Showing papers on "Random effects model published in 1997"

A joint model for survival and longitudinal data measured with error.

Abstract: The relationship between a longitudinal covariate and a failure time process can be assessed using the Cox proportional hazards regression model We consider the problem of estimating the parameters in the Cox model when the longitudinal covariate is measured infrequently and with measurement error We assume a repeated measures random effects model for the covariate process Estimates of the parameters are obtained by maximizing the joint likelihood for the covariate process and the failure time process This approach uses the available information optimally because we use both the covariate and survival data simultaneously Parameters are estimated using the expectation-maximization algorithm We argue that such a method is superior to naive methods where one maximizes the partial likelihood of the Cox model using the observed covariate values It also improves on two-stage methods where, in the first stage, empirical Bayes estimates of the covariate process are computed and then used as time-dependent covariates in a second stage to find the parameters in the Cox model that maximize the partial likelihood

Linear Mixed Models in Practice: A SAS-Oriented Approach

Abstract: 1 Introduction.- 2 An Example-Based Tour in Linear Mixed Models.- 2.1 Fixed Effects and Random Effects in Mixed Models.- 2.2 General Linear Mixed Models.- 2.3 Variance Components Estimation and Best Linear Unbiased Prediction.- 2.3.1 Variance Components Estimation.- 2.3.2 Best Linear Unbiased Prediction (BLUP).- 2.3.3 Examples and the SAS Procedure MIXED.- 2.4 Fixed Effects: Estimation and Hypotheses Testing.- 2.4.1 General Considerations.- 2.4.2 Examples and the SAS Procedure MIXED.- 2.5 Case Studies.- 2.5.1 Cell Proliferation.- 2.5.2 A Cross-Over Experiment.- 2.5.3 A Multicenter Trial.- 3 Linear Mixed Models for Longitudinal Data.- 3.1 Introduction.- 3.2 The Study of Natural History of Prostate Disease.- 3.3 A Two-Stage Analysis.- 3.4 The General Linear Mixed-Effects Model.- 3.4.1 The Model.- 3.4.2 Maximum Likelihood Estimation.- 3.4.3 Restricted Maximum Likelihood Estimation.- 3.4.4 Comparison between ML and REML Estimation.- 3.4.5 Model-Fitting Procedures.- 3.5 Example.- 3.5.1 The SAS Program.- 3.5.2 The SAS Output.- 3.5.3 Estimation Problems due to Small Variance Components.- 3.6 The RANDOM and REPEATED Statements.- 3.7 Testing and Estimating Contrasts of Fixed Effects.- 3.7.1 The CONTRAST Statement.- 3.7.2 Model Reduction.- 3.7.3 The ESTIMATE Statement.- 3.8 PROC MIXED versus PROC GLM.- 3.9 Tests for the Need of Random Effects.- 3.9.1 The Likelihood Ratio Test.- 3.9.2 Applied to the Prostate Data.- 3.10 Comparing Non-Nested Covariance Structures.- 3.11 Estimating the Random Effects.- 3.12 General Guidelines for Model Construction.- 3.12.1 Selection of a Preliminary Mean Structure.- 3.12.2 Selection of Random-Effects.- 3.12.3 Selection of Residual Covariance Structure.- 3.12.4 Model Reduction.- 3.13 Model Checks and Diagnostic Tools ?.- 3.13.1 Normality Assumption for the Random Effects ?.- 3.13.2 The Detection of Influential Subjects ?.- 3.13.3 Checking the Covariance Structure ?.- 4 Case Studies.- 4.1 Example 1: Variceal Pressures.- 4.2 Example 2: Growth Curves.- 4.3 Example 3: Blood Pressures.- 4.4 Example 4: Growth Data.- 4.4.1 Model 1.- 4.4.2 Model 2.- 4.4.3 Model 3.- 4.4.4 Graphical Exploration.- 4.4.5 Model 4.- 4.4.6 Model 5.- 4.4.7 Model 6.- 4.4.8 Model 7.- 4.4.9 Model 8.- 5 Linear Mixed Models and Missing Data.- 5.1 Introduction.- 5.2 Missing Data.- 5.2.1 Missing Data Patterns.- 5.2.2 Missing Data Mechanisms.- 5.2.3 Ignorability.- 5.3 Approaches to Incomplete Data.- 5.4 Complete Case Analysis.- 5.4.1 Growth Data.- 5.5 Simple Forms of Imputation.- 5.5.1 Last Observation Carried Forward.- 5.5.2 Imputing Unconditional Means.- 5.5.3 Buck's Method: Conditional Mean Imputation.- 5.5.4 Discussion of Imputation Techniques.- 5.6 Available Case Methods.- 5.6.1 Growth Data.- 5.7 Likelihood-Based Ignorable Analysis and PROC MIXED.- 5.7.1 Growth Data.- 5.7.2 Summary.- 5.8 How Ignorable Is Missing At Random ? ?.- 5.8.1 Information and Sampling Distributions ?.- 5.8.2 Illustration ?.- 5.8.3 Example ?.- 5.8.4 Implications for PROC MIXED.- 5.9 The Expectation-Maximization Algorithm ?.- 5.10 Multiple Imputation ?.- 5.10.1 General Theory ?.- 5.10.2 Illustration: Growth Data ?.- 5.11 Exploring the Missing Data Process.- 5.11.1 Growth Data.- 5.11.2 Informative Non-Response.- 5.11.3 OSWALD for Informative Non-Response.- A Inference for Fixed Effects.- A.1 Estimation.- A.2 Hypothesis Testing.- A.3 Determination of Degrees of Freedom.- A.4 Satterthwaite's Procedure.- B Variance Components and Standard Errors.- C Details on Table 2.10: Expected Mean Squares.- D Example 2.8: Cell Proliferation.- References.

