title: 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).
abstract: BACKGROUND
  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.
  
  
  METHODS
  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.
  
  
  RESULTS
  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.
  
  
  CONCLUSIONS
  This case study shows that life expectancy growth is widely linear, but it might occur on different levels.
authors.affiliation: Southampton Statistical Sciences Research Institute, Mathematics and Medicine, University of Southampton, Southampton SO17 1BJ, UK. d.a.bohning@soton.ac.uk
authors.forename: Dankmar
authors.initials: D
authors.lastname: Böhning
authors.forename: Sarah
authors.initials: S
authors.lastname: Karasek
authors.forename: Claudia
authors.initials: C
authors.lastname: Terschüren
authors.forename: Rolf
authors.initials: R
authors.lastname: Annuß
authors.forename: Rainer
authors.initials: R
authors.lastname: Fehr
mesh_terms: D000293:Adolescent; D000328:Adult; D000368:Aged; D016000:Cluster Analysis; D005260:Female; D005858:Germany / Q000453:epidemiology; D006305:Health Status Indicators; D006801:Humans; D008017:Life Expectancy / Q000639:trends*; D016014:Linear Models; D008297:Male; D008875:Middle Aged; D012041:Regional Medical Programs; D018570:Risk Assessment; D012424:Rural Population / Q000706:statistics & numerical data; D062206:Spatial Analysis; D018709:Statistics, Nonparametric; D014505:Urban Population / Q000706:statistics & numerical data