Beyond standardized mortality ratios; some uses of smoothed age-specific mortality rates on small areas studies

Abstract

Background: Most epidemiological risk indicators strongly depend on the age composition of populations, which makes the direct comparison of raw (unstandardized) indicators misleading because of the different age structures of the spatial units of study. Age-standardized rates (ASR) are a common solution for overcoming this confusing effect. The main drawback of ASRs is that they depend on age-specific rates which, when working with small areas, are often based on very few, or no, observed cases for most age groups. A similar effect occurs with life expectancy at birth and many more epidemiological indicators, which makes standardized mortality ratios (SMR) the omnipresent risk indicator for small areas epidemiologic studies.

Methods: To deal with this issue, a multivariate smoothing model, the M-model, is proposed in order to fit the age-specific probabilities of death (PoDs) for each spatial unit, which assumes dependence between closer age groups and spatial units. This age-space dependence structure enables information to be transferred between neighboring consecutive age groups and neighboring areas, at the same time, providing more reliable age-specific PoDs estimates.

Results: Three case studies are presented to illustrate the wide range of applications that smoothed age specific PoDs have in practice . The first case study shows the application of the model to a geographical study of lung cancer mortality in women. This study illustrates the convenience of considering age-space interactions in geographical studies and to explore the different spatial risk patterns shown by the different age groups. Second, the model is also applied to the study of ischaemic heart disease mortality in women in two cities at the census tract level. Smoothed age-standardized rates are derived and compared for the census tracts of both cities, illustrating some advantages of this mortality indicator over traditional SMRs. In the latest case study, the model is applied to estimate smoothed life expectancy (LE), which is the most widely used synthetic indicator for characterizing overall mortality differences when (not so small) spatial units are considered.

Conclusion: Our age-space model is an appropriate and flexible proposal that provides more reliable estimates of the probabilities of death, which allow the calculation of enhanced epidemiological indicators (smoothed ASR, smoothed LE), thus providing alternatives to traditional SMR-based studies of small areas.

Keywords: Age-specific smoothing; Age-standardized rates; Disease mapping; Life expectancy.

Fig. 1

Comparison between raw and smoothed probabilities of death (PoDs) for each area from lung cancer in women in 2008–2017. Denia and Almazora are two illustrative municipalities. Comunitat Valenciana, CV, is the whole study region

Fig. 2

Spatial and interaction terms for the smoothed age-specific PoDs for each area. Denia and Almazora are two illustrative municipalities

Fig. 3

Age–space interaction for several of the age groups considered

Fig. 4

Smoothed age-standardized mortality rate from ischaemic heart disease in Valencia and Alicante. Women over 45 years, period 1996–2015

Fig. 5

Raw and smoothed life expectancy at birth, for men and women, period 2014–2017