Ariel Alonso Abad

Testing for misspecification in generalized linear mixed models

Generalized linear mixed models have become a frequently used tool for the analysis of non-Gaussian longitudinal data. Estimation is often based on maximum likelihood theory, which assumes that the underlying probability model is correctly specified. Recent research shows that the results obtained from these models are not always robust against departures from the assumptions on which they are based. Therefore, diagnostic tools for the detection of model misspecifications are of the utmost importance. In this paper, we propose 2 diagnostic tests that are based on 2 equivalent representations of the model information matrix. We evaluate the power of both tests using theoretical considerations as well as via simulation. In the simulations, the performance of the new tools is evaluated in many settings of practical relevance, focusing on misspecification of the random-effects structure. In all the scenarios, the results were encouraging, however, the tests also exhibited inflated Type I error rates when the sample size was small or moderate. Importantly, a parametric bootstrap version of the tests seems to overcome this problem, although more research in this direction may be needed. Finally, both tests were also applied to analyze a real case study in psychiatry.

Choice of units of analysis and modeling strategies in multilevel hierarchical models

Hierarchical models are common in complex surveys, psychometric applications, as well as agricultural and biomedical applications, to name but a few. The context of interest here is meta-analysis, with emphasis on the use of such an approach in the evaluation of surrogate endpoints in randomized clinical trials. The methodology rests on the ability to replicate the effect of treatment on both the true endpoint, as well as the candidate surrogate endpoint, across a number of trials. However, while a meta-analysis of clinical trials in the same indication seems the natural hierarchical structure, some authors have considered center or country as the unit, either because no meta-analytic data were available or because, even when available, they might not allow for a sufficient level of replication. This leaves us with two important, related questions. First, how sensible is it to replace one level of replication by another one? Second, what are the consequences when a truly three- or higher-level model (e.g., trial, center, patient) is replaced by a coarser two-level structure (either trial and patient or center and patient). The same or similar questions may occur in a number of different settings, as soon as interest is placed on the validity of a conclusion at a certain level of the hierarchy, such as in sociological or genetic studies. Using the framework of normally distributed endpoints, these questions will be studied, using both analytic calculation as well as Monte Carlo simulation.

Generalizability in nongaussian longitudinal clinical trial data based on generalized linear mixed models.

This work investigates how generalizability, an extension of reliability, can be defined and estimated based on longitudinal data sequences resulting from, for example, clinical studies. Useful and intuitive approximate expressions are derived based on generalized linear mixed models. Data from four double-blind, randomized clinical trials into schizophrenia motivate the research and are used to estimate generalizability for a binary response parameter.