The geometric mean of the age-specific death rates as a summary index of mortality

Even though a single summary index of mortality can never replace the set of age-specific death rates, it has been found to be extremely useful for a wide variety of purposes. Such indexes are generally one of two types: aggregative indexes, such as directly standardized rates which reflect absolute differences between corresponding age-specific mortality rates; and average of relatives indexes which reflect proportional differences between those rates. The choice of index depends upon the purposes for which it is to be used, and is important as different indexes can produce very different results. While directly standardized rates are widely used, they depend upon the selection of an appropriate standard population and give disproportionately heavy weight to the high ages. Average of relatives indexes give equal weight to all ages, but are infrequently used as no index of that type has gained wide acceptability. This paper recommends the use of the geometric mean of the age-specific mortality rates as such an index, and shows that this index is readily calculable, unbiased, needs no standard population, is directly comparable to all other indexes so calculated, and accurately reflects exponential mortality patterns.