Showing papers on "Random effects model published in 2003"

Improved tests for a random effects meta-regression with a single covariate

Abstract: The explanation of heterogeneity plays an important role in meta-analysis. The random effects meta-regression model allows the inclusion of trial-specific covariates which may explain a part of the heterogeneity. We examine the commonly used tests on the parameters in the random effects meta-regression with one covariate and propose some new test statistics based on an improved estimator of the variance of the parameter estimates. The approximation of the distribution of the newly proposed tests is based on some theoretical considerations. Moreover, the newly proposed tests can easily be extended to the case of more than one covariate. In a simulation study, we compare the tests with regard to their actual significance level and we consider the log relative risk as the parameter of interest. Our simulation study reflects the meta-analysis of the efficacy of a vaccine for the prevention of tuberculosis originally discussed in Berkey et al. The simulation study shows that the newly proposed tests are superior to the commonly used test in holding the nominal significance level.

Specification and Estimation of Spatial Panel Data Models

Abstract: This article provides a survey of the specification and estimation of spatial panel data models. These models include spatial error autocorrelation, or the specification is extended with a spatially lagged dependent variable. In particular, the author focuses on the specification and estimation of four panel data models commonly used in applied research: the fixed effects model, the random effects model, the fixed coefficients model, and the random coefficients model. The survey discusses the asymptotic properties of the estimators and provides guidance with respect to the estimation procedures, which should be useful for practitioners.

Generalized Linear Mixed Models

Abstract: This article provides an overview of generalized linear mixed models (GLMMs), how they are fit to data, and the inferences possible when using them. GLMMs are a class of statistical models that handle a wide variety of distributions for the outcome, accommodate nonlinear models, and model correlated data. As regression methods, they are not only capable of estimation and testing of covariate effects but also can be used to draw inferences about correlation structures in the data and are able to calculate predicted values that take into account not only covariates but also observed outcomes. We briefly describe software available for fitting GLMMs.

Lower level mediation in multilevel models.

Abstract: Multilevel models are increasingly used to estimate models for hierarchical and repeated measures data. The authors discuss a model in which there is mediation at the lower level and the mediational links vary randomly across upper level units. One repeated measures example is a case in which a person's daily stressors affect his or her coping efforts, which affect his or her mood, and both links vary randomly across persons. Where there is mediation at the lower level and the mediational links vary randomly across upper level units, the formulas for the indirect effect and its standard error must be modified to include the covariance between the random effects. Because no standard method can estimate such a model, the authors developed an ad hoc method that is illustrated with real and simulated data. Limitations of this method and characteristics of an ideal method are discussed.

Distinguishing between Heterogeneity and Inefficiency: Stochastic Frontier Analysis of the World Health Organization S Panel Data on National Health Care Systems

Abstract: The most commonly used approaches to parametric (stochastic frontier) analysis of efficiency in panel data, notably the fixed and random effects models, fail to distinguish between cross individual heterogeneity and inefficiency. This blending of effects is particularly problematic in the World Health Organization s (WHO) panel data set on health care delivery, which is a 191 country, five year panel. The wide variation in cultural and economic characteristics of the worldwide sample of countries produces a large amount of unmeasured heterogeneity in the data. Familiar approaches to inefficiency estimation mistakenly measure that heterogeneity as inefficiency. This study will examine a large number of recently developed alternative approaches to stochastic frontier analysis with panel data, and apply some of them to the WHO data. A more general, flexible model and several measured indicators of cross country heterogeneity are added to the analysis done by previous researchers. Results suggest that in these data, there is considerable evidence of heterogeneity that in other studies using the same data, has masqueraded as inefficiency. Our results differ substantially from those obtained by several earlier researchers.

