Statistical methods for testing carryover effects: A mixed effects model approach

Carryover, or the effects of treatment after it ceases, has been largely ignored in statistical literature except as a nuisance parameter. When testing for carryover, comparing cumulative incidence rates is biased when diagnosis is based on a noisy measurement crossing a threshold (such as in blood pressure) then followed by open-label treatment. This issue was raised in the context of preventing hypertension by the TROPHY trial. We show that modelling the noisy measurement itself using linear mixed effect models, then computing the expected proportion over the threshold, gives valid tests and consistent estimates. The key insight is that the data made unavailable by open-label treatment after diagnosis are missing at random. We demonstrate the analysis in simulations based on a large set of blood pressure measurements from a New Zealand healthcare organisation and show that properly specified random effects models accurately estimate carryover effects even in the presence of data censored at diagnosis.