Using distance correlation and SS-ANOVA to assess associations of familial relationships, lifestyle factors, diseases, and mortality

Abstract

We present a method for examining mortality as it is seen to run in families, and lifestyle factors that are also seen to run in families, in a subpopulation of the Beaver Dam Eye Study. We observe that pairwise distance between death age in related persons is on average less than pairwise distance in death age between random pairs of unrelated persons. Our goal is to examine the hypothesis that pairwise differences in lifestyle factors correlate with the observed pairwise differences in death age that run in families. Szekely and Rizzo [Szekely GJ, Rizzo ML (2009) Ann Appl Stat 3(4): 1236–1265] have recently developed a method called distance correlation, which is suitable for this task with some enhancements. We build a Smoothing Spline ANOVA (SS-ANOVA) model for predicting death age based on four major lifestyle factors generally known to be related to mortality and four major diseases contributing to mortality, to develop a lifestyle mortality risk vector and a disease mortality risk vector. We then examine to what extent pairwise differences in these scores correlate with pairwise differences in mortality as they occur between family members and between unrelated persons. We find significant distance correlations between death ages, lifestyle factors, and family relationships. Considering only sib pairs compared with unrelated persons, distance correlation between siblings and mortality is, not surprisingly, stronger than that between more distantly related family members and mortality. The methodological approach here adapts to exploring relationships between multiple clusters of variables with observable (real-valued) attributes, and other factors for which only possibly nonmetric pairwise dissimilarities are observed.

Distance correlation coefficients for Lancaster distributions

“…The concepts of distance covariance and distance correlation, introduced by Székely, et al [27,31], have been shown to be widely applicable for measuring dependence between collections of random variables. As examples of the ubiquity of distance correlation methods, we note the results on distance correlation given recently by: Székely, et al [21,28,29,30,31], on statistical inference; Sejdinovic, et al [26], on machine learning; Kong, et al [10], on familial relationships and mortality; Zhou [33], on nonlinear time series; Lyons [17], on abstract metric spaces; Martínez-Gomez, et al [18] and Richards, et al [20], on large astrophysical databases; Dueck, et al [5], on high-dimensional inference and the analysis of wind data; and Dueck, et al [6], on a connection with singular integrals on Euclidean spaces.…”

Fast Computing for Distance Covariance

“…Since its induction (Székely, Rizzo and Bakirov 2007), distance correlation has had many applications in, e.g., life science (Kong, Klein, Klein and Wahba 2012) and variable selection (Li, Zhong and Zhu 2012), and has been analyzed (Székely and Rizzo 2012;Lyons 2013), extended (Székely and Rizzo 2009;Székely and Rizzo To appear) in various aspects. If distance correlation were implemented straightforwardly from its definition, its computational complexity can be as high as a constant times n 2 for a sample size n. This fact has been cited for numerous times in the literature as a disadvantage of adopting the distance correlation.…”

Using distance covariance for improved variable selection with application to learning genetic risk models

“…The method has been successfully applied to various problem, see [4] for example. To be specific, the authors defined the distance covariance between X ∈ ℝ p and Y ∈ ℝ q to be…”