Estimating correlation between multivariate longitudinal data in the presence of heterogeneity
Abstract Background Estimating correlation coefficients among outcomes is one of the most important analytical tasks in epidemiological and clinical research. Availability of multivariate longitudinal data presents a unique opportunity to assess joint evolution of outcomes over time. Bivariate linea...
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| Format: | Article |
| Language: | English |
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BMC
2017-08-01
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| Series: | BMC Medical Research Methodology |
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| Online Access: | http://link.springer.com/article/10.1186/s12874-017-0398-1 |
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| author | Feng Gao J. Philip Miller Chengjie Xiong Jingqin Luo Julia A. Beiser Ling Chen Mae O. Gordon |
| author_facet | Feng Gao J. Philip Miller Chengjie Xiong Jingqin Luo Julia A. Beiser Ling Chen Mae O. Gordon |
| author_sort | Feng Gao |
| collection | DOAJ |
| description | Abstract Background Estimating correlation coefficients among outcomes is one of the most important analytical tasks in epidemiological and clinical research. Availability of multivariate longitudinal data presents a unique opportunity to assess joint evolution of outcomes over time. Bivariate linear mixed model (BLMM) provides a versatile tool with regard to assessing correlation. However, BLMMs often assume that all individuals are drawn from a single homogenous population where the individual trajectories are distributed smoothly around population average. Methods Using longitudinal mean deviation (MD) and visual acuity (VA) from the Ocular Hypertension Treatment Study (OHTS), we demonstrated strategies to better understand the correlation between multivariate longitudinal data in the presence of potential heterogeneity. Conditional correlation (i.e., marginal correlation given random effects) was calculated to describe how the association between longitudinal outcomes evolved over time within specific subpopulation. The impact of heterogeneity on correlation was also assessed by simulated data. Results There was a significant positive correlation in both random intercepts (ρ = 0.278, 95% CI: 0.121–0.420) and random slopes (ρ = 0.579, 95% CI: 0.349–0.810) between longitudinal MD and VA, and the strength of correlation constantly increased over time. However, conditional correlation and simulation studies revealed that the correlation was induced primarily by participants with rapid deteriorating MD who only accounted for a small fraction of total samples. Conclusion Conditional correlation given random effects provides a robust estimate to describe the correlation between multivariate longitudinal data in the presence of unobserved heterogeneity (NCT00000125). |
| first_indexed | 2024-12-11T07:53:40Z |
| format | Article |
| id | doaj.art-f0715532e59d4a3cad86b2c0329b5eed |
| institution | Directory Open Access Journal |
| issn | 1471-2288 |
| language | English |
| last_indexed | 2024-12-11T07:53:40Z |
| publishDate | 2017-08-01 |
| publisher | BMC |
| record_format | Article |
| series | BMC Medical Research Methodology |
| spelling | doaj.art-f0715532e59d4a3cad86b2c0329b5eed2022-12-22T01:15:17ZengBMCBMC Medical Research Methodology1471-22882017-08-0117111110.1186/s12874-017-0398-1Estimating correlation between multivariate longitudinal data in the presence of heterogeneityFeng Gao0J. Philip Miller1Chengjie Xiong2Jingqin Luo3Julia A. Beiser4Ling Chen5Mae O. Gordon6Department of Surgery, Division of Public Health Sciences, Washington University School of MedicineDivision of Biostatistics, Washington University School of MedicineDivision of Biostatistics, Washington University School of MedicineDepartment of Surgery, Division of Public Health Sciences, Washington University School of MedicineDepartment of Ophthalmology & Visual Sciences, Washington University School of MedicineDivision of Biostatistics, Washington University School of MedicineDivision of Biostatistics, Washington University School of MedicineAbstract Background Estimating correlation coefficients among outcomes is one of the most important analytical tasks in epidemiological and clinical research. Availability of multivariate longitudinal data presents a unique opportunity to assess joint evolution of outcomes over time. Bivariate linear mixed model (BLMM) provides a versatile tool with regard to assessing correlation. However, BLMMs often assume that all individuals are drawn from a single homogenous population where the individual trajectories are distributed smoothly around population average. Methods Using longitudinal mean deviation (MD) and visual acuity (VA) from the Ocular Hypertension Treatment Study (OHTS), we demonstrated strategies to better understand the correlation between multivariate longitudinal data in the presence of potential heterogeneity. Conditional correlation (i.e., marginal correlation given random effects) was calculated to describe how the association between longitudinal outcomes evolved over time within specific subpopulation. The impact of heterogeneity on correlation was also assessed by simulated data. Results There was a significant positive correlation in both random intercepts (ρ = 0.278, 95% CI: 0.121–0.420) and random slopes (ρ = 0.579, 95% CI: 0.349–0.810) between longitudinal MD and VA, and the strength of correlation constantly increased over time. However, conditional correlation and simulation studies revealed that the correlation was induced primarily by participants with rapid deteriorating MD who only accounted for a small fraction of total samples. Conclusion Conditional correlation given random effects provides a robust estimate to describe the correlation between multivariate longitudinal data in the presence of unobserved heterogeneity (NCT00000125).http://link.springer.com/article/10.1186/s12874-017-0398-1Bivariate linear mixed model (BLMM)Multivariate longitudinal dataCorrelationHeterogeneity |
| spellingShingle | Feng Gao J. Philip Miller Chengjie Xiong Jingqin Luo Julia A. Beiser Ling Chen Mae O. Gordon Estimating correlation between multivariate longitudinal data in the presence of heterogeneity BMC Medical Research Methodology Bivariate linear mixed model (BLMM) Multivariate longitudinal data Correlation Heterogeneity |
| title | Estimating correlation between multivariate longitudinal data in the presence of heterogeneity |
| title_full | Estimating correlation between multivariate longitudinal data in the presence of heterogeneity |
| title_fullStr | Estimating correlation between multivariate longitudinal data in the presence of heterogeneity |
| title_full_unstemmed | Estimating correlation between multivariate longitudinal data in the presence of heterogeneity |
| title_short | Estimating correlation between multivariate longitudinal data in the presence of heterogeneity |
| title_sort | estimating correlation between multivariate longitudinal data in the presence of heterogeneity |
| topic | Bivariate linear mixed model (BLMM) Multivariate longitudinal data Correlation Heterogeneity |
| url | http://link.springer.com/article/10.1186/s12874-017-0398-1 |
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