Advisory Committee Chair
Lloyd J Edwards
Advisory Committee Members
Timothy M Beasley
Date of Award
Degree Name by School
Doctor of Philosophy (PhD) School of Public Health
The linear mixed model has become a popular technique for the analysis of longitudinal data, but Wald test statistics of fixed effects for these models frequently lack well defined distributions. A common approach to this problem uses the Kenward-Roger adjustment, which attempts to approximate the distribution of the Wald statistic by matching its moments obtained via Taylor expansion to those of an F distribution. However, this approach only matches moments obtained under the null hypothesis of no effect and cannot currently be used to approximate the distribution of the test statistic under some alternative hypothesis. This limitation prevents a straightforward approach to calculating power for the Kenward-Roger adjusted Wald statistic. In chapter 2, we introduce a novel power calculation that extends the original methodology of Kenward and Roger to obtain an approximate noncentral distribution of this adjusted Wald statistic from which power for tests of linear trend can then be calculated. This method is then extended to calculate expected power for designs with anticipated rates of missing follow-up data in Chapter 3, and finally to the calculation of sample size for such designs in Chapter 4. A variety of other techniques are also examined and compared to this method, with the newly developed method consistently outperforming other approaches in the calculation of both power and sample size.
McPherson, Tarrant Oliver, "Power and Sample Size Calculations for Linear Mixed Models of Longitudinal Data Using the Kenward-Roger Adjusted Wald Test" (2022). All ETDs from UAB. 475.