Volume 20, Issue 1 (6-2021)                   JIRSS 2021, 20(1): 347-370 | Back to browse issues page

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Torabi M, R. de Leon A. Conditional Dependence in Longitudinal Data Analysis. JIRSS. 2021; 20 (1) :347-370
URL: http://jirss.irstat.ir/article-1-789-en.html
Departments of Community Health Sciences and Statistics, University of Manitoba, Winnipeg, Manitoba, CANADA R3E 0W3 , Mahmoud.Torabi@umanitoba.ca
Abstract:   (228 Views)

Mixed models are widely used to analyze longitudinal data.

In their conventional formulation as linear mixed models (LMMs) and generalized LMMs (GLMMs), a commonly indispensable assumption in settings involving longitudinal non-Gaussian data is that the longitudinal observations from subjects are conditionally independent, given subject-specific random effects. Although conventional Gaussian LMMs are able to incorporate conditional dependence of longitudinal observations, they require that the data are, or some transformation of them is, Gaussian, a serious limitation in a wide variety of practical applications. Here, we introduce the class of Gaussian copula conditional regression models (GCCRMs) as flexible alternatives to conventional LMMs and GLMMs. One advantage of GCCRMs is that they extend conventional LMMs and GLMMs in a way that reduces to conventional LMMs, when the data are Gaussian, and to conventional GLMMs, when conditional independence is assumed. We implement likelihood analysis of GCCRMs using existing software and statistical packages and evaluate the finite-sample performance of maximum likelihood estimates for GCCRM empirically via simulations vis-a-vis the `naive' likelihood analys is that incorrectly assumes conditionally independent longitudinal data. Our results show that the `naive' analysis yields estimates with possibly severe bias and incorrect standard errors, leading to misleading inferences. We use bolus count data on patients' controlled analgesia comparing dosing regimes and data on serum creatinine from a renal graft study to illustrate the applications of GCCRMs.

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Type of Study: Original Paper | Subject: 62Exx: Distribution theory
Received: 2020/11/17 | Accepted: 2021/02/8 | Published: 2021/06/20

1. Brown, H. and Prescott, R. (2015). Applied Mixed Models in Medicine. New York: John Wiley & Sons.
2. Clemen, R. and Reilly, T. (1999). Correlation and copulas for decision and risk analysis. Management Science 45, 208-224. [DOI:10.1287/mnsc.45.2.208]
3. Das, K., Li, R., Sengupta, S., and Wu, R. (2013). A Bayesian semiparametric model for bivariate sparse longitudinal data. Statistics in Medicine 32, 3899-3910. [DOI:10.1002/sim.5790]
4. de Leon, A. and Wu, B. (2011). Copula-based regression models for a bivariate mixed discrete and continuous outcome. Statistics in Medicine 30, 175-185. [DOI:10.1002/sim.4087]
5. Fieuws, S. and Verbeke, G. (2008). Predicting renal graft failure using multivariate longitudinal profiles. Biostatistics 9, 419-431. [DOI:10.1093/biostatistics/kxm041]
6. Klaassen, C. and Wellner, J. (1997). E cient estimation in the bivariate normal copula: normal margins are least favourable. Bernoulli 3, 55-77. [DOI:10.2307/3318652]
7. Kugiumtzis, D. and Bora-Senta, E. (2010). Normal correlation coefficient of non-normal variables using piece-wise linear approximation. Computational Statistics 25, 645-662. [DOI:10.1007/s00180-010-0195-3]
8. Magezi, D. A. (2015). Linear mixed-effects models for within-participant psychology experiments: an introductory tutorial and free, graphical user interface (LMMgui). Frontiers in Psychology 6(2), 1664-1078 [DOI:10.3389/fpsyg.2015.00002]
9. Masarotto, G. and Varin, C. (2012). Gaussian copula marginal regression. Electronic Journal of Statistics 6, 1517-1549. [DOI:10.1214/12-EJS721]
10. McCulloch, C. E., Searle, S. R., and Neuhaus, J. M. (2008). Generalized, Linear, and Mixed Models. New York: John Wiley & Sons.
11. Molenberghs, G. and Verbeke, G. (2005). Models for Discrete Longitudinal Data. New York: Springer.
12. R Core Team. (2020). R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing.
13. Renard, D., Geys, H., Molenberghs, G., Burzykowski, T., and Buyse, M. (2002). Validation of surrogate end points in multiple randomized clinical trials with discrete outcomes. Biometrical Journal 44, 921-935. [DOI:10.1002/bimj.200290004]
14. Searle, S. R., Casella, G., and McCulloch, C. E. (2006). Variance Components. New Jersey: John Wiley & Sons.
15. Vangeneugden, T., Molenberghs, G., Verbeke, G., and Demetrio, C. (2011). Marginal correlation from an extended random-effects model for repeated and overdispersed counts. Journal of Applied Statistics 38, 215-232. [DOI:10.1080/02664760903406405]
16. Weiss, E. W. (2005). Modeling Longitudinal Data. New York: Springer.
17. Wu, B. and de Leon, A. R. (2014). Gaussian copula mixed models for clustered mixed outcomes, with application in developmental toxicology. Journal of Agricultural, Biological and Environmental Statistics 19, 39-56. [DOI:10.1007/s13253-013-0155-9]
18. Wu, B., de Leon, A., and Withanage, N. (2013). Joint analysis of mixed discrete and continuous outcomes via copulas. In Analysis of Mixed Data: Methods and Applications, de Leon A and Carrie're Chough K (eds), 139-156, Chap 10. CRC/Chapman & Hall.
19. Young, J. H. (2002). Blood pressure and decline in kidney function: findings from the systolic hypertension in the elderly program (SHEP). Journal of the American Society of Nephrology 11, 2776-2782. [DOI:10.1097/01.ASN.0000031805.09178.37]

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