Modified logistic model for mortality rates in Malaysia

Abstract

Rapid improvement and changes in mortality trends signify the growing percentage of older people in the population of a country. However, this remains challenging to study due to data limitations, particularly the lack of data for all ages and the sparseness characteristics in the data due to number of death compared to the living at older ages are small. Besides this, the current changes in the mortality curvature have caused the existing mortality models to be accurate at a certain age range only. This research improves an old-age mortality model namely Wilmoth model by combining it with Akima spline to produce smooth rate estimates at younger ages. This approach allows mortality estimates to be calculated for the oldest ages while accounting for uncertainty in the age and gender parameter estimates. This research also introduces a threshold age where the transition between Akima spline and the extended mortality model is optimal. The proposed model can also extrapolate the oldest age mortality rate beyond the available age. This research applies the proposed model to Malaysian mortality data from the years 2010 to 2016 and compares it with six other mortality models, namely Gompertz, Makeham, Beard, Kannisto, Wilmoth, and Heligman Pollard models. The comparison is done using root mean squared error and mean absolute percentage error via a cross-validation method as well as simulation study using bootstrap method. The results show that the proposed logistic model significantly improves Malaysian mortality estimation for all ages in terms of accuracy and prediction performance, as well as its ability to capture the important mortality features such as accident hump, mortality crossover, and deceleration of mortality at old ages. Moreover, the simulation study has also proved that the proposed model is unbiased and consistent. In summary, the proposed model better fits Malaysian mortality rates when compared to the other six mortality models.