A Beta Regression Framework with Intentional Left-Censoring for Quantifying Familial Longevity

Defining and quantifying exceptional familial human survival is a persistent challenge in longevity research. Traditional approaches rely on binary thresholds, arbitrary cutoffs, or simple descriptive measures, which discard information on variation among the oldest individuals, ignore differences in background mortality, and yield unstable family-level summaries. We propose a principled, model-based framework that transforms survival times into percentiles relative to population life tables, standardizing across birth cohorts, sexes, and populations. We extend beta mixed-effects regression to accommodate intentional left-censoring, which downweights early deaths while retaining their contribution to the likelihood, thereby focusing inference on extreme survival. Family-specific random effects provide interpretable, statistically grounded longevity scores, overcoming the limitations of ad hoc measures and enabling robust identification of long-lived families. Simulation studies and application to a large multigenerational Dutch cohort demonstrate that the method reliably identifies families enriched for longevity. This framework provides a flexible, interpretable, and robust tool for analyzing familial survival, offering a paradigm shift in the statistical study of exceptional human lifespan.