Confidence intervals for exposure‐adjusted rate differences in randomized trials

Abstract

Exposure-adjusted event rate is a quantity often used in clinical trials to describe average event count per unit of person-time. The event count may represent the number of patients experiencing first (incident) event episode, or the total number of event episodes, including recurring events. For inference about difference in the exposure-adjusted rates between interventions, many methods of interval estimation rely on the assumption of Poisson distribution for the event counts. These intervals may suffer from substantial undercoverage both, asymptotically due to extra-Poisson variation, and in the settings with rare events even when the Poisson assumption is satisfied. We review asymptotically robust methods of interval estimation for the rate difference that do not depend on distributional assumptions for the event counts, and propose a modification of one of these methods. The new interval estimator has asymptotically nominal coverage for the rate difference with an arbitrary distribution of event counts, and good finite sample properties, avoiding substantial undercoverage with small samples, rare events, or over-dispersed data. The proposed method can handle covariate adjustment and can be implemented with commonly available software. The method is illustrated using real data on adverse events in a clinical trial. K E Y W O R D Sexposure-adjusted rate, incidence rate, rate difference | INTRODUCTIONExposure-adjusted event rate is a quantity expressing average event count per unit of person-time. Consider a cohort ω of n patients exposed to a specific medication until some maximum exposure time τ, and followed for occurrence of treatment-emergent adverse events (i.e., events occurring during the exposure). The exposure period is time to the last dose plus a pre-defined washout period determined by the drug elimination kinetics, anticipated duration of pharmacodynamic effects, or similar considerations. For the i-th patient in ω, let Z i ≤ τ denote the planned exposure time, let Y i ≤ Z i denote the actual exposure time at-risk for the treatment-emergent adverse event of interest, and let X i be the number of the event episodes during time at-risk. The planned exposure time may be the same for all patients (Z i τ) or may vary (e.g., due to staggered entry). The actual time at-risk Y i is less than Z i in the case of early discontinuation of study drug exposure (e.g., due to death or a non-fatal adverse event), which can be considered a competing risk for any subsequent treatment emergent adverse event. The observed exposure-adjusted event rate is the ratio

Treatment effect measures under nonproportional hazards

“…The exposure-adjusted incidence rate is widely used in clinical trials, 14 with the difference between groups calculated as P j e 0,j…”

“…The exposure‐adjusted incidence rate is widely used in clinical trials, 14 with the difference between groups calculated as . While this calculation is typically based on all available follow‐up, it can easily be modified to consider only follow‐up through time, .…”