Combining multiple microarray studies and modeling interstudy variation

Abstract: We have established a method for systematic integration of multiple microarray datasets. The method was applied to two different sets of cancer profiling studies. The change of gene expression in cancer was expressed as 'effect size', a standardized index measuring the magnitude of a treatment or covariate effect. The effect sizes were combined to obtain the estimate of the overall mean. The statistical significance was determined by a permutation test extended to multiple datasets. It was shown that the data integration promotes the discovery of small but consistent expression changes with increased sensitivity and reliability. The effect size methods provided the efficient modeling framework for addressing interstudy variation as well. Based on the result of homogeneity tests, a fixed effects model was adopted for one set of datasets that had been created in controlled experimental conditions. By contrast, a random effects model was shown to be appropriate for the other set of datasets that had been published by independent groups. We also developed an alternative modeling procedure based on a Bayesian approach, which would offer flexibility and robustness compared to the classical procedure.

A mixed-effects multinomial logistic regression model.

Abstract: A mixed-effects multinomial logistic regression model is described for analysis of clustered or longitudinal nominal or ordinal response data. The model is parameterized to allow flexibility in the choice of contrasts used to represent comparisons across the response categories. Estimation is achieved using a maximum marginal likelihood (MML) solution that uses quadrature to numerically integrate over the distribution of random effects. An analysis of a psychiatric data set, in which homeless adults with serious mental illness are repeatedly classified in terms of their living arrangement, is used to illustrate features of the model.

Environmental Kuznets Curve for sulfur: evidence using GMM estimation and random coefficient panel data models

Abstract: The purpose of this study is to test empirically the hypothesis of the inverted U-shaped relationship between environmental damage from sulfur emissions and economic growth as expressed by GDP. Using a large database of panel data consisting of 73 OECD and non-OECD countries for 31 years (1960–1990) we apply for the first time random coefficients and Arellano-Bond Generalized Method of Moments (A–B GMM) econometric methods. Our findings indicate that the EKC hypothesis is not rejected in the case of the A–B GMM. On the other hand there is no support for an EKC in the case of using a random coefficients model. Our turning points range from 6230/c. These results are completely different compared to the results derived using the same database and fixed and random effects models.

Frailty modeling for spatially correlated survival data, with application to infant mortality in Minnesota.

Abstract: SUMMARY The use of survival models involving a random effect or ‘frailty’ term is becoming more common. Usually the random effects are assumed to represent different clusters, and clusters are assumed to be independent. In this paper, we consider random effects corresponding to clusters that are spatially arranged, such as clinical sites or geographical regions. That is, we might suspect that random effects corresponding to strata in closer proximity to each other might also be similar in magnitude. Such spatial arrangement of the strata can be modeled in several ways, but we group these ways into two general settings: geostatistical approaches, where we use the exact geographic locations (e.g. latitude and longitude) of the strata, and lattice approaches, where we use only the positions of the strata relative to each other (e.g. which counties neighbor which others). We compare our approaches in the context of a dataset on infant mortality in Minnesota counties between 1992 and 1996. Our main substantive goal here is to explain the pattern of infant mortality using important covariates (sex, race, birth weight, age of mother, etc.) while accounting for possible (spatially correlated) differences in hazard among the counties. We use the GIS ArcView to map resulting fitted hazard rates, to help search for possible lingering spatial correlation. The DIC criterion (Spiegelhalter et al. ,J ournal of the Royal Statistical Society, Series B 2002, to appear) is used to choose among various competing models. We investigate the quality of fit of our chosen model, and compare its results when used to investigate neonatal versus post-neonatal mortality. We also compare use of our time-to-event outcome survival model with the simpler dichotomous outcome logistic model. Finally, we summarize our findings and suggest directions for future research.

Incentive effects in the demand for health care: a bivariate panel count data estimation

Abstract: This paper contributes in three dimensions to the literature on health care demand. First, it features the first application of a bivariate random effects estimator in a count data setting, to permit the efficient estimation of this type of model with panel data. Second, it provides an innovative test of adverse selection and confirms that high-risk individuals are more likely to acquire supplemental add-on insurance. Third, the estimations yield that in accordance with the theory of moral hazard, we observe a much lower frequency of doctor visits among the self-employed, and among mothers of small children. Copyright © 2002 John Wiley & Sons, Ltd.

