bluuebunny/crossref_metadata_2025 huggingface dataset:
GEE with Gaussian Estimation of the Correlations When Data Are Incomplete
Authors: Lipsitz Stuart R. , Molenberghs Geert , Fitzmaurice Garrett M. , Ibrahim Joseph
Published: May 2004

Summary.This paper considers a modification of generalized estimating equations GEE) for handling missing binary response data. The proposed method uses Gaussian estimation of the correlation parameters, i.e., the estimating function that yields an estimate of the correlation parameters is obtained from the multivariate normal likelihood. The proposed method yields consistent estimates of the regression parameters when data are missing completely at random (MCAR). However, when data are missing at random (MAR), consistency may not hold. In a simulation study with repeated binary outcomes that are missing at random, the magnitude of the potential bias that can arise is examined. The results of the simulation study indicate that, when the working correlation matrix is correctly specified, the bias is almost negligible for the modified GEE. In the simulation study, the proposed modification of GEE is also compared to the standard GEE, multiple imputation, and weighted estimating equations approaches. Finally, the proposed method is illustrated using data from a longitudinal clinical trial comparing two therapeutic treatments, zidovudine (AZT) and didanosine (ddI), in patients with HIV.
Combining Contingency Tables with Missing Dimensions
Authors: Dominici Francesca
Published: May 2004

Summary.We propose a methodology for estimating the cell probabilities in a multiway contingency table by combining partial information from a number of studies when not all of the variables are recorded in all studies. We jointly model the full set of categorical variables recorded in at least one of the studies, and we treat the variables that are not reported as missing dimensions of the study‐specific contingency table. For example, we might be interested in combining several cohort studies in which the incidence in the exposed and nonexposed groups is not reported for all risk factors in all studies while the overall numbers of cases and cohort size is always available. To account for study‐to‐study variability, we adopt a Bayesian hierarchical model. At the first stage of the model, the observation stage, data are modeled by a multinomial distribution with fixed total number of observations. At the second stage, we use the logistic normal (LN) distribution to model variability in the study‐specific cells' probabilities. Using this model and data augmentation techniques, we reconstruct the contingency table for each study regardless of which dimensions are missing, and we estimate population parameters of interest. Our hierarchical procedure borrows strength from all the studies and accounts for correlations among the cells' probabilities. The main difficulty in combining studies recording different variables is in maintaining a consistent interpretation of parameters across studies. The approach proposed here overcomes this difficulty and at the same time addresses the uncertainty arising from the missing dimensions. We apply our modeling strategy to analyze data on air pollution and mortality from 1987 to 1994 for six U.S. cities by combining six cross‐classifications of low, medium, and high levels of mortality counts, particulate matter, ozone, and carbon monoxide with the complication that four of the six cities do not report all the air pollution variables. Our goals are to investigate the association between air pollution and mortality by reconstructing the tables with missing dimensions, to determine the most harmful pollutant combinations, and to make predictions about these key issues for a city other than the six sampled. We find that, for high levels of ozone and carbon monoxide, the number of cases with a high number of deaths increases as the levels of particulate matter,PM10, increases and that the most harmful combinations corresponds to high levels ofPM10, confirming prior findings that levels ofPM10higher than the NAAQS standard are harmful.
Nonparametric Analysis of Recurrent Events and Death
Authors: Ghosh Debashis , Lin D. Y.
Published: May 2004

Summary. This article is concerned with the analysis of recurrent events in the presence of a terminal event such as death. We consider the mean frequency function, defined as the marginal mean of the cumulative number of recurrent events over time. A simple nonparametric estimator for this quantity is presented. It is shown that the estimator, properly normalized, converges weakly to a zero‐mean Gaussian process with an easily estimable covariance function. Nonparametric statistics for comparing two mean frequency functions and for combining data on recurrent events and death are also developed. The asymptotic null distributions of these statistics, together with consistent variance estimators, are derived. The small‐sample properties of the proposed estimators and test statistics are examined through simulation studies. An application to a cancer clinical trial is provided.
Graphical Exploration of Covariate Effects on Survival Data Through Nonparametric Quantile Curves
Authors: Bowman A. W. , Wright E. M.
Published: May 2004

