# Life expectancy calculation: METHODOLOGY

1. Documentation

Search for medical literature and selection of the most pertinent publications concerning the medical condition.This selection must be rigorous, including the most recent publications with large series of patients, with sufficient data on mortality, long duration of follow-up, and if possible similar demographic characteristics as of the studied case.

2.  Mortality analysis

Most of the calculations are being performed in order to determine two parameters: standardized mortality ratio (SMR) and excess death rate (EDR). Mean age of patients at entry in the study, repartition male/female, duration of follow-up, and data on mortality are essential in those calculation.

The objective is to determine the excess risk of mortality in person with the medical condition by comparing the observed mortality in person with the condition versus the expected mortality for the same age and in the general population

We used the usual mortality analysis methodology adopted by the American Academy of Insurance Medicine (AAIM) 1, 5.

2.1- Observed mortality:

a) Cumulative mortality (Q): reported in the text, or calculated by dividing the total number of death during the follow-up by the number of the living entrants in the study. It can also be obtained from a Kaplan-Meier survival curve 2

b) Cumulative survival rates (P): reported in the text or derived from survival curves.

c) Geometric Average Annual mortality

Mortality should be expressed on annual basis, allowed by calculating geometric average  annual  mortality rate (q) that is derived from cumulative survival rate (P) as 1-P1/Δt (Δt being the length of follow-up in years reported in the study).

Survival rate (P) is the complement of mortality rate (Q) (i.e.:  P+Q =1) and then, it could be calculated from cumulative mortality as: P = 1-Q.

2.2- Expected mortality:

Sometimes reported in some studies providing control group without the medical condition; most often calculated from the appropriate life tables for the general population.

Expected cumulative survival rate (P’) is calculated from Life tables, and expected geometric average annual mortality rate (q’) could be derived by the same way as seen with observed mortality (q).Details on methodology were previously published by our team in Journal of insurance medicine3.

2.3- Comparative mortality:

a. SMR, or Standardized Mortality Ratio, is the quotient of the observed mortality rate due to a medical condition over the expected mortality rate in the general population. Normal SMR is 1.0; a SMR of 2 means twice as many deaths due to the medical condition over a period of time as compared to what occurs in the general population.

This parameter could also, be expressed as percentage by multiplying SMR by 100 this give us MR (Mortality ratio), and generally used for underwriting purposes. Normal MR being 100%. (MR of 200% mean 2 fold risk of mortality)

b. EDR, or Excess Death Rate, is the number of extra deaths that occur per 1000 individuals exposed to the risk of death per year. It is the difference between the observed and the expected mortality rates.

Both, SMR and EDR could also, be calculated from the number of death (observed – expected) per 1000 persons-year.

We note that terminology could change according to the methodology. For instance, mortality rate is also noted (mx), and standardised mortality ratio (SMR) noted as relative risk (RR).This did not dramatically change results

SMR for given age could be considered as Relative Risk (RR), and sometimes used in calculating mortality rate related to the condition, (by multiplying RR by mortality rate of the same age in general population). EDR for this age could be then easily calculated.

3. Estimation of life expectancy

Based on life table construction methodology, using series of excess death rate (EDR) calculated for current age of interest and future attained ages until age 109.

These values of EDR are added to the standard (normal) mortality rate of each age, thus creating series of specific mortality rates for the considered medical condition. A new life table is then built using these mortality rates.

Proportional Life expectancy method4, consider variations of mortality with age in certain conditions (SMR decrease with age, EDR increase with age) allows calculation of these EDRs.

By summating EDRs of several conditions added to normal mortality rates5., we generate a new set of mortality rate used to build life table for different combinations as described above.

Results are presented as tables   and figures, reproducing life expectancy curves showing remaining years of life expectancy and percent reduction from normal expected life expectancy.

Cumulative survival curves with median survival time are also added.

References:

1. Pokorski RJ. Mortality methodology and analysis seminar. J Insur Med 1988; 20: 20-45.
2. Steven J. Rigatti. A simple method for computer-based survival curve measurement. J Insur Med 2009; 41:107–109.
3. Naslafkih A, Sestier. A quicker method for calculating mortality ratios based on survival rates in clinical trials and other follow-up studies. J Insur Med. 2001; 33(4): 339-348.
4. Strauss, DJ, Vachon PJ and Shavelle RM. Estimation of future mortality rates and life expectancy in chronic medical conditions. J Insur Med 2005; 37: 20–34.
5. Singer, RB. How to prepare a life expectancy report for an attorney in a tort case. J Insur Med 2005; 37:42–51.