Estimating probability of non-response to treatment using mixture distributions

Repeat measurements of patient characteristics are often used to assess response to treatment. In this paper we discuss a normal mixture model for the observed change in the characteristic of interest in treated patients. The methods described can be used to estimate the overall proportion of non-response to treatment and also the probability that a patient has not responded to treatment given his or her observed change. The model parameters are estimated using maximum likelihood, and the delta method is used to construct a pointwise confidence band for the conditional probability that a patient is a non-responder to treatment. The work was initially motivated by analysis issues in the Fracture Intervention Trial (FIT), a randomized trial of the osteoporosis drug alendronate, and the method is illustrated with data from that study. We also evaluate key aspects of the estimation procedure with two simulation studies. In the first, the data generation model is the assumed normal mixture model, and in the second, the data are generated according to a shifted and scaled central t-distribution model suggested by the FIT data.