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Open Access Research article

A nonparametric random coefficient approach for life expectancy growth using a hierarchical mixture likelihood model with application to regional data from North Rhine-Westphalia (Germany)

Dankmar Böhning1*, Sarah Karasek2, Claudia Terschüren3, Rolf Annuß3 and Rainer Fehr3

Author Affiliations

1 Southampton Statistical Sciences Research Institute, Mathematics and Medicine, University of Southampton, Southampton SO17 1BJ, UK

2 Institute of Statistics, Graz University of Technology, Kopernikusgasse 24/III, 8010 Graz, Austria

3 , Landeszentrum Gesundheit Nordrhein-Westfalen / NRW Centre for Health, Westerfeldstr. 35/37, 33609 Bielefeld, Germany

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BMC Medical Research Methodology 2013, 13:36  doi:10.1186/1471-2288-13-36

Published: 9 March 2013



Life expectancy is of increasing prime interest for a variety of reasons. In many countries, life expectancy is growing linearly, without any indication of reaching a limit. The state of North Rhine–Westphalia (NRW) in Germany with its 54 districts is considered here where the above mentioned growth in life expectancy is occurring as well. However, there is also empirical evidence that life expectancy is not growing linearly at the same level for different regions.


To explore this situation further a likelihood-based cluster analysis is suggested and performed. The modelling uses a nonparametric mixture approach for the latent random effect. Maximum likelihood estimates are determined by means of the EM algorithm and the number of components in the mixture model are found on the basis of the Bayesian Information Criterion. Regions are classified into the mixture components (clusters) using the maximum posterior allocation rule.


For the data analyzed here, 7 components are found with a spatial concentration of lower life expectancy levels in a centre of NRW, formerly an enormous conglomerate of heavy industry, still the most densely populated area with Gelsenkirchen having the lowest level of life expectancy growth for both genders. The paper offers some explanations for this fact including demographic and socio-economic sources.


This case study shows that life expectancy growth is widely linear, but it might occur on different levels.

Likelihood–based cluster analysis; Random coefficient modelling; Finite mixture model; Life expectancy