Statistical estimation and comparison of group-specific bivariate correlation coefficients in family-type clustered studies

Abstract

Bivariate correlation coefficients (BCCs) are often calculated to gauge the relationship between two variables in medical research. In a family-type clustered design where multiple participants from same units/families are enrolled, BCCs can be defined and estimated at various hierarchical levels (subject level, family level and marginal BCC). Heterogeneity usually exists between subject groups and, as a result, subject level BCCs may differ between subject groups. In the framework of bivariate linear mixed effects modeling, we define and estimate BCCs at various hierarchical levels in a family-type clustered design, accommodating subject group heterogeneity. Simplified and modified asymptotic confidence intervals are constructed to the BCC differences and Wald type tests are conducted. A real-world family-type clustered study of Alzheimer disease (AD) is analyzed to estimate and compare BCCs among well-established AD biomarkers between mutation carriers and non-carriers in autosomal dominant AD asymptomatic individuals. Extensive simulation studies are conducted across a wide range of scenarios to evaluate the performance of the proposed estimators and the type-I error rate and power of the proposed statistical tests.

Abbreviations: BCC: bivariate correlation coefficient; BLM: bivariate linear mixed effects model; CI: confidence interval; AD: Alzheimer’s disease; DIAN: The Dominantly Inherited Alzheimer Network; SA: simple asymptotic; MA: modified asymptotic

KEYWORDS:

• Bivariate correlation coefficient
• bivariate linear mixed effects model
• parameter estimation
• confidence interval
• hypothesis testing
• type-I error/size and power

Acknowledgements

The authors thank the Genetics Core (Alison Goate, DPhil, Core Leader) of the DIAN (UF1 AG03243807) for the genetic data, Biomarker Core (Anne Fagan, PhD, Core leader) for the CSF data, and Imaging Core (Tammie Benzinger, MD, PhD, Core leader) for the imaging data. J Luo and CX conceptualized the paper and designed the study. JL performed the analyses and wrote the manuscript. J Lu and Chen helped with missing data analyses. GW, AF, GD, JV contributed to DIAN data. All authors participated in discussion, reviewed and revised the paper and approved the final version of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Availability of data and materials

The simulation and real data analysis programming codes will be available at request from the corresponding author.

Competing interests

AMF has received research funding from the National Institute on Aging of the National Institutes of Health, Biogen, Centene, Fujirebio and Roche Diagnostics. She is a member of the scientific advisory boards for Roche Diagnostics, Genentech and AbbVie and also consults for Araclon/Grifols, Diadem, and DiamiR. There are no conflicts. GSD is supported by a career development grant from the NIH (K23AG064029). He owns stock (>$10,000) in ANI Pharmaceuticals (a generic pharmaceutical company). He serves as a topic editor for DynaMed (EBSCO), overseeing development of evidence-based educational content, and as the Clinical Director of the Anti-NMDA Receptor Encephalitis Foundation (Inc, Canada; uncompensated). All the authors declare no competing interests related to this work.

Ethics approval and consent to the participant

The use of the DIAN observational study data was approved by the DIAN Steering Committee for data analysis and publication.

Additional information

Funding

This study was partly supported by National Institute of Health/National Cancer Institute grant P30 CA91842 (Dr. Eberlein), U10 CA180860 (Dr. Mutch/Dr. Ellis/Dr. Luo), National Institute on Aging (NIA) grant UF1 AG03243807 (Dr Bateman) and P50 AG005681 (Dr. Morris), NIA R01 AG034119 (Dr. Xiong).