New improved estimators for overdispersion in models with clustered multinomial data and unequal cluster sizes

It is usual to rely on the quasi-likelihood methods for deriving statistical methods applied to clustered multinomial data with no underlying distribution. Even though extensive literature can be encountered for these kind of data sets, there are few investigations to deal with unequal cluster sizes. This paper aims to contribute to fill this gap by proposing new estimators for the intracluster correlation coefficient

Influence Diagnostics for Generalized Estimating Equations Applied to Correlated Categorical Data

Influence diagnostics in regression analysis allow analysts to identify observations that have a strong influence on model fitted probabilities and parameter estimates. The most common influence diagnostics, such as Cook’s Distance for linear regression, are based on a deletion approach where the results of a model with and without observations of interest are compared. Here, deletion-based influence diagnostics are proposed for generalized estimating equations (GEE) for correlated, or clustered, nominal multinomial responses. The proposed influence diagnostics focus on GEEs with the baseline-category logit link function and a local odds ratio parameterization of the association structure. Formulas for both observation- and cluster-deletion diagnostics are provided which are multivariate extensions of the current one-step approximation approaches used for GEEs with univariate marginal responses. Simulation studies were conducted to evaluate the accuracies of the one-step diagnostics in multinomial GEE as well as in other commonly used categorical response models. Applications are presented on 2017-2018 English Premier League shot-outcome data and on a cohort study on small renal mass histologic subtype distributions

Analysis of dose-response data from developmental toxicity studies

Ph.DDOCTOR OF PHILOSOPH

Análisis inferencial basado en medidas de Fi-divergencia para modelos loglineales con muestreo Multinomial y sobredispersión

En los últimos años se han incrementado de forma importante los métodos estadísticospara analizar datos cualitativos. Quizá esto se ha debido en parte a la gran demanda, porparte de las Ciencias Biomédicas (particularmente en relación a estudios epidemiológicos),Sociales y del Comportamiento, de técnicas estadísticas especí cas para el tratamiento dela gran cantidad de datos cualitativos de que disponían. El desarrollo de técnicas especí- cas para el tratamiento de datos cualitativos o categóricos ha permitido descartar, porinnecesarios y muchas veces inapropiadas, muchas de las técnicas para variables continuasque se venían utilizando para este tipo de datos..

Overdispersion models for correlated multinomial data: Applications to blinding assessment

Overdispersion models have been extensively studied for correlated normal and binomial data but much less so for correlated multinomial data. In this work, we describe a multinomial overdispersion model that leads to the specification of the first two moments of the outcome and allows the estimation of the global parameters using generalized estimating equations (GEE). We introduce a Global Blinding Index as a target parameter and illustrate the application of the GEE method to its estimation from (1) a clinical trial with clustering by practitioner and (2) a meta-analysis on psychiatric disorders. We examine the impact of a small number of clusters, high variability in cluster sizes, and the magnitude of the intraclass correlation on the performance of the GEE estimators of the Global Blinding Index using the data simulated from different models. We compare these estimators with the inverse-variance weighted estimators and a maximum-likelihood estimator, derived under the Dirichlet-multinomial model. Our results indicate that the performance of the GEE estimators was satisfactory even in situations with a small number of clusters, whereas the inverse-variance weighted estimators performed poorly, especially for larger values of the intraclass correlation coefficient. Our findings and illustrations may be instrumental for practitioners who analyze clustered multinomial data from clinical trials and/or meta-analysis

Overdispersion models for correlated multinomial data: Applications to blinding assessment

Overdispersion models have been extensively studied for correlated normal and binomial data but much less so for correlated multinomial data. In this work, we describe a multinomial overdispersion model that leads to the specification of the first two moments of the outcome and allows the estimation of the global parameters using generalized estimating equations (GEE). We introduce a Global Blinding Index as a target parameter and illustrate the application of the GEE method to its estimation from (1) a clinical trial with clustering by practitioner and (2) a meta-analysis on psychiatric disorders. We examine the impact of a small number of clusters, high variability in cluster sizes, and the magnitude of the intraclass correlation on the performance of the GEE estimators of the Global Blinding Index using the data simulated from different models. We compare these estimators with the inverse-variance weighted estimators and a maximum-likelihood estimator, derived under the Dirichlet-multinomial model. Our results indicate that the performance of the GEE estimators was satisfactory even in situations with a small number of clusters, whereas the inverse-variance weighted estimators performed poorly, especially for larger values of the intraclass correlation coefficient. Our findings and illustrations may be instrumental for practitioners who analyze clustered multinomial data from clinical trials and/or meta-analysis