Variance component testing in generalised linear models with random effects

Abstract: SUMMARY There is considerable interest in testing for overdispersion, correlation and heterogeneity across groups in biomedical studies In this paper, we cast the problem in the framework of generalised linear models with random effects We propose a global score test for the null hypothesis that all the variance components are zero This test is a locally asymptotically most stringent test and is robust in the special sense that the test does not require specifying the joint distribution of the random effects We also propose individual score tests and their approximations for testing the variance components separately Both tests can be easily implemented using existing statistical software We illustrate these tests with an application to the study of heterogeneity of mating success across males and females in an experiment on salamander matings, and evaluate their performance through simulation

Sampling from the posterior distribution in generalized linear mixed models

Abstract: Generalized linear mixed models provide a unified framework for treatment of exponential family regression models, overdispersed data and longitudinal studies. These problems typically involve the presence of random effects and this paper presents a new methodology for making Bayesian inference about them. The approach is simulation-based and involves the use of Markov chain Monte Carlo techniques. The usual iterative weighted least squares algorithm is extended to include a sampling step based on the Metropolis–Hastings algorithm thus providing a unified iterative scheme. Non-normal prior distributions for the regression coefficients and for the random effects distribution are considered. Random effect structures with nesting required by longitudinal studies are also considered. Particular interests concern the significance of regression coefficients and assessment of the form of the random effects. Extensions to unknown scale parameters, unknown link functions, survival and frailty models are outlined.

