Analysis of Hybrid Life-tests in Presence of Competing Risks

The mixture of type-I and type-II censoring schemes, called the hybrid censoring scheme is quite common in life-testing or reliability experiments. In this paper, we consider the competing risks model in presence of hybrid censored data. Under this set up, it is assumed that the item may fail due to various causes and the corresponding lifetime distributions are independent and exponentially distributed with different scale parameters. We obtain the maximum likelihood estimators of the mean life of the different causes and derive their exact distributions. Using the exact distributions, all the moments can be obtained. Asymptotic confidence intervals and two bootstrap confidence intervals are also proposed. Bayes estimates and credible intervals of the unknown parameters are obtained under the assumptions of independent inverted gamma priors of the mean life of the different causes. Different methods have been compared using Monte Carlo simulations. Onereal data set has been analyzed for illustrative purposes. Part of the work was supported by a grant from the Natural Sciences and Engineering Research Council.     

Consistent Estimation of Censored Demand Systems Using Panel Data

We derive a joint continuous/censored commodity demand system for panel data applications. Unobserved heterogeneity is controlled for using a correlated random effects specification and a generalized method of moments framework used to estimate the model. While relatively small differences in elasticity estimates are found between a flexible random effects specification and one that restricts the random effect coefficient to be time invariant, larger differences are observed when comparing the flexible model to a pooled cross-sectional estimator. The results suggest the limited ability of such estimators to control for preference heterogeneity and unit-value endogeneity leads to parameter bias.     

Maximum likelihood methods for fitting the burr type XII distribution to multiply (progressively) censored life test data

Summary This paper develops mathematical and computational methodology for fitting, by the method of maximum likelihood (ML), the Burr Type XII distribution to multiply (or progressively) censored life test data. Mathematical expressions are given for approximating the asymptotic variances and covariances of the ML estimates (MLEs) of the parameters of the Burr Type XII distribution. A rigorous mathematical analysis is undertaken to investigate the existence and uniqueness of the MLEs for arbitrary sample data. The methodology of this paper is applied to progressively censored sample data arising in a life test experiment.     

Nonparametric Bayes inference for concave distribution functions

Bayesian inference for concave distribution functions is investigated. This is made by transforming a mixture of Dirichlet processes on the space of distribution functions to the space of concave distribution functions. We give a method for sampling from the posterior distribution using a Pólya urn scheme in combination with a Markov chain Monte Carlo algorithm. The methods are extended to estimation of concave distribution functions for incompletely observed data.     

A count data model with endogenous household specific censoring: the number of nights to stay

In this paper a count data regression model accounting for endogenous censoring with household specific censoring thresholds is presented. The presented modelling approach is utilized in an analysis of household choice of total number of nights to spend on monthly recreational trips. The empirical study reveals that the suggested approach is feasible and that accounting for endogenous censoring gives a better fit to the data. For helpful comments on an earlier version of the paper we thank two anonymous referees.     

Quasi- and Simulated-Likelihood Approaches to Censored Demand Systems: Food Consumption by Food Stamp Recipients in the United States

A quasi-maximum-likelihood estimator is proposed and applied to a censored Translog demand system for foods, using a sample of food stamp recipients in the United States. The procedure produces remarkably close parameter and elasticity estimates to those of the simulated-maximum-likelihood procedure. A two-step procedure is also considered but it produces different elasticities. Demands are found to be price elastic for pork and fish but price inelastic for all other food products. Gross complementarity and net substitutability are obvious but these cross-price effects are much less pronounced than own-price and total food expenditure effects.     

Constructive identification of the mixed proportional hazards model

We give a new proof of the identifiably of the MPH model. This proof is constructive: it is a recipe for constructing the triple—regression function, base-line hazard, and distribution of the individual effect—from the observed cumulative distribution functions.
We then prove that the triples do not depend continuously on the observed cumulative distribution functions. Uniformly consistent estimators do not exist.
Finally we show that the MPH model is even identifiable from two-sided censored observations. This proof is constructive, too.     

Non‐parametric Analysis of Gap Times for Multiple Event Data: An Overview

Multiple event data are frequently encountered in medical follow‐up, engineering and other applications when the multiple events are considered as the major outcomes. They may be repetitions of the same event (recurrent events) or may be events of different nature. Times between successive events (gap times) are often of direct interest in these applications. The stochastic‐ordering structure and within‐subject dependence of multiple events generate statistical challenges for analysing such data, including induced dependent censoring and non‐identifiability of marginal distributions. This paper provides an overview of a class of existing non‐parametric estimation methods for gap time distributions for various types of multiple event data, where sampling bias from induced dependent censoring is effectively adjusted. We discuss the statistical issues in gap time analysis, describe the estimation procedures and illustrate the methods with a comparative simulation study and a real application to an AIDS clinical trial. A comprehensive understanding of challenges and available methods for non‐parametric analysis can be useful because there is no existing standard approach to identifying an appropriate gap time method that can be used to address research question of interest. The methods discussed in this review would allow practitioners to effectively handle a variety of real‐world multiple event data.     

Estimation of a survival curve with randomly censored data in the presence of a covariate

This paper deals with the estimation of a survival curve in models with random right censoring and dependent censoring mechanism. We consider a specific dependent censorship model in which conditional on a covariate, the survival and censoring times are assumed to be independent. We investigate asymptotic properties of a corrected version of a survival curve estimator introduced by Cheng (1989). In particular we show uniform strong consistency and weak convergence to a Gaussian process. Comparisons of this estimator with the well-known Kaplan-Meier-estimator are included. Finally, some examples illustrate how the estimator performs. Received: February 2000