Clinical endpoints measured in terms of duration, such as intensive care unit (ICU) length of stay (LOS), are widely used in randomized clinical trials (RCTs) and observational research. In analyses of patient-level data from a recent RCT, in which ICU LOS was the primary endpoint, and in administrative data, we show that additional ICU time is often accrued by patients after they are deemed ready for discharge. This "immutable" time (which cannot plausibly be altered by interventions under study) varies by day, week, and year, adding on average one-third of a day to total LOS. We then use statistical simulations, informed by the administrative data and RCT, to assess the impact of immutable time on the measurement and statistical comparison of patients' ICU LOS. These simulations demonstrate that immutable time combines with clinically necessary ICU time (neither of which is likely to be normally distributed) to produce overall LOS distributions that may either mask true treatment effects or suggest false treatment effects relative to analyses of time-to-discharge-readiness. The extent and direction of bias are complex functions of the statistical method used, mortality rates and distributions, and the magnitude of immutable time relative to intervention-associated reductions in LOS.