Practical Data Analysis for Designed Experiments

Abstract: Preface Part A: Placing Data in Context Practical Data Analysis Effect of Factors Nature of Data Summary Tables Plots for Statistics Computing Interpretation Problems Collaboration in Science Asking Questions Learning from Plots Mechanics of a Consulting Session Philosophy and Ethics Intelligence, Culture and Learning Writing Problems Experimental Design Types of Studies Designed Experiments Design Structure Treatment Structure Designs in This Book Problems Part B: Working with Groups of Data Group Summaries Graphical Summaries Estimates of Means and Variance Assumptions and Pivot Statistics Interval Estimates of Means Testing Hypotheses about Means Formal Inference on the Variance Problems Comparing Several Means Linear Contrasts of Means Overall Test of Difference Partitioning Sums of Squares Expected Mean Squares Power and Sample Size Problems Multiple Comparisons of Means Experiment- and Comparison-Wise Error Rates Comparisons Based on F-Tests Comparisons Based on Range of Means Comparisons of Comparisons Problems Part C: Sorting Out Effects with Data Factorial Designs Cell Means Models Effects Models Estimable Functions Linear Constraints General Form of Estimable Functions Problems Balanced Experiments Additive Models Full Models with Two Factors Interaction Plots Higher Orders Models Problems Model Selection Pooling Interactions Selected the "Best" Model Model Selection Criteria One Observation per Cell Tukey's Test for Interaction Problems Part D: Dealing with Imbalance Unbalanced Experiments Unequal Samples Additive Model Types I, II, III and IV Problems Missing Cells What Are Missing Cells? Connected Cells and Incomplete Designs Type IV Comparisons Latin Square Designs Fractional Factorial Designs Problems Linear Models Inference Matrix Preliminaries Ordinary Least Squares Weighted Least Squares Maximum Likelihood Restricted Maximum Likelihood Inference for Fixed Effect Models Anova and Regression Models Problems Part E: Questioning Assumptions Residual Plots Departures from Assumptions Incorrect Model Correlated Responses Unequal Variance Non-Normal Data Problems Comparisons with Unequal Variance Comparing Means When Variances Are Unequal Weighted Analysis of Variances Satterthwaite Approximation Generalized Inference Testing for Unequal Variances Problems Getting Free from Assumptions Transforming Data Comparisons Using Ranks Randomization Monte Carlo Methods Problems Part F: Regressing with Factors Ordered Groups Groups in a Line Testing for Linearity Path Analysis Diagrams Regression Calibration Classical Error in Variables Problems Parallel Lines Parallel Lines Model Adjusted Estimates Plots with Symbols Sequential Tests with Multiple Responses Sequential Tests with Driving Covariate Adjusted (Type III) Tests of Hypotheses Different Slopes for Different Groups Problems Multiple Responses Overall Tests for Group Differences Matrix Analog to F Test How Do Groups Differ? Causal Models Part G: Deciding on Fixed or Random Effects Models with Random Effects Single Factor Random Model Test for Class Variation Distribution of Sums of Squares Variance Components Grand Menu Problems General Random Models Two Factor Random Models Unbalanced Two-Factor Random Model General Random Model Quadratic Forms in Random Effects Application to Two Factor Random Model Problems Mixed Effect Models Two Factor Mixed Models General Mixed Models Problems Part H: Nesting Experimental Units Nested Designs Sub-Sampling Blocking Nested and Crossed Factors Nesting of Fixed Effects Nesting of Random Effects Problems Split Plot Design Several Views of Split Plot Split Plot Model Contrasts in a Split Plot Problems General Nested Designs Extensions of Split Plot Split Plot Imbalance in Nested Designs Covariates in Nested Designs Explained Variation in Nested Designs Problems Part I: Repeating Measures on Subjects Repeated Measures as Split Plot Repeated Measures Designs Repeated Measures Model Split Plot More or Less Expected Mean Squares under Sphericity Contrasts under Sphericity Problems Adjustments for Correlation Adjustments to Split Plot Contrasts over Time Multivariate Repeated Measures Problems Cross-Over Design Cross-Over Model Confounding in Cross-Over Designs Partition of Sum of Squares Replicated Latin Square Design General Cross-Over Designs Problems References Index

Short-term Effects of Ambient Oxidant Exposure on Mortality: A Combined Analysis within the APHEA Project

Abstract: The Air Pollution and Health: a European Approach (APHEA) project is a coordinated study of the short-term effects of air pollution on mortality and hospital admissions using data from 15 European cities, with a wide range of geographic, sociodemographic, climatic, and air quality patterns. The objective of this paper is to summarize the results of the short-term effects of ambient oxidants on daily deaths from all causes (excluding accidents). Within the APHEA project, six cities spanning Central and Western Europe provided data on daily deaths and NO2 and/or O3 levels. The data were analyzed by each center separately following a standardized methodology to ensure comparability of results. Poisson autoregressive models allowing for overdispersion were fitted. Fixed effects models were used to pool the individual regression coefficients when there was no evidence of heterogeneity among the cities and random effects models otherwise. Factors possibly correlated with heterogeneity were also investigated. Significant positive associations were found between daily deaths and both NO2 and O3. Increases of 50 micrograms/m3 in NO2 (1-hour maximum) or O3 (1-hour maximum) were associated with a 1.3% (95% confidence interval 0.9-1.8) and 2.9% (95% confidence interval 1.0-4.9) increase in the daily number of deaths, respectively. Stratified analysis of NO2 effects by low and high levels of black smoke or O3 showed no significant evidence for an interaction within each city. However, there was a tendency for larger effects of NO2 in cities with higher levels of black smoke. The pooled estimate for the O3 effect was only slightly reduced, whereas the one for NO2 was almost halved (although it remained significant) when two pollutant models including black smoke were applied. The internal validity (consistency across cities) as well as the external validity (similarities with other published studies) of our results on the O3 effect support the hypothesis of a causal relation between O3 and all cause daily mortality. However, the short-term effects of NO2 on mortality may be confounded by other vehicle-derived pollutants. Thus, the issue of independent NO2 effects requires additional investigation.