A Multivariate, Multilevel Rasch Model with Application to Self–Reported Criminal Behavior

Abstract: In studying correlates of social behavior, attitudes, and beliefs, a measurement model is required to combine information across a large number of item responses. Multiple constructs are often of interest, and covariates are often multilevel (e.g., measured at the person and neighborhood level). Some item-level missing data can be expected. This paper proposes a multivariate, multilevel Rasch model with random effects for these purposes and illustrates its application to self-reports of criminal behavior. Under assumptions of conditional independence and additivity, the approach enables the investigator to calibrate the items and persons on an interval scale, assess reliability at the person and neighborhood levels, study the correlations among crime types at each level, assess the proportion of variation in each crime type that lies at each level, incorporate covariates at each level, and accommodate data missing at random. Using data on 20 item responses from 2842 adolescents ages 9 to 18 nested within ...

Shrinkage Estimation for Functional Principal Component Scores with Application to the Population Kinetics of Plasma Folate

Abstract: We present the application of a nonparametric method to performing functional principal component analysis for functional curve data that consist of measurements of a random trajectory for a sample of subjects. This design typically consists of an irregular grid of time points on which repeated measurements are taken for a number of subjects. We introduce shrinkage estimates for the functional principal component scores that serve as the random effects in the model. Scatterplot smoothing methods are used to estimate the mean function and covariance surface of this model. We propose improved estimation in the neighborhood of and at the diagonal of the covariance surface, where the measurement errors are reflected. The presence of additive measurement errors motivates shrinkage estimates for the functional principal component scores. Shrinkage estimates are developed through best linear prediction and in a generalized version, aiming at minimizing one-curve-leave-out prediction error. The estimation of individual trajectories combines data obtained from that individual as well as all other individuals. We apply our methods to new data regarding the analysis of the level of 14C-folate in plasma as a function of time since dosing of healthy adults with a small tracer dose of 14C-folic acid. A time transformation was incorporated to handle design irregularity concerning the time points on which the measurements were taken. The proposed methodology, incorporating shrinkage and data-adaptive features, is seen to be well suited for describing population kinetics of 14C-folate-specific activity and random effects, and can also be applied to other functional data analysis problems.

Approximate cross-validatory predictive checks in disease mapping models.

Abstract: When fitting complex hierarchical disease mapping models, it can be important to identify regions that diverge from the assumed model. Since full leave-one-out cross-validatory assessment is extremely time-consuming when using Markov chain Monte Carlo (MCMC) estimation methods, Stern and Cressie consider an importance sampling approximation. We show that this can be improved upon through replication of both random effects and data. Our approach is simple to apply, entirely generic, and may aid the criticism of any Bayesian hierarchical model.

Multivariate meta-analysis

Abstract: Meta-analysis is now a standard statistical tool for assessing the overall strength and interesting features of a relationship, on the basis of multiple independent studies. There is, however, recent acknowledgement of the fact that in many applications responses are rarely uniquely determined. Hence there has been some change of focus from a single response to the analysis of multiple outcomes. In this paper we propose and evaluate three Bayesian multivariate meta-analysis models: two multivariate analogues of the traditional univariate random effects models which make different assumptions about the relationships between studies and estimates, and a multivariate random effects model which is a Bayesian adaptation of the mixed model approach. Our preferred method is then illustrated through an analysis of a new data set on parental smoking and two health outcomes (asthma and lower respiratory disease) in children.

Random effects Cox models: A Poisson modelling approach

Abstract: SUMMARY We propose a Poisson modelling approach to nested random effects Cox proportional hazards models. An important feature of this approach is that the principal results depend only on the first and second moments of the unobserved random effects. The orthodox best linear unbiased predictor approach to random effects Poisson modelling techniques enables us to justify appropriate consistency and optimality. The explicit expressions for the random effects given by our approach facilitate incorporation of a relatively large number of random effects. The use of the proposed methods is illustrated through the reanalysis of data from a large-scale cohort study of particulate air pollution and mortality previously reported by Pope et al. (1995).

