Graft patency risk set

A graft patency risk set contains the observed grafts still eligible to experience the specified patency endpoint immediately before a given time. It is the denominator for a time-specific failure calculation, not simply the original number of operations or the number of open grafts at the last recorded visit.

The endpoint must be chosen first. Primary graft patency, assisted primary graft patency and secondary graft patency use different intervention and occlusion histories. An intervention that ends one endpoint need not end another. The vascular reporting standards define these categories and discuss life-table and Kaplan–Meier estimator methods for unequal follow-up.^[ref]

For a single time-to-first-failure endpoint, let $T_i$ be graft $i$'s failure time and $C_i$ its last observable follow-up time. With a specified common time origin, defineAt an observed failure time $t_j$, the risk set size $n_j=n(t_j)$ is evaluated just before the failures. If $d_j$ qualifying failures occur then, the Kaplan–Meier estimator of patency isTies between failure and censoring times require a consistent observation convention.

In an original example, ten grafts enter follow-up. Two meet the chosen endpoint at day 10, three of the remaining grafts are last observed without failure at day 15, and one of the five still followed fails at day 20. ThenThe three censored grafts do not cause a survival-curve drop at day 15; they reduce the later denominator. The crude expression $1-3/10=0.70$ answers neither the same follow-up-adjusted question nor the question of what happened after censoring.

The censoring assumptions are substantive. If grafts are preferentially lost when failure is imminent, observed risk sets may not represent those no longer followed. Death also prevents later graft-failure observation and can be a competing risks, rather than merely an ordinary missed visit. A cumulative incidence question with death as a competing event differs from a net-patency analysis that censors deaths. Endpoint definition, time origin, observation process and treatment of death must accompany a patency estimate.