bluuebunny/crossref_metadata_2025 huggingface dataset:
A Transitional Model for Longitudinal Binary Data Subject to Nonignorable Missing Data
Authors: Albert Paul S.
Published: May 2004

Summary.Binary longitudinal data are often collected in clinical trials when interest is on assessing the effect of a treatment over time. Our application is a recent study of opiate addiction that examined the effect of a new treatment on repeated urine tests to assess opiate use over an extended follow‐up. Drug addiction is episodic, and a new treatment may affect various features of the opiate‐use process such as the proportion of positive urine tests over follow‐up and the time to the first occurrence of a positive test. Complications in this trial were the large amounts of dropout and intermittent missing data and the large number of observations on each subject. We develop a transitional model for longitudinal binary data subject to nonignorable missing data and propose an EM algorithm for parameter estimation. We use the transitional model to derive summary measures of the opiate‐use process that can be compared across treatment groups to assess treatment effect. Through analyses and simulations, we show the importance of properly accounting for the missing data mechanism when assessing the treatment effect in our example.
On the Accuracy of Efficiency of Estimating Equation Approach
Authors: Sutradhar Brajendra C. , Das Kalyan
Published: May 2004

Summary.Liang and Zeger (1986,Biometrika73, 13–22) introduced a generalized estimating equation (GEE) approach based on a working correlation matrix to obtain efficient estimators of regression parameters in the class of generalized linear models for repeated measures data. As demonstrated by Crowder (1995,Biometrika82, 407–410), because of uncertainty of the definition of the working correlation matrix, the Liang‐Zeger approach may, in some cases, lead to a complete breakdown of the estimation of the regression parameters. After taking this comment of Crowder into account, recently Sutradhar and Das (1999,Biometrika86, 459–465) examined the loss of efficiency of the regression estimators due to misspecification of the correlation structures. But their study was confined to the regression estimation with cluster‐level covariates, as in the original paper of Liang and Zeger. In this paper, we study this efficiency loss problem for the generalized regression models with within‐cluster covariates by utilizing the approach of Sutsadhar and Das (1999).
The One‐Sample Problem from Eradication Studies of Chronic Viral Infections
Authors: Cheng Debbie M. , Lagakos Stephen W.
Published: May 2004

Summary. In studies of chronic viral infections, the objective is to estimate probabilities of developing viral eradication and resistance. Complications arise as the laboratory methods used to assess eradication status result in unusual types of censored observations. This paper proposes nonparametric methods for the one‐sample analysis of viral eradication/resistance data. We show that the unconstrained nonparametric maximum likelihood estimator of the subdistributions of eradication and resistance are obtainable in closed form. In small samples, these estimators may be inadmissible; thus, we also present an algorithm for obtaining the constrained MLEs based on an isotonic regression of the unconstrained MLEs. Estimators of several functionals of the eradication and resistance subdistributions are also developed and discussed. The methods are illustrated with results from recent hepatitis C clinical trials.
Effects of Covariate Measurement Error in the Initial Level and Rate of Change of an Exposure Variable
Authors: Lyles Robert H. , McFarlane Glen
Published: May 2004

Summary. When repeated measures of an exposure variable are obtained on individuals, it can be of epidemiologic interest to relate the slope of this variable over time to a subsequent response. Subject‐specific estimates of this slope are measured with error, as are corresponding estimates of the level of exposure, i.e., the intercept of a linear regression over time. Because the intercept is often correlated with the slope and may also be associated with the outcome, each error‐prone covariate (intercept and slope) is a potential confounder, thereby tending to accentuate potential biases due to measurement error. Under a familiar mixed linear model for the exposure measurements, we present closed‐form estimators for the true parameters of interest in the case of a continuous outcome with complete and equally timed follow‐up for all subjects. Generalizations to handle incomplete follow‐up, other types of outcome variables, and additional fixed covariates are illustrated via maximum likelihood. We provide examples using data from the Multicenter AIDS Cohort Study. In these examples, substantial adjustments are made to uncorrected parameter estimates corresponding to the health‐related effects of exposure variable slopes over time. We illustrate the potential impact of such adjustments on the interpretation of an epidemiologic analysis.
A Note on Robust Variance Estimation for Cluster‐Correlated Data
Authors: Williams Rick L.
Published: May 2004

Summary. There is a simple robust variance estimator for cluster‐correlated data. While this estimator is well known, it is poorly documented, and its wide range of applicability is often not understood. The estimator is widely used in sample survey research, but the results in the sample survey literature are not easily applied because of complications due to unequal probability sampling. This brief note presents a general proof that the estimator is unbiased for cluster‐correlated data regardless of the setting. The result is not new, but a simple and general reference is not readily available. The use of the method will benefit from a general explanation of its wide applicability.
The Problematic Unity of Biometrics*
Authors: Stigler Stephen M.
Published: May 2004

