Maximum Likelihood and Bayesian Estimation of Repeatability Index: Application of Estimating Ratio of Variance Components


  • Maha Al-Eid Department of Biostatistics, Epidemiology and Scientific Computing, King Faisal Specialist Hospital and Research Center, P.O. Box 3354, Riyadh, Saudi Arabia
  • Mohamed M. Shoukri Department of Epidemiology and Biostatistics, Schulich School of Medicine and Dentistry, London, Ontario, Canada



One-way random effects model, Functions of variance components, Fisher’s information matrix, Gamma-glutamyl-transferase (GGT), Delta method, Jefferey’s priors, Monte-Carlo integration, Sampling Importance Resampling


An index of repeatability is constructed to evaluate the relative magnitude of measurement error. This index is constructed as a ratio of two variance components. Estimation of the index is derived under the one-way random effects model. We compare the well-known maximum likelihood estimator to the Bayesian estimation procedure using non-informative prior. Large sample variance of the of the maximum likelihood estimator are obtained using the inverse of Fisher’s information matrix and the delta method. Inference procedure using the. We also construct a test statistic on the equality of two repeatability indices using the Monte Carlo integration and sampling Importance re-sampling method. We illustrate the methodologies on the estimation of the index of repeatability of Gamma-glutamyl-transferase, an enzyme found in many organs all over the human body, with the highest concentrations found in the liver. This enzyme’s level is raised in the blood in most diseases that cause damage to the liver or bile ducts and is considered an essential serum marker for alcohol-related liver disease.


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How to Cite

Al-Eid, M., & Shoukri, M. M. (2020). Maximum Likelihood and Bayesian Estimation of Repeatability Index: Application of Estimating Ratio of Variance Components. International Journal of Statistics in Medical Research, 9, 1–9.



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