The Penn Statistics in Imaging and Visualization Endeavor (PennSIVE), Department of Biostatistics, Epidemiology, and Informatics, University of Pennsylvania, 423 Guardian Drive, Philadelphia, PA, 19104, USA.
Section on Developmental Neurogenomics, National Institutes of Mental Health, 10 Center Drive, Bethesda, MD, 20892, USA.
Biostatistics. 2023 Dec 15;25(1):154-170. doi: 10.1093/biostatistics/kxac032.
Many scientific questions can be formulated as hypotheses about conditional correlations. For instance, in tests of cognitive and physical performance, the trade-off between speed and accuracy motivates study of the two variables together. A natural question is whether speed-accuracy coupling depends on other variables, such as sustained attention. Classical regression techniques, which posit models in terms of covariates and outcomes, are insufficient to investigate the effect of a third variable on the symmetric relationship between speed and accuracy. In response, we propose a conditional correlation model with association size, a likelihood-based statistical framework to estimate the conditional correlation between speed and accuracy as a function of additional variables. We propose novel measures of the association size, which are analogous to effect sizes on the correlation scale while adjusting for confound variables. In simulation studies, we compare likelihood-based estimators of conditional correlation to semiparametric estimators adapted from genomic studies and find that the former achieves lower bias and variance under both ideal settings and model assumption misspecification. Using neurocognitive data from the Philadelphia Neurodevelopmental Cohort, we demonstrate that greater sustained attention is associated with stronger speed-accuracy coupling in a complex reasoning task while controlling for age. By highlighting conditional correlations as the outcome of interest, our model provides complementary insights to traditional regression modeling and partitioned correlation analyses.
许多科学问题可以被表述为关于条件相关的假设。例如，在认知和身体表现的测试中，速度和准确性之间的权衡促使人们一起研究这两个变量。一个自然的问题是，速度-准确性的耦合是否取决于其他变量，例如持续注意力。经典的回归技术，根据协变量和结果来假设模型，不足以研究第三个变量对速度和准确性之间对称关系的影响。为此，我们提出了一个具有关联大小的条件相关模型，这是一种基于似然的统计框架，可以估计速度和准确性之间的条件相关作为附加变量的函数。我们提出了关联大小的新度量标准，这些度量标准类似于相关尺度上的效应大小，同时调整了混淆变量。在模拟研究中，我们将基于似然的条件相关估计与来自基因组研究的半参数估计进行比较，发现前者在理想条件和模型假设失配下都具有更低的偏差和方差。使用费城神经发育队列的神经认知数据，我们证明在控制年龄的情况下，更大的持续注意力与复杂推理任务中更强的速度-准确性耦合相关。通过将条件相关作为感兴趣的结果，我们的模型为传统的回归建模和分区相关分析提供了补充见解。
