Table 1 Calculation of the within-cluster, within-period correlation (WPC) and within-cluster, between-period correlation (BPC) for intensive care unit (ICU) log-length of stay (LOS) in the Australian and New Zealand Intensive Care Society – Adult Patient Database (ANZICS-APD)

\( {\widehat{\sigma}}_{ICU}^2=0.045 \)

\( {\widehat{\sigma}}_{CP}^2=0.008 \)

\( {\widehat{\sigma}}_I^2=1.360 \)

\( \widehat{\rho}=\frac{{\widehat{\sigma}}_{ICU}^2+{\widehat{\sigma}}_{CP}^2}{{\widehat{\sigma}}_{ICU}^2+{\widehat{\sigma}}_{CP}^2+{\widehat{\sigma}}_I^2}\kern0.5em =\kern0.5em \frac{0.045+0.008}{0.045+0.008+1.360}\kern0.5em =\kern0.5em 0.038 \)

\( \widehat{\eta}=\frac{{\widehat{\sigma}}_{ICU}^2}{{\widehat{\sigma}}_{ICU}^2+{\widehat{\sigma}}_{CP}^2+{\widehat{\sigma}}_I^2}\kern0.5em =\kern0.5em \frac{0.045}{0.045+0.008+1.360}\kern0.5em =\kern0.5em 0.032 \)