Figure 2.

Illustration of the ODAL algorithm. Step I: Use patient-level data within each site to obtain ${\overline{\beta }}_j$ and its variance $\overline{V_j}$, then broadcast $\left\{{\overline{\beta }}_j{\overline{V}}_j\right\}$, where j = 1,...,K. Step II: Obtain the initial value $\overline{\beta }$ with ${\overline{\beta }}_{\text{j}}$ and calculate the intermediate terms $\nabla L_j$ and at $\nabla L_j^2$ at j-th site. With intermediate information, construct local surrogate likelihoods to obtain and broadcast ${\tilde{\beta }}_j$ and H_j. Step III: Synthesize the evidence to get output $\tilde{\beta }$.