bluuebunny/crossref_metadata_2025 huggingface dataset:
A Quantitative Genetic Model for Analyzing Species Differences in Outcrossing Species
Authors: Wu Rongling , Li Bailian
Published: May 2004

Summary.A genetic model based on a two‐level intra‐ and interspecific mating design is proposed to estimate the genetic architecture of species differences and heterosis for outcrossing species. The underlying genetic analyses make use of classical quantitative genetic theories and recent results from molecular genetic studies. Gene effects across different quantitative trait loci (QTL) can be approximated by a geometric series. Under natural selection, gene effects are often associated with allele frequencies in a particular way, which can be approximated by the gamma distribution. By incorporating these approximations into family structural analyses in the mating design, we are able to estimate a number of genetic parameters that contribute to quantitative genetic variation based on a nonlinear optimization approach. These parameters include the number of QTL, their gene effects, and their allele frequencies in the parental populations. We perform simulation studies and illustrate an example to demonstrate the statistical property and procedure of the method.
Analysis of Exposure‐Time‐Response Relationships Using a Spline Weight Function
Authors: Hauptmann Michael , Wellmann Jürgen , Lubin Jay H. , Rosenberg Philip S. , Kreienbrock Lothar
Published: May 2004

Summary.To examine the time‐dependent effects of exposure histories on disease, we estimate a weight function within a generalized linear model. The shape of the weight function, which is modeled as a cubic B‐spline, gives information about the impact of exposure increments at different times on disease risk. The method is evaluated in a simulation study and is applied to data on smoking histories and lung cancer from a recent case‐control study in Germany.
Confidence Intervals for the Mean of Diagnostic Test Charge Data Containing Zeros
Authors: Zhou Xiao‐Hua , Tu Wanzhu
Published: May 2004

Summary. In this paper, we consider the problem of interval estimation for the mean of diagnostic test charges. Diagnostic test charge data may contain zero values, and the nonzero values can often be modeled by a log‐normal distribution. Under such a model, we propose three different interval estimation procedures: a percentile‐t bootstrap interval based on sufficient statistics and two likelihood‐based confidence intervals. For theoretical properties, we show that the two likelihood‐based one‐sided confidence intervals are only first‐order accurate and that the bootstrap‐based one‐sided confidence interval is second‐order accurate. For two‐sided confidence intervals, all three proposed methods are second‐order accurate. A simulation study in finite‐sample sizes suggests all three proposed intervals outperform a widely used minimum variance unbiased estimator (MVUE)‐based interval except for the case of one‐sided lower end‐point intervals when the skewness is very small. Among the proposed one‐sided intervals, the bootstrap interval has the best coverage accuracy. For the two‐sided intervals, when the sample size is small, the bootstrap method still yields the best coverage accuracy unless the skewness is very small, in which case the bias‐corrected ML method has the best accuracy. When the sample size is large, all three proposed intervals have similar coverage accuracy. Finally, we analyze with the proposed methods one real example assessing diagnostic test charges among older adults with depression.
Regression Models for Disease Prevalence with Diagnostic Tests on Pools of Serum Samples
Authors: Vansteelandt S. , Goetghebeur E. , Verstraeten T.
Published: May 2004

Summary. Whether the aim is to diagnose individuals or estimate prevalence, many epidemiological studies have demonstrated the successful use of tests on pooled sera. These tests detect whether at least one sample in the pool is positive. Although originally designed to reduce diagnostic costs, testing pools also lowers false positive and negative rates in low prevalence settings and yields more precise prevalence estimates. Current methods are aimed at estimating the average population risk from diagnostic tests on pools. In this article, we extend the original class of risk estimators to adjust for covariates recorded on individual pool members. Maximum likelihood theory provides a flexible estimation method that handles different covariate values in the pool, different pool sizes, and errors in test results. In special cases, software for generalized linear models can be used. Pool design has a strong impact on precision and cost efficiency, with covariate‐homogeneous pools carrying the largest amount of information. We perform joint pool and sample size calculations using information from individual contributors to the pool and show that a good design can severely reduce cost and yet increase precision. The methods are illustrated using data from a Kenyan surveillance study of HIV. Compared to individual testing, age‐homogeneous, optimal‐sized pools of average size seven reduce cost to 44% of the original price with virtually no loss in precision.
A Permutation Test to Compare Receiver Operating Characteristic Curves
Authors: Venkatraman E. S.
Published: May 2004

Summary. We developed a permutation test in our earlier paper (Venkatraman and Begg, 1996, Biometrika83, 835–848) to test the equality of receiver operating characteristic curves based on continuous paired data. Here we extend the underlying concepts to develop a permutation test for continuous unpaired data, and we study its properties through simulations.
Semiparametric Regression Analysis of Interval‐Censored Data
Authors: Goetghebeur Els , Ryan Louise
Published: May 2004