Incorporating variability in estimates of heterogeneity in the random effects model in meta‐analysis

Abstract: When combining results from separate investigations in a meta-analysis, random effects methods enable the modelling of differences between studies by incorporating a heterogeneity parameter tau 2 that accounts explicitly for across-study variation. We develop a simple form for the variance of Cochran's homogeneity statistic Q, leading to interval estimation of tau 2 utilizing an approximating distribution for Q; this enables us to extend the point estimation of DerSimonian and Laird. We also develop asymptotic likelihood methods and compared them with this method. We then use these approximating distributions to give a new method of calculating the weight given to the individual studies' results when estimating the overall mean which takes into account variation in these point estimates of tau 2. Two examples illustrate the methods presented, where we show that the new weighting scheme is between the standard fixed and random effects models in down-weighting the results of large studies and up-weighting those of small studies.

Statistical Methods for Health Sciences

Abstract: COMPARING GROUP MEANS WHEN THE STANDARD ASSUMPTIONS ARE VIOLATED Introduction Non-Normality Heterogeneity of Variances Non-Independence STATISTICAL ANALYSIS OF MEASUREMENTS RELIABILITY: THE CASE OF INTERVAL SCALE MEASUREMENTS Introduction Models for Reliability Studies Case 1: The One-Way Random Effects Model Case 2: The Two-Way Random Effects Model Case 3: The Two-Way Mixed Effects Model Covariate Adjustment in the One-Way Random Effects Model Comparison of Measurement Methods Comparing the Reliability of Two Methods Comparing the Precisions of Two Methods Concordance Correlation as a Measure of Reproducibility STATISTICAL ANALYSIS OF CROSS-CLASSIFIED DATA Introduction Measures of Association in 2x2 Tables Cross Sectional Sampling (Historical Cohort Studies) Cohort and Case-Control Studies Statistical Inference on Odds Ratio Significance Tests Interval Estimation Analysis of Several 2x2 Contingency Tables Statistical Methods for Bias Reduction Analysis of Matched Pairs (One Case and One Control) Estimating the Odds Ratio Testing the Equality of Marginal Distributions Statistical Analysis of Clustered Binary Data Testing Homogeneity Inference on the Common Odds Ratio Measure of Interclinician Agreement for Categorical Data Agreement in 2x2 Tables (Two Clinicians and Two Categories) Confidence Interval on Kappa in 2x2 Table Agreement between Two Raters with Multiple Categories More than Two Clinicians Assessment of Bias Statistical Analysis of Medical Screening Tests Introduction Estimating Prevalence Estimating Predictive Value Positive and Predictive Value Negative Estimation in Double Sampling Dependent Screening Tests (Multiple Readings) Estimation of Parameters Special Topics Group Testing Evaluating the Performance of Medical Screening Tests in the Absence of a Gold Standard (Latent Class Models) LOGISTIC REGRESSION Introduction The Logistic Transformation Coding Categorical Explanatory Variables and Interpretation of Coefficients Interaction and Confounding The Goodness of Fit and Model Comparisons Pearson's X2 - Statistic The Likelihood Ratio Criterion (Deviance) Logistic Regression of Clustered Binary Data Introduction Intracluster Effects Analysis of Overdispersed Binomial Data Full Likelihood Models Estimating Equations Approach Logistic Regression for Case-Control Studies Cohort versus Case-Control Models Matched Analysis Conditional Likelihood Fitting Matched Case-Control Study Data in SAS THE ANALYSIS OF TIME SERIES Introduction Simple Descriptive Methods Fundamental Concepts in the Analysis of Time Series Stochastic Process Stationary Series The Autocovariance and Autocorrelation Functions Models for Stationary Time Series Autoregressive Processes Moving Average Processes The Mixed Autoregressive Moving Average Process Models for Nonstationary Time Series Nonstationarity in the Mean Differencing Arima Models Nonstationarity in the Variance Model Specification and Parameter Estimation Specification Estimation Forecasting The One-Way and Two-Way Analysis of Variance with Time-Series Data Introduction One-Way Anova with Correlated Errors Two-Way Anova with Correlated Errors REPEATED MEASURES ANALYSIS Introduction Examples Effect of Mycobacterium Inoculation on Weight Variation in Teenage Pregnancy Rates (TAPR) in Canada Methods for the Analysis of Repeated Measures Experiments Basic Models Hypothesis Testing Recommended Analysis for Example A Recommended Analysis for Example B Missing Observations The Generalized Estimating Equations Approach

