Comparison of Logistic Force of Mortality Models for Predicting Life Table Probabilities of Death: A Simulation-Based Approach

Abstract

A program was written in the statistical software package R for conducting Monte Carlo studies based on simulated life tables, and then used in a study to compare two different models for predicting life table probabilities of death. A parametric probability model was used by the program to generate the cohort distribution of deaths, based on supplied life table data. For the present study a cohort life table was constructed using mortality data from the Social Security Death Index, Master File. The models evaluated in the present Monte Carlo study are alternative three-parameter versions of the logistic force of mortality model. The models were fit to simulated life table data for ages 80 to 99, and then used to make probability of death predictions for ages 80 to 105. The Monte Carlo simulations were used to obtain the average values and standard deviations of the probability of death predictions generated by the two models, which were then compared to one another and to the actual probabilities of death based on the probability model that generated the simulated life table data. Results of the simulations showed that the mean probabilities of death predicted by the two models were very similar over the range of ages considered, but usually deviated somewhat from the actual probabilities of death. In the age range of 80-99, the average percentage deviation was less than 2% for each model, while in the age range of 100-105, the average percentage deviation for the models was around 5-6%. In the age range of 100-105, both models always underestimated the true probability of death.