Figure 1.

Schematic illustration of the ODACH algorithm. The first step is initialization, where each site reports the local estimation of the log hazard ratio (${\widehat{\beta }}_j$) and the corresponding variance estimate (${\widehat{V}}_j$). The lead site then computes the initial estimate $\overline{\beta }$ as the weighted average of all local estimates and sends it back to each site. In the second step, each site calculates and shares the local gradients $\mathrm{\nabla }{L}_j(\overline{\beta })$ and ${\mathrm{\nabla }}^2{L}_j(\overline{\beta })$. In the third step, the lead site constructs a surrogate likelihood function $\tilde{L}(\beta )$ with these gradients and obtains the surrogate estimate $\stackrel{\sim }{\beta }$.