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The method of expected number of deaths, 1786-1886-1986. (English) Zbl 0616.62001
Expected numbers of deaths were used by W. Dale (1777) in full detail, and J. N. Tetens (1786) demonstrated their calculation and corrections to loss to follow-up, and he gave an early parametric model for relative mortality.
This method was reinvented in connection with 19th century studies of geographical and occupational variations of mortality by F. G. F. Neison (1884), W. Farr (1859), H. Westergaard (1882), see also M. Rubin and H. Westergaard (1886). Standardization of vital rates - of which the above method is a part - was later primarily used in official statistics. G. U. Yule [On some points relating to vital statistics, more especially statistics of occupational mortality (with discussion). J. R. Stat. Soc. 97, 1-84 (1934)] was the first to derive the standard error of standardized rates. H. Westergaard (1882) gave a rather careful discussion of sampling errors of mortality statistics.
A full theoretical perspective has been given recently by G. Berry [The analysis of mortality by the subject-years method. Biometrics 39, 173-184 (1983)], N. E. Breslow [Int. Stat. Rev. 43, 45-58 (1975; Zbl 0316.62042)], and J. M. Hoem [Statistical analysis of a multiplicative model and its application to the standardization of vital rates: A review. ibid. 55, 119-152 (1987)] by interpreting standardized mortality ratio as a maximum likelihood estimator in a proportional hazards model. A brief description of recent generalizations to regression models with continuous time and continuous covariates were developed by N. E. Breslow, J. H. Lubin, P. Marek and B. Langholz [J. Am. Stat. Assoc. 78, 1-12 (1983; Zbl 0503.62090)].
Reviewer: H.Grimm

62-03 History of statistics
01A55 History of mathematics in the 19th century
62P05 Applications of statistics to actuarial sciences and financial mathematics
01A50 History of mathematics in the 18th century
01A60 History of mathematics in the 20th century
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