Confidence estimation via the parametric bootstrap in logistic joinpoint regression

We consider asymptotic properties of the maximum likelihood and related estimators in a clustered logistic joinpoint model with an unknown joinpoint. Sufficient conditions are given for the consistency of confidence bounds produced by the parametric bootstrap; one of the conditions required is that the true location of the joinpoint is not at one of the observation times. A simulation study is presented to illustrate the lack of consistency of the bootstrap confidence bounds when the joinpoint is an observation time. A removal algorithm is presented which corrects this problem, but at the price of an increased mean square error. Finally, the methods are applied to data on yearly cancer mortality in the US for individuals age 65 and over.