Summary.Kaplan‐Meier curves provide an effective means of presenting the distributional pattern in a sample of survival data. However, in order to assess the effect of a covariate, a standard scatterplot is often difficult to interpret because of the presence of censored observations. Several authors have proposed a running median as an effective way of indicating the effect of a covariate. This article proposes a form of kernel estimation, employing double smoothing, that can be applied in a simple and efficient manner to construct an estimator of a percentile of the survival distribution as a function of one or two covariates. Permutations and bootstrap samples can be used to construct reference bands that help identify whether particular features of the estimates indicate real features of the underlying curve or whether this may be due simply to random variation. The techniques are illustrated on data from a study of kidney transplant patients.
Estimation of Regression Parameters and the Hazard Function in Transformed Linear Survival Models
Authors: Gray Robert J.
Published: May 2004

Summary. An estimator of the regression parameters in a semiparametric transformed linear survival model is examined. This estimator consists of a single Newton‐like update of the solution to a rank‐based estimating equation from an initial consistent estimator. An automated penalized likelihood algorithm is proposed for estimating the optimal weight function for the estimating equations and the error hazard function that is needed in the variance estimator. In simulations, the estimated optimal weights are found to give reasonably efficient estimators of the regression parameters, and the variance estimators are found to perform well. The methodology is applied to an analysis of prognostic factors in non‐Hodgkin's lymphoma.
Bayesian Inference for Kappa from Single and Multiple Studies
Authors: Basu Sanjib , Banerjee Mousumi , Sen Ananda
Published: May 2004

Summary. Cohen's kappa coefficient is a widely popular measure for chance‐corrected nominal scale agreement between two raters. This article describes Bayesian analysis for kappa that can be routinely implemented using Markov chain Monte Carlo (MCMC) methodology. We consider the case of m≥ 2 independent samples of measured agreement, where in each sample a given subject is rated by two rating protocols on a binary scale. A major focus here is on testing the homogeneity of the kappa coefficient across the different samples. The existing frequentist tests for this case assume exchangeability of rating protocols, whereas our proposed Bayesian test does not make any such assumption. Extensive simulation is carried out to compare the performances of the Bayesian and the frequentist tests. The developed methodology is illustrated using data from a clinical trial in ophthalmology.
Interval Estimation of the Kappa Coefficient with Binary Classification and an Equal Marginal Probability Model
Authors: Nam Jun‐Mo
Published: May 2004

Summary. We derive a likelihood score method for interval estimation of the intraclass version of the kappa coefficient of agreement with binary classification using a general theory of Bartlett (1953, Biometrika40, 306–317). By exact evaluation, we investigate statistical properties of the score method, the chi‐square goodness‐of‐fit procedure (Donner and Eliasziw, 1992, Statistics in Medicine11, 1511–1519; Hale and Fleiss, 1993, Biometrics49, 523–534), and a crude confidence interval for small and medium sample sizes. Actual coverage percentages of the score and chi‐square methods are satisfactorily close to the nominal confidence coefficient, while that of the crude method is quite unsatisfactory. The expected length of the score method is shorter than that of the chi‐square procedure when the response rate is very small or very large.
A Curve‐Free Method for Phase I Clinical Trials
Authors: Gasparini Mauro , Eisele Jeffrey
Published: May 2004

Summary. Consider the problem of finding the dose that is as high as possible subject to having a controlled rate of toxicity. The problem is commonplace in oncology Phase I clinical trials. Such a dose is often called the maximum tolerated dose (MTD) since it represents a necessary trade‐off between efficacy and toxicity. The continual reassessment method (CRM) is an improvement over traditional up‐and‐down schemes for estimating the MTD. It is based on a Bayesian approach and on the assumption that the dose‐toxicity relationship follows a specific response curve, e.g., the logistic or power curve. The purpose of this paper is to illustrate how the assumption of a specific curve used in the CRM is not necessary and can actually hinder the efficient use of prior inputs. An alternative curve‐free method in which the probabilities of toxicity are modeled directly as an unknown multidimensional parameter is presented. To that purpose, a product‐of‐beta prior (PBP) is introduced and shown to bring about logical improvements. Practical improvements are illustrated by simulation results.
Sample Size Estimation for Survival Outcomes in Cluster‐Randomized Studies with Small Cluster Sizes
Authors: Manatunga Amita K. , Chen Shande
Published: May 2004

Summary.We present a method for computing sample size for cluster‐randomized studies involving a large number of clusters with relatively small numbers of observations within each cluster. For multivariate survival data, only the marginal bivariate distribution is assumed to be known. The validity of this assumption is also discussed.
Testing Secondary Hypotheses Following Sequential Clinical Trials
Authors: Liu Aiyi , Tan Ming , Boyett James M. , Xiong Xiaoping
Published: May 2004

