https://doi.org/10.1140/epjp/s13360-024-05746-3
Regular Article
Nonlinear multiparametric modeling of life-table data with adaptive distributions: time evolution of hazard ratios
, Sechsschimmelgasse 1/21-22, 1090, Vienna, Austria
Received:
12
August
2024
Accepted:
14
October
2024
Published online:
7
November
2024
Factorizing multiparameter densities are proposed for the analytic continuum modeling of human life tables. The formalism is developed based on mortality data of the female, male, and total population of France for the year 2021. The data sets cover the age range from birth up to 110 years. The cumulative hazard function is a multiply broken exponential density, admitting a differential hazard rate capable of describing the observed late-life mortality deceleration and exhibiting exponential asymptotic increase rather than a mortality plateau. The nonlinear least-squares regression is performed with the survival function, which admits double-exponential decay in the high-age limit. The minimization of the multiparametric least-squares functional is facilitated by invoking the product structure of the cumulative hazard, the number of factors and fitting parameters being adapted to the data set. More generally, new techniques are developed to deal with probability densities exhibiting a nonlinear multiparameter dependence. Such densities are increasingly needed to represent extended data sets, as exemplified by recent mortality data across the tree of life. In the case of the mentioned human life tables, the residual deviations of the regressed survival functions and cumulative distributions from the data points are within at most two percent, uniformly over the entire empirical age range. The analytic probability density and age-conditioned survival probabilities are calculated for the total population and the female and male cohorts. The lifetime evolution of the cumulative and differential female/male hazard ratios is studied, from birth up to the asymptotic high-age regime.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
