Modeling U.S. Mortality and Risk-Cost Optimization on Life Expectancy

Abstract

Human life expectancy has risen in most developed countries over several decades, causing observed demographic shifts. Many researchers have developed models to determine the expectancy of life at birth. Yet due to the complexity of the real-world mortality data, and recent global economy impacts, there is a great demand to search for new models to accurately predict the life expectancy, especially in the United States. In this paper, we focus on the analysis of mortality rate in the United States over a period of six decades (data from 1946 to 2005) with considerations of the six most common distribution functions in the mortality area. These functions are: Gompertz, Gompertz-Makeham, logistic, log logistic, loglog, and Weibull. Given complex mortality data, we develop models including algorithms to compute the mortality measures such as mortality rate, and then select the best function for predicting the life expectancy in the United States. The modeling results include life expectancy at birth, life expectancy at each age, mortality rate, and forecasting models. We also discuss a new risk-cost function with respect to life expectancy, and determine the optimal threshold lifetime level that maximizes the expected risk cost. Numerical examples are given to illustrate the expected risk-cost results. The proposed risk-cost optimization model, and the optimal lifetime threshold value can help the policy-decision makers of related healthcare organizations including insurance companies to carefully perform the tradeoff between the cost and benefits. This approach can affect both short term and long term related healthcare policies and plans. The results show that the logistic distribution uniquely out performs other distributions based on the mean square error criterion. We find that on average the life expectancy at birth in the United States in 2005 for both sexes, males, and females are 84.0, 81.9, and 84.6 years, respectively. This new result shows that the true life expectancy on average in the U.S. is significantly larger than in existing reports. Life expectancy obviously changes as one will get older. By late adulthood, a person's chances of living longer increase as is reflected by the life expectancy function. For example, although the life expectancy from birth in the United States in 2005 is 84.0 years, those who live to age 65 will have an average of 20.4 additional years left to live, making their life expectancy almost 85.4 years. Similarly, those who live to age 75 will gain an additional few years, making their life expectancy almost 87.6 years. On average, a child who will be born in the US in 2015 can expect to live 85.5 years, and in 2025 a child born can expect to live nearly 87 years.