title: Multivariable flexible modelling for estimating complete, smoothed life tables for sub-national populations.
abstract: The methods currently available to estimate age- and sex-specific mortality rates for sub-populations are subject to a number of important limitations. We propose two alternative multivariable approaches: a relational model and a Poisson model both using restricted cubic splines.
  
  
  
  We evaluated a flexible Poisson and flexible relational model against the Elandt-Johnson approach in a simulation study using 100 random samples of population and death counts, with different sampling proportions and data arrangements. Estimated rates were compared to the original mortality rates using goodness-of-fit measures and life expectancy. We further investigated an approach for determining optimal knot locations in the Poisson model.
  
  
  
  The flexible Poisson model outperformed the flexible relational and Elandt-Johnson methods with the smallest sample of data (1%). With the largest sample of data (20%), the flexible Poisson and flexible relational models performed comparably, though the flexible Poisson model displayed a slight advantage. Both approaches tended to underestimate infant mortality and thereby overestimate life expectancy at birth. The flexible Poisson model performed much better at young ages when knots were fixed a priori. For ages 30 and above, results were similar to the model with no fixed knots.
  
  
  
  The flexible Poisson model is recommended because it derives robust and unbiased estimates for sub-populations without making strong assumptions about age-specific mortality profiles. Fixing knots a priori in the final model greatly improves fit at the young ages.
authors.affiliation: Cancer Survival Group, Department of Non-Communicable Disease Epidemiology, London School of Hygiene and Tropical Medicine, Keppel street, London, WC1E 7HT, UK. bernard.rachet@lshtm.ac.uk.
authors.forename: Bernard
authors.initials: B
authors.lastname: Rachet
authors.affiliation: Cancer Survival Group, Department of Non-Communicable Disease Epidemiology, London School of Hygiene and Tropical Medicine, Keppel street, London, WC1E 7HT, UK.
authors.forename: Camille
authors.initials: C
authors.lastname: Maringe
authors.affiliation: Cancer Survival Group, Department of Non-Communicable Disease Epidemiology, London School of Hygiene and Tropical Medicine, Keppel street, London, WC1E 7HT, UK.
authors.forename: Laura M
authors.initials: LM
authors.lastname: Woods
authors.affiliation: Cancer Survival Group, Department of Non-Communicable Disease Epidemiology, London School of Hygiene and Tropical Medicine, Keppel street, London, WC1E 7HT, UK.
authors.forename: Libby
authors.initials: L
authors.lastname: Ellis
authors.affiliation: Cancer Survival Group, Department of Non-Communicable Disease Epidemiology, London School of Hygiene and Tropical Medicine, Keppel street, London, WC1E 7HT, UK.
authors.forename: Devon
authors.initials: D
authors.lastname: Spika
authors.affiliation: Cancer Survival Group, Department of Non-Communicable Disease Epidemiology, London School of Hygiene and Tropical Medicine, Keppel street, London, WC1E 7HT, UK.
authors.forename: Claudia
authors.initials: C
authors.lastname: Allemani
mesh_terms: D000293:Adolescent; D000328:Adult; D000368:Aged; D000369:Aged, 80 and over; D002648:Child; D002675:Child, Preschool; D004739:England / Q000453:epidemiology; D005260:Female; D006801:Humans; D007223:Infant; D007231:Infant, Newborn; D008017:Life Expectancy; D015993:Life Tables; D008297:Male; D008875:Middle Aged; D015233:Models, Statistical; D015999:Multivariate Analysis; D016012:Poisson Distribution; D055815:Young Adult
keywords: Cubic splines; Deprivation; Generalised linear model; Life expectancy; Life tables; Model life tables; Mortality rates; Small areas