We have recently constructed tables of the estimated life expectancies of impaired lives on the basis of mortality ratios and the cohort life expectancy tables given in the 8th edition of the Ogden Tables, which are derived from the ONS 2018-based population projections for the United Kingdom.1,2
The life expectancy of impaired lives may also be estimated using excess death rates. In this paper, we give tables of life expectancies for impaired lives using a range of excess death rates for males and females from age 0 to age 100. As both mortality ratios and excess death rates are widely used in medical and legal settings, it is hoped that these additional tables of life expectancies will be of practical value.
Background
In the United Kingdom, projections of life expectancy are used to determine quantum in legal cases where damages are awarded following injury or negligence. This is a key element in the assessment of the financial loss of claimants, as the estimation of the remaining years of life allows projection of care costs and lost earnings or pensions.
The assumption is made that an average survival can be projected using the cohort or period tables relying on current or estimated future trends in mortality. These projections are published by the Government Actuary's Department based on the Office for National Statistics (ONS) principal population projections, as the Ogden Tables. Where an individual is thought to be atypical as a result of pre-existing conditions or an accident, an impaired lives calculation may be required.
In 2014, tables were published that allowed for projection of life expectancies of impaired lives, using mortality ratios between 100% and 1000%. These calculations relied on the 7th edition of the Ogden Tables.3
Following publication of the 8th edition of the Ogden Tables in July 2020, we used mortality ratios to construct new cohort tables for the valuation of impaired life expectancy in the United Kingdom. The 8th edition is based on mortality probabilities from the 2018-based projections, which were published in 2019, and refer to a date of trial or assessment in 2022.4
An alternative approach to that of mortality ratios is to assume a constant addition to the death rate experienced by impaired lives. The excess death rate (EDR) is the difference, rather than the ratio, of two mortality rates, and it is usually expressed as a rate per thousand, or per k. For example, an EDR of 2 per k translates (roughly speaking) into 2 additional deaths in 1000 persons observed over a 1-year period.
To assist with practical calculations, we give tables that estimate the future life expectancies of male and female impaired lives between the ages of 0 and 100, on the basis of a range of EDRs.
Methods
By applying life table methodology to the adjusted age-specific mortality rates () estimates of life expectancy were calculated for EDR's ranging from 0 to 500.
The excess death rate (EDR) is the expected annual number of deaths in an impaired population of size 1000, minus those expected in a standard population of the same size. Thus, an EDR of 4 means that there are about 4 extra deaths per annum in the impaired population, per 1000 individuals. An EDR of 0 corresponds to the standard mortality experience.
Results
Tables 1 and 2 give cohort life expectancy by excess death rate (EDR) for men and women separately in the United Kingdom. Life expectancies were calculated up to age 100, as this is the age range given in the 8th edition of the Ogden Tables.
Regardless of the standard mortality tables being used, impaired lives will only have their life expectancy adjusted if there is clear evidence that their life expectancy is ‘atypical.’2
The life expectancy of a standard life can be seen in column 1, where the excess death rate is 0. The subsequent columns allow for the additional mortality risks of impaired lives, up to an EDR of 500 excess deaths per 1000 individuals.
The EDR is generally estimated by an analysis of the most relevant clinical follow-up studies, assuming that the extra mortality may be reasonably represented by a constant addition to the standard mortality rate.
As an example, let us consider survivors of corrective surgical repair for tetralogy of Fallot, as discussed by Hickey et al.5 The average age at the date of corrective surgery was 6.7 years, and survivors were followed for up to 40 years (with a median follow-up period of 20 years). The overall mortality rate of those with classic tetralogy of Fallot was about 0.003 per annum. Allowing for mortality from all causes among standard lives of about 0.001 per annum at ages up to about 40, an excess death rate of about 2 per k is indicated.
Under the assumption that this EDR pertains for life, we can use Tables 1 and 2 to estimate the impaired life expectancy. For a male aged 7 who has had successful corrective surgery, there is a reduction in life expectancy from 80.7 to 74.4 years. For a female of the same age, there is a reduction in life expectancy from 83.4 to 76.6 years.
Compared with the 7th edition of the Ogden Tables, the 8th shows a fall in life expectancy at all ages (and particularly at older ages).2 This is because mortality rates did not improve as much as expected between 2008 and 2018, and because less favourable assumptions have been adopted by the ONS regarding future changes in mortality.
Life expectancy estimates for impaired lives are also lower than those based on the 7th edition of the Ogden Tables. When the life expectancies for the tetralogy of Fallot example were recalculated using the ONS 2008-based population projections (as used in the 7th edition of the Ogden Tables), male life expectancy at age 7 fell from 81.7 to 75.1 years, and female life expectancy at the same age fell from 85.3 to 78.2 years. The reductions in projected life expectancy are therefore slightly smaller when the 8th edition of the Ogden Tables is used rather than the 7th edition.
Constant excess death rates and constant mortality ratios are widely used in practice, though in reality both measures may fluctuate over time, and with age. For older impaired lives, excess death rates are sometimes preferable to mortality ratios.6 This is because mortality ratios imply a constant relative risk, whereas in reality the relative risk of mortality generally declines with age.7 Thus, the use of mortality ratios may lead to an underestimation of life expectancy. On the other hand, the use of excess death rates may lead to underestimation of the mortality rates of impaired lives at older ages, leading to overestimation of life expectancy. See Singer (1988, 1998) for comparisons of the observed mortality ratios and excess death rates of patients who have experienced a myocardial infarction, or those with prostate cancer.6,8
Regardless of whether excess death rates or mortality ratios are used to compute estimates of life expectancy, the values used are estimated on the basis of evidence from clinical or scientific follow-up studies, which are often of limited size and duration. Furthermore, the excess death rate or mortality ratio may need to be estimated for ages outside the range of ages of those who participated in the follow-up studies. It follows that the excess death rates and mortality ratios used in practice should be viewed with some caution, though they may give reasonable estimates of life expectancy for practical purposes.
Conclusions
Following the publication of the 8th edition of the Ogden Tables, we have provided estimates of life expectancy for impaired lives using excess death rates.
We hope that the tables presented in this article, along with the corresponding tables based on mortality ratios,1 will be helpful in both medical and legal settings.
Madeleine Reid gratefully acknowledges the financial support of MAC-MIGS in the form of a vacation grant.