Robust Bayesian growth curve modelling using conditional medians

Nonparametric percentile curve estimation for a nonnegative marker with excessive zeros

Norm curves for the head circumference, height, and weight of newborns and infants are widely known examples of percentile curves over age, and early accounts date back 50 years. The advent of the Agatston score for coronary calcification based on coronary computed tomography in 1990 heralded the era of a new marker in preventive medicine, in addition to well-known cardiovascular risk factors. A peculiarity of the nonnegative Agatston score in populations that are free of coronary artery disease is the overexpression of zeros. In a case study, we have demonstrated a nonparametric approach for percentile curve estimation using markers such as the Agatston score. This method is based on lowess smoothing of marker-positive scores on age, and the resulting percentile curves are subsequently transposed according to the estimated proportions of zeros. The approach does not involve any parametric assumptions, is robust against outliers, and fulfills the noncrossing property for percentile curves. A simulation study using samples of N=1,000, 2,000, 5,000, and 10,000 subjects illuminates the closeness of the estimated 50^th, 75^th, and 90^th percentile curves to the respective true curves, assuming an exponentially distributed marker and a proportion of zero scores that increase with age.•

The method is applicable to highly skewed data and exemplified here with subgroup data of the referenced procedure.

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The consistency and general performance of the method is shown by means of simulation.

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The method is an explicit, transferable, and reproducible procedure that is applicable to a wide spectrum of markers and scores across various scientific disciplines, far beyond cardiovascular medicine.

Conditional median-based Bayesian growth mixture modeling for nonnormal data

Growth mixture modeling is a common tool for longitudinal data analysis. One of the key assumptions of traditional growth mixture modeling is that repeated measures within each class are normally distributed. When this normality assumption is violated, traditional growth mixture modeling may provide misleading model estimation results and suffer from nonconvergence. In this article, we propose a robust approach to growth mixture modeling based on conditional medians and use Bayesian methods for model estimation and inferences. A simulation study is conducted to evaluate the performance of this approach. It is found that the new approach has a higher convergence rate and less biased parameter estimation than the traditional growth mixture modeling approach when data are skewed or have outliers. An empirical data analysis is also provided to illustrate how the proposed method can be applied in practice.