Further Developments of the Fisher Information Matrix in Nonlinear Mixed Effects Models with Evaluation in Population Pharmacokinetics

Abstract: We extend the development of the expression of the Fisher information matrix in nonlinear mixed effects models for designs evaluation. We consider the dependence of the marginal variance of the observations with the mean parameters and assume an heteroscedastic variance error model. Complex models with interoccasions variability and parameters quantifying the influence of covariates are introduced. Two methods using a Taylor expansion of the model around the expectation of the random effects or a simulated value, using then Monte Carlo integration, are proposed and compared. Relevance of the resulting standard errors is investigated in a simulation study with NONMEM.

The use of fixed- and random-effects models for classifying hospitals as mortality outliers: a Monte Carlo assessment.

Abstract: Background. There is an increasing movement towards the release of hospital “report-cards.” However, there is a paucity of research into the abilities of the different methods to correctly classify hospitals as performance outliers.Objective.To examine the ability of risk-adjusted mortality rates computed using conventional logistic regression and random-effects logistic regression models to correctly identify hospitals that have higher than acceptable mortality.Research Design.Monte Carlo simulations.Measures.Sensitivity, specificity, and positive predictive value of a classification as a high-outlier for identifying hospitals with higher than acceptable mortality rates.Results.When the distribution of hospital-specific log-odds of death was normal, random-effects models had greater specificity and positive predictive value than fixed-effects models. However, fixed-effects models had greater sensitivity than random-effects models.Conclusions.Researchers and policy makers need to carefully consider the ba...

Matching conditional and marginal shapes in binary random intercept models using a bridge distribution function

Abstract: SUMMARY Random effects logistic regression models are often used to model clustered binary response data. Regression parameters in these models have a conditional, subject-specific interpretation in that they quantify regression effects for each cluster. Very often, the logistic functional shape conditional on the random effects does not carry over to the marginal scale. Thus, parameters in these models usually do not have an explicit marginal, population-averaged interpretation. We study a bridge distribution function for the random effect in the random intercept logistic regression model. Under this distributional assumption, the marginal functional shape is still of logistic form, and thus regression parameters have an explicit marginal interpretation. The main advantage of this approach is that likelihood inference can be obtained for either marginal or conditional regression inference within a single model framework. The generality of the results and some properties of the bridge distribution functions are discussed. An example is used for illustration.

Functional quasi-likelihood regression models with smooth random effects

Abstract: Summary. We propose a class of semiparametric functional regression models to describe the influence of vector-valued covariates on a sample of response curves. Each observed curve is viewed as the realization of a random process, composed of an overall mean function and random components. The finite dimensional covariates influence the random components of the eigenfunction expansion through single-index models that include unknown smooth link and variance functions. The parametric components of the single-index models are estimated via quasi-score estimating equations with link and variance functions being estimated nonparametrically. We obtain several basic asymptotic results. The functional regression models proposed are illustrated with the analysis of a data set consisting of egg laying curves for 1000 female Mediterranean fruit-flies (medflies).

Developing a well-behaved dynamic site equation using a modified Hossfeld IV function y3 = (axm)/(c + xm-1), a simplified mixed-model and scant subalpine fir data

Abstract: I developed a dynamic height growth model by using a simplified form of mixed effects modeling and subalpine fir (Abies lasiocarpa [Hook.] Nutt.) stem analysis data. The new dynamic equation uses directly heights at any age to predict consistent heights (e.g., y 2 = f(t 2 ,t 1 ,y 1 ) ⇔ y 1 = f(t 1 ,t 2 ,y 2 )) and f(t 3 ,t 1 ,y 1 ) = f(t 3 ,t 2 ,f(t 2 ,t 1 ,y 1 ))), and therefore constitutes compatible site indexand height models in one common equation. The parametersforthe model were estimated by analysis of fixed and random effects with corrections for first- and second-order serial autocorrelation. The correction for second-order autocorrelation was necessary to assure the model's proper representation of the data and to remove a seeming cross-sectional autocorrelation across different sites/series. Estimating the errors in site indices as random effects eliminated the effects of stochastic predictive variables. The proposed model has outperformed all other base-age specific and base-age invariant models in both the fit to the data and in its behavior during extrapolations. It also outperforms the model (developed on amabilis fir data) that is currently, operationally used for subalpine fir. The new model's advantages are parsimony, mathematical tractability, base-age invariance, and greater consistency in curvatures of the generated height-age trajectories. FOR. Sci. 49(4):539-554.