Random Effects Probit and Logistic Regression Models for Three-Level Data

Abstract: In analysis of binary data from clustered and longitudinal studies, random effect models have been recently developed to accommodate two-level problems such as subjects nested within clusters or repeated classifications within subjects. Unfortunately, these models cannot be applied to three-level problems that occur frequently in practice. For example, multicenter longitudinal clinical trials involve repeated assessments within individuals and individuals are nested within study centers. This combination of clustered and longitudinal data represents the classic three-level problem in biometry. Similarly, in prevention studies, various educational programs designed to minimize risk taking behavior (e.g., smoking prevention and cessation) may be compared where randomization to various design conditions is at the level of the school and the intervention is performed at the level of the classroom. Previous statistical approaches to the three-level problem for binary response data have either ignored one level of nesting, treated it as a fixed effect, or used first- and second-order Taylor series expansions of the logarithm of the conditional likelihood to linearize these models and estimate model parameters using more conventional procedures for measurement data. Recent studies indicate that these approximate solutions exhibit considerable bias and provide little advantage over use of traditional logistic regression analysis ignoring the hierarchical structure. In this paper, we generalize earlier results for two-level random effects probit and logistic regression models to the three-level case. Parameter estimation is based on full-information maximum marginal likelihood estimation (MMLE) using numerical quadrature to approximate the multiple random effects. The model is illustrated using data from 135 classrooms from 28 schools on the effects of two smoking cessation interventions.

A nested frailty model for survival data, with an application to the study of child survival in northeast Brazil.

Abstract: This article presents a multivariate hazard model for survival data that are clustered at two hierarchical levels. The model provides corrected parameter estimates and standard errors, as well as estimates of the intragroup correlation at both levels. The model is estimated using the expectation-maximization (EM) algorithm. We apply the model to an analysis of the covariates of child survival using survey data from northeast Brazil collected via a hierarchically clustered sampling scheme. We find that family and community frailty effects are fairly small in magnitude but are of importance because they alter the results in a systematic pattern.

A Random-Effects Model for Multiple Characteristics with Possibly Missing Data

Abstract: The use of random-effects models for the analysis of longitudinal data with missing responses has been discussed by several authors. This article extends the random-effects model for a single characteristic to the case of multiple characteristics, allowing for arbitrary patterns of observed data. Two different structures for the covariance matrix of measurement error are considered: uncorrelated error between responses and correlation of error terms at the same measurement times. Parameters for this model are estimated via the EM algorithm. The set of equations for this estimation procedure is derived; these equations are appropriately modified to deal with missing data. The methodology is illustrated with an example from clinical trials.

Hierarchical Generalized Linear Models and Frailty Models with Bayesian Nonparametric Mixing

Abstract: SUMMARY This paper proposes Bayesian nonparametric mixing for some well-known and popular models. The distribution of the observations is assumed to contain an unknown mixed effects term which includes a fixed effects term, a function of the observed covariates, and an additive or multiplicative random effects term. Typically these random effects are assumed to be independent of the observed covariates and independent and identically distributed from a distribution from some known parametric family. This assumption may be suspect if either there is interaction between observed covariates and unobserved covariates or the fixed effects predictor of observed covariates is misspecified. Another cause for concern might be simply that the covariates affect more than just the location of the mixed effects distribution. As a consequence the distribution of the random effects could be highly irregular in modality and skewness leaving parametric families unable to model the distribution adequately. This paper therefore proposes a Bayesian nonparametric prior for the random effects to capture possible deviances in modality and skewness and to explore the observed covariates' effect on the distribution of the mixed effects.

