= Solution
For a population question use a <population-averaged logistic model for repeated binary outcomes>. Code $z_i=1$ for the new treatment and $0$ for the control, with visit times $t_j=2j$ months for $j=1,2,3$. Let $w_{ij}=(1,z_i,x_i^T,t_j)^T$, $\gamma_M=(\alpha_M,\phi_M,\beta_M^T,\delta_M)^T$, and
$$
m_{ij}=P(Y_{ij}=1\mid z_i,x_i,t_j),\qquad\operatorname{logit}m_{ij}=w_{ij}^T\gamma_M.
$$
Different subjects are independent. Each response has a <Bernoulli distribution> with this marginal mean, but no independence of a subject's three responses is assumed. The linear time effect and absence of treatment-by-time <interaction> are substantive mean assumptions; if inappropriate they can be replaced by time indicators and <interaction terms>.
For complete data, set $m_i=(m_{i1},m_{i2},m_{i3})^T$, $A_i=\operatorname{diag}(m_{ij}(1-m_{ij}))$, and $D_i=\partial m_i/\partial\gamma_M^T=A_iW_i$, where $W_i$ has rows $w_{ij}^T$. A working exchangeable <correlation matrix> has unit diagonal and off-diagonal value $\rho\in(-1/2,1)$; set $V_i=A_i^{1/2}C(\rho)A_i^{1/2}$. The <generalized estimating equation> is
$$
\sum_iD_i^TV_i^{-1}(Y_i-m_i)=0.
$$
With correct means and independent subjects, a positive-definite working <covariance matrix> and regularity give consistency even if the working correlation is wrong. Write $H=\sum_iD_i^TV_i^{-1}D_i$ and $u_i=D_i^TV_i^{-1}(Y_i-m_i)$. The fitted subject-level <sandwich covariance matrix> is
$$
\widehat{\operatorname{Var}}(\widehat\gamma_M)=H^{-1}\left(\sum_i u_iu_i^T\right)H^{-1},
$$
evaluated at the estimates. This inference is asymptotic in the number of independent subjects, not the number of visits.
For the actual incomplete data, define $R_{ij}=1$ if visit $j$ is observed, with $R_{i0}=1$ and monotone dropout. Let $\mathcal H_{i,j-1}$ contain treatment, baseline <covariates> and responses observed before visit $j$. Under sequential <missing at random>, specify
$$
q_{ij}=P(R_{ij}=1\mid R_{i,j-1}=1,\mathcal H_{i,j-1}),\qquad \rho_{ij}=\prod_{k=1}^j q_{ik}>0.
$$
The assumption is that the retention decision, conditional on this history, does not additionally depend on unseen current or future outcomes. Fit the $q_{ij}$, for example by visit-specific <logistic regressions>. A simple valid choice uses working independence and the <inverse-observation-weighted estimating equations for longitudinal dropout>:
$$
\boxed{\sum_i\sum_{j=1}^3 w_{ij}\frac{R_{ij}}{\rho_{ij}}(Y_{ij}-m_{ij})=0.}
$$
Terms with $R_{ij}=0$ are zero and require no missing response. Given the full response vector, sequential <missing at random> makes $\mathbb E(R_{ij}/\rho_{ij}\mid Y_i,z_i,x_i)=1$. Consequently the weighted score has the same <expectation> as the complete-data score, proving its mean-zero property. Correct retention probabilities, positivity and a correctly specified marginal mean are required. Use cluster-robust uncertainty, accounting for fitted retention-model coefficients, or resample entire subjects and refit both models. Under <missing completely at random>, the simpler unweighted observed-response <GEE> can suffice; ordinary unweighted <GEE> is not valid under arbitrary history-dependent <missing at random>.
The treatment coefficient gives a population conditional-on-baseline <odds ratio> $e^{\phi_M}$ at each visit. To communicate an absolute population treatment benefit, standardize predicted <probabilities> over the full baseline population, rather than only completers:
$$
\widehat p_z(t)=\frac1m\sum_i\operatorname{logit}^{-1}(\widehat\alpha_M+\widehat\phi_M z+\widehat\beta_M^Tx_i+\widehat\delta_M t),\qquad \widehat p_1(t)-\widehat p_0(t).
$$
A causal reading additionally uses the <randomized controlled trial> assignment, consistency of the treatment definition, no interference and the dropout assumptions; the statistical model alone does not supply those conditions.
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