Summary.We propose a semiparametric approach to the proportional hazards regression analysis of interval‐censored data. An EM algorithm based on an approximate likelihood leads to an M‐step that involves maximizing a standard Cox partial likelihood to estimate regression coefficients and then using the Breslow estimator for the unknown baseline hazards. The E‐step takes a particularly simple form because all incomplete data appear as linear terms in the complete‐data log likelihood. The algorithm of Turnbull (1976,Journal of the Royal Statistical Society, Series B38, 290–295) is used to determine times at which the hazard can take positive mass. We found multiple imputation to yield an easily computed variance estimate that appears to be more reliable than asymptotic methods with small to moderately sized data sets. In the right‐censored survival setting, the approach reduces to the standard Cox proportional hazards analysis, while the algorithm reduces to the one suggested by Clayton and Cuzick (1985,Applied Statistics34, 148–156). The method is illustrated on data from the breast cancer cosmetics trial, previously analyzed by Finkelstein (1986,Biometrics42, 845–854) and several subsequent authors.
Bivariate Binary Data Analysis with Nonignorably Missing Outcomes
Authors: Cho Paik Myunghee , Sacco Ralph , Lin I.‐Feng
Published: May 2004

Summary.One of the objectives in the Northern Manhattan Stroke Study is to investigate the impact of stroke subtype on the functional status 2 years after the first ischemic stroke. A challenge in this analysis is that the functional status at 2 years after stroke is not completely observed. In this paper, we propose a method to handle nonignorably missing binary functional status when the baseline value and the covariates are completely observed. The proposed method consists of fitting four separate binary regression models: for the baseline outcome, the outcome 2 years after the stroke, the product of the previous two, and finally, the missingness indicator. We then conduct a sensitivity analysis by varying the assumptions about the third and the fourth binary regression models. Our method belongs to an imputation paradigm and can be an alternative to the weighting method of Rotnitzky and Robins (1997,Statistics in Medicine16, 81–102). A jackknife variance estimate is proposed for the variance of the resulting estimate. The proposed analysis can be implemented using statistical software such as SAS.
Multiple Imputation and Posterior Simulation for Multivariate Missing Data in Longitudinal Studies
Authors: Liu Minzhi , Taylor Jeremy M. G. , Belin Thomas R.
Published: May 2004

Summary. This paper outlines a multiple imputation method for handling missing data in designed longitudinal studies. A random coefficients model is developed to accommodate incomplete multivariate continuous longitudinal data. Multivariate repeated measures are jointly modeled; specifically, an i.i.d. normal model is assumed for time‐independent variables and a hierarchical random coefficients model is assumed for time‐dependent variables in a regression model conditional on the time‐independent variables and time, with heterogeneous error variances across variables and time points. Gibbs sampling is used to draw model parameters and for imputations of missing observations. An application to data from a study of startle reactions illustrates the model. A simulation study compares the multiple imputation procedure to the weighting approach of Robins, Rotnitzky, and Zhao (1995, Journal of the American Statistical Association90, 106–121) that can be used to address similar data structures.
SMR Analysis of Historical Follow‐Up Studies with Missing Death Certificates
Authors: Rittgen Werner , Becker Nikolaus
Published: May 2004

Summary. The evaluation of epidemiological follow‐up studies is frequently based on a comparison of the number O of deaths observed in the cohort from a specified cause with the expected number E calculated from person years in the cohort and mortality rates from a reference population. The ratio SMR = 100 ×O/E is called the standardized mortality ratio (SMR). While person years can easily be calculated from the cohort and reference rates are generally available from the national statistical offices or the World Health Organization (WHO), problems can arise with the accessibility of the causes of death of the deceased study participants. However, the information that a person has died may be available, e.g., from population registers. In this paper, a statistical model for this situation is developed to derive a maximum likelihood (ML) estimator for the true (but unknown) number O* of deaths from a specified cause, which uses the known number O of deaths from this cause and the proportion p of all known causes of death among all deceased participants. It is shown that the standardized mortality ratio SMR * based on this estimated number is just SMR *= SMR/p. Easily computable confidence limits can be obtained by dividing the usual confidence limits of the SMR by the opposite limit of the proportion p. However, the confidence level α has to be adjusted appropriately.
Interim Analysis and Sample Size Reassessment
Authors: Posch Martin , Bauer Peter
Published: May 2004

Summary. This article deals with sample size reassessment for adaptive two‐stage designs based on conditional power arguments utilizing the variability observed at the first stage. Fisher's product test for the p‐values from the disjoint samples at the two stages is considered in detail for the comparison of the means of two normal populations. We show that stopping rules allowing for the early acceptance of the null hypothesis that are optimal with respect to the average sample size may lead to a severe decrease of the overall power if the sample size is a priori underestimated. This problem can be overcome by choosing designs with low probabilities of early acceptance or by midtrial adaptations of the early acceptance boundary using the variability observed in the first stage. This modified procedure is negligibly anticonservative and preserves the power.
An Improved Double Sampling Procedure Based on the Variance
Authors: Proschan Michael A. , Wittes Janet
Published: May 2004