Summary. Sequential monitoring in a clinical trial poses difficulty in hypotheses testing on secondary endpoints after the trial is terminated. The conventional likelihood‐based testing procedure that ignores the sequential monitoring inflates Type I error and undermines power. In this article, we show that the power of the conventional testing procedure can be substantially improved while the Type I error is controlled. The method is illustrated with a real clinical trial.
A Century of Biometrical Genetics
Authors: Elston Robert C. , Thompson Elizabeth A.
Published: May 2004

Summary. We briefly review the major contribution of biometrics to genetics over the last century (population genetic models, familial correlations, segregation analysis, and gene mapping) and current areas of active research and then speculate about what problems will be tackled in the next century.
Structural Time Series Models with Feedback Mechanisms
Authors: Guo Wensheng , Brown Morton B.
Published: May 2004

Summary.Structural time series models have applications in many different fields such as biology, economics, and meteorology. A structural time series model can be represented as a state‐space model where the states of the system represent the unobserved components and the structural parameters have clear interpretations. This paper introduces a class of structural time series models that incorporate feedback from the latent components of the history. An iterative procedure is proposed for estimation. These models allow flexible and robust feedback mechanisms, have clear interpretations, and have a computationally efficient estimation procedure. They are applied to hormone data to characterize hormone secretion and to explore a potential feedback mechanism.
Modeling Nonstationary Longitudinal Data
Authors: Núñez‐Antón Vicente , Zimmerman Dale L.
Published: May 2004

Summary. An important theme of longitudinal data analysis in the past two decades has been the development and use of explicit parametric models for the data's variance‐covariance structure. A variety of these models have been proposed, of which most are second‐order stationary. A few are flexible enough to accommodate nonstationarity, i.e., nonconstant variances and/or correlations that are not a function solely of elapsed time between measurements. We review five nonstationary models that we regard as most useful: (1) the unstructured covariance model, (2) unstructured antedependence models, (3) structured antedependence models, (4) autoregressive integrated moving average and similar models, and (5) random coefficients models. We evaluate the relative strengths and limitations of each model, emphasizing when it is inappropriate or unlikely to be useful. We present three examples to illustrate the fitting and comparison of the models and to demonstrate that nonstationary longitudinal data can be modeled effectively and, in some cases, quite parsimoniously. In these examples, the antedependence models generally prove to be superior and the random coefficients models prove to be inferior. We conclude that antedependence models should be given much greater consideration than they have historically received.
Multivariate Continuation Ratio Models: Connections and Caveats
Authors: Heagerty Patrick J. , Zeger Scott L.
Published: May 2004

Summary.We develop semiparametric estimation methods for a pair of regressions that characterize the first and second moments of clustered discrete survival times. In the first regression, we represent discrete survival times through univariate continuation indicators whose expectations are modeled using a generalized linear model. In the second regression, we model the marginal pairwise association of survival times using the Clayton‐Oakes cross‐product ratio (Clayton, 1978,Biometrika65, 141–151; Oakes, 1989,Journal of the American Statistical Association84, 487–493). These models have recently been proposed by Shih (1998,Biometrics54, 1115–1128). We relate the discrete survival models to multivariate multinomial models presented in Heagerty and Zeger (1996,Journal of the American Statistical Society91, 1024–1036) and derive a paired estimating equations procedure that is computationally feasible for moderate and large clusters. We extend the work of Guo and Lin (1994,Biometrics50, 632–639) and Shih (1998) to allow covariance weighted estimating equations and investigate the impact of weighting in terms of asymptotic relative efficiency. We demonstrate that the multinomial structure must be acknowledged when adopting weighted estimating equations and show that a naive use of GEE methods can lead to inconsistent parameter estimates. Finally, we illustrate the proposed methodology by analyzing psychological testing data previously summarized by TenHave and Uttal (1994,Applied Statistics43, 371–384) and Guo and Lin (1994).
Modeling Markers of Disease Progression by a Hidden Markov Process: Application to Characterizing CD4 Cell Decline
Authors: Guihenneuc‐Jouyaux Chantal , Richardson Sylvia , Longini Ira M.
Published: May 2004

Summary.Multistate models have been increasingly used to model natural history of many diseases as well as to characterize the follow‐up of patients under varied clinical protocols. This modeling allows describing disease evolution, estimating the transition rates, and evaluating the therapy effects on progression. In many cases, the staging is defined on the basis of a discretization of the values of continuous markers (CD4 cell count for HIV application) that are subject to great variability due mainly to short time‐scale noise (intraindividual variability) and measurement errors. This led us to formulate a Bayesian hierarchical model where, at a first level, a disease process (Markov model on the true states, which are unobserved) is introduced and, at a second level, the measurement process making the link between the true states and the observed marker values is modeled. This hierarchical formulation allows joint estimation of the parameters of both processes. Estimation of the quantities of interest is performed via stochastic algorithms of the family of Markov chain Monte Carlo methods. The flexibility of this approach is illustrated by analyzing the CD4 data on HIV patients of the Concorde clinical trial.
Likelihood‐Ratio Tests for Hidden Markov Models
Authors: Giudici Paolo , Ryden Tobias , Vandekerkhove Pierre
Published: May 2004

