For the DTS study, use subjects with all five assessments in HamD scores in the CAU group for this question. The intraclass correlation coefficient among the repeated measures in Ham-D scores can be estimated by fitting the following mixed-effects model:

\[\operatorname{HamD}_{i j}=\mu+r_{i}+\varepsilon_{i j}, j=0,3,6,9,12,\]

where \(H a m D_{i j}\) is the HamD score for the \(i\) th subject measured \(j\) months after baseline, \(\mu\) is the population average of the scores, \(r_{i} \sim N\left(0, u^{2}\right)\) is the random effect for the \(i\) th subject, \(\varepsilon_{i j} \sim N\left(0, \sigma^{2} I_{4}\right)\), and \(r_{i} \perp\left(\varepsilon_{i 0}, \varepsilon_{i 3}, \varepsilon_{i 6}, \varepsilon_{i 9}, \varepsilon_{i 12}\right)\).

(a) Write the model in an equivalent multivariate regression form without random effects.

(b) Give an estimate of \(\mu\) based on the mixed-effects model. Is it significantly different from 10 ?

(c) Estimate the intraclass correlation coefficient among the repeated HamD scores.

(d) Write down the corresponding marginal model and use the GEE to estimate \(\mu\). Is it significantly different from \(10 ?\)