An exact upper limit for the variance bias in the carry-over model with correlated errors
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Date
2009-04-30T10:31:47Z
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Abstract
The analysis of crossover designs assuming i.i.d. errors leads to biased variance estimates whenever the true covariance structure is not spherical. As a result, the OLS F-Test for treatment differences is not
valid. Bellavance et al. (Biometrics 52:607-612, 1996) use simulations
to show that a modified F-Test based on an estimate of the within
subjects covariance matrix allows for nearly unbiased tests. Kunert
and Utzig (JRSS B 55:919-927, 1993) propose an alternative test that
does not need an estimate of the covariance matrix. However, for
designs with more than three observations per subject Kunert and
Utzig (1993) only give a rough upper bound for the worst-case variance
bias. This may lead to overly conservative tests. In this paper we
derive an exact upper limit for the variance bias due to carry-over for
an arbitrary number of observations per subject. The result holds for
a certain class of highly efficient carry-over balanced designs.
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Keywords
bias, correlated errors, crossover designs, fixed effects model, upper limit, variance estimation