Abstract
This paper presents a variant of the survival function proposed by Wong and Tsui, in which we include a component reflecting heterogeneity among individuals (frailty), together with a covariate describing the influence of certain characteristics of individuals on the response variable. Using mortality statistics for the entire Spanish population, we estimated survival functions according to the variants of the model considered, also determining life expectancies and mortality ratios at each age. The advantage of the proposed variant is that it incorporates gender differences, by including sex as a covariate. Furthermore, it reflects the intrinsic randomness of individuals. With this approach, additional parameters must be considered, but all were found to be significant.
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Notes
These estimated values for the scale parameters in the Spanish population are very similar to those obtained by Won-Tsui in the US population in 2010. The youth-to-adulthood component is 66.5329 for males and 66.2780 for females and the old-oldest component is 80.2327 for males and 83.8294 for females. The greater the survival of the population, the higher these values.
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Funding
This work was supported by the Research Group “Survival Analysis and Probability Distributions” and by the Vice-Rector’s Office for Political Science and Research, through the project “Social-Labour Statistics and Demography” [30.BB.11.1101] at the Faculty of Human Resources and Labor Relations, at the University of Granada (Spain).
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Huete-Morales, MD., Navarrete-Álvarez, E., Rosales-Moreno, MJ. et al. Modelling the survival function of the Spanish population by the Wong–Tsui model with the incorporation of frailty and covariates. Lett Spat Resour Sci 13, 151–163 (2020). https://doi.org/10.1007/s12076-020-00250-5
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DOI: https://doi.org/10.1007/s12076-020-00250-5