title: Modelling childhood growth using fractional polynomials and linear splines.
abstract: BACKGROUND
  There is increasing emphasis in medical research on modelling growth across the life course and identifying factors associated with growth. Here, we demonstrate multilevel models for childhood growth either as a smooth function (using fractional polynomials) or a set of connected linear phases (using linear splines).
  
  
  METHODS
  We related parental social class to height from birth to 10 years of age in 5,588 girls from the Avon Longitudinal Study of Parents and Children (ALSPAC). Multilevel fractional polynomial modelling identified the best-fitting model as being of degree 2 with powers of the square root of age, and the square root of age multiplied by the log of age. The multilevel linear spline model identified knot points at 3, 12 and 36 months of age.
  
  
  RESULTS
  Both the fractional polynomial and linear spline models show an initially fast rate of growth, which slowed over time. Both models also showed that there was a disparity in length between manual and non-manual social class infants at birth, which decreased in magnitude until approximately 1 year of age and then increased.
  
  
  CONCLUSIONS
  Multilevel fractional polynomials give a more realistic smooth function, and linear spline models are easily interpretable. Each can be used to summarise individual growth trajectories and their relationships with individual-level exposures.
authors.affiliation: School of Social and Community Medicine and MRC Integrative Epidemiology Unit, University of Bristol, Bristol, UK.
authors.forename: Kate
authors.initials: K
authors.lastname: Tilling
authors.forename: Corrie
authors.initials: C
authors.lastname: Macdonald-Wallis
authors.forename: Debbie A
authors.initials: DA
authors.lastname: Lawlor
authors.forename: Rachael A
authors.initials: RA
authors.lastname: Hughes
authors.forename: Laura D
authors.initials: LD
authors.lastname: Howe
mesh_terms: D001827:Body Height; D002648:Child; D002657:Child Development / Q000502:physiology*; D002675:Child, Preschool; D005260:Female; D006801:Humans; D007223:Infant; D016014:Linear Models; D008137:Longitudinal Studies; D015233:Models, Statistical; D012923:Social Class