Summary.We consider hidden Markov models as a versatile class of models for weakly dependent random phenomena. The topic of the present paper is likelihood‐ratio testing for hidden Markov models, and we show that, under appropriate conditions, the standard asymptotic theory of likelihood‐ratio tests is valid. Such tests are crucial in the specification of multivariate Gaussian hidden Markov models, which we use to illustrate the applicability of our general results. Finally, the methodology is illustrated by means of a real data set.
On the Analysis of Accumulation Curves
Authors: Christen J. Andrés , Nakamura Miguel
Published: May 2004

Summary. Identifying and counting the total number of biological species observed, when plotted against a measure of the effort used to record them, gives rise to a species accumulation curve. We investigate estimation of the total number of species and other relevant properties of accumulation by elaborating on the multinomial model (Nakamura and Peraza, 1998, Journal of Agricultural, Biological, and Environmental Statistics, 3, 17–36) that includes specification of a beta density for recording probabilities. We consider a unified description including complete and incomplete (aggregated) curves, a more general scheme for recording, and a Bayesian framework to allow for inclusion of the biologist's knowledge with regard to typical recording probabilities and the total number of species. The beta distribution is used as a prior, but recording probabilities are not restrained to be beta distributed. The methods yield either closed analytical expressions for inference or relatively simple numerical procedures. Predictive distributions of future recordings that would eventually lead to an optimal decision‐theoretical rule for stopping collection effort may be easily calculated. A case study regarding species of bats is considered, including some guidelines for elicitation of an informative prior.
Nonparametric and Parametric Estimation for a Linear Germination‐Growth Model
Authors: Chiu S. N. , Quine M. P. , Stewart M.
Published: May 2004

Summary. Seeds are planted on the interval [0, L] at various locations. Each seed has a location x and a potential germination time tε [0, ∞), and it is assumed that the collection of such (x, t) pairs forms a Poisson process in [0, L] × [0, ∞) with intensity measure dxdΛ(t). From each seed that germinates, an inhibiting region grows bidirectionally at rate 2v. These regions inhibit germination of any seed in the region with a later potential germination time. Thus, seeds only germinate in the uninhibited part of [0, L]. We want to estimate Λ on the basis of one or more realizations of the process, the data being the locations and germination times of the germinated seeds. We derive the maximum likelihood estimator of v and a nonparametric estimator of Λ and describe methods of obtaining parametric estimates from it, illustrating these with reference to gamma densities. Simulation results are described and the methods applied to some neurobiological data. An Appendix outlines the S‐PLUS code used.
Standard Errors for EM Estimates in Generalized Linear Models with Random Effects
Authors: Friedl Herwig , Kauermann Göran
Published: May 2004

Summary.A procedure is derived for computing standard errors of EM estimates in generalized linear models with random effects. Quadrature formulas are used to approximate the integrals in the EM algorithm, where two different approaches are pursued, i.e., Gauss‐Hermite quadrature in the case of Gaussian random effects and nonparametric maximum likelihood estimation for an unspecified random effect distribution. An approximation of the expected Fisher information matrix is derived from an expansion of the EM estimating equations. This allows for inferential arguments based on EM estimates, as demonstrated by an example and simulations.
Nonconjugate Bayesian Analysis of Variance Component Models
Authors: Wolfinger Russell D. , Kass Robert E.
Published: May 2004

Summary. We consider the usual normal linear mixed model for variance components from a Bayesian viewpoint. With conjugate priors and balanced data, Gibbs sampling is easy to implement; however, simulating from full conditionals can become difficult for the analysis of unbalanced data with possibly nonconjugate priors, thus leading one to consider alternative Markov chain Monte Carlo schemes. We propose and investigate a method for posterior simulation based on an independence chain. The method is customized to exploit the structure of the variance component model, and it works with arbitrary prior distributions. As a default reference prior, we use a version of Jeffreys' prior based on the integrated (restricted) likelihood. We demonstrate the ease of application and flexibility of this approach in familiar settings involving both balanced and unbalanced data.
Proportional Means Regression for Censored Medical Costs
Authors: Lin D. Y.
Published: May 2004

