• Changepoint;
  • Empirical distribution;
  • Likelihood ratio;
  • Maximum empirical likelihood estimation;
  • Profile likelihood

Summary.  A two-sample changepoint model is proposed to investigate the difference between two treatments or devices. Under our semiparametric approach, no assumptions are made about the underlying distributions of the measurements from the two treatments or devices, but a parametric link is assumed between the two. The parametric link contains the possible changepoint where the two distributions start to differ. We apply the maximum empirical likelihood for model estimation and show the consistency of the changepoint estimator. An extended changepoint model is studied to handle data censored because of detection limits in viral load assays of human immunodeficiency virus (HIV). Permutation and bootstrap procedures are proposed to test the existence of a changepoint and the goodness of fit of the model. The performance of the semiparametric changepoint model is compared with that of parametric models in a simulation study. We provide two applications in HIV studies: one is a randomized placebo-controlled study to evaluate the effects of a recombinant glycoprotein 120 vaccine on HIV viral load; the other is a study to compare two types of tubes in handling plasma samples for viral load determination.