Statistical considerations for cross-sectional data relating to tracheal reconstruction over time

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.