Individualizing Life Expectancy Estimates for Older Adults Using the Gompertz Law of Human Mortality

Abstract

Background

Guidelines recommend incorporating life expectancy (LE) into clinical decision-making for preventive interventions such as cancer screening. Previous research focused on mortality risk (e.g. 28% at 4 years) which is more difficult to interpret than LE (e.g. 7.3 years) for both patients and clinicians. Our objective was to utilize the Gompertz Law of Human Mortality which states that mortality risk doubles in a fixed time interval to transform the Lee mortality index into a LE calculator.

Methods

We examined community-dwelling older adults age 50 and over enrolled in the nationally representative 1998 wave of the Health and Retirement Study or HRS (response rate 81%), dividing study respondents into development (n = 11701) and validation (n = 8009) cohorts. In the development cohort, we fit proportional hazards Gompertz survival functions for each of the risk groups defined by the Lee mortality index. We validated our LE estimates by comparing our predicted LE with observed survival in the HRS validation cohort and an external validation cohort from the 2004 wave of the English Longitudinal Study on Ageing or ELSA (n = 7042).

Results

The ELSA cohort had a lower 8-year mortality risk (14%) compared to our HRS development (23%) and validation cohorts (25%). Our model had good discrimination in the validation cohorts (Harrell’s c 0.78 in HRS and 0.80 in the ELSA). Our predicted LE’s were similar to observed survival in the HRS validation cohort without evidence of miscalibration (Hosmer-Lemeshow, p = 0.2 at 8 years). However, our predicted LE’s were longer than observed survival in the ELSA cohort with evidence of miscalibration (Hosmer-Lemeshow, p<0.001 at 8 years) reflecting the lower mortality rate in ELSA.

Conclusion

We transformed a previously validated mortality index into a LE calculator that incorporated patient-level risk factors. Our LE calculator may help clinicians determine which preventive interventions are most appropriate for older US adults.