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Table 2 Estimated ICC values under five different correlation structures for the example trial on the logit scale, unadjusted and adjusted for prespecified covariates

From: Accounting for complex intracluster correlations in longitudinal cluster randomized trials: a case study in malaria vector control

 

Unadjusted

Adjusted

Correlation structures

WPICC (ρw)

CAC

Intra-cluster correlation matrixa

WPICC (ρw)

CAC

Intra-cluster correlation matrixa

Exchangeable

0.160

1

\(\left(\begin{array}{ccc}0.160& 0.160& 0.160\\ {}0.160& 0.160& 0.160\\ {}0.160& 0.160& 0.160\end{array}\right)\)

0.054

1

\(\left(\begin{array}{ccc}0.054& 0.054& 0.054\\ {}0.054& 0.054& 0.054\\ {}0.054& 0.054& 0.054\end{array}\right)\)

Nested Exchangeable

0.187

0.774

\(\left(\begin{array}{ccc}0.187& 0.145& 0.145\\ {}0.145& 0.187& 0.145\\ {}0.145& 0.145& 0.187\end{array}\right)\)

0.084

0.421

\(\left(\begin{array}{ccc}0.084& 0.035& 0.035\\ {}0.035& 0.084& 0.035\\ {}0.035& 0.035& 0.084\end{array}\right)\)

Exponential decay

0.189

0.822

\(\left(\begin{array}{ccc}0.189& 0.156& 0.128\\ {}0.156& 0.189& 0.156\\ {}0.128& 0.156& 0.189\end{array}\right)\)

0.084

0.505

\(\left(\begin{array}{ccc}0.084& 0.043& 0.021\\ {}0.043& 0.084& 0.043\\ {}0.021& 0.043& 0.084\end{array}\right)\)  

Toeplitz

0.189

\(\left(\begin{array}{ccc}0.189& 0.153& 0.136\\ {}0.153& 0.189& 0.153\\ {}0.136& 0.153& 0.189\end{array}\right)\)

0.084

\(\left(\begin{array}{ccc}0.084& 0.041& 0.028\\ {}0.041& 0.084& 0.041\\ {}0.028& 0.041& 0.084\end{array}\right)\)

Unstructured

\(\left(\begin{array}{ccc}0.216& 0.140& 0.149\\ {}0.140& 0.156& 0.150\\ {}0.149& 0.150& 0.199\end{array}\right)\)

\(\left(\begin{array}{ccc}0.091& 0.017& 0.039\\ {}0.017& 0.052& 0.054\\ {}0.039& 0.054& 0.118\end{array}\right)\)

  1. WPICC: Within-period ICC, CAC: Cluster autocorrelation coefficient
  2. aEach cell [i, j] represent correlation between two within-cluster individuals collected in different i and j periods