An Unconditional Test for Change Point Detection in Binary Sequences with Applications to Clinical Registries.

Abstract

Methods for change point (also sometimes referred to as threshold or breakpoint) detection in binary sequences are not new and were introduced as early as 1955. Much of the research in this area has focussed on asymptotic and exact conditional methods. Here we develop an exact unconditional test. An unconditional exact test is developed which assumes the total number of events as random instead of conditioning on the number of observed events. The new test is shown to be uniformly more powerful than Worsley's exact conditional test and means for its efficient numerical calculations are given. Adaptions of methods by Berger and Boos are made to deal with the issue that the unknown event probability imposes a nuisance parameter. The methods are compared in a Monte Carlo simulation study and applied to a cohort of patients undergoing traumatic orthopaedic surgery involving external fixators where a change in pin site infections is investigated. The unconditional test controls the type I error rate at the nominal level and is uniformly more powerful than (or to be more precise uniformly at least as powerful as) Worsley's exact conditional test which is very conservative for small sample sizes. In the application a beneficial effect associated with the introduction of a new treatment procedure for pin site care could be revealed. We consider the new test an effective and easy to use exact test which is recommended in small sample size change point problems in binary sequences.