Inconsistencies in methodologies of calculating expectation of life

Shavelle et al.¹ recently wrote to Spinal Cord with a re-calculation of the life expectancies in the paper of the current authors (Middleton et al.²).

The letter authors departed from theoretical correctness and consistency with both their own previous publications and well-recognized methodology in insurance and actuarial mathematics.

In Table 1 to their letter, they failed to adhere to the principle of concordance between mortality and exposure in applying empirical mortality rates to a life table developed more than 10 years after the mean period of exposure. Justifying this departure based on the secular trend in crude death rate in a small sample is inappropriate when over the same period the sample age standardized death rate for C5–8ABC decreased by about 20%, and for the whole Australian population by 34% from 1990 to 2010.³

Table 1 Life expectancy for C5–8ABC

In Table 2, they derive a life table using a methodology of constant mortality beyond age 80, which produces absurdities at older ages and also distorts life expectancy results at younger ages. Moreover, this methodology is inconsistent with the approach the same authors have taken in different communications,⁴ which have involved empirical standardized mortality ratios (SMRs) followed by constant SMRs after a certain age. This methodology can produce discontinuities, and also fails at older ages if the ‘constant age’ is too low (for example, age 60 years), giving crude mortality rates greater than 1.0. For the current example, a ‘constant age’ of 80 years gives results quite close to Middleton et al.,² and is theoretically more correct.

Table 1 demonstrates the error in the Shavelle letter, correctly determines SMRs on the principle of concordance using ALT1995–97, and reproduces expectations of life for C5–8ABC using the alternative Strauss methodology and that used in the Middleton paper. This methodology is also consistent with standard actuarial practice and provides equitable results compared to the purchase price of annuities and structured settlements.