Statistics and Data Science Seminar
Shi Zhao, PhD Candidate
MSCS, UIC
Graeco-Latin Square Crossover Designs for Higher Order Carryover Effects
Abstract: Latin square constructed crossover designs balanced for first order
carryover effects, commonly referred to as Williams designs, are commonly
used in many PK, PD, and other clinical studies. These designs are used to
investigate treatment (t) effects in the presence of two nuisance factors,
subjects (s) and periods (p), while evaluating and accommodating first
order carryover effects with equal precision among treatment comparisons. In
some studies, an additional design factor and higher order carryover
effects are of interest. For example, in capsaicin cough challenge studies, the
additional design factor cough counter (c) is of interest, as is the
possibility of higher order carryover effects given the nature of the
capsaicin induced cough endpoint, and the human interaction between the
cough counters and the study subjects.
Graeco-Latin square crossover designs balanced for up to t-1 and c-1 order
residual effects need to be constructed. We illustrate for the case where t = p
= c = 4. Specifically, two sets of three 4x4 mutually orthogonal Latin square
(MOLS) crossover designs with 12 sequences are constructed. Then
permutations of each set of three 4x4 MOLS are enumerated. Particular
permutations from the first set of three 4x4 MOLS are selected and
superimposed upon selected permutations from the second set of three 4x4
MOLS, to construct the desired Graeco-Latin square crossover design with 24
sequences of treatment and evaluator combinations. Using field theory, this
result is generalized to any case where t is prime number or a power of a
prime number. Open questions related to these results such as: how to
partially balance the treatment and evaluator combinations across periods;
how to construct designs for numbers of treatments which are not primes or
powers of primes; will also be discussed. Appropriate intellectual building
blocks will be presented throughout the talk.
Wednesday September 12, 2007 at 3:30 PM in SEO 712