Statistical considerations for crosssectional data relating to tracheal reconstruction over time

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Abstract
Complementary statistical analyses are performed on data concerning tracheal reconstruction in rats. The principal response criterion is vessel area as defined by the area of a graft onto the trachea covered by blood vessels. Postoperatively, this vessel area changes in a nonlinear fashion over time. Starting at 0% immediately postoperation, the vessel area increases to a peak and then sharply decreases to a certain level at which it remains. A total of 64 independently observed cross-sectional pairs (postop day, vessel area) are distributed among four treated groups. Analysis consists of two-way analysis of variance and piecewise linear regression under the usual assumptions of normality and variance homogeneity. Other analyses that relax these assumptions are also considered; treatment differences are established by nonparametric tests, and a quasi-likelihood analysis of the piecewise linear regression model is applied under the assumption of a binomial-like variance function. The resulting fit of the normal-theory-based piecewise linear model is compared to that of a nonlinear model whose shape is that of a gamma function integrand.