Analysis of multivariate longitudinal kidney function outcomes using generalized linear mixed models

Journal of Translational Medicine

Ayad A Jaffa¹  Mulugeta Gebregziabher²  Miran A Jaffa³ 

[1] Department of Biochemistry and Molecular Genetics, Faculty of Medicine, American University of Beirut, Riad El-Solh, Beirut 1107 2020, Lebanon;Department of Public Health Sciences, Medical University of South Carolina, Charleston 29425, SC, USA;Epidemiology and Population Health Department, Faculty of Health Sciences, American University of Beirut, Riad El-Solh, Beirut 1107 2020, Lebanon

关键词: Random coefficients;    Multivariate longitudinal outcomes;    Joint modeling;   

Others  :  1212305
DOI  :  10.1186/s12967-015-0557-2

 received in 2015-01-26, accepted in 2015-06-01,  发布年份 2015

【 摘 要 】

Background

Renal transplant patients are mandated to have continuous assessment of their kidney function over time to monitor disease progression determined by changes in blood urea nitrogen (BUN), serum creatinine (Cr), and estimated glomerular filtration rate (eGFR). Multivariate analysis of these outcomes that aims at identifying the differential factors that affect disease progression is of great clinical significance. Thus our study aims at demonstrating the application of different joint modeling approaches with random coefficients on a cohort of renal transplant patients and presenting a comparison of their performance through a pseudo-simulation study. The objective of this comparison is to identify the model with best performance and to determine whether accuracy compensates for complexity in the different multivariate joint models.

Methods and results

We propose a novel application of multivariate Generalized Linear Mixed Models (mGLMM) to analyze multiple longitudinal kidney function outcomes collected over 3 years on a cohort of 110 renal transplantation patients. The correlated outcomes BUN, Cr, and eGFR and the effect of various covariates such patient’s gender, age and race on these markers was determined holistically using different mGLMMs. The performance of the various mGLMMs that encompass shared random intercept (SHRI), shared random intercept and slope (SHRIS), separate random intercept (SPRI) and separate random intercept and slope (SPRIS) was assessed to identify the one that has the best fit and most accurate estimates. A bootstrap pseudo-simulation study was conducted to gauge the tradeoff between the complexity and accuracy of the models. Accuracy was determined using two measures; the mean of the differences between the estimates of the bootstrapped datasets and the true beta obtained from the application of each model on the renal dataset, and the mean of the square of these differences. The results showed that SPRI provided most accurate estimates and did not exhibit any computational or convergence problem.

Conclusion

Higher accuracy was demonstrated when the level of complexity increased from shared random coefficient models to the separate random coefficient alternatives with SPRI showing to have the best fit and most accurate estimates.

