Modelling and Projecting Mortality Rates Using Adaptive P-splines

Abstract

In this thesis we propose models for estimating and projecting mortality rates using adaptive splines. Mortality modelling has various applications from social planning to insurance. However, raw mortality data often exhibits irregular patterns due to randomness. The data at the oldest ages are also very scarce and unreliable as there are only very little survivors at these ages, adding difficulty to estimation. Graduation refers to the act of smoothing crude mortality rates, during which extrapolation to older ages where data is non-existent is usually also performed. We first propose a flexible and robust model for mortality graduation of static life tables using adaptive splines. Male and female mortality rates are graduated jointly, as opposed to previous English Life Tables (ELTs) where they were smoothed independently. Therefore our model borrows information across sexes, which is especially helpful at the oldest ages. Often
when male and female mortality rates are estimated independently, implausible age patterns may occur, such as intersecting male and female mortality schedules. This has been addressed using rather ad hoc procedures in previous ELTs, for example, by calculating the weighted average of the estimated mortality rates starting at the age where they intersect or by discarding data at the oldest ages. By utilising the locality of B-spline basis, constraints can be imposed effectively such that female mortality rates are always lower than or equal to male mortality rates at all ages, even at extrapolation ages, hence does not involve subjective adjustments.

We then extend the model to forecast mortality rates. Building upon models by Dodd et al. (2020) and Hilton et al. (2019), we jointly model and project male and female mortality rates of England Wales and Scotland. The joint sex model produces more reasonable long term male and female mortality projections that are non intersecting. Information is borrowed at the highest ages where exposures are small. By doing so the extrapolation to higher ages beyond data range gives more plausible estimates, especially for the mortality improvement rates for females at the oldest ages where a worsening mortality is otherwise projected. We also jointly model mortality rates of the same sex across the two countries, as they are expected to have similar mortality structures for the same sex. England Wales populations have a wider age range with available
data, therefore the joint country model provides a way for the smaller Scottish populations to
borrow information and learn from the bigger English Welsh populations. The joint country
model is able to produce non-divergent long term projections between the countries for both
males and females.
Finally, a joint model for all of the four populations is proposed. The model combines features
of the joint sex and joint country models, and borrows strength across sexes and countries.

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Identifiers

ORCID for Erengul Dodd: orcid.org/0000-0001-6658-0990

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