Dependency modeling approach of cause-related mortality and longevity risks: HIV/AIDS

Disaggregation of mortality by cause has advanced the development of life tables for life insurance and pension purposes. However, the assumption that the causes of death are independent is a challenge in reality. Furthermore, models that determine relationships among causes of death such as HIV/AIDS and their impact on mortality and longevity risks seem trivial or inflexible. To address these problems, we aim to determine and build an appropriate copula dependence model for HIV/AIDS against other causes of death in the presence of age, gender, and time. A bivariate copula model is proposed to capture the dependence structure of HIV/AIDS on life expectancy. This approach allows the fitting of flexible and interpretable bivariate copulas for a two-dimensional case. The dataset was derived from the World Health Organization database that constituted annualized death numbers, causes, age, gender, and years (2000 to 2019). Using Kendall's tau and Pearson linear coefficient values, the survival Joe copulas proved to be a suitable model. The contribution and implication of this research are the quantification of the impact of HIV/AIDS on a life table, and, thus, the establishment of an alternative to the subjective actuarial judgment approach.