Andrew Cairns, Torsten Kleinow and Jie Wen introduce the new Longevity Index for England and the accompanying open access app
The new Longevity Index for England (LIFE) grew out of the need for actuaries and external organisations to better understand and quantify mortality inequalities. Developing the index has formed a key part of a research programme based at Heriot-Watt University and supported by the Actuarial Research Centre of the IFoA, the Society of Actuaries and the Canadian Institute of Actuaries.
Starting point: the Index of Multiple Deprivation
Our initial challenge was to identify the strongest association between socioeconomic predictive variables and mortality outcomes using publicly available data. A good starting point is the widely used Index of Multiple Deprivation (IMD), as greater levels of deprivation are known to be associated with higher levels of mortality.
However, the IMD is a general measure of relative deprivation and was not developed with a view towards explaining mortality differences. We propose an alternative index that focuses on mortality and uses a range of predictive variables to explain the differences in mortality and life expectancy between small neighbourhoods.
Data was sourced from the Office for National Statistics for 32,844 Lower Layer Super Output Areas (LSOAs): socially homogeneous neighbourhoods with an average population of 1,600. Predictive variables at the LSOA level include all the domains and sub-domains of the IMD (most importantly unemployment, and income deprivation among the elderly), urban-rural classification and a variety of census-related data, including the proportion of people in an LSOA who live in a care home. Urban-rural differences turn out to be key in getting a good fit, as Figure 1 illustrates. This reveals a flaw in the IMD as a mortality predictor. For example, within Decile 4, death rates in rural areas are 20% lower than the decile average, while death rates in non-London conurbations are nearly 10% higher. The proposed LIFE index closes this gap.
The objectives of a new index
In developing the new index, we aim to:
- Publish a robust, reliable and open-access mortality index at neighbourhood (LSOA) level
- Explain as much as possible of the variation we observe in LSOA-level mortality, using publicly available data, socioeconomic predictive variables, care home population, and urban-rural class
- Minimise unexplained urban-rural and regional differences
- Provide an open-access toolkit for actuaries
- Provide a tool and benchmark for actuaries for comparison with alternative ratings and valuation models
- Facilitate debate and action on how to tackle mortality inequality.
The LIFE index is estimated using the random forest algorithm. A random forest is a collection of uncorrelated regression trees. Each tree estimates relative risk as a piecewise constant function of the predictive variables fitted optimally to a randomly selected subset of LSOAs. As with simple linear regression, each function can be evaluated at any point – not just the LSOAs that it is fitted to. The random forest estimator is then the arithmetic average of the individual tree estimators.
Random forests are known to be more robust than individual trees and, more generally, hyperparameters are tuned to achieve the right balance between over and underfitting. As a further check on robustness, results were compared with those for local linear regression and generalised linear models.
LIFE index values are available for the 32,844 LSOAs in England for males and females aged 40-89. The index itself is a relative risk, with English national mortality by age and year as the base table: for example, an index value of 2 means the mortality rate at a particular age is double the national rate. The spread of values across all LSOAs is illustrated in Figure 2. This shows that there is considerable inequality at younger ages, with a narrowing gap at higher ages. To give context, we also calculate period remaining life expectancies (Figure 3).
Examples of LSOAs with particularly high or low LIFE index values (for males and females) are listed in Table 1. More generally, many of the LSOAs with high LIFE values (high mortality) are in the North West of England (particularly Manchester, Liverpool and areas up the coast from Liverpool), but this is mainly the result of the underlying socioeconomic factors rather than any unexplained regional variation.
The LIFE app
The research team has produced an open access app (bit.ly/LIFEindex) that allows non-expert users to explore mortality variation across the country. The app has two main tabs. Tab 1 provides data at the LSOA level. The user inputs a postcode or the name of an LSOA, alongside sex and age. Outputs include the LIFE index and life expectancy for that LSOA/sex/age combination, along with decile and percentile values that indicate how the LSOA ranks alongside other LSOAs.
Figure 4 gives an example.
Tab 2 is a mapping tool that zooms out from the LSOA to either region, NHS clinical commissioning group (CCG) or parliamentary constituency. Users can zoom in to focus on areas of interest. Clicking on individual LSOAs produces a pop-up that gives summary information for the LSOA, similarly to Tab 1.
The LIFE index and app can help policymakers compare CCGs on a like-for-like basis: after adjusting for socioeconomic and urban-rural variation, they can see which have higher or lower mortality than expected. CCG-specific variation in relative risk is small but still significant, pushing life expectancies up or down by as much as six months from age 65. The app allows users to choose whether to include this additional CCG-level variation in the relative risk.
While the app provides open access to the index values and allows users to compare index values in different areas, details of the underlying methodology are also available. We invite readers to contact us with any feedback via the webpage on the construction of the index or the app. You can watch a webinar of Andrew and Torsten demonstrating them at bit.ly/3eBL6x6
Andrew Cairns is a professor in actuarial mathematics and statistics at Heriot-Watt University
Torsten Kleinow is an associate professor in actuarial mathematics and statistics at Heriot-Watt University
Jie Wen is a PhD candidate at Heriot-Watt University and works at Lloyds Banking Group