Testing the trajectory difference in a semi-parametric longitudinal model

Motivated by a genetic investigation on the progressive decline in renal function in a clinical trial study of kidney disease, we develop a practical test for evaluating the group difference in trajectories under a semi-parametric modeling framework. For the temporal patterns or trajectories of longitudinal data, B-splines are used to approximate the function non-parametrically. Such approximation asymptotically converts the problem of testing trajectory difference into the significance test of regression coefficients that can be simply estimated by generalized estimating equations. To select the optimal number of inner knots for B-splines, a cross-validation procedure is performed using the criterion of the generalized residual sum of squares. The new proposed test successfully detects a significant difference of underlying genetic impact on the progression of renal disease, which is not captured by the parametric approach.