Summary. Sample size calculations for a continuous outcome require specification of the anticipated variance; inaccurate specification can result in an underpowered or overpowered study. For this reason, adaptive methods whereby sample size is recalculated using the variance of a subsample have become increasingly popular. The first proposal of this type (Stein, 1945, Annals of Mathematical Statistics16, 243–258) used all of the data to estimate the mean difference but only the first stage data to estimate the variance. Stein's procedure is not commonly used because many people perceive it as ignoring relevant data. This is especially problematic when the first stage sample size is small, as would be the case if the anticipated total sample size were small. A more naive approach uses in the denominator of the final test statistic the variance estimate based on all of the data. Applying the Helmert transformation, we show why this naive approach underestimates the true variance and how to construct an unbiased estimate that uses all of the data. We prove that the type I error rate of our procedure cannot exceed α.
On Power and Sample Size Calculations for Likelihood Ratio Tests in Generalized Linear Models
Authors: Shieh Gwowen
Published: May 2004

Summary.A direct extension of the approach described in Self, Mauritsen, and Ohara (1992,Biometrics48, 31–39) for power and sample size calculations in generalized linear models is presented. The major feature of the proposed approach is that the modification accommodates both a finite and an infinite number of covariate configurations. Furthermore, for the approximation of the noncentrality of the noncentral chi‐square distribution for the likelihood ratio statistic, a simplification is provided that not only reduces substantial computation but also maintains the accuracy. Simulation studies are conducted to assess the accuracy for various model configurations and covariate distributions.
Applications of Likelihood Asymptotics for Nonlinear Regression in Herbicide Bioassays
Authors: Bellio R. , Jensen J. E. , Seiden P.
Published: May 2004

Summary. Dose–response models are intensively used in herbicide bioassays. Despite recent advancements the development of new herbicides, statistical analyses are commonly based on asymptotic approximations are sometimes poor. This paper presents the use of recent results in higher order asymptotics for likelihood‐based inference in nonlinear regression. The methods presented provide accurate approximation the distribution of test statistics and for prediction limits. Analyses of the fit and measures of detection limits of the bioassays are considered, and the potential of the methods is illustrated by examples with real data.
Definition of the Probability Efficiency Index for Optimization of the Stepwise Yield Selection Procedures of Plant Varieties
Authors: Yonezawa Katsuei , Ishii Takuro , Yano Kentaro
Published: May 2004

Summary.Equations to give exact predictions for the multistep yield selection in a finite population of plant varieties were defined. Not only the optimum resource allocation within a selection trial but also the optimum resource investment for a trial as a whole can be obtained based on the cost‐efficiency index defined in this article.
A Generalized Nonparametric Test for Lattice‐Ordered Means
Authors: Strand Matthew
Published: May 2004

Summary. Treatment means in factorial experiments are lattice ordered when there is an increase in mean response as the level of any factor is increased while holding the other factors fixed. Such means occur naturally in many experiments. A nonparametric test for lattice‐ordered means involving a Kendall‐type statistic will be summarized for k‐factor factorial experiments. Specifically, the form of the test statistic and variance under the null hypothesis will be presented. In addition, a normalized version of the test statistic will be discussed and applied to relevant data.
Capture‐Recapture, Epidemiology, and List Mismatches: Two Lists
Authors: Seber George A. F. , Huakau John T. , Simmons David
Published: May 2004

Summary. In recent years, capture‐recapture methods for closed populations have been extensively applied to epidemiology. For example, suppose we have several incomplete lists of diabetics and we wish to estimate the total number of diabetics by estimating the number missing from all the lists. A major problem is that the information about individuals on the lists may have been given incorrectly or the information may have been typed incorrectly so that some list matches are missed. Using the concept of tag loss borrowed from animal population studies, we consider methods for estimating both the probabilities of making list errors and the population size for just two independent lists. The effect of heterogeneity on the errors is examined. The methods are applied to a large data set of diabetic persons consisting of a list obtained from a survey and a list obtained from doctors’ records. It was found that the error rates were high and that ignoring the errors led to a gross overestimate of the total number of diabetic persons.
Tests of Proportional Hazards and Proportional Odds Models for Grouped Survival Data
Authors: Colosimo Enrico A. , Chalita Liciana V. A. S. , Demétrio Clarice G. B.
Published: May 2004

Summary.In this paper, we derive score test statistics to discriminate between proportional hazards and proportional odds models for grouped survival data. These models are embedded within a power family transformation in order to obtain the score tests. In simple cases, some small‐sample results are obtained for the score statistics using Monte Carlo simulations. Score statistics have distributions well approximated by the chi‐squared distribution. Real examples illustrate the proposed tests.
Reparameterizing the Pattern Mixture Model for Sensitivity Analyses Under Informative Dropout
Authors: Daniels Michael J. , Hogan Joseph W.
Published: May 2004

