Rectangularization of the survival curve reconsidered: The maximum inner rectangle approach.

Rectangularization of the survival curve-a key analytical framework in mortality research-relies on assumptions that have become partially obsolete in high-income countries due to mortality reductions among the oldest old. We propose refining the concept to adjust for recent and potential future mortality changes. Our framework, the 'maximum inner rectangle approach' (MIRA) considers two types of rectangularization. Outer rectangularization captures progress in mean lifespan relative to progress in maximum lifespan. Inner rectangularization captures progress in lifespan equality relative to progress in mean lifespan. Empirical applications show that both processes have generally increased since 1850. However, inner rectangularization has displayed country-specific patterns since the onset of sustained old-age mortality declines. Results from separating premature and old-age mortality, using the MIRA, suggest there has been a switch from reducing premature deaths to extending the premature age range; a shift potentially signalling a looming limit to the share of premature deaths.