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Tu D, Mahony B, Moore TM, Bertolero MA, Alexander-Bloch AF, Gur R, Bassett DS, Satterthwaite TD, Raznahan A, Shinohara RT. CoCoA: conditional correlation models with association size. Biostatistics 2023; 25:154-170. [PMID: 35939558 PMCID: PMC10724258 DOI: 10.1093/biostatistics/kxac032] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2022] [Revised: 07/14/2022] [Accepted: 07/18/2022] [Indexed: 11/13/2022] Open
Abstract
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.
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Affiliation(s)
- Danni Tu
- 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
| | - Bridget Mahony
- Section on Developmental Neurogenomics, National Institutes of Mental Health, 10 Center Drive, Bethesda, MD, 20892, USA
| | - Tyler M Moore
- Department of Psychiatry, Perelman School of Medicine, 3400 Spruce Street, Philadelphia, PA, 19104, USA
| | - Maxwell A Bertolero
- Department of Psychiatry, Perelman School of Medicine, Philadelphia, PA, USA and Penn Lifespan Informatics and Neuroimaging Center, 3700 Hamilton Walk, Philadelphia, PA, 19104, USA
| | | | - Ruben Gur
- Department of Psychiatry, Perelman School of Medicine, Philadelphia, PA, USA
| | - Dani S Bassett
- Department of Bioengineering, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA, 19104, USA, Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA, 19104, USA, Department of Electrical and Systems Engineering, University of Pennsylvania, 200 South 33rd Street, Philadelphia, PA, 19104, USA and Department of Neurology, University of Pennsylvania, 3400 Spruce Street, Philadelphia, PA, 19104, USA
| | - Theodore D Satterthwaite
- Department of Psychiatry, Perelman School of Medicine, Philadelphia, PA, USA and Penn Lifespan Informatics and Neuroimaging Center, Philadelphia, PA, USA
| | - Armin Raznahan
- Section on Developmental Neurogenomics, National Institutes of Mental Health, Bethesda, MD, USA
| | - Russell T Shinohara
- The Penn Statistics in Imaging and Visualization Endeavor (PennSIVE), Department of Biostatistics, Epidemiology, and Informatics, University of Pennsylvania, Philadelphia, PA, USA
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