Fitting mixture models to birth weight data: a case study

Birth weights by gestational age are compared in two birth cohorts from Northern Finland, the first from 1966 and the second from 1985-1986. A curious fact in the data is that mean birth weight before the 39th week was lower in the latter series although the mean birth weight for the total series was higher. Similar findings have been reported in other series. A mixture model with the nonparametric regression function is proposed for studying the hypothesis that the difference was caused by more frequent gross errors in gestational assessment in the earlier cohort. The probability of an error in gestational assessment then greatly depends on the observed gestational age, which makes the mixture model nonstandard. Maximum likelihood solutions to the parameters in the proposed model were computed employing the general expectation-maximization (EM) algorithm. A technique for studying the effect of errors on the intrauterine weight gain curve is proposed and applied to our two birth cohorts. The risk of underestimation of gestational age seems to be larger in the previous series and the differences between the growth curves almost totally vanish when "corrected" by means of the mixture model.