Bayesian Approach for Nonlinear Random Effects Models

Abstract: SUMMARY In this paper, we propose a general model-determination strategy based on Bayesian methods for nonlinear mixed effects models. Adopting an exploratory data analysis viewpoint, we develop diagnostic tools based on conditional predictive ordinates that conveniently get tied in with Markov chain Monte Carlo fitting of models. Sampling-based methods are used to carry out these diagnostics. Two examples are presented to illustrate the effectiveness of these criteria. The first one is the famous Langmuir equation, commonly used in pharmacokinetic models, whereas the second model is used in the growth curve model for longitudinal data.

A discrete survival model with random effects : an application to time to pregnancy

Abstract: Time to pregnancy, the number of menstrual cycles it takes a couple to conceive, and various covariates have been collected among couples ultimately achieving conception. To assess the influence of the covariates, we constructed a discrete survival model that allows time-dependent covariates. A random effect was included to account for unobserved heterogeneity. The collected waiting times are obtained through retrospective ascertainment and are analyzed as truncated data. Maximum likelihood estimation was implemented by Fisher scoring through iteratively reweighted least squares.

Now You See It, Now You Don't A Comparison of Traditional Versus Random-Effects Regression Models in the Analysis of Longitudinal Follow-Up Data From a Clinical Trial

Abstract: To illustrate the limitations of commonly used methods of handling missing data when using traditional analysis of variance (ANOVA) models and highlight the relative advantages of random-effects regression models, multiple analytic strategies were applied to follow-up data from a clinical trial. Traditional ANOVA and random-effects models produced similar results when underlying assumptions were met and data were complete. However, analyses based on subsamples, to which investigators would have been limited with traditional models, would have led to different conclusions about treatment effects over time than analyses based on intention-to-treat samples using random-effects regression models. These findings underscore the advantages of models that use all data collected and the importance of complete data collection to minimize sample bias.

Influence Diagnostics for Linear Longitudinal Models

Abstract: Influence diagnostics are important for analyzing cross-sectional regression studies, because they allow the analyst to understand the impact of individual observations on the estimated regression model. In this article we consider the role of influence diagnostics in subject-specific longitudinal models. Diagnostics are proposed under both fixed and random subject effects. Our approach is based on subject deletion, which in this setting involves deleting a group of correlated observations. We develop partial influence statistics to understand the combined impact of observations from a subject on population parameters. Simple computational formulas make the procedures feasible. Finally, we illustrate the use of our new influence statistics by examining a dataset to model a taxpayer's charitable givings.

Maximum likelihood estimation for probit-linear mixed models with correlated random effects

Abstract: The probit-normal model for binary data (McCulloch, 1994, Journal of the American Statistical Association 89, 330-335) is extended to allow correlated random effects. To obtain maximum likelihood estimates, we use the EM algorithm with its M-step greatly simplified under the assumption of a probit link and its E-step made feasible by Gibbs sampling. Standard errors are calculated by inverting a Monte Carlo approximation of the information matrix rather than via the SEM algorithm. A method is also suggested that accounts for the Monte Carlo variation explicitly. As an illustration, we present a new analysis of the famous salamander mating data. Unlike previous analyses, we find it necessary to introduce different variance components for different species of animals. Finally, we consider models with correlated errors as well as correlated random effects.

Credibility theory and generalized linear models

Abstract: Thus paper shows how credibility theory can be encompassed within the theory of Hierarchical Genezahzed Linear Models. It is shown that credtbdnty estimates are obtained by including random effects m the model. The framework of Hierarchical Generalized Linear Models allows a more extensive range of models to be used than straightforward credibility theory. The model fitting and testing procedures can be carried out using a standard statistical package Thus, the paper contributes a further range of models which may be useful m a wide range of actuarial apphcations, including premmm rating and clmms reserving

A stochastic model for the analysis of bivariate longitudinal AIDS data.

