Bayesian Ordinal Quantile Regression for Early Puberty

Abstract

The average age of female puberty onset in the United States is trending downwards, particularly in low-income and African-American populations, but the underlying reasons are not well understood. Previous research has identified links between early puberty and socioeconomic factors, harsh family environments, nutrition, and childhood obesity, but there are many contradicting studies and no clear consensus in the literature. Early puberty is associated with increased health risks later in life, including for cardiovascular disease, breast cancer, type 2 diabetes, and all-cause mortality, so identifying the childhood factors related to early puberty is essential to the development of intervention strategies. In this work, we use the Fragile Families and Child Wellbeing Study, which provides longitudinal data on children from high-risk populations. However, as with most surveys, this dataset contains a large number of ordinal variables, distinguished from categorical data because they are ordered and from count data because there is no underlying interval. Ordinal data result in a high incidence of misclassification error because of the subjectivity in choosing the best category for an intended response. Our preliminary analyses on the Fragile Families data reveal a prevalence of misclassification error in general, and this effect is compounded in the ordinal variables. Quantile regression is a robust way to study associations in such noisy datasets, but we show that existing ordinal quantile regression methods do not produce stable and reliable parameter estimates. Here, we develop and present a new Bayesian ordinal quantile regression method, PCGSD, that outperforms existing methods on our set of simulations and can be applied to answer questions such as those introduced by our motivating case study, early puberty.