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

Sub-Saharan Africa has seen steep increases in life expectancy over the past few decades, but there is sparse research into mortality modelling and forecasting for this region. Kenya's life expectancy, for example, has been increasing at a rate of 0.88 per year over the last two decades. We propose a cause-of-death (CoD) mortality modelling technique that, to the best of our knowledge, has not previously been applied to CoD mortality modelling. Compared to aggregate mortality, CoD mortality data enables a clearer understanding of critical drivers of mortality and incorporation of cause-specific insights. Kenyan CoD data for the 10 most common causes of death for males and females from 1990 to 2017 are analysed and modelled. We apply the novel constrained penalised splines (CPS) model to individual causes of death. Forecast reconciliation approaches are applied to ensure coherence between individual causes and aggregate mortality. We show that varying constraints through the CPS model, motivated for example by expert judgement into the persistency and representativeness of past mortality patterns for future forecasts, can potentially improve forecast accuracy, especially for causes that have historically experienced steep changes in mortality rates. 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 the LC and PS models, demonstrating the flexibility of the CPS model. 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 of 3.3 years to 73.3 when compared with the United Nations (UN) estimate of 70.0. These differences in mortality and life expectancy forecasts have potential implications to future healthcare system costs, life insurance product costing, and other areas