Restricted mean survival time ($\mathrm{RMST}(\tau )={\int }_0^{\tau }S(t)dt$)

The restricted mean survival time to a fixed cutoff $\tau$ is $\mathbb{E}[\min (T,\tau )]={\int }_0^{\tau }S(t)dt$ for a nonnegative event time. This follows by the tail integral formula for moments. Unlike the unrestricted mean, it uses no tail beyond $\tau$; under independent censoring it can be estimated by integrating a Kaplan–Meier estimator over adequately observed follow-up.