Motivated by comparing the distribution of longitudinal quality of life (QoL) data among different treatment groups from a cancer clinical trial, we propose a semiparametric test statistic for the homogeneity of the distributions of multigroup longitudinal measurements, which are bounded in a closed interval with excess observations taking the boundary values. Our procedure is based on a three-component mixed density ratio model and a composite empirical likelihood for the longitudinal data taking values inside the interval. A nonparametric bootstrap method is applied to calculate the p-value of the proposed test. Simulation studies are conducted to evaluate the proposed procedure, which show that the proposed test is effective in controlling type I errors and more powerful than the procedure which ignores the values on the boundaries. It is also robust to the model mispecification than the parametric test. The proposed procedure is also applied to compare the distributions of the scores of Physical Function subscale and Global Heath Status between the patients randomized to two treatment groups in a cancer clinical trial.
Keywords: Bootstrap; Box-Cox transformation; composite likelihood; density ratio model; interval-bounded; longitudinal data.