Summary.The word “biometry” may be less than 200 years old, but it can be argued that work we would now consider biometric dates back even to the pre‐Christian era. The unity of biometry is attested through examples spanning two millennia, and a lesson from Francis Galton is recalled from a century ago.
Modeling Repeated Count Data Subject to Informative Dropout
Authors: Albert Paul S. , Follmann Dean A.
Published: May 2004

Summary. In certain diseases, outcome is the number of morbid events over the course of follow‐up. In epilepsy, e.g., daily seizure counts are often used to reflect disease severity. Follow‐up of patients in clinical trials of such diseases is often subject to censoring due to patients dying or dropping out. If the sicker patients tend to be censored in such trials, estimates of the treatment effect that do not incorporate the censoring process may be misleading. We extend the shared random effects approach of Wu and Carroll (1988, Biometrics44, 175–188) to the setting of repeated counts of events. Three strategies are developed. The first is a likelihood‐based approach for jointly modeling the count and censoring processes. A shared random effect is incorporated to introduce dependence between the two processes. The second is a likelihood‐based approach that conditions on the dropout times in adjusting for informative dropout. The third is a generalized estimating equations (GEE) approach, which also conditions on the dropout times but makes fewer assumptions about the distribution of the count process. Estimation procedures for each of the approaches are discussed, and the approaches are applied to data from an epilepsy clinical trial. A simulation study is also conducted to compare the various approaches. Through analyses and simulations, we demonstrate the flexibility of the likelihood‐based conditional model for analyzing data from the epilepsy trial.
Bayesian Predictive Inference for Time Series Count Data
Authors: Chen Ming‐Hui , Ibrahim Joseph G.
Published: May 2004

Summary.Correlated count data arise often in practice, especially in repeated measures situations or instances in which observations are collected over time. In this paper, we consider a parametric model for a time series of counts by constructing a likelihood‐based version of a model similar to that of Zeger (1988,Biometrika75, 621–629). The model has the advantage of incorporating both over‐dispersion and autocorrelation. We consider a Bayesian approach and propose a class of informative prior distributions for the model parameters that are useful for prediction. The prior specification is motivated from the notion of the existence of data from similar previous studies, called historical data, which is then quantified into a prior distribution for the current study. We derive the Bayesian predictive distribution and use a Bayesian criterion, called the predictive L measure, for assessing the predictions for a given time series model. The distribution of the predictive L measure is also derived, which will enable us to compare the predictive ability for each model under consideration. Our methodology is motivated by a real data set involving yearly pollen counts, which is examined in some detail.
Modeling Longitudinal Data with Ordinal Response by Varying Coefficients
Authors: Kauermann Göran
Published: May 2004

Summary.This paper presents a smooth regression model for ordinal data with longitudinal dependence structure. A marginal model with cumulative logit link is applied to cope with the ordinal scale and the main and covariate effects in the model are allowed to vary with time. Local fitting is pursued and asymptotic properties of the estimates are discussed. In a second step, the longitudinal dependence of the observations is considered. Cumulative log odds ratios are fitted locally, which allows investigation of how the longitudinal dependence of the ordinal observations changes with time.
Inference about Misclassification Probabilities from Repeated Binary Responses
Authors: Fujisawa Hironori , Izumi Shizue
Published: May 2004

Summary. Repeated binary responses provide efficient information for two purposes: (1) estimating two misclassification (false‐positive and false‐negative error) probabilities and (2) testing the hypothesis that either is zero in a reliability study. We focus on the assessment of reliability of a diagnostic test when there is no gold standard. This paper uses a latent class model and illustrates some of its properties. In addition, application to data containing variation among individuals is considered. We apply this model to the serological data on the MNSs blood group of atomic bomb survivors and their children. The results provide valuable information for examining measurement reliability.
Association Models for a Multivariate Binary Response
Authors: Ekholm Anders , McDonald John W. , Smith Peter W. F.
Published: May 2004