Summary. Pattern mixture models are frequently used to analyze longitudinal data where missingness is induced by dropout. For measured responses, it is typical to model the complete data as a mixture of multivariate normal distributions, where mixing is done over the dropout distribution. Fully parameterized pattern mixture models are not identified by incomplete data; Little (1993, Journal of the American Statistical Association88, 125–134) has characterized several identifying restrictions that can be used for model fitting. We propose a reparameterization of the pattern mixture model that allows investigation of sensitivity to assumptions about nonidentified parameters in both the mean and variance, allows consideration of a wide range of nonignorable missing‐data mechanisms, and has intuitive appeal for eliciting plausible missing‐data mechanisms. The parameterization makes clear an advantage of pattern mixture models over parametric selection models, namely that the missing‐data mechanism can be varied without affecting the marginal distribution of the observed data. To illustrate the utility of the new parameterization, we analyze data from a recent clinical trial of growth hormone for maintaining muscle strength in the elderly. Dropout occurs at a high rate and is potentially informative. We undertake a detailed sensitivity analysis to understand the impact of missing‐data assumptions on the inference about the effects of growth hormone on muscle strength.
Minimax D‐Optimal Designs for the Logistic Model
Authors: King Joy , Wong Weng‐Kee
Published: May 2004

Summary. We propose an algorithm for constructing minimax D‐optimal designs for the logistic model when only the ranges of the values for both parameters are assumed known. Properties of these designs are studied and compared with optimal Bayesian designs and Sitter's (1992, Biometrics, 48, 1145–1155) minimax D‐optimal kk‐designs. Examples of minimax D‐optimal designs are presented for the logistic and power logistic models, including a dose‐response design for rheumatoid arthritis patients.
A Comment on Testing for a Decline in Upper Cretaceous Dinosaur Diversity
Authors: Solow Andrew R.
Published: May 2004

Summary. A common problem in ecology is to determine whether the diversity of a. biological community has changed over time or in response to a disturbance. This involves testing the null hypothesis that diversity is constant against the alternative hypothesis that it has changed. As the power of this test may be low, Fritsch and Hsu (1999, Biometrics55, 1300–1305) proposed reversing the null and alternative hypothesis. Here, I return to the original formulation and point out that power can be improved by adopting a parametric model for relative abundances and by testing against an ordered alternative.
Book Reviews
Authors: Ridout M. S.
Published: May 2004

STEIN, A. and PENNING DE VRIES, F. W. T. (editors).Data and Models in Action: Methodological Issues in Production Ecology.

RAO, C. R. and SZEKELY, G. J. (editors).Statistics for the 21st Century: Methodologies for Applications of the Future.

BARTHOLOMEW, D. J. and. KNOTT, M.Latent Variable Models and Factor Analysis, 2nd edition.

KRZANOWSKI, W. J.An Introduction to Statistical Modelling.

JOLICOEUR,P. Introduction to Biometry.

DONNELLY, C. A. and FERGUSON, N. M.Statistical Aspects of BSE and vCJD: Models for Epidemics.

YOUNG, L. J. and YOUNG, J. H.Statistical Ecology: A Population Perspective.

LEONARD, T.A Course in Categorical Data Analysis.

STIGLER, S. M.Statistics on the Table: The History of Statistical Concepts and Methods.

EVANS, M. and SWARTZ, T.Approximating Integrals via Monte Carlo and Deterministic Methods.

DUNN, G.Statistics in Psychiatry.

MIGON, H. S. and GAMERMAN,D. Statistical Inference: An Integrated Approach.

WU, C. F. J. and HAMADA, M.Experiments: Planning, Analysis and Parameter Design Optimisation.

WEBER, D. C. and SKILLINGS, J. H.A First Course in the Design of Experiments: A Linear Models Approach.

DE MUTH, J. E.Basic Statistics and Pharmaceutical Applications.

CHOW, S.‐C. (editor)Encyclopedia of Biopharmaceutical Statistics.

PETRIE, A. and WATSON,P. Statistics for Veterinary and Animal Science.

BOSSOMAIER, T. R. J. and GREEN, D. G.Complex Systems.

Brief reports by the editor

GRASSMAN, W. K. (editor)Computational Probability.

GLAZ, J. and BALAKRISHNAN, N. (editors).Scan Statistics.

HEALEY, M. J. R.Matrices for Statistics, 2nd edition.
Survival Analysis in Clinical Trials: Past Developments and Future Directions
Authors: Fleming Thomas R. , Lin D. Y.
Published: May 2004

Summary.The field of survival analysis emerged in the 20th century and experienced tremendous growth during the latter half of the century. The developments in this field that have had the most profound impact on clinical trials are the Kaplan‐Meier (1958,Journal of the American Statistical Association53, 457–481) method for estimating the survival function, the log‐rank statistic (Mantel, 1966,Cancer Chemotherapy Report50, 163–170) for comparing two survival distributions, and the Cox (1972,Journal of the Royal Statistical Society, Series B34, 187–220) proportional hazards model for quantifying the effects of covariates on the survival time. The counting‐process martingale theory pioneered by Aalen (1975, Statistical inference for a family of counting processes, Ph.D. dissertation, University of California, Berkeley) provides a unified framework for studying the small‐ and large‐sample properties of survival analysis statistics. Significant progress has been achieved and further developments are expected in many other areas, including the accelerated failure time model, multivariate failure time data, interval‐censored data, dependent censoring, dynamic treatment regimes and causal inference, joint modeling of failure time and longitudinal data, and Baysian methods.
Masking Unmasked in the Proportional Hazards Model
Authors: Wei Wen Hsiang , Kosorok Michael R.
Published: May 2004

