Statistical Testing and Power for MH Research

描述(申请人提供)：在过去的十年里，精神卫生服务的研究人员广泛使用了广义混合效应回归模型来分析聚集和纵向数据。这一领域的许多工作涉及开发基于最大边际似然、经验贝叶斯和完全贝叶斯估计策略的有效统计估计方法。将连续正态分布数据的原始模型推广到二元、有序、名义和泊松分布的非线性混合效应回归模型的情况下，现在普遍可用并得到广泛使用。此外，现在已经开发了计算机软件，可以通过因特网免费获得，也可以在商业上获得。随着这一发展的速度和被研究界接受，因此令人惊讶的是，关于广义混合效应回归模型的假设检验问题的研究如此之少。事实上，基于似然比和Wald-type统计量的大样本检验的传统方法是普遍可用的。这些方法由于它们的大样本属性以及众所周知的用于测试具有不同数量的随机效果的模型的局限性而受到限制。 此外，除了缺乏用于统计测试的工具库之外，文献在计算集群和纵向设计的统计能力的统计严谨方法方面也相当有限。对于非线性混合模型(例如，二元和有序情况)，有关统计能力的文献几乎不存在，必须使用研究设计、估计和测试程序的过度简单化来获得对每一嵌套水平所需的测量数量的任何估计，这些估计是检验假设与类型I和类型II的合理平衡所需的。这一建议的主要目标是通过以下方式填补这一空白：(1)研究适用于广义线性和非线性混合效应回归模型的各种现有和新测试的大样本和小样本特性，(2)开发统计严格的方法来计算这类模型的统计能力，这类模型现在被行为、社会和生物科学家广泛使用，特别是健康和心理健康服务研究人员，以及(3)开发用于计算线性和非线性混合效应回归模型的统计能力的计算机程序(MIXPWR)，并将这些新测试合并到现有的程序(MIXREG，MIXOR，MIXPREG，MIXNO)，可从www.uic.edu/IABS/BioStat免费分发。初步结果表明，我们得出的新的小样本测试提供了在小样本中检测显著较小的影响的能力，并且即使在样本量较大的情况下，也比传统的大样本测试具有更强的统计能力。最终结果是能够使用严格的统计方法分析纵向和集群数据，即使是在少数族裔、无家可归者和自杀高危人群等规模较小且难以招募的人群中也是如此。

DESCRIPTION (provided by applicant): 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.