Summary.Models for a multivariate binary response are parameterized by univariate marginal proba‐bilities and dependence ratios of all orders. Thew‐order dependence ratio is the joint success probability ofwbinary responses divided by the joint success probability assuming independence. This parameterization supports likelihood‐based inference for both regression parameters, relating marginal probabilities to explanatory variables, and association model parameters, relating dependence ratios to simple and meaningful mechanisms. Five types of association models are proposed, where responses are (1) independent given a necessary factor for the possibility of a success, (2) independent given a latent binary factor, (3) independent given a latent beta distributed variable, (4) follow a Markov chain, and (5) follow one of two first‐order Markov chains depending on the realization of a binary latent factor. These models are illustrated by reanalyzing three data sets, foremost a set of binary time series on auranofin therapy against arthritis. Likelihood‐based approaches are contrasted with approaches based on generalized estimating equations. Association models specified by dependence ratios are contrasted with other models for a multivariate binary response that are specified by odds ratios or correlation coefficients.
Bias Correction for Segregation Ratio Estimation in Human Genetics
Authors: Yao Yi‐Ching , Tai John Jen
Published: May 2004

Summary.Segregation ratio estimation has long been important in human genetics. A simple truncated binomial model is considered that assumes complete ascertainment and a deterministic genotype‐phenotype relationship. A simple but intuitively appealing estimator of the segregation ratio, previously proposed, is shown to have a negative bias. It is also shown that the bias of this estimator can be largely reduced via a randomization device, resulting in a new estimator that has the same large‐sample behavior but with a negligible bias (decaying at a geometric rate). Numerical results are given to show the small‐sample performance of this new estimator. An extension to incomplete ascertainment is also considered.
Qualified Testing of Single‐Locus Codominant Inheritance Using Single Tree Progenies
Authors: Gillet Elizabeth M. , Gregorius Hans‐Rolf
Published: May 2004

Summary. In forest trees, classical techniques of studying modes of inheritance are usually not feasible due to the difficulty of performing controlled crosses. The limited information on inheritance extractable from readily available data, such as the large progenies collectable from single seed trees, must be compensated by the design of appropriately parameterized models. For this purpose, a system analytic approach is used to develop a new inferential framework for testing a single‐locus codominant mode of inheritance of genetic traits using the inferred genotypes within progenies of single trees of inferred heterozygous genotype. Model assumptions are random gametic fusion between the local gamete pools and absence of postzygotic selection; ovule segregation distortion is allowed. The method yields estimates of the allele frequencies in both local gamete pools. Since tests of modes of inheritance must be tests of models rather than of parameters, the utility of the classical statistical testing procedures is limited, particularly concerning the qualification of a sampling method to attain a preassigned level of precision. Consistent application of this principle makes it possible to design qualified sampling methods prior to the actual experiment as well as to specify qualification levels for tests of completed experiments.
Nonparametric Estimation for the Three‐Stage Irreversible Illness–Death Model
Authors: Datta Somnath , Satten Glen A. , Datta Susmita
Published: May 2004

Summary. In this paper, we present new nonparametric estimators of the stage‐occupation probabilities in the three‐stage irreversible illness‐death model. These estimators use a fractional risk set and a reweighting approach and are valid under stage‐dependent censoring. Using a simulated data set, we compare the behavior of our estimators with previously proposed estimators. We also apply our estimators to data on time to Pneumocystis pneumonia and death obtained from an AIDS cohort study.
Regression Models for Convex ROC Curves
Authors: Lloyd Chris J.
Published: May 2004

Summary. The performance of a diagnostic test is summarized by its receiver operating characteristic (ROC) curve. Under quite natural assumptions about the latent variable underlying the test, the ROC curve is convex. Empirical data on a test's performance often comes in the form of observed true positive and false positive relative frequencies under varying conditions. This paper describes a family of regression models for analyzing such data. The underlying ROC curves are specified by a quality parameter μ and a shape parameter Δ and are guaranteed to be convex provided Δ > 1. Both the position along the ROC curve and the quality parameter Δ are modeled linearly with covariates at the level of the individual. The shape parameter μ enters the model through the link functions log(pμ) ‐ log(1 ‐ pμ) of a binomial regression and is estimated either by search or from an appropriate constructed variate. One simple application is to the meta‐analysis of independent studies of the same diagnostic test, illustrated on some data of Moses, Shapiro, and Littenberg (1993). A second application, to so‐called vigilance data, is given, where ROC curves differ across subjects and modeling of the position along the ROC curve is of primary interest.
A Simulation Study of Measurement Error Correction Methods in Logistic Regression
Authors: Thoresen Magne , Laake Petter
Published: May 2004

Summary. Measurement error models in logistic regression have received considerable theoretical interest over the past 10–15 years. In this paper, we present the results of a simulation study that compares four estimation methods: the so‐called regression calibration method, probit maximum likelihood as an approximation to the logistic maximum likelihood, the exact maximum likelihood method based on a logistic model, and the naive estimator, which is the result of simply ignoring the fact that some of the explanatory variables are measured with error. We have compared the behavior of these methods in a simple, additive measurement error model. We show that, in this situation, the regression calibration method is a very good alternative to more mathematically sophisticated methods.
Simultaneously Model‐Unbiased, Design‐Unbiased Estimation
Authors: Gerow Ken , McCulloch Charles E.
Published: May 2004

