propose a novel method for the analysis of cure rate data with competing risks using defective distributions. We develop two defective regression models for the analysis of competing risk data subjected to random right censoring. The proposed models enable us to estimate the cure fraction directly from the model. Simultaneously, we also estimate the regression parameters corresponding to each cause of failure using the method of maximum likelihood. We conduct a simulation study to evaluate the finite sample performance of the proposed estimators. The practical usefulness of the procedures is illustrated using two real-life data sets.

In some experiments such as stress testing and industrial quality control experiments, only values which are larger or smaller than all previous ones are observed. Study of such extremes are of great importance. An extensive research on record values using distribution function are available in literature; however, a quantile-based study on the same have not been considered so far. Motivated with these, in this article, we introduce a quantile function approach of record values, which is an equivalent and alternative to the traditional distribution function approach. We study various properties of quantile-based measures of record values. We also obtain some stochastic comparison and ageing properties of quantile-based record values. The L-moment estimation method of hazard quantile function of record values is explained using a real-data example.

Information generating functions have been used for generating various entropy and divergence measures. In the present work, we introduce quantile based relative information generating function and study its properties. The proposed generating function provides well-known Kullback-Leibler divergence measure. The quantile based relative information generating function for residual and past lifetimes are presented. A non parametric estimator for the function is derived. A simulation study is conducted to assess performance of the estimators. Finally, the proposed method is applied to a real life data.

In this paper, we introduce a class of distributions with bilinear mean residual quantile function. We study various distributional properties and reliability characteristics of the proposed class. Characterizations of the model are presented and the method of L-moments is employed to estimate parameters of the class of distributions. Finally, we illustrate the usefulness of the proposed claim to a real data set.

In survival analysis, interval censoring case I or current status censoring happens if each subject is observed only once for status of occurrence of the event of interest. Current status data often appear along with covariates in cross sectional studies and tumorigenicity studies. Cox's proportional hazards model has been widely used to explore the relationship between lifetime variable and covariates. In this paper we propose a novel and easy to implement Bayesian approach for analyzing current status data. Under proportional hazards model, baseline survival function and regression parameters are estimated assuming proper prior distributions and implementing Metropolis Hastings algorithm for posterior computation. Methods for both model selection and model validation are suggested. Finite sample performance of the proposed method is evaluated using simulation studies. Intraocular lenses calcification data are analyzed for illustration.

In reliability studies, the data is often truncated and hence the residual random variable plays a vital role in the modelling and analysis of lifetime data. Like various reliability measures such as hazard rate, mean residual life function, variance residual life function, the residual coefficient of variation is also an important tool considered by many. In this paper, we study a quantile version of coefficient of variation of residual life, an alternative to the traditional distribution function measure. We study various properties of it and obtain characterizations based on some well-known probability models. We introduce a class of distributions with linear quantile-based residual coefficient of variation and study their basic reliability properties. We also obtain some stochastic comparison and aging properties using quantile-based residual coefficient of variation. The L-moment method of estimation for the class of distributions with linear quantile-based residual coefficient of variation has also been illustrated using two real data sets.

This article deals with the regression analysis of recurrent event data with multiple causes of failure that are collected in disconnected observation windows with gaps. These type of data are referred to as window-observation recurrence data and we introduce a proportional cause specific mean model for analyzing multiple causes of failure. We also develop methods for estimating the regression parameters and the baseline cause specific mean function. The asymptotic properties of the estimators are analyzed, and their performance is evaluated through simulation studies. The proposed techniques are then illustrated using a real data set.