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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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Ma Z, Davis SW, Ho YY. Flexible copula model for integrating correlated multi-omics data from single-cell experiments. Biometrics 2022. [PMID: 35622236 DOI: 10.1111/biom.13701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2021] [Accepted: 05/18/2022] [Indexed: 11/27/2022]
Abstract
With recent advances in technologies to profile multi-omics data at the single-cell level, integrative multi-omics data analysis has been increasingly popular. It is increasingly common that information such as methylation changes, chromatin accessibility, and gene expression are jointly collected in a single-cell experiment. In biomedical studies, it is often of interest to study the associations between various data types and to examine how these associations might change according to other factors such as cell types and gene regulatory components. However, since each data type usually has a distinct marginal distribution, joint analysis of these changes of associations using multi-omics data is statistically challenging. In this paper, we propose a flexible copula-based framework to model covariate-dependent correlation structures independent of their marginals. In addition, the proposed approach could jointly combine a wide variety of univariate marginal distributions, either discrete or continuous, including the class of zero-inflated distributions. The performance of the proposed framework is demonstrated through a series of simulation studies. Finally, it is applied to a set of experimental data to investigate the dynamic relationship between single-cell RNA-sequencing, chromatin accessibility, and DNA methylation at different germ layers during mouse gastrulation. This article is protected by copyright. All rights reserved.
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Affiliation(s)
- Zichen Ma
- Department of Public Health Sciences, Clemson University, Clemson, SC, USA
| | - Shannon W Davis
- Department of Biological Sciences, University of South Carolina, Columbia, SC, USA
| | - Yen-Yi Ho
- Department of Statistics, University of South Carolina, Columbia, SC, USA
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