Summary. This paper proposes a class of inferential procedures (incorporating both design and estimation elements) that yield estimates of means that are simultaneously model unbiased and design unbiased. Classical regression procedures yield conditionally unbiased estimators for the mean (conditioning on the model and choice of observation points). In contrast, design‐based methods yield estimators that are unconditionally unbiased no matter what the form of the underlying model. Variance properties of the proposed class are examined, and applications to bioavailability, water quality from mine run‐off, and finite population regression estimation are considered. The proposed procedures perform well, especially in the typical case where a model is only approximately correct.
Estimating Number of Events from the Kaplan–Meier Curve for Incorporation in a Literature‐Based Meta‐Analysis: What You Don't See You Can't Get!
Authors: Duchateau Luc , Collette Laurence , Sylvester Richard , Pignon Jean‐Pierre
Published: May 2004

Summary. In literature‐based meta‐analyses of time‐to‐event data, the number of events in the treated and control groups together with the total number of patients randomized to the two treatment arms are often used as summary statistics. If interest is in mortality at a specified moment in time, the number of events can, in most cases, only be obtained from the Kaplan–Meier curve. The estimated number of events, however, is typically larger than the true number of events. The effect of this overestimation on the Mantel–Haenszel test and the odds ratio is studied in this paper. From these results, it can be concluded that the number of events should not be estimated from the Kaplan–Meier curves for meta‐analytic purposes unless virtually no patients are lost to follow‐up or censored and there are still many patients at risk in the two groups at the time at which the number of events is to be determined.
A Simple Test of Association for Contingency Tables with Multiple Column Responses
Authors: Decady Y. J. , Thomas D. R.
Published: May 2004

Summary. Loughin and Scherer (1998, Biometrics54, 630–637) investigated tests of association in two‐way tables when one of the categorical variables allows for multiple‐category responses from individual respondents. Standard chi‐squared tests are invalid in this case, and they developed a bootstrap test procedure that provides good control of test levels under the null hypothesis. This procedure and some others that have been proposed are computationally involved and are based on techniques that are relatively unfamiliar to many practitioners. In this paper, the methods introduced by Rao and Scott (1981, Journal of the American Statistical Association76, 221–230) for analyzing complex survey data are used to develop a simple test based on a corrected chi‐squared statistic.
Approximating the Distribution of Maximally Selected McNemar's Statistics
Authors: Rabinowitz Daniel , Betensky Rebecca A.
Published: May 2004

Summary. It is common in epidemiologic analyses to summarize continuous outcomes as falling above or below a threshold. With paired data and with a threshold chosen without reference to the outcomes, McNemar's test of marginal homogeneity may be applied to the resulting dichotomous pairs when testing for equality of the marginal distributions of the underlying continuous outcomes. If the threshold is chosen to maximize the test statistic, however, referring the resulting test statistic to the nominal x2 distribution is incorrect; instead, the p‐value must be adjusted for the multiple comparisons. Here the distribution of a maximally selected McNemar's statistic is derived, and it is shown that an approximation due to Durbin (1985, Journal of Applied Probability22, 99–122) may be used to estimate approximate p‐values. The methodology is illustrated by an application to measurements of insulin‐like growth factor‐I (IGF‐I) in matched prostate cancer cases and controls from the Physicians' Health Study. The results of simulation experiments that assess the accuracy of the approximation in moderate sample sizes are reported.
Statistical Comparison of Axon‐Scaled Neurochemical Production
Authors: Baileru A. John , Liu Siyu , Smith Michelle L. , Isaacson Lori G.
Published: May 2004

Summary. Treatments designed to increase neurochemical levels may also result in increases in the numbers of axons that produce the neurochemicals of interest. A natural research question is how does one compare the average neurochemical production per axon between two (or more) experimental groups. Two statistical methods are proposed for this problem. The first method utilizes a delta‐method approximation to the variance of a function of random variables while the second method is based on the bootstrap. These methods are illustrated with data obtained from perivascular norepinephrine following intracerebroventricular infusion of neurotrophin nerve growth factor in adult rats and are studied in a small simulation experiment. The delta‐method confidence intervals exhibited better coverage properties than the bootstrap alternative.
A Proportional Hazards Model for Multivariate Interval‐Censored Failure Time Data
Authors: Goggins William B. , Finkelstein Dianne M.
Published: May 2004