Summary. The semiparametric proportional means model specifies that the mean function for the cumulative medical cost over time conditional on a set of covariates is equal to an arbitrary baseline mean function multiplied by an exponential regression function. We demonstrate how to estimate the vector‐valued regression parameter using possibly censored lifetime costs. The estimator is consistent and asymptotically normal with an easily estimable covariance matrix. Simulation studies show that the proposed methodology is appropriate for practical use. An application to AIDS is provided.
Correcting for Noncompliance and Dependent Censoring in an AIDS Clinical Trial with Inverse Probability of Censoring Weighted (IPCW) Log‐Rank Tests
Authors: Robins James M. , Finkelstein Dianne M.
Published: May 2004

Summary. AIDS Clinical Trial Group (ACTG) randomized trial 021 compared the effect of bactrim versus aerosolized pentamidine (AP) as prophylaxis therapy for pneumocystis pneumonia (POP) in AIDS patients. Although patients randomized to the bactrim arm experienced a significant delay in time to POP, the survival experience in the two arms was not significantly different (p= .32). In this paper, we present evidence that bactrim therapy improves survival but that the standard intent‐to‐treat comparison failed to detect this survival advantage because a large fraction of the subjects either crossed over to the other therapy or stopped therapy altogether. We obtain our evidence of a beneficial bactrim effect on survival by artificially regarding the subjects as dependently censored at the first time the subject either stops or switches therapy; we then analyze the data with the inverse probability of censoring weighted Kaplan‐Meier and Cox partial likelihood estimators of Robins (1993, Proceedings of the Biopharmaceutical Section, American Statistical Association, pp. 24–33) that adjust for dependent censoring by utilizing data collected on time‐dependent prognostic factors.
Nonparametric and Semiparametric Trend Analysis for Stratified Recurrence Times
Authors: Wang Mei‐Cheng , Chen Ying‐Qing
Published: May 2004

Summary. Recurrent event data are frequently encountered in longitudinal follow‐up studies when the occurrences of multiple events are considered as the major outcomes. Suppose that the recurrent events are of the same type and the variable of interest is the recurrence time between successive events. In many applications, the distributional pattern of recurrence times can be used as an index for the progression of a disease. Such a distributional pattern is important for understanding the natural history of a disease or for confirming long‐term treatment effect. In this article, we discuss and define the comparability of recurrence times. Nonparametric and semiparametric methods are developed for testing trend of recurrence time distributions and estimating trend parameters in regression models. The construction of the methods is based on comparable recurrence times from stratified data. A real data example is presented to illustrate the use of methodology.
Estimation of Individual Genetic Effects from Binary Observations on Relatives Applied to a Family History of Respiratory Illnesses and Chronic Lung Disease of Newborns
Authors: Houwing‐Duistermaat Jeanine J. , van Houwelingen Hans C. , de Winter J. Peter
Published: May 2004

Summary.This paper considers methods for estimating the relationship between a binary responseYand the genetic effects responsible for a second binary traitZ.The responsesYare observed only for target individuals, and the responsesZare observed only for the relatives of these targets. The analysis consists of two parts. The first part concerns the analysis of the family dataZand the second part estimates the relation between the genetic effects andY.For the family data, a generalized linear mixed model with a logit link and Gaussian genetic (random) effects is used. Estimates of the variances of the genetic effects are obtained by using a pseudo‐profile log‐likelihood method. Estimation of the log likelihood involves averaging overn‐dimensional normal distributions, which is done by importance sampling. The methods used in the second part are straightforward. The methods are applied to a data set containing chronic lung disease (CLDN) responses of newborns and asthma (AS), allergy (AL), chronic bronchitis (CB) and eczema (EC) responses observed for the relatives of these newborns. The clinical question is whether genetic effects of AS, AL, CB, and EC have an effect on the risk for CLDN. It can be concluded that for AS, AL, CB, and EC, the influence of genetic effects is significant. However, these genetic predispositions have no significant effect on CLDN.
A Frailty Model of Segregation Analysis: Understanding the Familial Transmission of Alcoholism
Authors: Zhang Heping , Merikangas Kathleen
Published: May 2004

