Table 12 Setup for a motivational example

\({\theta }_{0}={\text{log}}\left(0.35/0.65\right)\)

the true log odds ratio of the outcome in the control group (\({W}_{ijk}=0\)) with reference group for binary covariate (\({X}_{ijk}=0\)) for k^th individual in i^th cluster at j^th period. We assume that prevalence of outcome is 15%

\({\gamma }_{1}=0, {\gamma }_{2}=0,{\gamma }_{3}=0,{\gamma }_{4}=0,{\gamma }_{5}=0\)

No secular trend

\({\theta }_{1}={\text{log}}\left(1.24\right)\)

\({\theta }_{2}={\text{log}}\left(0.33\right)\)

\({\theta }_{3}={\text{log}}\left(1.96\right)\)

Assuming minority group is 33%, OTE and main effect of minority status are based on the hypothesis: GoC increases in minority and non-minority patients are from 15 to 30% and from 35 to 40%, respectively

\(I=8,J=5,m=15\)

Number of clusters, and time steps. Equal sizes for every cluster

\(ICC=0.1\); \(CAC=0.8\)

For a nested exchangeable correlation structure