Measures of Interobserver Agreement and Reliability

Abstract: General Introduction Review Probability and Its Application in Medical Research Reliability for Continuous Scale Measurements Introduction Models for Reliability Studies Testing the Equality of Two Independent ICCs Testing the Equality of Two Dependent ICCs Large Sample Confidence Interval on rho2 Raters Agreement for Continuous Scale Measurements Estimating Agreement When Gold Standard Is Present Several Faulty Methods and a Gold Standard Sample Size Requirements for the Design of Reliability Study under One-Way ANOVA Sample Size for Case 2 Estimation of ICC from Two-Way Random Effects Model with Replicated Measurements Method-Comparison Studies Introduction Literature Review Bland and Altman's Approach Bradley-Blackwood Procedure Regression Methods for Methods-Comparison Correlated Measurement Errors Assessing Agreement in Methods-Comparison Studies with Replicate Measurements Discussion Population Coefficient of Variation as a Measure of Precision and Reproducibility Introduction Inference from Single Normal Sample Coefficient of Variation from the Gamma Distribution Tests for Equality of Coefficients of Variation Statistical Inference on Coefficient of Variation under the One-Way Random Effects Model Maximum Likelihood Estimation Variance Stabilizing Transformation Estimating the WSCV When the Error Variance Is Not Common Sample Size Estimation Analysis of WSCF from Two Dependent Samples Measures of Agreement for Dichotomous Outcomes Introduction Indices of Adjusted Agreement Cohen's Kappa: Chance Corrected Measure of Agreement Intraclass Kappa The 2 x 2 Kappa in the Context of Association Stratified Kappa Conceptual Issues Sample Size Requirements Dependent Dichotomous Assessments Adjusting for Covariates Simultaneous Assessment of Two Binary Traits by Two Raters Coefficients of Agreement for Multiple Rates and Multiple Categories Introduction Multiple Categories and Two Raters Agreement for Multiple Raters and Dichotomous Classification Probability Models Multiple Raters and Multiple Categories Testing the Homogeneity of Kappa Statistic from Independent Studies References Index Exercises appear at the end of each chapter.

Predicting the spatial distribution of ground flora on large domains using a hierarchical Bayesian model

Abstract: Accomodation of important sources of uncertainty in ecological models is essential to realistically predicting ecological processes. The purpose of this project is to develop a robust methodology for modeling natural processes on a landscape while accounting for the variability in a process by utilizing environmental and spatial random effects. A hierarchical Bayesian framework has allowed the simultaneous integration of these effects. This framework naturally assumes variables to be random and the posterior distribution of the model provides probabilistic information about the process. Two species in the genus Desmodium were used as examples to illustrate the utility of the model in Southeast Missouri, USA. In addition, two validation techniques were applied to evaluate the qualitative and quantitative characteristics of the predictions.

Combining multiple outcome measures in a meta-analysis: an application.

Abstract: In meta-analysis of clinical trials published in the medical literature it is customary to restrict oneself to standard univariate fixed or random effects models. If multiple endpoints are present, each endpoint is analysed separately. A few articles have been written in the statistical literature on multivariate methods for multiple outcome measures. However, these methods were not easy to apply in practice, because self-written programs had to be used, and the examples were only two-dimensional. In this paper we consider a meta-analysis on the effect on stroke-free survival of surgery compared to conservative treatment in patients with increased risk of stroke. Three summary measures per trial are available: short-term post-operative morbidity/mortality in the surgical group; long-term event rate in the surgical group, and the event rate in the conservative group. We analyse the three outcomes jointly with a general linear MIXED model, compare the results with the standard univariate approaches and discuss the many advantages of multivariate modelling. It turns out that the general linear MIXED model is a very convenient framework for multivariate meta-analysis. All analyses could be carried out in standard general linear MIXED model software.