Estimation of Parent-Sib Correlations for Quantitative Traits Using the Linear Mixed Regression Model: Applications to Arterial Blood Pressures Data Collected From Nuclear Families


  • Maha Al-Eid Department of Biostatistics, Epidemiology and Scientific Computing, King Faisal SpecialistHospital and Research Center, Riyadh, Saudi Arabia
  • Sarah AL-Gahtani Department of Internal Medicine, King Fahd Medical City, Riyadh, Saudi Arabia
  • Mohamed M. Shoukri Department of Epidemiology and Biostatistics, Schulich of Medicine and Dentistry University of Western Ontario, London, Ontario Canada



Genetic epidemiology, Familial correlations, Heritability, Linear Mixed normal models, Maximum Likelihood estimation, Estimating Ratio of parameters, Bootstrap Confidence interval.


A fundamental question in quantitative genetics is whether observed variation in the phenotypic values of a particular trait is due to environmental or to biological factors. Proportion of variations attributed to genetic factors is known as heritability of the trait. Heritability is a concept that summarizes how much of the variation in a trait is due to variation in genetic factors. Often, this term is used in reference to the resemblance between parents and their offspring. In this context, high heritability implies a strong resemblance between parents and offspring with regard to a specific trait, while low heritability implies a low level of resemblance. While many applications measure the offspring resemblance to their parents using the mid-parental value of a quantitative trait of interest as an input parameter, others focus on estimating maternal and paternal heritability. In this paper we address the problem of estimating parental heritability using the nuclear family as a unit of analysis. We derive moment and maximum likelihood estimators of parental heritability, and test their equality using the likelihood ratio test, the delta method. We also use Fieller’s interval on the ratio of parental heritability to address the question of bioequivalence. The methods are illustrated on published arterial blood pressures data collected from nuclear families.


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How to Cite

Al-Eid, M. ., AL-Gahtani, S. ., & Shoukri, M. M. . (2020). Estimation of Parent-Sib Correlations for Quantitative Traits Using the Linear Mixed Regression Model: Applications to Arterial Blood Pressures Data Collected From Nuclear Families. International Journal of Statistics in Medical Research, 9, 59–68.



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