Summary.Influence measures based on the pairwise deletion approach and the differentiation approach are developed for unmasking observations masked by other observations in the proportional hazards model. These influential observations might have substantial impact on statistical inference and might provide important information for model adequacy. One numerical example based on real data is presented and discussed.
Post Blocking Gone Too Far! Recovery of Information and Spatial Analysis in Field Experiments
Authors: Gilmour Arthur R.
Published: May 2004

Summary. Federer (1998, Biometrics54, 471–481) presents two analyses of field data in which high‐order polynomials are fitted as random regressions to remove spatial variation. We challenge the justification of this approach and suggest some alternatives.
On a Likelihood‐Based Goodness‐of‐Fit Test of the Beta‐Binomial Model
Authors: Garren Steven T. , Smith Richard L. , Piegorsch Walter W.
Published: May 2004

Summary.When faced with proportion data that exhibit extra‐binomial variation, data analysts often consider the beta‐binomial distribution as an alternative model to the more common binomial distribution. A typical example occurs in toxicological experiments with laboratory animals, where binary observations on fetuses within a litter are often correlated with each other. In such instances, it may be of interest to test for the goodness of fit of the beta‐binomial model; this effort is complicated, however, when there is large variability among the litter sizes. We investigate a recent goodness‐of‐fit test proposed by Brooks et al. (1997,Biometrics53, 1097–1115) but find that it lacks the ability to distinguish between the beta‐binomial model and some severely non‐beta‐binomial models. Other tests and models developed in their article are quite useful and interesting but are not examined herein.
Review Times in Statistical Journals: Tilting at Windmills?
Authors: Carroll Raymond J.
Published: May 2004

Summary. Using limited data, I argue that the review times in statistics are far too long for the field to keep pace with the rapidly changing environment in science. I note that statisticians do not appear to believe in statistics because data on the review process are not widely available to members of the profession. I suggest a few changes that could be made to speed up the review process, although it would appear that a change in our culture is required before the problem will be solved.
Sensitivity Analysis for Nonrandom Dropout: A Local Influence Approach
Authors: Verbeke Geert , Molenberghs Geert , Thijs Herbert , Lesaffre Emmanuel , Kenward Michael G.
Published: May 2004

Summary.Diggle and Kenward (1994,Applied Statistics43, 49–93) proposed a selection model for continuous longitudinal data subject to nonrandom dropout. It has provoked a large debate about the role for such models. The original enthusiasm was followed by skepticism about the strong but untestable assumptions on which this type of model invariably rests. Since then, the view has emerged that these models should ideally be made part of a sensitivity analysis. This paper presents a formal and flexible approach to such a sensitivity assessment based on local influence (Cook, 1986,Journal of the Royal Statistical Society, Series B48, 133–169). The influence of perturbing a missing‐at‐random dropout model in the direction of nonrandom dropout is explored. The method is applied to data from a randomized experiment on the inhibition of testosterone production in rats.
Bias in Estimating Association Parameters for Longitudinal Binary Responses with Drop‐Outs
Authors: Fitzmaurice Garrett M. , Lipsitz Stuart R. , Molenberghs Geert , Ibrahim Joseph G.
Published: May 2004

Summary.This paper considers the impact of bias in the estimation of the association parameters for longitudinal binary responses when there are drop‐outs. A number of different estimating equation approaches are considered for the case where drop‐out cannot be assumed to be a completely random process. In particular, standard generalized estimating equations (GEE), GEE based on conditional residuals, GEE based on multivariate normal estimating equations for the covariance matrix, and second‐order estimating equations (GEEZ) are examined. These different GEE estimators are compared in terms of finite sample and asymptotic bias under a variety of drop‐out processes. Finally, the relationship between bias in the estimation of the association parameters and bias in the estimation of the mean parameters is explored.
Multiple Imputation for Multivariate Data with Missing and Below‐Threshold Measurements: Time‐Series Concentrations of Pollutants in the Arctic
Authors: Hopke Philip K. , Liu Chuanhai , Rubin Donald B.
Published: May 2004

Summary.Many chemical and environmental data sets are complicated by the existence of fully missing values or censored values known to lie below detection thresholds. For example, week‐long samples of airborne particulate matter were obtained at Alert, NWT, Canada, between 1980 and 1991, where some of the concentrations of 24 particulate constituents were coarsened in the sense of being either fully missing or below detection limits. To facilitate scientific analysis, it is appealing to create complete data by filling in missing values so that standard complete‐data methods can be applied. We briefly review commonly used strategies for handling missing values and focus on the multiple‐imputation approach, which generally leads to valid inferences when faced with missing data. Three statistical models are developed for multiply imputing the missing values of airborne particulate matter. We expect that these models are useful for creating multiple imputations in a variety of incomplete multivariate time series data sets.
Maximum Likelihood Methods for Cure Rate Models with Missing Covariates
Authors: Chen Ming‐Hui , Ibrahim Joseph G.
Published: May 2004

