Gamma shared frailty model based on reversed hazard rate

Abstract

Frailty models are used in survival analysis to account for unobserved heterogeneity in individual risks to disease and death. To analyze bivariate data on related survival times (e.g., matched pairs experiments, twin, or family data), shared frailty models were suggested. Shared frailty models are frequently used to model heterogeneity in survival analysis. The most common shared frailty model is a model in which hazard function is a product of random factor(frailty) and baseline hazard function which is common to all individuals. There are certain assumptions about the baseline distribution and distribution of frailty. In this paper, we introduce shared gamma frailty models with reversed hazard rate. We introduce Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in the model. We present a simulation study to compare the true values of the parameters with the estimated values. Also, we apply the proposed model to the Australian twin data set.     

Modeling bivariate survival data using shared inverse Gaussian frailty model

ABSTRACT

The shared frailty models are often used to model heterogeneity in survival analysis. The most common shared frailty model is a model in which hazard function is a product of a random factor (frailty) and the baseline hazard function which is common to all individuals. There are certain assumptions about the baseline distribution and the distribution of frailty. In this paper, we consider inverse Gaussian distribution as frailty distribution and three different baseline distributions, namely the generalized Rayleigh, the weighted exponential, and the extended Weibull distributions. With these three baseline distributions, we propose three different inverse Gaussian shared frailty models. We also compare these models with the models where the above-mentioned distributions are considered without frailty. We develop the Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in these models. We present a simulation study to compare the true values of the parameters with the estimated values. A search of the literature suggests that currently no work has been done for these three baseline distributions with a shared inverse Gaussian frailty so far. We also apply these three models by using a real-life bivariate survival data set of McGilchrist and Aisbett (1991 McGilchrist, C.A., Aisbett, C.W. (1991). Regression with frailty in survival analysis. Biometrics 47:461–466.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) related to the kidney infection data and a better model is suggested for the data using the Bayesian model selection criteria.     

Some inference results in several symmetric multivariate exponential models

In this paper, we consider multivariate exponential models with identical marginals. We obtain MLEs of the parameters and large sample tests for mutual independence of k components in the multivariate exponential models proposed by Weinman (1966), Marshall-Olkin (1967) and Block (1975).     

More flexible sequential and non-sequential designs in long-term clinical trial

In this paper, we describe decision making procedures as they exist in most clinical trials,review some recently suggested approaches to monitoring and clarify how these methods allow greater flexibility in monitoring and explicit specification of data monitoring methods in the protocol.     

Nonparametric estimation of the survival distribution in censored data

Two nonparametric estimators o f the survival distributionare discussed. The estimators were proposed by Kaplan and Meier (1958) and Breslow (1972) and are applicable when dealing with censored data. It is known that they are asymptotically unbiased and uniformly strongly consistent, and when properly normalized that they converge weakly to the same Gaussian process. In this paper, the properties of the estimators are carefully inspected in small or moderate samples. The Breslow estimator, a shrinkage version of the Kaplan-Meier, nearly always has the smaller mean square error (MSE) whenever the truesurvival probabilityis at least 0.20, but has considerably larger MSE than the Kaplan-Meier estimator when the survivalprobability is near zero.     

On Energy Policy Models

Many energy models cannot be relied upon in forecasting or policy analysis. The quality of the data is often poor, and the theoretical underpinnings tend to be inadequate. These points are illustrated by example.     

A Nonstochastic Interpretation of Reported Significance Levels

Tests of significance are often made in situations where the standard assumptions underlying the probability calculations do not hold. As a result, the reported significance levels become difficult to interpret. This article sketches an alternative interpretation of a reported significance level, valid in considerable generality. This level locates the given data set within the spectrum of other data sets derived from the given one by an appropriate class of transformations. If the null hypothesis being tested holds, the derived data sets should be equivalent to the original one. Thus, a small reported significance level indicates an unusual data set. This development parallels that of randomization tests, but there is a crucial technical difference: our approach involves permuting observed residuals; the classical randomization approach involves permuting unobservable, or perhaps nonexistent, stochastic disturbance terms.     

A Case Study in Nonresponse: Plaintiff vs. California State Board of Equalization

In any sample survey, nonresponse bias is a potential issue. Even with a moderately high nonresponse rate, however, covariates can sometimes be used to show that the nonresponse bias is likely to be small. This note presents such an argument, which was used by the winning side in a tax case.     

A Bootstrap Stationarity Test for Predictive Regression Invalidity

In order for predictive regression tests to deliver asymptotically valid inference, account has to be taken of the degree of persistence of the predictors under test. There is also a maintained assumption that any predictability in the variable of interest is purely attributable to the predictors under test. Violation of this assumption by the omission of relevant persistent predictors renders the predictive regression invalid, and potentially also spurious, as both the finite sample and asymptotic size of the predictability tests can be significantly inflated. In response, we propose a predictive regression invalidity test based on a stationarity testing approach. To allow for an unknown degree of persistence in the putative predictors, and for heteroscedasticity in the data, we implement our proposed test using a fixed regressor wild bootstrap procedure. We demonstrate the asymptotic validity of the proposed bootstrap test by proving that the limit distribution of the bootstrap statistic, conditional on the data, is the same as the limit null distribution of the statistic computed on the original data, conditional on the predictor. This corrects a long-standing error in the bootstrap literature whereby it is incorrectly argued that for strongly persistent regressors and test statistics akin to ours the validity of the fixed regressor bootstrap obtains through equivalence to an unconditional limit distribution. Our bootstrap results are therefore of interest in their own right and are likely to have applications beyond the present context. An illustration is given by reexamining the results relating to U.S. stock returns data in Campbell and Yogo (2006 Campbell, J. Y. and Yogo, M. (2006), “Efficient Tests of Stock Return Predictability,” Journal of Financial Economics, 81, 27–60.[Crossref], [Web of Science ®] , [Google Scholar]). Supplementary materials for this article are available online.