The additional changes all relate to the way in which the default Initial Rates of Mortality Improvement (in 2011) are determined. Once these Initial Rates have been determined the age-period-cohort split and the projection of future mortality improvements will be done in the usual way. Users of the Model will still be able to use their own Advanced assumptions for Initial Rates if they prefer.
The starting point for determining the Initial Rates is to fit a P-spline model to past mortality data. The Committee has analysed the deviance residuals of the P-spline fit and proposes to make the following related changes for CMI_2014 as a result:
- Move to a rolling data window
As time progresses, older data becomes less relevant for determining future improvements – having a rolling window on past data reflects this. Analysis of the deviance residuals indicates that the Model fit in the 1960s is less good than in more recent years. The precise choice of the window to use is somewhat arbitrary but the Committee proposes to use a rolling 40-year period, i.e. the first data year will be 1974 for CMI_2014, 1975 for CMI_2015 and so on. (For the avoidance of doubt, the age-period-cohort split will also be determined based on data in the same window.)
- Exclude extreme “outliers”
Certain age/year combinations have an implausibly high deviance residual; this is particularly true for the 1919/1920 birth cohorts. Comparison with CMI SAPS data strongly suggests that these outliers are not due to genuine mortality effects, and this is supported by external research by Cairns et al (2014). The Committee proposes that age/year combinations with a deviance residual outside a reasonable range will be given less or no weight in the P-spline fit.
- Allow for overdispersion
The degree of smoothing in the P-spline fit is currently determined by the Bayesian Information Criterion (BIC). The Committee proposes to instead use a quasi-BIC (QBIC) method that makes explicit allowance for the presence of overdispersion. (Overdispersion is commonly encountered in mortality experience data and means that the variability of observed mortality rates is higher than would be expected with a Poisson distribution of deaths.) This method leads to a smoother fit to the data and less extreme cohort patterns in particular.
- Allow for experience in the first part of 2014
The ONS publishes data on weekly deaths, which means that as at time of writing we have a good picture on how mortality has developed over the first 7 or 8 months of 2014. In order to ensure that the Model reflects the latest experience data available, the Committee proposes to include this data in the dataset used to fit the P-spline model. Making this change brings the Model into line with industry best-practice.
Reference: Cairns, A.J.G., Blake, D., Dowd, K., and Kessler, A. (2014), Phantoms Never Die: Living with Unreliable Mortality Data, Working paper, Heriot-Watt University. Available from http://www.macs.hw.ac.uk/~andrewc/papers/ajgc71.pdf
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