title: Misspecification of at-risk periods and distributional assumptions in estimating COPD exacerbation rates: The resultant bias in treatment effect estimation.
abstract: In trials comparing the rate of chronic obstructive pulmonary disease exacerbation between treatment arms, the rate is typically calculated on the basis of the whole of each patient's follow-up period. However, the true time a patient is at risk should exclude periods in which an exacerbation episode is occurring, because a patient cannot be at risk of another exacerbation episode until recovered. We used data from two chronic obstructive pulmonary disease randomized controlled trials and compared treatment effect estimates and confidence intervals when using two different definitions of the at-risk period. Using a simulation study we examined the bias in the estimated treatment effect and the coverage of the confidence interval, using these two definitions of the at-risk period. We investigated how the sample size required for a given power changes on the basis of the definition of at-risk period used. Our results showed that treatment efficacy is underestimated when the at-risk period does not take account of exacerbation duration, and the power to detect a statistically significant result is slightly diminished. Correspondingly, using the correct at-risk period, some modest savings in required sample size can be achieved. Using the proposed at-risk period that excludes recovery times requires formal definitions of the beginning and end of an exacerbation episode, and we recommend these be always predefined in a trial protocol.
authors.affiliation: MRC Biostatistics Unit, Cambridge, UK.
authors.forename: M
authors.initials: M
authors.lastname: Law
authors.affiliation: Department of Public Health and Primary Care, University of Cambridge, Cambridge, UK.
authors.forename: M J
authors.identifier: 0000-0003-0980-8965
authors.initials: MJ
authors.lastname: Sweeting
authors.affiliation: National Heart and Lung Institute, Imperial College London, Cambridge, UK.
authors.forename: G C
authors.initials: GC
authors.lastname: Donaldson
authors.affiliation: National Heart and Lung Institute, Imperial College London, Cambridge, UK.
authors.forename: J A
authors.initials: JA
authors.lastname: Wedzicha
mesh_terms: D006801:Humans; D029424:Pulmonary Disease, Chronic Obstructive; D016032:Randomized Controlled Trials as Topic; D012307:Risk Factors
keywords: chronic obstructive pulmonary disease; exacerbation rate; negative binomial; recurrent events