= Solution
For conditional individual response profiles use a <logistic random-intercept model for repeated binary outcomes>. Introduce a subject effect $B_i\sim N(0,\tau^2)$ independently across subjects and independently of treatment and baseline <covariates>, under the specified model. Conditional on $B_i,z_i,x_i$, assume the three responses are independent <Bernoulli random variables> with
$$
p_{ij}(b)=P(Y_{ij}=1\mid B_i=b,z_i,x_i),\qquad \operatorname{logit}p_{ij}(b)=\alpha_C+\phi_C z_i+\beta_C^Tx_i+\delta_C t_j+b.
$$
Here $B_i$ is persistent unmeasured subject heterogeneity and $\tau^2$ its <variance>. It induces dependence after integration: for distinct visits, the response <covariance> is $\operatorname{Cov}_B(p_{ij}(B),p_{ik}(B))$, generally positive. This is a complete joint <generalized linear mixed model>, unlike a mean-only <GEE> specification.
Under <missing at random> conditional on the observed responses and baseline variables, with <distinct parameters> for missingness and outcomes, the missingness model is ignorable for likelihood inference. Let $\mathcal O_i=\{j:R_{ij}=1\}$. The outcome <observed-data likelihood> is
$$
L(\gamma_C,\tau^2)=\prod_i\int_{-\infty}^{\infty}\prod_{j\in\mathcal O_i}p_{ij}(b)^{y_{ij}}[1-p_{ij}(b)]^{1-y_{ij}}\frac{e^{-b^2/(2\tau^2)}}{\sqrt{2\pi\tau^2}}\,db.
$$
The omitted Bernoulli factors sum to one over missing outcomes. Fit the fixed coefficients and $\tau^2$ by maximizing this integrated <likelihood>, with suitable quadrature or another justified integration method. If $\tau=0$, use the limiting point-mass model. Correct response and random-effect distributions, identifiable coefficients and regularity are needed; the latent distribution assumption is not merely a convenient working covariance.
For patient $i$, combine the fitted model with the posterior density of $B_i$ proportional to its normal density times that patient's observed Bernoulli factors. Integrating $p_{ij}(b)$ over this posterior gives a patient-specific predicted response profile. The treatment <odds ratio> for a fixed $b$ and the same baseline variables is $e^{\phi_C}$. This conditional contrast does not by itself identify each person's unobserved causal treatment effect: a parallel-arm trial observes only one treatment per person. Random slopes or heterogeneous treatment effects require further modelling and sufficient information; they are not implied by fitting a <random intercept>.
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