Date of Award


Degree Type


Degree Name

Master of Science (MS)


Mathematics and Statistics

Committee Chair(s)

Chris Corcoran


Chris Corcoran


The rapid improvement of genotyping technology holds the promise of better understanding the genetic causes of complex disease. While traits of interest often include the presence or absence of disease, there is growing interest in intermediate phenotypes (or so-called endophenotypes) that may yield more information about disease onset or course. In particular, changes over time with respect to an investigative ordinal measure often contain significant predictive power, and rate-of-change phenotypes are becoming important in their own right when studying genetic association. Initial steps in assessing the potential genetic determinants of a continuous trait often involve estimating the degree of the trait 's heritability, or the proportion of phenotypic variation in the population that is due to genetic variation between individuals. Although heritability estimators for cross-sectional measures are well-defined, estimating heritability for rate-of-change traits has received surprisingly little attention. In this paper we describe three options: a commonly used summary-response approach, a joint analysis, and a recently-proposed Bayesian hierarchical model. We applied the first to data from the Cache County Study on Memory, Health, and Aging (CCSMHA), a longitudinal study of the elderly in Cache County, Utah, that was initiated over fourteen years ago to explore the role of APOE genotype and other environmental factors in dementia risk and cognitive function. Collaboration between the CCSMHA and investigators with the Utah Population Database (UPDB) at the University of Utah has revealed a significant number of sibships among the original 5,092 CCSMHA participants, along with complex pedigrees that include additional thousands of ancestors and relatives not enrolled in the Cache Study. Information about these pedigrees raises the potential for family-based studies of the genetic epidemiology of age-related traits. Heritability of global cognition and cognitive decline for the Cache cohort has been previously estimated; however, the subscales that comprise the global measures have not yet been examined either cross-sectionally or in terms of rate of change. Individual subscales measure more specific aspects of cognitive function (e.g., learning, memory, orientation, and abstract reasoning), and examining these more refined metrics can reveal which aspects of cognition may be influenced most strongly by genetic effects.