Abstract Mode-based Measures

1. Introduction

The concept of compression of mortality is closely linked to that of rectangularization of the survival curve which means, according to Fries, a state in which mortality from exogenous causes is eliminated and the remaining variability in the age at death is caused by genetic factors [Fries 1980]. Though the primary concern of Fries was the compression of morbidity, and much of the discussion has followed this line, compression of mortality was naturally recognized as having an important relationship with the former. The present paper is concerned exclusively with the question of the compression of mortality.

An index of mortality entropy, known as "Keyfitz' H" [Keyfitz and Golini 1975] has been used in studying the compression of mortality [e.g. Hill 1993, Nusselder and Mackenbach 1996] while some other studies have focused on changes in standard deviation [Myers and Manton 1984]. The median, mode and the upper percentiles have also been studied [e.g. Paccaud et al. 1998] and have the merit of being organically related to important benchmarks in the survival process instead of just chronological age.

Lexis gave much importance to the mode as an expression of the natural life span. His view was that if, in an age-at-death distribution, we replicate on the left side of the mode a mirror image of the right side, the result is a normal curve describing the natural life span. Deaths further left or above the normal curve represented premature deaths, ascribed to abnormal conditions or external influences [Lexis 1877]. This approach was used later by him and other authors [Ballod 1899, Dublin 1923, Lexis 1903].

For definition, we start from the simple premise that mortality is being compressed when a given proportion of deaths takes place in a shorter age interval than before. The measurement is best done with life table data. Both period and cohort life tables can be used but in the following we shall examine only period tables which are of greater practical interest for analysis of mortality.

As the concept of compression of mortality is not linked to any particular age, it should be measured free from the age scale. Infant and childhood mortality, however, may be excluded because the whole theory and discussion of compression is directed to what happens in late life. Instead of chronological age, an indicator may be placed on the scale of mortality percentiles where it is related to ranking in survival. An indicator may also be selected so that it has not even this connection but is free to measure compression wherever it may occur.


Abstract Mode-based Measures

Measuring the Compression of Mortality
Väinö Kannisto
© 2000 Max-Planck-Gesellschaft ISSN 1435-9871