Abstract: We present a model for multivariate repeated measures that incorporates random effects, correlated stochastic processes, and measurement errors. The model is a multivariate generalization of the model for univariate longitudinal data given by Taylor, Cumberland, and Sy (1994, Journal of the American Statistical Association 89, 727-736). The stochastic process used in this paper is the multivariate integrated Ornstein-Uhlenbeck (OU) process, which includes Brownian motion and a random effects model as special limiting cases. This process is an underlying continuous-time autoregressive order [AR(1)] process for the derivatives of the multivariate observations. The model allows unequally spaced observations and missing values for some of the variables. We analyze CD4 T-cell and beta-2-microglobulin measurements of the seroconverters at multiple time points from the Los Angeles section of the Multicenter AIDS Cohort Study. The model allows us to investigate the relationship between CD4 and beta-2-microglobulin through the correlations between their random effects and their serial correlation. The data suggest that CD4 and beta-2-microglobulin follow a bivariate Brownian motion process. The fit of the model implies that an increase in beta-2-microglobulin is associated with a decrease in future CD4 but not vice versa, agreeing with immunologic postulates about the relationship between these two variables.

A prospectively planned cumulative meta‐analysis applied to a series of concurrent clinical trials

Abstract: Sequential designs are now a familiar part of clinical trial methodology. In particular, the triangular test has been used in several individual studies. Methods of combining studies are also well-known from the literature on meta-analysis. However, the combination of the two approaches is new. Consider the situation where a series of studies is to be conducted, following broadly similar protocols comparing a new treatment with a control treatment. In order to obtain an answer as quickly as possible to an efficacy or safety question it may be desirable to perform a cumulative meta-analysis on one particular variable. This could, for example, be the primary efficacy variable, an expensive assessment conducted in only a subgroup of patients, or a serious side-effect. To allow for the size of the treatment difference varying from study to study we might wish to provide a global estimate. Hence a random effects combined analysis, within a sequential framework, would appear to be appropriate. A methodology which utilizes efficient score statistics and Fisher's information is presented. Simulations show that the proposed methodology will achieve the specified error probabilities with reasonable accuracy provided that any random effect is relatively small. Ignoring random effects when they are present can lead to inaccuracies. A simulated example illustrates a number of practical issues.

Proceedings of the First Seattle Symposium in Biostatistics: Survival Analysis

Abstract: Some remarks on the analysis of survival data.- Multivariate failure time data: Representation and analysis.- Analysis of multivariate survival times with non-proportional hazards models.- Analysis of mean and rate functions for recurrent events.- Extending the Cox model.- Model-based and/or marginal analysis for multiple event-time data.- Artificial insemination by donor: discrete time survival data with crossed and nested random effects.- Interval censored survival data: A review of recent progress.- Singly and doubly censored current status data with extensions to multistate counting processes.- Additive hazards regression models for survival data.- Some exploratory tools for survival analysis.- Survival analysis in the regulatory setting.- Proposed strategies for designing and analyzing sepsis trials.- Coarsening at random: characterizations, conjectures, counter-examples.- Sequential models for coarsening and missingness.- Addresses for Contact Authors.- List of Referees.

Generalized Score Test of Homogeneity Based on Correlated Random Effects Models

Abstract: SUMMARY We present a family of tests based on correlated random effects models which provides a synthesis and a generalization of recent work on homogeneity testing. In these models each subject has a particular random effect, but the random effects between subjects are correlated. We derive the general form of the score statistic for testing that the random effects have a variance equal to 0. We apply this result to both parametric and semiparametric models. In both cases we show that under certain conditions the score statistic has an asymptotic normal distribution. We consider several applications of this theory, including overdispersion, heterogeneity between groups, spatial correlations and genetic linkage.

Bivariate modelling of clustered continuous and ordered categorical outcomes.

