Statistical Modeling of Carryover Effects After Cessation of Treatments

Abstract

Hypertension, high cholesterol, and diabetes are responsible for significant mortality, morbidity, and cost in both developed and developing countries. Rather than intervening after these high-risk conditions develop, it would be preferable to intervene to prevent incident hypertension, high cholesterol, and diabetes. In this thesis we discuss trial design and analysis for evaluating interventions that prevent them, in particular, the problem of estimating the duration of response to treatment. Put simply, how long does the effect continue after the active intervention ceases? Randomised controlled trials are generally considered the gold standard when testing for the efficacy of an administered treatment. Recently, a new genre of trial has emerged to test for long-term impact of a treatment, or carryover effect. For analysis, these trials used naive comparisons of cumulative incidence at the end of the post-treatment follow up period. Diagnosis of hypertension, diabetes, and high cholesterol occurs when a noisy measurement crosses a threshold so incident is difficult to localise. The purpose of this thesis is to explore sound methodologies to test a carryover hypothesis in these circumstances. We explore four different approaches: parallel-group trial, crossover trial, linear mixed models, and survival analysis. We conducted systematic simulation studies over varying combinations of parameters to assess both parallel and crossover trials and compared incidence of systolic hypertension to deter- mine power and Type I error rates. The linear mixed model was also assessed via simulation with coverage of relative risks used to measure efficacy. We assessed the survival analysis model by comparing results found from maximising our adjusted likelihood with true hazards found from simulated data without error. We conclude that for the applications of interest researchers will need to apply a linear mixed model and parametric bootstrap to find relative risks.