Summary.This paper focuses on the methodology developed for analyzing a multivariate interval‐censored data set from an AIDS observational study. A purpose of the study was to determine the natural history of the opportunistic infection cytomeglovirus (CMV) in an HIV‐infected individual. For this observational study, laboratory tests were performed at scheduled clinic visits to test for the presence of the CMV virus in the blood and in the urine (called CMV shedding in the blood and urine). The study investigators were interested in determining whether the stage of HIV disease at study entry was predictive of an increased risk for CMV shedding in either the blood or the urine. If all patients had made each clinic visit, the data would be multivariate grouped failure time data and published methods could be used. However, many patients missed several visits, and when they returned, their lab tests indicated a change in their blood and/or urine CMV shedding status, resulting in interval‐censored failure time data. This paper outlines a method for applying the proportional hazards model to the analysis of multivariate interval‐censored failure time data from a study of CMV in HIV‐infected patients.
On the Bayesian Analysis of Ring‐Recovery Data
Authors: Brooks S. P. , Catchpole E. A. , Morgan B. J. T. , Barry S. C.
Published: May 2004

Summary.Vounatsou and Smith (1995,Biometrics51, 687–708) describe the modern Bayesian analysis of ring‐recovery data. Here we discuss and extend their work. We draw different conclusions from two major data analyses. We emphasize the extreme sensitivity of certain parameter estimates to the choice of prior distribution and conclude that naive use of Bayesian methods in this area can be misleading. Additionally, we explain the discrepancy between the Bayesian and classical analyses when the likelihood surface has a flat ridge. In this case, when there is no unique maximum likelihood estimate, the Bayesian estimators are remarkably precise.
Bayesian Analysis of Discrete Survival Data with a Hidden Markov Chain
Authors: Kozumi Hideo
Published: May 2004

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.
Bayesian Estimators for Conditional Hazard Functions
Authors: McKeague Ian W. , Tighiouart Mourad
Published: May 2004

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.
Parameter Estimation in a Gompertzian Stochastic Model for Tumor Growth
Authors: Ferrante L. , Bompadre S. , Possati L. , Leone L.
Published: May 2004

Summary. The problem of estimating parameters in the drift coefficient when a diffusion process is observed continuously requires some specific assumptions. In this paper, we consider a stochastic version of the Gompertzian model that describes in vivo tumor growth and its sensitivity to treatment with antiangiogenic drugs. An explicit likelihood function is obtained, and we discuss some properties of the maximum likelihood estimator for the intrinsic growth rate of the stochastic Gompertzian model. Furthermore, we show some simulation results on the behavior of the corresponding discrete estimator. Finally, an application is given to illustrate the estimate of the model parameters using real data.
Identifying Combinations of Cancer Markers for Further Study as Triggers of Early Intervention
Authors: Baker Stuart G.
Published: May 2004

Summary. In many long‐term clinical trials or cohort studies, investigators repeatedly collect and store tissue or serum specimens and later test specimens from cancer cases and a random sample of controls for potential markers for cancer. An important question is what combination, if any, of the molecular markers should be studied in a future trial as a trigger for early intervention. To answer this question, we summarized the performance of various combinations using Receiver Operating Characteristic (ROC) curves, which plot true versus false positive rates. To construct the ROC curves, we proposed a new class of nonparametric algorithms which extends the ROC paradigm to multiple tests. We fit various combinations of markers to a training sample and evaluated the performance in a test sample using a target region based on a utility function. We applied the methodology to the following markers for prostate cancer, the last value of total prostate‐specific antigen (PSA), the last ratio of total to free PSA, the last slope of total PSA, and the last slope of the ratio. In the test sample, the ROC curve for last total PSA was slightly closer to the target region than the ROC curve for a combination of four markers. In a separate validation sample, the ROC curve for last total PSA intersected the target region in 77% of bootstrap replications, indicating some promise for further study. We also discussed sample size calculations.
Estimation of Operating Characteristics for Dependent Diagnostic Tests Based on Latent Markov Models
Authors: Cook Richard J. , Ng Edmund T. M. , Meade Maureen O.
Published: May 2004

Summary.We describe a method for making inferences about the joint operating characteristics of multiple diagnostic tests applied longitudinally and in the absence of a definitive reference test. Log‐linear models are adopted for the classification distributions conditional on the latent state, where inclusion of appropriate interaction terms accommodates conditional dependencies among the tests. A marginal likelihood is constructed by marginalizing over a latent two‐state Markov process. Specific latent processes we consider include a first‐order Markov model, a second‐order Markov model, and a time‐nonhomogeneous Markov model, although the method is described in full generality. Adaptations to handle missing data are described. Model diagnostics are considered based on the bootstrap distribution of conditional residuals. The methods are illustrated by application to a study of diffuse bilateral infiltrates among patients in intensive care wards in which the objective was to assess aspects of validity and clinical agreement.
Sequential Designs for Phase I Clinical Trials with Late‐Onset Toxicities
Authors: Cheung Ying Kuen , Chappell Rick
Published: May 2004

