Most studies of continuous health-related outcomes examine differences in mean levels (location) of the outcome by exposure. However, identifying effects on the variability (scale) of an outcome, and combining tests of mean and variability (location-and-scale), could provide additional insights into biological mechanisms. A joint test could improve power for studies of high-dimensional phenotypes, such as epigenome-wide association studies of DNA methylation at CpG sites. One possible cause of heterogeneity of variance is a variable interacting with exposure in its effect on outcome, so a joint test of mean and variability could help in the identification of effect modifiers. Here, we review a scale test, based on the Brown-Forsythe test, for analysing variability of a continuous outcome with respect to both categorical and continuous exposures, and develop a novel joint location-and-scale score (JLSsc) test. These tests were compared to alternatives in simulations and used to test associations of mean and variability of DNA methylation with gender and gestational age using data from the Accessible Resource for Integrated Epigenomics Studies (ARIES). In simulations, the Brown-Forsythe and JLSsc tests retained correct type I error rates when the outcome was not normally distributed in contrast to the other approaches tested which all had inflated type I error rates. These tests also identified > 7500 CpG sites for which either mean or variability in cord blood methylation differed according to gender or gestational age. The Brown-Forsythe test and JLSsc are robust tests that can be used to detect associations not solely driven by a mean effect.

大多数关于持续健康相关结果的研究检查了暴露导致的结果平均水平（位置）的差异。然而，识别对结果的可变性（规模）的影响，并结合均值和可变性（位置和规模）的测试，可以提供对生物学机制的更多见解。联合测试可以提高高维表型研究的能力，例如 CpG 位点 DNA 甲基化的表观基因组关联研究。方差异质性的一个可能原因是变量与暴露在其对结果的影响中相互作用，因此均值和变异性的联合测试可以帮助识别效果修饰符。在这里，我们回顾了基于 Brown-Forsythe 检验的量表检验，用于分析连续结果在分类和连续暴露方面的可变性，并开发一种新颖的联合位置和尺度评分 (JLSsc) 测试。将这些测试与模拟中的替代方法进行比较，并使用来自综合表观基因组学研究 (ARIES) 的可访问资源的数据来测试 DNA 甲基化的平均值和变异性与性别和胎龄的关联。在模拟中，当结果不是正态分布时，Brown-Forsythe 和 JLSsc 测试保留了正确的 I 类错误率，而其他测试的方法都夸大了 I 类错误率。这些测试还确定了超过 7500 个 CpG 位点，其脐带血甲基化的平均值或变异性因性别或胎龄而异。Brown-Forsythe 检验和 JLSsc 是稳健的检验，可用于检测不仅仅由平均效应驱动的关联。