Over the last decade, mental health services researchers have made widespread use of generalized mixed-effects regression models for analysis of clustered and longitudinal data. Much of the work in this area has involved the development of efficient methods of statistical estimation, based on maximum marginal likelihood, empirical Bayes, and fully Bayesian estimation strategies. Generalization of the original model for continuous and normally distributed data to the case of non-linear mixed-effects regression models for binary, ordinal, nominal, and Poisson, distributions are now generally available and enjoy widespread use. Furthermore, computer software has now been developed and is either freely available over the Internet or commercially available. With the speed of this development and acceptance by the research community, it is therefore somewhat surprising that so little research has been conducted on the issue of hypothesis testing for generalized mixed-effects regression models. Indeed, traditional approaches of large sample tests based on likelihood ratios and Wald-type statistics are all that are generally available. These approaches are limited due to their large sample properties in addition to well-known limitations for testing models with varying numbers of random effects. Furthermore, in addition to the absence of an arsenal of tools for statistical testing, the literature is also quite limited with respect to statistically rigorous approaches to computing statistical power for clustered and longitudinal designs. For non-linear mixed-models (e.g., binary and ordinal cases), the literature on statistical power is virtually nonexistent, and gross oversimplification of the study design, estimation, and testing procedures must be used to obtain any estimates of the number of measurements needed at each level of nesting that are required to test a hypothesis with a reasonable balance of Type I and II errors. The primary goal of this proposal is to fill this void by (1) studying the large and small sample properties of various existing and new tests suitable for generalized linear and non-linear mixed-effects regression models, (2) to develop statistically rigorous approaches to computing statistical power for this class of models that is now so widely used by behavioral, social, and biological scientists in general, and health and mental health services researchers in particular, and (3) to develop a computer program for computing statistical power for linear and non-linear mixed-effects regression models (MIXPWR), and to incorporate these new tests into the existing programs (MIXREG, MIXOR, MIXPREG, MIXNO), which are distributed freely from ww.uic.edu/Iabs/biostat. Preliminary results reveal that the new small sample tests that we have derived provide the ability to detect dramatically smaller effects in small samples and increased statistical power over traditional large sample tests even when sample sizes are large. The net result is the ability to use rigorous statistical methods for analysis of longitudinal and clustered data, even in small and difficult to recruit populations such as minorities, homeless, and those at high risk for suicide.
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