Summary.We propose maximum likelihood methods for parameter estimation for a novel class of semi‐parametric survival models with a cure fraction, in which the covariates are allowed to be missing. We allow the covariates to be either categorical or continuous and specify a parametric distribution for the covariates that is written as a sequence of one‐dimensional conditional distributions. We propose a novel EM algorithm for maximum likelihood estimation and derive standard errors by using Louis's formula (Louis, 1982,Journal of the Royal Statistical Society, Series B44, 226–233). Computational techniques using the Monte Carlo EM algorithm are discussed and implemented. A real data set involving a melanoma cancer clinical trial is examined in detail to demonstrate the methodology.
Semiparametric Maximum Likelihood for Measurement Error Model Regression
Authors: Schafer Daniel W.
Published: May 2004

Summary.This paper presents an EM algorithm for semiparametric likelihood analysis of linear, generalized linear, and nonlinear regression models with measurement errors in explanatory variables. A structural model is used in which probability distributions are specified for (a) the response and (b) the measurement error. A distribution is also assumed for the true explanatory variable but is left unspecified and is estimated by nonparametric maximum likelihood. For various types of extra information about the measurement error distribution, the proposed algorithm makes use of available routines that would be appropriate for likelihood analysis of (a) and (b) if the true x were available. Simulations suggest that the semiparametric maximum likelihood estimator retains a high degree of efficiency relative to the structural maximum likelihood estimator based on correct distributional assumptions and can outperform maximum likelihood based on an incorrect distributional assumption. The approach is illustrated on three examples with a variety of structures and types of extra information about the measurement error distribution.
Covariate Measurement Error Adjustment for Matched Case–Control Studies
Authors: McShane Lisa M. , Midthune Douglas N. , Dorgan Joanne F. , Freedman Laurence S. , Carroll Raymond J.
Published: May 2004

Summary. We propose a conditional scores procedure for obtaining bias‐corrected estimates of log odds ratios from matched case‐control data in which one or more covariates are subject to measurement error. The approach involves conditioning on sufficient statistics for the unobservable true covariates that are treated as fixed unknown parameters. For the case of Gaussian nondifferential measurement error, we derive a set of unbiased score equations that can then be solved to estimate the log odds ratio parameters of interest. The procedure successfully removes the bias in naive estimates, and standard error estimates are obtained by resampling methods. We present an example of the procedure applied to data from a matched case–control study of prostate cancer and serum hormone levels, and we compare its performance to that of regression calibration procedures.
Nonparametric Maximum Likelihood Estimation for Competing Risks Survival Data Subject to Interval Censoring and Truncation
Authors: Hudgens Michael G. , Satten Glen A. , Longini Ira M.
Published: May 2004

Summary.We derive the nonparametric maximum likelihood estimate (NPMLE) of the cumulative incidence functions for competing risks survival data subject to interval censoring and truncation. Since the cumulative incidence function NPMLEs give rise to an estimate of the survival distribution which can be undefined over a potentially larger set of regions than the NPMLE of the survival function obtained ignoring failure type, we consider an alternative pseudolikelihood estimator. The methods are then applied to data from a cohort of injecting drug users in Thailand susceptible to infection from HIV‐1 subtypes B and E.
Multilevel Models for Survival Analysis with Random Effects
Authors: Yau Kelvin K. W.
Published: May 2004

Summary.A method for modeling survival data with multilevel clustering is described. The Cox partial likelihood is incorporated into the generalized linear mixed model (GLMM) methodology. Parameter estimation is achieved by maximizing a log likelihood analogous to the likelihood associated with the best linear unbiased prediction (BLUP) at the initial step of estimation and is extended to obtain residual maximum likelihood (REML) estimators of the variance component. Estimating equations for a three‐level hierarchical survival model are developed in detail, and such a model is applied to analyze a set of chronic granulomatous disease (CGD) data on recurrent infections as an illustration with both hospital and patient effects being considered as random. Only the latter gives a significant contribution. A simulation study is carried out to evaluate the performance of the REML estimators. Further extension of the estimation procedure to models with an arbitrary number of levels is also discussed.
Methods for Conducting Sensitivity Analysis of Trials with Potentially Nonignorable Competing Causes of Censoring
Authors: Andrea Rotnitzky , Scharfstein Daniel , Su Ting‐Li , Robins James
Published: May 2004

