Cause of Death Mortality Modelling using Constrained Penalised Splines and Forecast Reconciliation Approach

Sub-Saharan Africa has seen sharp increases in life expectancy over the past few decades and is one of the regions experiencing the fastest mortality improvements. Although vast literature on mortality modelling and forecasting exists, most of this literature relates to developed countries, with sparse literature focusing on this region. Kenya's life expectancy, for example, has been increasing at a rate of 0.88 per year over the last two decades. Here, we propose a cause-of-death (CoD) mortality modelling technique that, to the best of our knowledge, has not been applied to CoD mortality modelling before. Compared to aggregate mortality, CoD mortality data contains detailed information on mortality trends, which enables us to understand the critical drivers of mortality and incorporate cause-specific insights on mortality patterns. CoD data for males and females from 1990 to 2017 are utilised, and the top 10 causes of death are used for modelling. We apply the novel constrained penalised splines (CPS) model to individual causes and aggregate mortality. Forecast reconciliation forecasting approaches are applied to ensure coherence. We show that incorporating prior knowledge of mortality patterns significantly improves forecast accuracy, especially for mortalities with irregular patterns. Additionally, we compare the results from the CPS model with those from an extension of the Lee-Carter (LC) model and the mainstream penalised splines (PS) model. We show that the constraint parameters can be appropriately chosen to produce similar results as those from LC and PS models. Finally, we apply the CPS model to calculate two lifespan measures: mean life span and life span variations and apply residual bootstrap to project these measures. These results show an increase in projected average life expectancy by 3.3 years to 73.3 when compared with the United Nations (UN) estimates and have implications when modelling future healthcare system costs, including life insurance implications and others.