= Solution
\b[The independence analysis is not justified without further assumptions.] Three binary responses from the same subject generally remain correlated after conditioning on baseline <covariates> and treatment. The fitted independent-Bernoulli <likelihood> discards that correlation and gives incorrect model-based <standard errors> and tests if it is present. Positive within-subject correlation commonly makes those errors too small.
There is an important distinction between estimating the mean and estimating uncertainty. If the stated marginal <logistic regression> is correct and responses are fully observed, the independence score $\sum_{i,j}w_{ij}(Y_{ij}-m_{ij})$ still has zero <expectation>. With independent subjects and regularity, its root can consistently estimate marginal coefficients despite within-subject dependence; a subject-level <sandwich covariance matrix> is then needed. True independence is a special case in which the original <standard errors> would be appropriate.
Dropout creates a separate issue. Restricting that score to observed responses need not preserve its zero <expectation> if observation depends on the response history or unseen depression outcomes. Therefore both point estimates and uncertainty may be wrong. Neither random treatment assignment nor baseline adjustment alone establishes an <ignorable missingness mechanism>. We need a model matched to the scientific estimand and explicit assumptions about <missing data>.
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