A random coefficient growth curve analysis of mental development in low‐birth‐weight infants

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Abstract
In many medical studies, longitudinal data are collected on each of a sample of patients. The objectives of such studies often are: to estimate and test bivariate or multivariate relationships within each of several groups of patients from these repeated measures data; to compare these relationships among groups; and to test for the effects of baseline covariates on the relationships. This paper illustrates the use of statistical methods for growth curve analysis recently proposed by Vonesh and Carter for achieving these goals by relating a measure of preschool cognitive development to age in four race by sex groups of low‐birth‐weight infants. Significant declines in Bayley's Mental Development Index (MDI) with increasing age were found in all groups. Birth‐weight did not significantly influence the rate of decline but did influence the overall level of performance. Even so, in the group most comparable to Bayley's normative population, predicted MDI was near the norm even for extremely low‐birth‐weight infants (that is, 1000 grams). Although there is some risk of mental deficit associated with prematurity, eventual developmental delays in low‐birth‐weight infants frequently are acquired with age. The rate of decline in MDI was significantly associated with race and mother's education. Assumptions required for the valid application of these methods are discussed and tested in the setting of this applied problem. The assumptions appeared valid in this application. We conclude with a brief discussion of available alternatives when the assumptions are violated and point to areas for future research.