Concomitant interventions are often introduced during a longitudinal clinical trial to patients who respond undesirably to the pre-specified treatments. In addition to the main objective of evaluating the pre-specified treatment effects, an important secondary objective in such a trial is to evaluate whether a concomitant intervention could change a patient's response over time. Because the initiation of a concomitant intervention may depend on the patient's general trend of pre-intervention outcomes, regression approaches that treat the presence of the intervention as a time-dependent covariate may lead to biased estimates for the intervention effects. Borrowing the techniques of Follmann and Wu (Biometrics 1995; 51:151-168) for modeling informative missing data, we propose a varying-coefficient mixed-effects model to evaluate the patient's longitudinal outcome trends before and after the patient's starting time of the intervention. By allowing the random coefficients to be correlated with the patient's starting time of the intervention, our model leads to less biased estimates of the intervention effects. Nonparametric estimation and inferences of the coefficient curves and intervention effects are developed using B-splines. Our methods are demonstrated through a longitudinal clinical trial in depression and heart disease and a simulation study.