Summary. We consider inference for the treatment‐arm mean difference of an outcome that would have been measured at the end of a randomized follow‐up study if, during the course of the study, patients had not initiated a nonrandomized therapy or dropped out. We argue that the treatment‐arm mean difference is not identified unless unverifiable assumptions are made. We describe identifying assumptions that are tantamount to postulating relationships between the components of a pattern‐mixture model but that can also be interpreted as imposing restrictions on the cause‐specific censoring probabilities of a selection model. We then argue that, although sufficient for identification, these assumptions are insufficient for inference due to the curse of dimensionality. We propose reducing dimensionality by specifying semiparametric cause‐specific selection models. These models are useful for conducting a sensitivity analysis to examine how inference for the treatment‐arm mean difference changes as one varies the magnitude of the cause‐specific selection bias over a plausible range. We provide methodology for conducting such sensitivity analysis and illustrate our methods with an analysis of data from the AIDS Clinical Trial Group (ACTG) study 002.
A Covariance Estimator for GEE with Improved Small‐Sample Properties
Authors: Mancl Lloyd A. , DeRouen Timothy A.
Published: May 2004

Summary. In this paper, we propose an alternative covariance estimator to the robust covariance estimator of generalized estimating equations (GEE). Hypothesis tests using the robust covariance estimator can have inflated size when the number of independent clusters is small. Resampling methods, such as the jackknife and bootstrap, have been suggested for covariance estimation when the number of clusters is small. A drawback of the resampling methods when the response is binary is that the methods can break down when the number of subjects is small due to zero or near‐zero cell counts caused by resampling. We propose a bias‐corrected covariance estimator that avoids this problem. In a small simulation study, we compare the bias‐corrected covariance estimator to the robust and jackknife covariance estimators for binary responses for situations involving 10–40 subjects with equal and unequal cluster sizes of 16–64 observations. The bias‐corrected covariance estimator gave tests with sizes close to the nominal level even when the number of subjects was 10 and cluster sizes were unequal, whereas the robust and jackknife covariance estimators gave tests with sizes that could be 2–3 times the nominal level. The methods are illustrated using data from a randomized clinical trial on treatment for bone loss in subjects with periodontal disease.
Bayesian Inference on Protective Antibody Levels Using Case‐Control Data
Authors: Carey Vincent J. , Baker Carol J. , Platt Richard
Published: May 2004

Summary. In the study of immune responses to infectious pathogens, the minimum protective antibody concentration (MPAC) is a quantity of great interest. We use case‐control data to estimate the posterior distribution of the conditional risk of disease given a lower bound on antibody concentration in an at‐risk subject. The concentration bound beyond which there is high credibility that infection risk is zero or nearly so is a candidate for the MPAC. A very simple Gibbs sampling procedure that permits inference on the risk of disease given antibody level is presented. In problems involving small numbers of patients, the procedure is shown to have favorable accuracy and robustness to choice/misspecification of priors. Frequentist evaluation indicates good coverage probabilities of credibility intervals for antibody‐dependent risk, and rules for estimation of the MPAC are illustrated with epidemiological data.
Bayesian Partitioning for Estimating Disease Risk
Authors: Denison D. G. T. , Holmes C. C.
Published: May 2004

Summary. This paper presents a Bayesian nonlinear approach for the analysis of spatial count data. It extends the Bayesian partition methodology of Holmes, Denison, and Mallick (1999, Bayesian partitioning for classification and regression, Technical Report, Imperial College, London) to handle data that involve counts. A demonstration involving incidence rates of leukemia in New York state is used to highlight the methodology. The model allows us to make probability statements on the incidence rates around point sources without making any parametric assumptions about the nature of the influence between the sources and the surrounding location.
Bayesian Semiparametric Analysis of Developmental Toxicology Data
Authors: Dominici Francesca , Parmigiani Giovanni
Published: May 2004

Summary. Modeling of developmental toxicity studies often requires simple parametric analyses of the dose‐response relationship between exposure and probability of a birth defect but poses challenges because of nonstandard distributions of birth defects for a fixed level of exposure. This article is motivated by two such experiments in which the distribution of the outcome variable is challenging to both the standard logistic model with binomial response and its parametric multistage elaborations. We approach our analysis using a Bayesian semiparametric model that we tailored specifically to developmental toxicology studies. It combines parametric dose‐response relationships with a flexible nonparametric specification of the distribution of the response, obtained via a product of Dirichlet process mixtures approach (PDPM). Our formulation achieves three goals: (1) the distribution of the response is modeled in a general way, (2) the degree to which the distribution of the response adapts nonparametrically to the observations is driven by the data, and (3) the marginal posterior distribution of the parameters of interest is available in closed form. The logistic regression model, as well as many of its extensions such as the beta‐binomial model and finite mixture models, are special cases. In the context of the two motivating examples and a simulated example, we provide model comparisons, illustrate overdispersion diagnostics that can assist model specification, show how to derive posterior distributions of the effective dose parameters and predictive distributions of response, and discuss the sensitivity of the results to the choice of the prior distribution.
On Sample Size and Inference for Two‐Stage Adaptive Designs
Authors: Liu Qing , Chi George Y. H.
Published: May 2004