Abstract: Simultaneous observation of continuous and ordered categorical outcomes for each subject is common in biomedical research but multivariate analysis of the data is complicated by the multiple data types. Here we construct a model for the joint distribution of bivariate continuous and ordinal outcomes by applying the concept of latent variables to a multivariate normal distribution. The approach is then extended to allow for clustering of the bivariate outcomes. The model can be parameterized in a way that allows writing the joint distribution as a product of a standard random effects model for the continuous variable and a correlated cumulative probit model for the ordinal outcome. This factorization suggests convenient parameter estimation using estimating equations. Foetal weight and malformation data from a developmental toxicity experiment illustrate the results.

Linear mixed models with heterogeneous within-cluster variances

Abstract: This paper describes an extension of linear mixed models to allow for heterogeneous within-cluster variances in the analysis of clustered data. Unbiased estimating equations based on quasilikelihood/pseudolikelihood and method of moments are introduced and are shown to give consistent estimators of the regression coefficients, variance components, and heterogeneity parameter under regularity conditions. Cluster-specific random effects and variances are predicted by the posterior modes. The method is illustrated through an analysis of menstrual diary data and its properties are evaluated in a simulation study.

Panel Estimators to Combine Revealed and Stated Preference Dichotomous Choice Data

Abstract: Combining stated and revealed preference data often involves multiple responses from the same individual. Panel estimators are appropriate to jointly model the decision to actually visit at current trip costs, the intention to visit at hypothetically higher trip costs, and the intention to visit at proposed quality levels. To incorporate data on all three choices, the random effects probit model is used to estimate the economic value of changes in instream flow. This model illustrates how the complementarity of revealed and stated preference data allows including of instream flow as a covariate in the model and calculating value under alternative flow regimes.

Exact confidence intervals for a variance ratio (or heritability) in a mixed linear model

Abstract: A family of procedures is given to construct confidence intervals for the heritability coefficient in a mixed linear model. The procedures are applicable for constructing confidence intervals for a ratio of variance components in a mixed linear model having two sources of variation. If the random effects are correlated, the procedure is valid even when there are zero degrees of freedom for error. The resulting intervals are evaluated in terms of bias and expected length. A sufficient condition for local unbiasedness is given and a numerical procedure is discussed for computing expected lengths. The investigator may select the best confidence interval procedure from the family of procedures based on these criteria. Computer software for obtaining the best interval is available from the authors.

A meta-analysis of the relation between cumulative exposure to asbestos and relative risk of lung cancer.

Abstract: OBJECTIVES: To obtain summary measures of the relation between cumulative exposure to asbestos and relative risk of lung cancer from published studies of exposed cohorts, and to explore the sources of heterogeneity in the dose-response coefficient with data available in these publications. METHODS: 15 cohorts in which the dose-response relation between cumulative exposure to asbestos and relative risk of lung cancer has been reported were identified. Linear dose-response models were applied, with intercepts either specific to the cohort or constrained by a random effects model; and with slopes specific to the cohort, constrained to be identical between cohorts (fixed effect), or constrained by a random effects model. Maximum likelihood techniques were used for the fitting procedures and to investigate sources of heterogeneity in the cohort specific dose-response relations. RESULTS: Estimates of the study specific dose-response coefficient (kappa 1.i) ranged from zero to 42 x 10(-3) ml/fibre-year (ml/f-y). Under the fixed effect model, a maximum likelihood estimate of the summary measure of the coefficient (k1) equal to 0.42 x 10(-3) (95% confidence interval (95% CI) 0.22 to 0.69 x 10(-3)) ml/f-y was obtained. Under the random effects model, implemented because there was substantial heterogeneity in the estimates of kappa 1.i and the zero dose intercepts (Ai), a maximum likelihood estimate of k1 equal to 2.6 x 10(-3) (95% CI 0.65 to 7.4 x 10(-3)) ml/f-y, and a maximum likelihood estimate of A equal to 1.36 (95% CI 1.05 to 1.76) were found. Industry category, dose measurements, tobacco habits, and standardisation procedures were identified as sources of heterogeneity. CONCLUSIONS: The appropriate summary measure of the relation between cumulative exposure to asbestos and relative risk of lung cancer depends on the context in which the measure will be applied and the prior beliefs of those applying the measure. In most situations, the summary measure of effect obtained under the random effects model is recommended. Under this model, potency, k1, is fourfold lower than that calculated by the United States Occupational Safety and Health Administration.