【 授权许可】

   
2015 Jaffa et al.

【 参考文献 】

• [1]James GD, Seally JE, Alderman M, Ljungman S, Mueller FB, Pecker MS et al.. A longitudinal study of urinary creatinine and creatinine clearance in normal subjects. Race, sex and age differences. Am J Hypertens. 1988; 1:124-131.
• [2]Schrier RW. Blood urea nitrogen and serum creatinine not married in heart failure. Circ Heart Fail. 2008; 1:25-33.
• [3]Froissart M, Rossert J, Jacquot C, Paillard M, Houillier P. Predictive performance of the modification of diet in renal disease and Cockcroft-Gault equations for estimating renal function. J Am Soc Nephrol. 2005; 16:763-773.
• [4]Verhave JC, Fesler P, Ribstein J, du Cailar G, Mimran A. Estimation of renal function in subjects with normal serum creatinine levels: influence of age and body mass index. Am J Kidney Dis. 2005; 46:233-241.
• [5]Cirillo M, Anastasio P, De Santo NG. Relationship of gender, age, and body mass index to errors in predicted kidney function. Nephrol Dial Transplant. 2005; 20:1791-1798.
• [6]Sammel M, Lin X, Ryan L. Multivariate linear mixed models for multiple outcomes. Stat Med. 1999; 18:2479-2492.
• [7]Xu J, Zeger SL. The evaluation of multiple surrogate endpoints. Biometrics. 2001; 57:81-87.
• [8]He B, Luo S (2013) Joint modeling of multivariate longitudinal measurements and survival data with applications to Parkinson’s disease. Stat Methods Med Res (In Press Published on line first on April 16, 2013)
• [9]Adams R, Wilson M, Wu M. Multilevel item response models: an approach to errors in variables regression. J Educ Behav Stat. 1997; 22(1):47-76.
• [10]Andersen E. Latent regression analysis based on the rating scale model. Psychol Sci. 2004; 46:209-226.
• [11]Christensen K, Bjorner J, Kreiner S, Petersen J. Latent regression in loglinear Rasch models. Commun Stat Theory Methods. 2004; 33(6):1295-1313.
• [12]Mislevy R. Estimation of latent group effects. J Am Stat Assoc. 1985; 80:993-997.
• [13]Zwinderman A. A generalized Rasch model for manifest predictors. Psychometrika. 1991; 56(4):589-600.
• [14]Maier K. A Rasch hierarchical measurement model. J Educ Behav Stat. 2001; 26(3):307-330.
• [15]Kamata A. Item analysis by the hierarchical generalized linear model. J Educ Meas. 2001; 38(1):79-93.
• [16]Fox J. Multilevel IRT using dichotomous and polytomous response data. Br J Math Stat Psychol. 2005; 58(1):145-172.
• [17]Pinheiro J, Liu C, Wu Y. Efficient algorithms for robust estimation in linear mixed-effects models using the multivariate t distribution. J Comput Graph Stat. 2001; 10(2):249-276.
• [18]Fieuws S, Verbeke G. Joint modeling of multivariate longitudinal profiles: pitfalls of the random effect approach. Stat Med. 2004; 23:3093-3104.
• [19]Fieuws S, Verbeke G, Molenberghs G. Random-effects models for multivariate repeated measures. Stat Methods Med Res. 2007; 16(5):387-397.
• [20]Bandyopadhyay S, Ganguli B, Chatterjee A. A review of multivariate longitudinal data analysis. Stat Methods Med Res. 2011; 20(4):299-330.
• [21]Lachos V, Bandyopadhyay D, Dey D. Linear and nonlinear mixed-effects models for censored HIV viral loads using normal/independent distributions. Biometrics. 2011; 67:1594-1604.
• [22]Gebregziabher M, Zhao Y, Dismuke CE, Axon N, Hunt KJ, Egede LE. Joint modeling of multiple longitudinal cost outcomes using multivariate generalized linear mixed models. Health Serv Outcomes Res Method. 2013; 13:39-57.
• [23]Zeier M, Dohler B, Oplez G, Ritz E. The effect of donor gender on graft failure. J Am Soc Nephrol. 2002; 13:2570-2576.
• [24]Kasiske BL, Umen JA. The influence of age, sex, race and body habitus on kidney weight in humans. Arch Pathol Lab Med. 1986; 110:55-60.
• [25]Brenner BM, Cohen RA, Milford EL. In renal transplantation, one size may not fit all. J Am Soc Nephrol. 1992; 3:162-169.
• [26]Jaffa MA, Woolson RF, Lipsitz SR. Slope estimation for bivariate longitudinal outcomes adjusting for informative right censoring by using a discrete survival model: application to the renal transplant cohort. J Royal Stat Soc A. 2011; 174:387-402.
• [27]Epidemiology of diabetes interventions and complications (EDIC): design, implementation and preliminary results of long-term follow up of diabetes control and complications trial cohort. Diabetes Care. 1999; 22:99-111.
• [28]The diabetes control and complications trial (DCCT): design and methodologic considerations for the feasibility phase. Diabetes. 1986; 35:530-545.