Performance of a Mixed Effects Logistic Regression Model for Binary Outcomes With Unequal Cluster Size

ABSTRACT

When a clustered randomized controlled trial is considered at a design stage of a clinical trial, it is useful to consider the consequences of unequal cluster size (i.e., sample size per cluster). Furthermore, the assumption of independence of observations within cluster does not hold, of course, because the subjects share the same cluster. Moreover, when the clustered outcomes are binary, a mixed effect logistic regression model is applicable. This article compares the performance of a maximum likelihood estimation of the mixed effects logistic regression model with equal and unequal cluster sizes. This was evaluated in terms of type I error rate, power, bias, and standard error through computer simulations that varied treatment effect, number of clusters, and intracluster correlation coefficients. The results show that the performance of the mixed effects logistic regression model is very similar, regardless of inequality in cluster size. This is illustrated using data from the Prevention Of Suicide in Primary care Elderly: Collaborative Trial (PROSPECT) study.

Key Words:

• Bias
• Clustered binary observations
• Clustered randomized controlled trials
• ICC
• Power
• Type I error rate.

ACKNOWLEDGMENTS

We are grateful to Mr. Jean Lefever for his assistance in SAS programming and to Dr. Bruce for her valuable comments. We are also indebted to the PROSPECT study group (R01MH59366, R01MH59380, R01MH59381) for their permission for use of data. This research is supported in part by NIMH grants P30MH49762 (Cornell ACISR) and R01MH060447 (ACL).

Notes

Note: K, number of clusters; N _tot  =  n _i , total number of observations; n, number of observations per cluster; U(a, b), a uniform distribution ranging from a to b.

^aIts normal-approximated 95% CI does not include the nominal alpha level 0.05.

Note: K, number of clusters; N _tot  =  n _i , total number of observations; n, number of observations per cluster; U(a, b), a uniform distribution ranging from a to b.

Note: K, number of clusters; N _tot  =  n _i , total number of observations; $n$, number of observations per cluster; U($a$, $b$), a uniform distribution ranging from a to b.

Note: K, number of clusters; N _tot  =  n _i , total number of observations; n, number of observations per cluster; U(a, b), a uniform distribution ranging from a to b.