Summary.Coupled with environmental factors, genes contribute to numerous human diseases and traits. While there are many epidemiological methods to assess the familial clustering of traits, few are flexible enough to accommodate interactions between covariates and familial factors. In this paper, we propose and develop a frailty model that establishes an integrated framework to evaluate familial transmission of a disease by controlling for covariate effects and conveniently testing the interactions between covariates and familial factors. We also present a peeling algorithm that dramatically reduces the computational burden. This frailty model is employed to examine the familial transmission of major subtypes of alcoholism, namely, alcohol abuse and dependence. We conclude that alcohol dependence is strongly familial whereas alcohol abuse expresses a marginally significant pattern of familial transmission. Moreover, females manifest alcoholism at a lower threshold, and there is no sex‐specific familial transmission of alcoholism after adjustment for the threshold effect.
Fractional Simplex Designs for Interaction Screening in Complex Mixtures
Authors: McConkey Brendan J. , Mezey Paul G. , Dixon D. George , Greenberg Bruce M.
Published: May 2004

Summary.In mixture experiments, one may be interested in estimating not only main effects but also some interactions. Main effects and significant interactions in a mixture may be estimated through appropriate mixture experiments, such as simplex‐centroid designs. However, for mixtures with a large number of factors, the run size for these designs becomes impractically large. A subset of a full simplex‐centroid design may be used, but the problem remains regarding which factor‐level settings should be selected. In this paper, we propose a solution that considers design points with either one orpindividual nonzero factor‐level settings. These fractional simplex designs provide a means of screening for interactions and of investigating the behavior of many‐component mixtures as a whole while greatly reducing the run size compared with full simplex‐centroid designs. The means of construction of the design arrays is described, and designs for ≤31 factors are presented. Some of the proposed methodology is illustrated using generated data.
Maximally Efficient Two‐Stage Screening
Authors: Berger Toby , Mandell James W. , Subrahmanya P.
Published: May 2004

Summary. In DNA library screening, blood testing, and monoclonal antibody generation, significant savings in the number of assays can be realized by employing group sampling. Practical considerations often limit the number of stages of group testing that can be performed. We address situations in which only two stages of testing are used. We define efficiency to be the expected number of positives isolated per assay performed and assume gold‐standard tests with unit sensitivity and specificity. Although practical tests never are golden, polymerase chain reaction (PCR) methods provide procedures for screening recombinant libraries that are strongly selective yet retain high sensitivity even when samples are pooled. Also, results for gold‐standard tests serve as bounds on the performance of practical testing procedures. First we derive formulas for the efficiency of certain extensions of the popular rows‐and‐columns technique. Then we derive an upper bound on the efficiency of any two‐stage strategy that lies well below the classical upper bound for situations with no constraint on the number of stages. This establishes that a restriction to only two stages necessitates performing many more assays than efficient multistage procedures need. Next, we specialize the bound to cases in which each item belonging only to pools that tested positive in stage 1 must be tested individually in stage 2. The specialized bound for such positive procedures is tight because we show that an appropriate multidimensional extension of the rows‐and‐columns technique achieves it. We also show that two‐stage positive procedures in which the stage‐l groups are selected at random perform suboptimally, thereby establishing that efficient tests must be structured carefully.
Estimating Transition Probabilities from Aggregate Samples Plus Partial Transition Data
Authors: Hawkins D. L. , Han Chien‐Pai
Published: May 2004

Summary.Longitudinal studies often collect only aggregate data, which allows only inefficient transition probability estimates. Barring enormous aggregate samples, improving the efficiency of transition probability estimates seems to be impossible without additional partial‐transition data. This paper discusses several sampling plans that collect data of both types,aswell as a methodology that combines them into efficient estimates of transition probabilities. The method handles both fixed and time‐dependent categorical covariates and requires no assumptions (e.g., time homogeneity, Markov) about the population evolution.
The Beta‐Binomial Model for Host Specificity among Organisms in Trophic Interactions
Authors: Diserud Ola H. , Ødegaard Rode
Published: May 2004

Summary. In this paper, we present a new stochastic model where the host specificity among organisms in trophic interactions in a community, say parasite‐host interactions, is estimated by a beta‐binomial model. The expected proportion of the host species in a community that a given parasite species is utilizing is modeled as a realization from an inhomogeneous Poisson process, where the rate of this process is assumed to be proportional to a beta probability distribution. The observed number of host species utilized by the parasites is then binomially distributed with the number of trials equaling the number of different host species in the sample. When the degree of polyphagy is estimated by the parameters of the beta‐binomial model, quantities like community host specificity and the expected total number of parasite species that will utilize the host species in the community can be predicted as functions of the number of host species available. The predictions can then be applied in analysis of, e.g., symbiotic interactions among organisms, local species richness, and community structure.
Sample Size Determination for Testing Whether an Identified Treatment Is Best
Authors: Horn Manfred , Vollandt Rudiger , Dunnett Charles W.
Published: May 2004

