Precise gaussian distribution functions of maternal serum α-fetoprotein and free β-subunit of human chorionic gonadotropin for trisomy 21 screening: Improved accuracy for patient counseling

OBJECTIVE: Gaussian equation curves are used to generate baseline curves against which a priori maternal age Down syndrome risks are adjusted to develop likelihood ratios for individual patients. We sought to evaluate the accuracy of these calculations, minimize the affects of outliers, and to make improvements. STUDY DESIGN: Gaussian distribution functions were used to investigate the best model for α-fetoprotein and free β-human chorionic gonadotropin multiples of the median with use of nonlinear regressions. Parameters from distribution functions can be used to compute a more precise likelihood ratio for the decision logic for trisomy 21. A total of 58,297 normal cases and 348 cases of trisomy 21 were computed. RESULTS: Log normal distribution functions generated by nonlinear regression produced excellent but exaggerated goodness of fit R² to the frequency distributions of the data. For normal cases values were as follows (in mean, SD, and R², respectively): log α-fetoprotein -0.07199, 0.15681, and 0.9970; log β- human chorionic gonadotropin -0.15203, 0.24284, and 0.9987. For trisomy 21 cases the values were (in mean, SD, and R², respectively) for log α- fetoprotein -0.19303, 0.15802, and 0.9828 and for log β-human chorionic gonadotropin 0.19996, 0.29760, and 0.9669. Distributions reconstructed with use of statistical means and SDs generated goodness of fit R² from 0.585 to 0.914. Use of means and SDs derived from distribution functions increased the R² to 0.855 and 0.999. The change in the model produces, at a 5% false- positive rate, a sensitivity of 57.18% (199/348). A 1 in 113 cutoff point risk is obtained and is tighter than the 1 in 251 without the distribution functions, as versus 1 in 270 by age calculations alone. CONCLUSIONS: Our data suggest that (1) normality of log transforms of α-fetoprotein and normality of log transforms of β-human chorionic gonadotropin are reasonable models, (2) distribution functions can minimize the effect of outliers, which produces more realistic risk estimates, and (3) the effect of distribution functions versus standard mean and SDs cannot automatically be extrapolated to other parameters, which must be tested individually.