#### Identifier

etd-03312006-100431

#### Degree

Doctor of Philosophy (PhD)

#### Department

Veterinary Medical Sciences - Pathobiological Sciences

#### Document Type

Dissertation

#### Abstract

In herd health studies, the mixed effects logistic regression model with random herd effects are commonly used for modeling clustered binary data. These models are well developed and widely used in the literature, among which is the logistic-normal regression model. In contrast to the rich literature in modeling methods, the sample size/power analysis methods for such mixed effects models are sparse. The sample size/power analysis method for the logistic-normal regression model is not readily available. This study is to develop a power analysis/sample size estimation method for the logistic-normal regression model. Extended from the sample size method for the likelihood ratio test in the generalized linear models (Self et al., 1992), a power analysis method for the logistic-normal model is developed based on a noncentral chi-square approximation to the distribution of the likelihood ratio statistic. The method described in this dissertation can be applied to both exchangeable and non-exchangeable responses. The power curves are presented with respect to the change of each of the planning values while holding other planning values fixed for two examples of the logistic-normal model containing one random cluster effect. The results from this proposed sample size/power analysis method for the logistic-normal model were compared to the results from the method for the fixed effects logistic regression model. For a given total sample size and the same applicable planning values, the power for the logistic-normal regression model is smaller than that for the fixed effects logistic regression model, suggesting that the minimum required sample size calculated from using the method for the fixed effects model is too small to achieve the desired power when the logistic-normal model is to be used in data analysis.

#### Date

2006

#### Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

#### Recommended Citation

Li, Yinmei, "Power analysis for a mixed effects logistic regression model" (2006). *LSU Doctoral Dissertations*. 244.

http://digitalcommons.lsu.edu/gradschool_dissertations/244

#### Committee Chair

Daniel Scholl