Summary. Proschan and Hunsberger (1995, Biometrics51, 1315–1324) proposed a two‐stage adaptive design that maintains the Type I error rate. For practical applications, a two‐stage adaptive design is also required to achieve a desired statistical power while limiting the maximum overall sample size. In our proposal, a two‐stage adaptive design is comprised of a main stage and an extension stage, where the main stage has sufficient power to reject the null under the anticipated effect size and the extension stage allows increasing the sample size in case the true effect size is smaller than anticipated. For statistical inference, methods for obtaining the overall adjusted p‐value, point estimate and confidence intervals are developed. An exact two‐stage test procedure is also outlined for robust inference.
Modeling Diurnal Variation of Marine Populations
Authors: Hjellvik Vidar , GodøS Olav Rune , TjøSstheim Dag
Published: May 2004

Summary. A number of marine populations exhibit diurnal variations in their behavioral pattern, and this phenomenon has been studied by several authors looking at a variety of species. But to our knowledge, fully adequate statistical tools have not been used in a comprehensive and systematic way. It is the goal of this article to bring forward relevant statistical techniques and to demonstrate how they can be used. Both parametric and nonparametric methods are employed, and we concentrate on such basic statistical issues as testing for the presence of diurnal variations using a nonparametric test and on estimating and testing the shape of diurnal oscillations. We indicate how this can be used to examine the effect of light on diurnal behavior. Our methods are illustrated using data from bottom trawl catches of cod (Gadus morhua) collected during winter surveys in the Barents Sea in the period 1985–1999.
Combining Datasets to Predict the Effects of Regulation of Environmental Lead Exposure in Housing Stock
Authors: Straws Warren J. , Carroll Raymond J. , Bortnick Steven M. , Menkedick John R. , Schultz Bradley D.
Published: May 2004

Summary. A model for children's blood lead concentrations as a function of environmental lead exposures was developed by combining two nationally representative sources of data that characterize the marginal distributions of blood lead and environmental lead with a third regional dataset that contains joint measures of blood lead and environmental lead. The complicating factor addressed in this article was the fact that methods for assessing environmental lead were different in the national and regional datasets. Relying on an assumption of transportability (that although the marginal distributions of blood lead and environmental lead may be different between the regional dataset and the nation as a whole, the joint relationship between blood lead and environmental lead is the same), the model makes use of a latent variable approach to estimate the joint distribution of blood lead and environmental lead nationwide.
A Score Test for Testing a Zero‐Inflated Poisson Regression Model Against Zero‐Inflated Negative Binomial Alternatives
Authors: Ridout Martin , Hinde John , Demétrio Clarice G. B.
Published: May 2004

Summary. Count data often show a higher incidence of zero counts than would be expected if the data were Poisson distributed. Zero‐inflated Poisson regression models are a useful class of models for such data, but parameter estimates may be seriously biased if the nonzero counts are overdispersed in relation to the Poisson distribution. We therefore provide a score test for testing zero‐inflated Poisson regression models against zero‐inflated negative binomial alternatives.
Likelihood Ratio Tests for a Mixture of Two von Mises Distributions
Authors: Grimshaw Scott D. , Whiting David G. , Morris Thomas H.
Published: May 2004

Summary. It is proposed that the orientation of elongate objects, such as bones, may be used to identify the flow direction of ancient river deposits. If true, elongate objects could be of great value when ancient bedforms such as ripples and dunes are not visible. Two sandstone quarries were investigated wherein the paleoflow direction was determined from both bedforms and elongate dinosaur bones. A mixture of two von Mises distributions captures the observation that elongate bones transported under unidirectional flow conditions will align both parallel and perpendicular to the flow direction. Likelihood ratio tests for a mixture of two von Mises distributions are given. The power of these tests is investigated by simulation since the direction of dinosaur bones agrees with the primary bedforms if the hypothesis test comparing the dominant mean direction of the bones to the paleoflow direction fails to reject. The likelihood ratio test on the dominant mean direction has reasonable power. If the two mean directions in the mixture distribution are π apart, a more powerful likelihood ratio test can be used. The likelihood ratio test on the hypothesis that the two mean directions are exactly π apart is useful in determining if the assumptions of the more powerful test are satisfied.
Robust Two‐Stage Estimation in Hierarchical Nonlinear Models
Authors: Yeap Beow Yong , Davidian Marie
Published: May 2004

Summary. Hierarchical models encompass two sources of variation, namely within and among individuals in the population; thus, it is important to identify outliers that may arise at each sampling level. A two‐stage approach to analyzing nonlinear repeated measurements naturally allows parametric modeling of the respective variance structure for the intraindividual random errors and interindividual random effects. We propose a robust two‐stage procedure based on Huber's (1981, Robust Statistics) theory of M‐estimation to accommodate separately aberrant responses within an experimental unit and subjects deviating from the study population when the usual assumptions of normality are violated. A toxicology study of chronic ozone exposure in rats illustrates the impact of outliers on the population inference and hence the advantage of adopting the robust methodology. The robust weights generated by the two‐stage M‐estimation process also serve as diagnostics for gauging the relative influence of outliers at each level of the hierarchical model. A practical appeal of our proposal is the computational simplicity since the estimation algorithm may be implemented using standard statistical software with a nonlinear least squares routine and iterative capability.