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Gamma Frailty Model (gamma + frailty_model)

Distribution by Scientific Domains
Mathematics and Statistics100%

Selected Abstracts

Aspects of the Armitage,Doll gamma frailty model for cancer incidence data

ENVIRONMETRICS, Issue 3 2004
Shizue Izumi
Abstract Using solid cancer incidence data from atomic bomb survivors in Japan, we examine some aspects of the Armitage,Doll gamma frailty (ADF) model. We consider the following two interpretations for lack of fit of the Armitage,Doll multistage (AD) model found with cancer data: the AD type individual hazards are heterogeneous or the individual hazards increase more slowly with age than the AD type hazards. In order to examine these interpretations, we applied the ADF model and the modified AD model to radiation-related cancer incidence rates. We assessed the magnitude of frailty by a frailty parameter at the ADF model and departures from the AD-type baseline hazard by a shape increment parameter at the modified AD model. Akaike's information criterion (AIC) was used to examine the goodness of fit of the models. The modified AD model provided as good a fit as the ADF model. Our results support both interpretations and imply that these interpretations may be practically unidentifiable in univariate failure time data. Thus, results from the frailty model for univariate failure time data should be interpreted carefully. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Meta-Analysis of Diagnostic Test Accuracy Studies with Multiple Thresholds using Survival Methods

BIOMETRICAL JOURNAL, Issue 1 2010
H. Putter
Abstract Diagnostic tests play an important role in clinical practice. The objective of a diagnostic test accuracy study is to compare an experimental diagnostic test with a reference standard. The majority of these studies dichotomize test results into two categories: negative and positive. But often the underlying test results may be categorized into more than two, ordered, categories. This article concerns the situation where multiple studies have evaluated the same diagnostic test with the same multiple thresholds in a population of non-diseased and diseased individuals. Recently, bivariate meta-analysis has been proposed for the pooling of sensitivity and specificity, which are likely to be negatively correlated within studies. These ideas have been extended to the situation of diagnostic tests with multiple thresholds, leading to a multinomial model with multivariate normal between-study variation. This approach is efficient, but computer-intensive and its convergence is highly dependent on starting values. Moreover, monotonicity of the sensitivities/specificities for increasing thresholds is not guaranteed. Here, we propose a Poisson-correlated gamma frailty model, previously applied to a seemingly quite different situation, meta-analysis of paired survival curves. Since the approach is based on hazards, it guarantees monotonicity of the sensitivities/specificities for increasing thresholds. The approach is less efficient than the multinomial/normal approach. On the other hand, the Poisson-correlated gamma frailty model makes no assumptions on the relationship between sensitivity and specificity, gives consistent results, appears to be quite robust against different between-study variation models, and is computationally very fast and reliable with regard to the overall sensitivities/specificities. [source]

Multivariate Survival Trees: A Maximum Likelihood Approach Based on Frailty Models

BIOMETRICS, Issue 1 2004
Xiaogang Su
Summary. A method of constructing trees for correlated failure times is put forward. It adopts the backfitting idea of classification and regression trees (CART) (Breiman et al., 1984, in Classification and Regression Trees). The tree method is developed based on the maximized likelihoods associated with the gamma frailty model and standard likelihood-related techniques are incorporated. The proposed method is assessed through simulations conducted under a variety of model configurations and illustrated using the chronic granulomatous disease (CGD) study data. [source]

A Semiparametric Estimate of Treatment Effects with Censored Data

BIOMETRICS, Issue 3 2001
Ronghui Xu
Summary. A semiparametric estimate of an average regression effect with right-censored failure time data has recently been proposed under the Cox-type model where the regression effect ,(t) is allowed to vary with time. In this article, we derive a simple algebraic relationship between this average regression effect and a measurement of group differences in K -sample transformation models when the random error belongs to the Gp family of Harrington and Fleming (1982, Biometrika69, 553,566), the latter being equivalent to the conditional regression effect in a gamma frailty model. The models considered here are suitable for the attenuating hazard ratios that often arise in practice. The results reveal an interesting connection among the above three classes of models as alternatives to the proportional hazards assumption and add to our understanding of the behavior of the partial likelihood estimate under nonproportional hazards. The algebraic relationship provides a simple estimator under the transformation model. We develop a variance estimator based on the empirical influence function that is much easier to compute than the previously suggested resampling methods. When there is truncation in the right tail of the failure times, we propose a method of bias correction to improve the coverage properties of the confidence intervals. The estimate, its estimated variance, and the bias correction term can all be calculated with minor modifications to standard software for proportional hazards regression. [source]