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Title: Bayesian hierarchical modeling of growth curve derivatives via sequences of quotient differences Authors:  Garritt Page - Brigham Young University (United States) [presenting]
Abstract: Growth curve studies are typically conducted to evaluate differences among group or treatment-specific curves. Most analysis focus solely on the growth curves, but it has been argued that growth curve derivatives are able to highlight differences among groups that may be masked when considering the raw curves only. Motivated by the desire to estimate derivative curves hierarchically, we introduce a new sequence of quotient differences (empirical derivatives) which, among other things, are well behaved near the boundaries compared to other sequences in the literature. Using on the sequence of quotient differences, we develop a Bayesian method to estimate curve derivatives in a multi-level setting (a common scenario in growth studies) and show how the method can be used to estimate individual and group derivative curves and make comparisons. We apply the new methodology to data collected from a study conducted to explore the impact that radiation-based therapies have on growth in female children diagnosed with acute lymphoblastic leukemia.