Summary. Laska and Meisner (1989, Biometrics45, 1139–1151) dealt with the problem of testing whether an identified treatment belonging to a set of k+ 1 treatments is better than each of the other k treatments. They calculated sample size tables for k= 2 when using multiple t‐tests or Wilcoxon–Mann–Whitney tests, both under normality assumptions. In this paper, we provide sample size formulas as well as tables for sample size determination for k≥ 2 when t‐tests under normality or Wilcoxon–Mann–Whitney tests under general distribution assumptions are used.
Unit–Treatment Interaction and Its Practical Consequences
Authors: Gadbury Gary L. , Iyer Hari K.
Published: May 2004

Summary. Most statistical characterizations of a treatment effect focus on the average effect of the treatment over an entire population. However, average effects may provide inadequate information, sometimes misleading information, when a substantial unit‐treatment interaction is present in the population. It is even possible that a nonnegligible proportion of the individuals in the population experience an unfavorable treatment effect even though the treatment might appear to be beneficial when considering population averages. This paper examines the extent to which information about unit–treatment interaction can be extracted using observed data from a two‐treatment completely randomized experiment. A method for utilizing the information from an available covariate is proposed. Although unit–treatment interaction is a nonidentifiable quantity, we show that mathematical bounds for it can be estimated from observed data. These bounds lead to estimated bounds for the probability of an unfavorable treatment effect. Maximum likelihood estimators of the bounds and their corresponding large‐sample distributions are given. The use of the estimated bounds is illustrated in a clinical trials data example.
Multiple‐Changepoint Testing for an Alternating Segments Model of a Binary Sequence
Authors: Halpern Aaron L.
Published: May 2004

Summary. A binary sequence may give the appearance of being composed of alternating segments with relatively high and relatively low probability of success. Determining whether such an alternating pattern is significant is a multiple‐changepoint problem where the number of segments and their success probabilities are unknown, with the added constraint of segment alternation. A dynamic programming method for determining the optimal segmentation into a given number of segments is provided. Given this, a variation on the simulation method of Venter and Steel (1996, Computational Statistics and Data Analysis22, 481–504) may be employed t o test the null hypothesis of a homogeneous sequence as well as to estimate the number and location of changepoints. A sample application, the assessment of the possibility of genetic recombination in HIV sequences, is presented.
Interpreting Parameters in the Logistic Regression Model with Random Effects
Authors: Larsen Klaus , Petersen Jørgen Holm , Budtz‐Jørgensen Esben , Endahl Lars
Published: May 2004

Summary.Logistic regression with random effects is used to study the relationship between explanatory variables and a binary outcome in cases with nonindependent outcomes. In this paper, we examine in detail the interpretation of both fixed effects and random effects parameters. As heterogeneity measures, the random effects parameters included in the model are not easily interpreted. We discuss different alternative measures of heterogeneity and suggest using a median odds ratio measure that is a function of the original random effects parameters. The measure allows a simple interpretation, in terms of well‐known odds ratios, that greatly facilitates communication between the data analyst and the subject‐matter researcher. Three examples from different subject areas, mainly taken from our own experience, serve to motivate and illustrate different aspects of parameter interpretation in these models.
When Should Epidemiologic Regressions Use Random Coefficients?
Authors: Greenland Sander
Published: May 2004

Summary.Regression models with random coefficients arise naturally in both frequentist and Bayesian approaches to estimation problems. They are becoming widely available in standard computer packages under the headings of generalized linear mixed models, hierarchical models, and multilevel models. I here argue that such models offer a more scientifically defensible framework for epidemiologic analysis than the fixed‐effects models now prevalent in epidemiology. The argument invokes an antiparsimony principle attributed to L. J. Savage, which is that models should be rich enough to reflect the complexity of the relations under study. It also invokes the countervailing principle that you cannot estimate anything if you try to estimate everything (often used to justify parsimony). Regression with random coefficients offers a rational compromise between these principles as well as an alternative to analyses based on standard variable‐selection algorithms and their attendant distortion of uncertainty assessments. These points are illustrated with an analysis of data on diet, nutrition, and breast cancer.
Bayesian Detection and Modeling of Spatial Disease Clustering
Authors: Gangnon Ronald E. , Clayton Murray K.
Published: May 2004

