On Analysis of the Difference of Two Exposure-Adjusted Poisson Rates with Stratification: From Asymptotic to Exact Approaches

Confidence intervals for exposure-adjusted rate differences in randomized trials

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.

Rethinking the Clinically Based Thresholds of TransCelerate BioPharma for Risk-Based Monitoring

BACKGROUND

The quality of data from clinical trials has received a great deal of attention in recent years. Of central importance is the need to protect the well-being of study participants and maintain the integrity of final analysis results. However, traditional approaches to assess data quality have come under increased scrutiny as providing little benefit for the substantial cost. Numerous regulatory guidance documents and industry position papers have described risk-based approaches to identify quality and safety issues. In particular, the position paper of TransCelerate BioPharma recommends defining risk thresholds to assess safety and quality risks based on past clinical experience. This exercise can be extremely time-consuming, and the resulting thresholds may only be relevant to a particular therapeutic area, patient or clinical site population. In addition, predefined thresholds cannot account for safety or quality issues where the underlying rate of observing a particular problem may change over the course of a clinical trial, and often do not consider varying patient exposure.

METHODS

In this manuscript, we appropriate rules commonly utilized for funnel plots to define a traffic-light system for risk indicators based on statistical criteria that consider the duration of patient follow-up. Further, we describe how these methods can be adapted to assess changing risk over time. Finally, we illustrate numerous graphical approaches to summarize and communicate risk, and discuss hybrid clinical-statistical approaches to allow for the assessment of risk at sites with low patient enrollment.

RESULTS

We illustrate the aforementioned methodologies for a clinical trial in patients with schizophrenia.

CONCLUSIONS

Funnel plots are a flexible graphical technique that can form the basis for a risk-based strategy to assess data integrity, while considering site sample size, patient exposure, and changing risk across time.

Combining one-sample confidence procedures for inference in the two-sample case

We present a simple general method for combining two one-sample confidence procedures to obtain inferences in the two-sample problem. Some applications give striking connections to established methods; for example, combining exact binomial confidence procedures gives new confidence intervals on the difference or ratio of proportions that match inferences using Fisher's exact test, and numeric studies show the associated confidence intervals bound the type I error rate. Combining exact one-sample Poisson confidence procedures recreates standard confidence intervals on the ratio, and introduces new ones for the difference. Combining confidence procedures associated with one-sample t-tests recreates the Behrens-Fisher intervals. Other applications provide new confidence intervals with fewer assumptions than previously needed. For example, the method creates new confidence intervals on the difference in medians that do not require shift and continuity assumptions. We create a new confidence interval for the difference between two survival distributions at a fixed time point when there is independent censoring by combining the recently developed beta product confidence procedure for each single sample. The resulting interval is designed to guarantee coverage regardless of sample size or censoring distribution, and produces equivalent inferences to Fisher's exact test when there is no censoring. We show theoretically that when combining intervals asymptotically equivalent to normal intervals, our method has asymptotically accurate coverage. Importantly, all situations studied suggest guaranteed nominal coverage for our new interval whenever the original confidence procedures themselves guarantee coverage.