Individual growth curves and longitudinal growth charts between 0 and 3 years

From a statistical viewpoint, the construction of longitudinal growth norms involves two classes of problems: (a) the choice of a mathematical function having a few constants as possible, but suitable for describing individual growth process in the growth period of concern; (b) the estimation of the mean growth constants for a homogeneous group of subjects, and of the covariance matrix of data collected longitudinally, to compute tolerance intervals which enable us to draw growth charts. Although growth constants should have some biological interpretation, the choice of functions rests mainly on the criterion of following observed growth as closely as possible. As to the second problem, the simplest situation implies that growth function is linear in the constants and all subjects have measures on the same prefixed occasions: in this case, multivariate Potthoff-Roy model (1964) directly applies. In longitudinal growth studies, however, it happens that subjects do not come for measurements at exactly the age specified: two-stage models seem to be more appropriate to this latter case. They consist of (a) fitting individual growth curve on each subject to obtain estimates of 1st-stage constants; (b) obtaining estimates of 2nd-stage constants, characteristic of the whole group of subjects, in terms of weighted averages of the estimates of the 1st-stage constants. This paper deals with the application of a two-stage model to the growth in length of 203 girls and 217 boys born in Naples between 1977 and 1981. Children, whose growth records are used to trace longitudinal standards, have been measured at birth, and at least 5 times in the course of a follow-up made up of 8 visits, between 3 months and 3 years of life.