Frailty models

(May 1, 2017)

A population consists of individuals, each with their own genetics, lifestyle, and yes, their very own force of mortality.  National mortality data, such as held by the Office for National Statistics (ONS), are observed only at the population level and the variation in the force of mortality across individuals of the same age is forever hidden.  The purpose of this blog is to show how we can attempt to model this hidden heterogeneity.

Let us suppose that Gompertz really was right and that the mortality of each individual follows their own Gompertz law from ages 40 to 90, say.  Notice that this is very different from saying that the mortality of the entire population (of individuals) follows the Gompertz law.  Let…

Tags: frailty

Pensioners — the youth of today

(Sep 9, 2016)

This blog focuses on two particular features of mortality improvements: improvements around retirement age and improvements for the (very) old.  Figure 1 shows $$\mu_{x,1961}/\mu_{x,2012}$$, the ratios of the forces of mortality over the ages $$x = 50,\ldots,95$$, in 1961 and 2012 for four countries.  The figure was obtained as follows: data for ages 50-95 and years 1961-2012 were downloaded from the Human Mortality Database and the raw 2D mortality table was smoothed using 2D P-splines (see my earlier blog for details on 2D smoothing with P-splines).  The ratios plotted in Figure 1 were obtained from the resulting smooth mortality surface.

Figure 1.  Mortality ratios, $$\mu_{x, 1961}/\mu_{x, 2012}$$,…

A chill wind

(Nov 27, 2015)

In a previous blogs I have looked at seasonal fluctuations in mortality, usually with lower mortality in summer and higher mortality in winter.  The subject of excess winter deaths is back in the news, as the UK experienced heavy mortality in the winter of 2014/15, as demonstrated in Figure 1.

Figure 1. Excess winter deaths in England & Wales. Source: ONS.

Figure 1 shows some important features, but some are less immediately obvious than others.  The most obvious feature is that the winter of 2014/15 is indeed the worst for excess winter deaths for fifteen years.  Another obvious feature of Figure 1 is that it is the elderly who bear the overwhelming brunt of excess winter mortality.  However, there is an easily…