  We develop inference procedures for longitudinal data where some of the
measurements are censored by fixed constants. We consider a semi-parametric
quantile regression model that makes no distributional assumptions. Our
research is motivated by the lack of proper inference procedures for data from
biomedical studies where measurements are censored due to a fixed
quantification limit. In such studies the focus is often on testing hypotheses
about treatment equality. To this end, we propose a rank score test for large
sample inference on a subset of the covariates. We demonstrate the importance
of accounting for both censoring and intra-subject dependency and evaluate the
performance of our proposed methodology in a simulation study. We then apply
the proposed inference procedures to data from an AIDS-related clinical trial.
We conclude that our framework and proposed methodology is very valuable for
differentiating the influences of predictors at different locations in the
conditional distribution of a response variable.