Summary.Many current statistical methods for disease clustering studies are based on a hypothesis testing paradigm. These methods typically do not produce useful estimates of disease rates or cluster risks. In this paper, we develop a Bayesian procedure for drawing inferences about specific models for spatial clustering. The proposed methodology incorporates ideas from image analysis, from Bayesian model averaging, and from model selection. With our approach, we obtain estimates for disease rates and allow for greater flexibility in both the type of clusters and the number of clusters that may be considered. We illustrate the proposed procedure through simulation studies and an analysis of the well‐known New York leukemia data.
Estimation of Multivariate Frailty Models Using Penalized Partial Likelihood
Authors: Ripatti Samuli , Palmgren Juni
Published: May 2004

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.
Multivariate Parametric Random Effect Regression Models for Fecundability Studies
Authors: Ecochard René , Clayton David G.
Published: May 2004

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.
Zero‐Inflated Poisson and Binomial Regression with Random Effects: A Case Study
Authors: Hall Daniel B.
Published: May 2004

Summary.In a 1992Technometricspaper, 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 probabilityp.Bothpand 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.
Calibration for Nonlinear Mixed Effects Models: An Application to the Withdrawal Time Prediction
Authors: Concordet Didier , Nunez Olivier G.
Published: May 2004

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.
Latent Variable Models for Longitudinal Data with Multiple Continuous Outcomes
Authors: Roy Jason , Lin Xihong
Published: May 2004

Summary.Multiple outcomes are often used to properly characterize an effect of interest. This paper proposes a latent variable model for the situation where repeated measures over time are obtained on each outcome. These outcomes are assumed to measure an underlying quantity of main interest from different perspectives. We relate the observed outcomes using regression models to a latent variable, which is then modeled as a function of covariates by a separate regression model. Random effects are used to model the correlation due to repeated measures of the observed outcomes and the latent variable. An EM algorithm is developed to obtain maximum likelihood estimates of model parameters. Unit‐specific predictions of the latent variables are also calculated. This method is illustrated using data from a national panel study on changes in methadone treatment practices.
Latent Class Model Diagnosis
Authors: Garrett Elizabeth S. , Zeger Scott L.
Published: May 2004

Summary.In many areas of medical research, such as psychiatry and gerontology, latent class variables are used to classify individuals into disease categories, often with the intention of hierarchical modeling. Problems arise when it is not clear how many disease classes are appropriate, creating a need for model selection and diagnostic techniques. Previous work has shown that the Pearson χ2statistic and the log likelihood ratioG2statistic are not valid test statistics for evaluating latent class models. Other methods, such as information criteria, provide decision rules without providing explicit information about where discrepancies occur between a model and the data. Identifiability issues further complicate these problems. This paper develops procedures for assessing Markov chain Monte Carlo convergence and model diagnosis and for selecting the number of categories for the latent variable based on evidence in the data using Markov chain Monte Carlo techniques. Simulations and a psychiatric example are presented to demonstrate the effective use of these methods.
Distinguishing Effects on Tumor Multiplicity and Growth Rate in Chemoprevention Experiments
Authors: Dunson David B. , Dinse Gregg E.
Published: May 2004

Summary. In some types of cancer chemoprevention experiments and short‐term carcinogenicity bioassays, the data consist of the number of observed tumors per animal and the times at which these tumors were first detected. In such studies, there is interest in distinguishing between treatment effects on the number of tumors induced by a known carcinogen and treatment effects on the tumor growth rate. Since animals may die before all induced tumors reach a detectable size, separation of these effects can be difficult. This paper describes a flexible parametric model for data of this type. Under our model, the tumor detection times are realizations of a delayed Poisson process that is characterized by the age‐specific tumor induction rate and a random latency interval between tumor induction and detection. The model accommodates distinct treatment and animal‐specific effects on the number of induced tumors (multiplicity) and the time to tumor detection (growth rate). A Gibbs sampler is developed for estimation of the posterior distributions of the parameters. The methods are illustrated through application to data from a breast cancer chemoprevention experiment.
Inferring the Location and Effect of Tumor Suppressor Genes by Instability‐Selection Modeling of Allelic‐Loss Data
Authors: Newton Michael A. , Lee Yoonjung
Published: May 2004

Summary. Cancerous tumor growth creates cells with abnormal DNA. Allelic‐loss experiments identify genomic deletions in cancer cells, but sources of variation and intrinsic dependencies complicate inference about the location and effect of suppressor genes; such genes are the target of these experiments and are thought to be involved in tumor development. We investigate properties of an instability‐selection model of allelic‐loss data, including likelihood‐based parameter estimation and hypothesis testing. By considering a special complete‐data case, we derive an approximate calibration method for hypothesis tests of sporadic deletion. Parametric bootstrap and Bayesian computations are also developed. Data from three allelic‐loss studies are reanalyzed to illustrate the methods.