Summary. Traditional designs for phase I clinical trials require each patient (or small group of patients) to be completely followed before the next patient or group is assigned. In situations such as when evaluating late‐onset effects of radiation or toxicities from chemopreventive agents, this may result in trials of impractically long duration. We propose a new method, called the time‐to‐event continual reassessment method (TITE‐CRM), that allows patients to be entered in a staggered fashion. It is an extension of the continual reassessment method (CRM; O'Quigley, Pepe, and Fisher, 1990, Biometrics46, 33–48). We also note that this time‐to‐toxicity approach can be applied to extend other designs for studies of short‐term toxicities. We prove that the recommended dose given by the TITE‐CRM converges to the correct level under certain conditions. A simulation study shows our method's accuracy and safety are comparable with CRM's while the former takes a much shorter trial duration: a trial that would take up to 12 years to complete by the CRM could be reduced to 2–4 years by our method.
Symmetrically Dependent Models Arising in Visual Assessment Data
Authors: Viana Marlos , Olkin Ingram
Published: May 2004

Summary. Given data from bilateral visual assessments on N subjects at k occasions, we consider inference for contralateral correlations (C) between fellow eyes and lateral correlations (L) among p different assessments of the same eye. Under permutation symmetric dependence structure between observations from fellow eyes and among observations from the same eye, we obtain maximum likelihood estimates of L, C, and L –‐ C. Based on the large‐sample estimates of the corresponding covariance structures, we test the hypothesis that the association between fellow eyes is constant across time and the hypothesis that lateral and contralateral associations between any two occasions are the same.
Estimating the Responsiveness of an Instrument Using More Than Two Repeated Measures
Authors: King Madeleine , Dobson Annette
Published: May 2004

Summary. The responsiveness of a measuring instrument is its ability to detect change over time. A commonly used index of responsiveness is the effect size for paired differences. This paper generalizes the effect size for paired differences to more than two repeated observations per subject. The sampling distribution of the generalized responsiveness statistic, Rt, is simulated for a range of plausible parameter values and for a range of sample sizes varying both the number of subjects (n) and the number of observations per subject (t). The coverage properties of confidence intervals constructed by four methods are compared. Confidence intervals based on jackknife estimates of the standard error and bias of Rt have good coverage properties even when n and t are small. The methods are used to determine which of two standard quality‐of‐life measures is more responsive to improvements in quality of life following surgery for early‐stage breast cancer.
Individual Toluene Exposure in Rotary Printing: Increasing Accuracy of Estimation by Linear Models Based on Protocols of Daily Activity and Other Measures
Authors: Wameling A. , Schäper M. , Kunert J. , Blaszkewicz M. , van Thriel C. , Zupanic M. , Seeber A.
Published: May 2004

Summary. Industrial exposure varies distinctly both between persons and for each person over time. It is often not possible to measure individual exposure repeatedly due to high costs. Therefore, a method for assessment of exposure is needed that accounts for inter‐ and intraindividual variability. We consider a strategy suggested by Preller et al. (1995, Scandinavian Journal of Work, Environment, and Health21, 504–512), the idea of which is to predict exposure on several days via a linear model using additional variables as regressors. Those additional variables are easier to obtain than exposure measurements and are assumed to influence exposure. The paper gives a theoretical proof of the use of this method. An example is given using toluene exposure data from a study in a rotogravure printing plant.
A Bayesian Approach to Finite Mixture Models in Bioassay via Data Augmentation and Gibbs Sampling and Its Application to Insecticide Resistance
Authors: Qu Pingping , Qu Yinsheng
Published: May 2004

Summary.After continued treatment with an insecticide, within the population of the susceptible insects, resistant strains will occur. It is important to know whether there are any resistant strains, what the proportions are, and what the median lethal doses are for the insecticide. Lwin and Martin (1989,Biometrics45, 721–732) propose a probit mixture model and use the EM algorithm to obtain the maximum likelihood estimates for the parameters. This approach has difficulties in estimating the confidence intervals and in testing the number of components. We propose a Bayesian approach to obtaining the credible intervals for the location and scale of the tolerances in each component and for the mixture proportions by using data augmentation and Gibbs sampler. We use Bayes factor for model selection and determining the number of components. We illustrate the method with data published in Lwin and Martin (1989).
ROC Curve Estimation When Covariates Affect the Verification Process
Authors: Rodenberg Cindy , Zhou Xiao‐Hua
Published: May 2004

