Subscribe to RSS
DOI: 10.1055/s-0038-1634097
Markov Models for Repeated Ordinal Data
Publication History
Publication Date:
06 February 2018 (online)
![](https://www.thieme-connect.de/media/10.1055-s-00035037/200604/lookinside/thumbnails/10-1055-s-0038-1634097-1.jpg)
Summary
Objectives: To demonstrate the application of Markov models, especially for ordinal outcomes, within the context of regression models for correlated data.
Methods: A brief review of regression methods for correlated data is given. A proportional odds model and a continuation ratio model is applied to repeated measurements of macular pigment density, obtained in an intervention study on the supplementation of macular carotenoids. The correlation between repeated assessments is assumed to follow a first-order Markov model. The models are implemented with standard statistical software.
Results: Both models, though not directly comparable, provide a similar conclusion. The application of these models with standard statistical software is straightforward.
Conclusions: Markov models can be valuable alternatives to random effects modes or procedures based on generalized estimation equations.
-
References
- 1 Dasch B, Fuhs A, Schmidt J, Behrens T, Meister A, Wellmann J, Fobker M, Pauleikhoff D, Hense HW. Serum levels of macular carotenoids in relation to age-related maculopathy. Graefe’s Arch Clin Exp Ophthalmol 2005; 243: 1028-35.
- 2 Diggle PJ, Heagerty PJ, Liang KY, Zeger SL. Analysis of Longitudinal Data. Oxford: Oxford University Press; 2nd edition 2002
- 3 Liang KY, Zeger SL. Longitudinal data analysis using generalized linear models. Biometrika 1986; 73: 13-22.
- 4 Zeger SL, Liang KY. Longitudinal data analysis for discrete and continuous outcomes. Biometrics 1986; 42: 121-30.
- 5 Prentice RL. Correlated binary regression with covariates specific to each binary observation. Biometrics 1988; 44: 1033-48.
- 6 Ananth CV, Kleinbaum DG. Regression models for ordinal responses: A review of methods and applications. Int J Epidemiol 1997; 26: 1323-33.
- 7 Armstrong BG, Sloan M. Ordinal regression models for epidemiologic data. Am J Epidemiol 1989; 129: 191-204.
- 8 Greenland S. Alternative models for ordinal logistic regression. Statist Med 1994; 13: 1665-77.
- 9 Cole SR, Ananth CV. Regression models for unconstrained, partially or fully constrained continuation odds ratios. Int J Epidemiol 2001; 30: 1379-82.
- 10 Cole SR, Allison PD, Ananth CV. Estimation of cumulative odds ratios. Ann Epidemiol 2004; 14: 172-78.
- 11 Choi T, Cole SR. A family of ordered logistic regression models fit by data expansion. Int J Epidemiol 2004; 33: 1413
- 12 Clayton D.. Repeated ordinal measurements: A generalized estimating equation approach. Technical report, Medical Research Council Biostatistics Unit, Cambridge, England, April 1992. http://www-gene.cimr.cam.ac.uk/clayton/tech_reports/ accessed Feb. 2005
- 13 Agresti A, Natarajan R. Modeling clustered ordered categorical data: A survey. International Statistical Review 2001; 69: 345-71.
- 14 Miller ME, Davis CS, Landis JR. The analysis of longitudinal polytomous data: Generalized Estimation Equations and connections with weighted least squares. Biometrics 1993; 49: 1033-44.
- 15 Lipsitz SR, Kim K, Zhao L. Analysis of repeated categorical data using generalized estimation equations. Statist Med 1994; 13: 1149-63.
- 16 Heagerty PJ, Zeger SL. Marginal regression models for clustered ordinal measurements. J Am Stat Assoc 1996; 91: 1024-36.
- 17 Ten Have TR, Uttal DH. Subject-specific and population averaged continuation ratio logit mod- els for multiple discrete time survival profiles. Applied Statistics 1994; 43: 371-84.
- 18 Heagerty PJ, Zeger SL. Multivariate continuation ratio models: Connections and caveats. Biometrics 2000; 56: 719-32.
- 19 Lindsey JK, Jones B, Ebbutt AF. Simple models for repeated ordinal responses with an application to a seasonal rhinitis clinical trial. Statist Med 1997; 16: 2873-82.
- 20 Wüstemeyer H, Moessner A, Jahn C, Wolf S. Macular pigment density in healthy subjects quantified with a modified confocal scanning laser ophthalmoscope. Graefe’s Arch Clin Exp Ophthalmol 2003; 241: 647-51.
- 21 Delori FC. Autofluorescence method to measure macular pigment optical densities fluorometry and autofluorescence imaging. Arch Biochem Biophys 2004; 430: 156-62.