Biometrics

Fleming, Thomas R.; Lin, D. Y.

doi: 10.1111/j.0006-341x.2000.0971.xpmid: 11129494

Summary. The field of survival analysis emerged in the 20th century and experienced tremendous growth during the latter half of the century. The developments in this field that have had the most profound impact on clinical trials are the Kaplan‐Meier (1958, Journal of the American Statistical Association53, 457–481) method for estimating the survival function, the log‐rank statistic (Mantel, 1966, Cancer Chemotherapy Report50, 163–170) for comparing two survival distributions, and the Cox (1972, Journal of the Royal Statistical Society, Series B34, 187–220) proportional hazards model for quantifying the effects of covariates on the survival time. The counting‐process martingale theory pioneered by Aalen (1975, Statistical inference for a family of counting processes, Ph.D. dissertation, University of California, Berkeley) provides a unified framework for studying the small‐ and large‐sample properties of survival analysis statistics. Significant progress has been achieved and further developments are expected in many other areas, including the accelerated failure time model, multivariate failure time data, interval‐censored data, dependent censoring, dynamic treatment regimes and causal inference, joint modeling of failure time and longitudinal data, and Baysian methods.

Murray, Susan

doi: 10.1111/j.0006-341x.2000.0984.xpmid: 11129495

Summary. This research gives methods for nonparametric sequential monitoring of paired censored survival data in the two‐sample problem using paired weighted log‐rank statistics with adjustments for dependence in survival and censoring outcomes. The joint asymptotic closed‐form distribution of these sequentially monitored statistics has a dependent increments structure. Simulations validating operating characteristics of the proposed methods highlight power and size consequences of ignoring even mildly correlated data. A motivating example is presented via the Early Treatment Diabetic Retinopathy Study.

Wei, Wen Hsiang; Kosorok, Michael R.

doi: 10.1111/j.0006-341x.2000.0991.xpmid: 11129496

Summary. Influence measures based on the pairwise deletion approach and the differentiation approach are developed for unmasking observations masked by other observations in the proportional hazards model. These influential observations might have substantial impact on statistical inference and might provide important information for model adequacy. One numerical example based on real data is presented and discussed.

Parker, Corette B.; Belong, Elizabeth R.

doi: 10.1111/j.0006-341x.2000.0996.xpmid: 11213761

Summary. Changes in maximum likelihood parameter estimates due to deletion of individual observations are useful statistics, both for regression diagnostics and for computing robust estimates of covariance. For many likelihoods, including those in the exponential family, these delete‐one statistics can be approximated analytically from a one‐step Newton‐Raphson iteration on the full maximum likelihood solution. But for general conditional likelihoods and the related Cox partial likelihood, the one‐step method does not reduce to an analytic solution. For these likelihoods, an alternative analytic approximation that relies on an appropriately augmented design matrix has been proposed. In this paper, we extend the augmentation approach to explicitly deal with discrete failure‐time models. In these models, an individual subject may contribute information at several time points, thereby appearing in multiple risk sets before eventually experiencing a failure or being censored. Our extension also allows the covariates to be time dependent. The new augmentation requires no additional computational resources while improving results.

Kozumi, Hideo

doi: 10.1111/j.0006-341x.2000.01002.xpmid: 11129454

Summary. This paper considers the discrete survival data from a Bayesian point of view. A sequence of the baseline hazard functions, which plays an important role in the discrete hazard function, is modeled with a hidden Markov chain. It is explained how the resultant model is implemented via Markov chain Monte Carlo methods. The model is illustrated by an application of real data.

McKeague, Ian W.; Tighiouart, Mourad

doi: 10.1111/j.0006-341x.2000.01007.xpmid: 11129455

Summary. This article introduces a new Bayesian approach to the analysis of right‐censored survival data. The hazard rate of interest is modeled as a product of conditionally independent stochastic processes corresponding to (1) a baseline hazard function and (2) a regression function representing the temporal influence of the covariates. These processes jump at times that form a time‐homogeneous Poisson process and have a pairwise dependency structure for adjacent values. The two processes are assumed to be conditionally independent given their jump times. Features of the posterior distribution, such as the mean covariate effects and survival probabilities (conditional on the covariate), are evaluated using the Metropolis‐Hastings‐Green algorithm. We illustrate our methodology by an application to nasopharynx cancer survival data.

Ripatti, Samuli; Palmgren, Juni

doi: 10.1111/j.0006-341x.2000.01016.xpmid: 11129456

Summary. There exists a growing literature on the estimation of gamma distributed multiplicative shared frailty models. There is, however, often a need to model more complicated frailty structures, but attempts to extend gamma frailties run into complications. Motivated by hip replacement data with a more complicated dependence structure, we propose a model based on multiplicative frailties with a multivariate log‐normal joint distribution. We give a justification and an estimation procedure for this generally structured frailty model, which is a generalization of the one presented by McGilchrist (1993, Biometrics49, 221‐225). The estimation is based on Laplace approximation of the likelihood function. This leads to estimating equations based on a penalized fixed effects partial likelihood, where the marginal distribution of the frailty terms determines the penalty term. The tuning parameters of the penalty function, i.e., the frailty variances, are estimated by maximizing an approximate profile likelihood. The performance of the approximation is evaluated by simulation, and the frailty model is fitted to the hip replacement data.

Ecochard, René; Clayton, David G.

doi: 10.1111/j.0006-341x.2000.01023.xpmid: 11129457

Summary. Delay until conception is generally described by a mixture of geometric distributions. Weinberg and Gladen (1986, Biometrics42, 547–560) proposed a regression generalization of the beta‐geometric mixture model where covariates effects were expressed in terms of contrasts of marginal hazards. Scheike and Jensen (1997, Biometrics53, 318–329) developed a frailty model for discrete event times data based on discrete‐time analogues of Hougaard's results (1984, Biometrika71, 75–83). This paper is on a generalization to a three‐parameter family distribution and an extension to multivariate cases. The model allows the introduction of explanatory variables, including time‐dependent variables at the subject‐specific level, together with a choice from a flexible family of random effect distributions. This makes it possible, in the context of medically assisted conception, to include data sources with multiple pregnancies (or attempts at pregnancy) per couple.

Hall, Daniel B.

doi: 10.1111/j.0006-341x.2000.01030.xpmid: 11129458

Summary. In a 1992 Technometrics paper, Lambert (1992, 34, 1–14) described zero‐inflated Poisson (ZIP) regression, a class of models for count data with excess zeros. In a ZIP model, a count response variable is assumed to be distributed as a mixture of a Poisson(λ) distribution and a distribution with point mass of one at zero, with mixing probability p. Both p and λ are allowed to depend on covariates through canonical link generalized linear models. In this paper, we adapt Lambert's methodology to an upper bounded count situation, thereby obtaining a zero‐inflated binomial (ZIP) model. In addition, we add to the flexibility of these fixed effects models by incorporating random effects so that, e.g., the within‐subject correlation and between‐subject heterogeneity typical of repeated measures data can be accommodated. We motivate, develop, and illustrate the methods described here with an example from horticulture, where both upper bounded count (binomial‐type) and unbounded count (Poisson‐type) data with excess zeros were collected in a repeated measures designed experiment.

Concordet, Didier; Nunez, Olivier G.

doi: 10.1111/j.0006-341x.2000.01040.xpmid: 11129459

Summary. We propose calibration methods for nonlinear mixed effects models. Using an estimator whose asymptotic properties are known, four different statistics are used to perform the calibration. Simulations are carried out to compare the performance of these statistics. Finally, the milk discard time prediction of an antibiotic, which has motivated this study, is performed on real data.