Summary.A receiver operating characteristic (ROC) curve is commonly used to measure the accuracy of a medical test. It is a plot of the true positive fraction (sensitivity) against the false positive fraction (1‐specificity) for increasingly stringent positivity criterion. Bias can occur in estimation of an ROC curve if only some of the tested patients are selected for disease verification and if analysis is restricted only to the verified cases. This bias is known as verification bias. In this paper, we address the problem of correcting for verification bias in estimation of an ROC curve when the verification process and efficacy of the diagnostic test depend on covariates. Our method applies the EM algorithm to ordinal regression models to derive ML estimates for ROC curves as a function of covariates, adjusted for covariates affecting the likelihood of being verified. Asymptotic variance estimates are obtained using the observed information matrix of the observed data. These estimates are derived under the missing‐at‐random assumption, which means that selection for disease verification depends only on the observed data, i.e., the test result and the observed covariates. We also address the issues of model selection and model checking. Finally, we illustrate the proposed method on data from a two‐phase study of dementia disorders, where selection for verification depends on the screening test result and age.
Fitting Nonlinear and Constrained Generalized Estimating Equations with Optimization Software
Authors: Contreras Martha , Ryan Louise M.
Published: May 2004

Summary.In this article, we present an estimation approach for solving nonlinear constrained generalized estimating equations that can be implemented using object‐oriented software for nonlinear programming, such as nlminb in Splus or fmincon and lsqnonlin in Matlab. We show how standard estimating equation theory includes this method as a special case so that our estimates, when unconstrained, will remain consistent and asymptotically normal. To illustrate this method, we fit a nonlinear dose‐response model with nonnegative mixed bound constraints to clustered binary data from a developmental toxicity study. Satisfactory confidence intervals are found using a nonparametric bootstrap method when a common correlation coefficient is assumed for all the dose groups and for some of the dose‐specific groups.
Nonparametric Rank‐Based Methods for Group Sequential Monitoring of Paired Censored Survival Data
Authors: Murray Susan
Published: May 2004

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.
A Diagnostic for Cox Regression with Discrete Failure‐Time Models
Authors: Parker Corette B. , Belong Elizabeth R.
Published: May 2004

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.
Maximum Likelihood Analysis of Logistic Regression Models with Incomplete Covariate Data and Auxiliary Information
Authors: Horton Nicholas J. , Laird Nan M.
Published: May 2004

Summary.This article presents a new method for maximum likelihood estimation of logistic regression models with incomplete covariate data where auxiliary information is available. This auxiliary information is extraneous to the regression model of interest but predictive of the covariate with missing data. Ibrahim (1990,Journal of the American Statistical Association85, 765–769) provides a general method for estimating generalized linear regression models with missing covariates using the EM algorithm that is easily implemented when there is no auxiliary data. Vach (1997,Statistics in Medicine16, 57–72) describes how the method can be extended when the outcome and auxiliary data are conditionally independent given the covariates in the model. The method allows the incorporation of auxiliary data without making the conditional independence assumption. We suggest tests of conditional independence and compare the performance of several estimators in an example concerning mental health service utilization in children. Using an artificial dataset, we compare the performance of several estimators when auxiliary data are available.
The Evaluation of Multiple Surrogate Endpoints
Authors: Xu Jane , Zeger Scott L.
Published: May 2004

Summary.Surrogate endpoints are desirable because they typically result in smaller, faster efficacy studies compared with the ones using the clinical endpoints. Research on surrogate endpoints has received substantial attention lately, but most investigations have focused on the validity of using a single biomarker as a surrogate. Our paper studies whether the use of multiple markers can improve inferences about a treatment's effects on a clinical endpoint. We propose a joint model for a time to clinical event and for repeated measures over time on multiple biomarkers that are potential surrogates. This model extends the formulation of Xu and Zeger (2001, in press) and Fawcett and Thomas (1996,Statistics in Medicine15, 1663–1685). We propose two complementary measures of the relative benefit of multiple surrogates as opposed to a single one. Markov chain Monte Carlo is implemented to estimate model parameters. The methodology is illustrated with an analysis of data from a schizophrenia clinical trial.
Nonparametric Models and Methods for Designs with Dependent Censored Data: Part I
Authors: O'Gorman John T. , Akritas Michael G.
Published: May 2004

