Dependent Right Censorship in the MOMW Distribution

In this paper, we consider paired survival data, in which pair members are subject to the same right censoring time, but they are dependent on each other. Assuming the Marshall–Olkin Multivariate Weibull distribution for the joint distribution of the lifetimes (X₁, X₂) and the censoring time X₃, we derive the joint density of the actual observed data and obtain maximum likelihood estimators, Bayes estimators and posterior regret Gamma minimax estimators of the unknown parameters under squared error loss and weighted squared error loss functions. We compare the performances of the maximum likelihood estimators and Bayes estimators numerically in terms of biases and estimated Mean Squared Error Loss.     

Estimation for exponential distribution based on competing risk middle censored data

Abstract

For a general censoring scheme called “middle censoring” scheme which was proposed by Jammalamadaka and Mangalam (2003 Jammalamadaka, S.R., Mangalam, V. (2003). Nonparametric estimation for middle censored data. J. Nonparametric Statist. 15:253–265.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) in nonparametric set up. In this article, point and interval estimation problems are considered for the exponential distribution when the failure data is middle censored with two independent competing failure risks. Different methods are introduced to estimate the unknown model parameters such as maximum likelihood estimation, midpoint approximation, equivalent quantities estimation. The Bayesian estimation is also considered with gamma priors. Two numerical examples are analyzed to show the performance of the proposed methods.     

Semiparametric Proportional Mean Residual Life Model With Censoring Indicators Missing at Random

For right-censored survival data, the information that whether the observed time is survival or censoring time is frequently lost. This is the case for the competing risk data. In this article, we consider statistical inference for the right-censored survival data with censoring indicators missing at random under the proportional mean residual life model. Simple and augmented inverse probability weighted estimating equation approaches are developed, in which the nonmissingness probability and some unknown conditional expectations are estimated by the kernel smoothing technique. The asymptotic properties of all the proposed estimators are established, while extensive simulation studies demonstrate that our proposed methods perform well under the moderate sample size. At last, the proposed method is applied to a data set from a stage II breast cancer trial.     

Exact fisher information for censored samples and the extended hazard rate functions

The question of how much information is contained in an ordered observation was studied by Tukey (1964) in terms of a linear sensitivity measure. This paper deals with exact Fisher information for censored data. The concept of hazard rate function is extended and some fundamental moment relations are established between them and the score functions. Some new moment equalities are obtained for the normal and gamma distributions.     

Bounds for the pearson type IV tail probabilities

Bounds for the tail probability of Pearson Type IV distribution are obtained, These bounds are simple to calculate.     

Multivariate analysis for the two-period repeated measures crossover design with application to clinical trials

Multivariate analysis techniques are applied to the two-period repeated measures crossover design. The approach considered in this paper has the advantage over the univariate analysis approach proposed recently by Wallenstein and Fisher (1977) that the former does not require any specific structure on the variance-covariance matrix of the repeated measures factor. (It should be noted that sums and differences of observations over periods are used for all tests. Therefore, there are two matrices under consideration, one for sums and one for differences.) Tests of significance are derived using the Wilks? criterion, and the procedure is illustrated with a numerical example from the area of clinical trials.     

Maximum likelihood estimation of bivariate survival probabilities and its existence and uniqueness

Nonparametric maximum likelihood estimation of bivariate survival probabilities is developed for interval censored survival data. We restrict our attention to the situation where response times within pairs are not distinguishable, and the univariate survival distribution is the same for any individual within any pair. Campbell's (1981) model is modified to incorporate this restriction. Existence and uniqueness of maximum likelihood estimators are discussed. This methodology is illustrated with a bivariate life table analysis of an angioplasty study where each patient undergoes two procedures.     

New polya and inverse polya distributions of order k

New Polya and inverse Polya distributions of order k are derived by means of generalized urn models and by compounding the binomial and negative binomial distributions of order k of Philippou (1986, 1983) with the beta distribution. It i s noted that the present Polpa distribution of order k includes as special cases a new hypergeometric distribution of order k, a negative one,an inverse one, and a discrete uniform of the same order. The probability generating functions, means and variances of the new distributions are obtained, and five asymptotic results are established relating them to the abovedmentioned binomial and negative binomial distributions of order k, and to the Poisson distribution of the same order of Philippou (1983).Moment estimates are also given and applications are indicated.     

Unbiased estimation in type II censored samples prom two-truncation parameter family

We consider a type II censored sample data from a two-truncation parameter density and obtain the UMVU estimator for an U-estimable parametric function. An explicit expression for the estimator is derived and some interesting special cases are developed. The shortest length confidence interval for the density is also obtained.     

Asymptotic efficiency of a competing risks model: A two-sample case

A generalized Cox regression model is studied for the covariance analysis of competing risks data subject to independent random censoring. The information of the maximum partial likelihood estimates is compared with that of maximum likelihood estimates assuming a log linear hazard function.The method of generalized variance is used to define the efficiency of estimation between the two models. This is then applied to two-sample problems with two exponentially censoring rates. Numerical results are summarized ane presented graphically.The detailed results indicate that the semi-parametric model wrks well for a higher rate of censoring. A method of generalizing the result to type 1 censoring and the efficiency of estimating the coefficient of the covariate are discussecd. A brief account of using the results to help design experiments is also given.