= Efron approximation for tied event times
{c}
{title2=$\displaystyle\frac{\prod_{i\in D}u_i}{\prod_{q=0}^{d-1}(S-qU_D/d)}$}
For $d$ events tied within a <risk set>, put $u_i=\exp(\beta^Tz_i)$, $S=\sum_{i\in R}u_i$ and $U_D=\sum_{i\in D}u_i$. The Efron approximation to <Cox partial likelihood> removes the average tied-event <hazard multiplier> from the denominator at each successive event. Unlike the <Breslow approximation for tied event times>, it accounts approximately for depletion of the <risk set> within the group. Factors independent of $\beta$ can be dropped for estimation. This is an approximation for coarsened continuous event times, not a full interval-observation <likelihood>.
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