Summary. We consider a nonparametric (NP) approach to the analysis of repeated measures designs with censored data. Using the NP model of Akritas and Arnold (1994, Journal of the American Statistical Association89, 336–343) for marginal distributions, we present test procedures for the NP hypotheses of no main effects, no interaction, and no simple effects. This extends the existing NP methodology for such designs (Wei and Lachin, 1984, Journal of the American Statistical Association79, 653‐661). The procedures do not require any modeling assumptions and should be useful in cases where the assumptions of proportional hazards or location shift fail to be satisfied. The large‐sample distribution of the test statistics is based on an i.i.d. representation for Kaplan–Meier integrals. The testing procedures apply also to ordinal data and to data with ties. Useful small‐sample approximations are presented, and their performance is examined in a simulation study. Finally, the methodology is illustrated with two real life examples, one with censored and one with missing data. It is indicated that one of the data sets does not conform to any set of assumptions underlying the available methods and also that the present method provides a useful additional analysis even when data sets conform to modeling assumptions.
A Solution to the Problem of Monotone Likelihood in Cox Regression
Authors: Heinze Georg , Schemper Michael
Published: May 2004

Summary.The phenomenon of monotone likelihood is observed in the fitting process of a Cox model if the likelihood converges to a finite value while at least one parameter estimate diverges to ±∞. Monotone likelihood primarily occurs in small samples with substantial censoring of survival times and several highly predictive covariates. Previous options to deal with monotone likelihood have been unsatisfactory. The solution we suggest is an adaptation of a procedure by Firth (1993,Biometrika80, 27–38) originally developed to reduce the bias of maximum likelihood estimates. This procedure produces finite parameter estimates by means of penalized maximum likelihood estimation. Corresponding Wald‐type tests and confidence intervals are available, but it is shown that penalized likelihood ratio tests and profile penalized likelihood confidence intervals are often preferable. An empirical study of the suggested procedures confirms satisfactory performance of both estimation and inference. The advantage of the procedure over previous options of analysis is finally exemplified in the analysis of a breast cancer study.
Akaike's Information Criterion in Generalized Estimating Equations
Authors: Pan Wei
Published: May 2004

Summary.Correlated response data are common in biomedical studies. Regression analysis based on the generalized estimating equations (GEE) is an increasingly important method for such data. However, there seem to be few model‐selection criteria available in GEE. The well‐known Akaike Information Criterion (AIC) cannot be directly applied since AIC is based on maximum likelihood estimation while GEE is nonlikelihood based. We propose a modification to AIC, where the likelihood is replaced by the quasi‐likelihood and a proper adjustment is made for the penalty term. Its performance is investigated through simulation studies. For illustration, the method is applied to a real data set.
Bayesian Approaches to Modeling the Conditional Dependence Between Multiple Diagnostic Tests
Authors: Dendukuri Nandini , Joseph Lawrence
Published: May 2004

Summary.Many analyses of results from multiple diagnostic tests assume the tests are statistically independent conditional on the true disease status of the subject. This assumption may be violated in practice, especially in situations where none of the tests is a perfectly accurate gold standard. Classical inference for models accounting for the conditional dependence between tests requires that results from at least four different tests be used in order to obtain an identifiable solution, but it is not always feasible to have results from this many tests. We use a Bayesian approach to draw inferences about the disease prevalence and test properties while adjusting for the possibility of conditional dependence between tests, particularly when we have only two tests. We propose both fixed and random effects models. Since with fewer than four tests the problem is nonidentifiable, the posterior distributions are strongly dependent on the prior information about the test properties and the disease prevalence, even with large sample sizes. If the degree of correlation between the tests is known aprioriwith high precision, then our methods adjust for the dependence between the tests. Otherwise, our methods provide adjusted inferences that incorporate all of the uncertainty inherent in the problem, typically resulting in wider interval estimates. We illustrate our methods using data from a study on the prevalence ofStrongyloidesinfection among Cambodian refugees to Canada.
Optimal Designs for Evaluating a Series of Treatments
Authors: Leung Denis Heng‐Yan , Wang You‐Gan
Published: May 2004

Summary. Several articles in this journal have studied optimal designs for testing a series of treatments to identify promising ones for further study. These designs formulate testing as an ongoing process until a promising treatment is identified. This formulation is considered to be more realistic but substantially increases the computational complexity. In this article, we show that these new designs, which control the error rates for a series of treatments, can be reformulated as conventional designs that control the error rates for each individual treatment. This reformulation leads to a more meaningful interpretation of the error rates and hence easier specification of the error rates in practice. The reformulation also allows us to use conventional designs from published tables or standard computer programs to design trials for a series of treatments. We illustrate these using a study in soft tissue sarcoma.