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.

Patient characteristics and healthcare utilisation among Danish patients with chronic conditions: a nationwide cohort study in general practice and hospitals

“…For calculating rates of outcomes that could not occur when a patients was hospitalised (e.g. a new admission or a GP contact), we subtracted any days spent in hospital in the follow-up period from the total time at risk [ 30 ]. To assess differences in outcomes between patients in general practice and hospital follow-up, we used a negative binomial regression model.…”

Effectiveness of a 24-hour access outpatient clinic for patients with chronic conditions in hospital outpatient follow-up: a registry-based controlled cohort study of healthcare utilisation and mortality

“…To calculate rates of outcomes that could not occur when a patients was hospitalised (eg, a new admission or a GP contact), we subtracted any days hospitalised from the total time at risk. 47 Differences in healthcare utilisation between groups were estimated using negative binomial regression model. We report incidence rate ratios (IRRs) with 95% CIs with robust SEs.…”

“…The comparative analyses of healthcare utilisation were based on intention-to-treat and included all eligible patients followed up for 18 months or until the patient was censored due to death or leaving the municipality. To calculate rates of outcomes that could not occur when a patients was hospitalised (eg, a new admission or a GP contact), we subtracted any days hospitalised from the total time at risk 47…”

Effectiveness of A 24-h Access Outpatient Clinic for Patients with Chronic Conditions in Hospital Outpatient Follow-Up: A Registry-Based Controlled Cohort Study of Healthcare Utilisation and Mortality

“…We subtracted days hospitalised when calculating rates of outcome types that could not occur when hospitalised. [40] Differences in healthcare utilisation between groups were estimated using a negative binomial regression model. We report incidence rate ratios (IRRs) with 95% con dence intervals (CIs) with robust standard errors.…”