Response Rate & Confidence Interval
Calculate a response rate and two-sided Wilson and Clopper–Pearson confidence intervals from response counts.
Response rate and binomial confidence intervals
Enter responses, denominator, and confidence level.
The denominator must follow the protocol/SAP definition of the analysis population and rules for missing or non-evaluable participants. Wilson and exact intervals have different coverage properties; this calculator does not select a preferred method. A single-arm response-rate CI does not replace a controlled comparison or determine causality or clinical significance.
Basis: NIST binomial-proportion CIs for two-sided Wilson score and Clopper–Pearson exact intervals, plus FDA review examples using exact 95% CIs for response rates.
Tool Guide
Definition
Response Rate & Confidence Interval — Calculates x/n and parallel two-sided Wilson score and Clopper–Pearson exact intervals from observed responses x and the protocol/SAP-defined analysis denominator n. Zero- and complete-response boundaries are handled directly.
Purpose
(1) Summarize binomial rates such as ORR, DCR, or assay positivity, (2) cross-check exact CIs at small n or extreme rates, (3) compare Wilson and exact intervals, and (4) copy count/percent/CI for tables or a CSR.
How to Use
① Determine response count and N under the analysis definition. ② Enter the two-sided confidence level. ③ Copy the point estimate and both intervals. ④ In the result table, state the interval method, analysis population, and missing/non-evaluable handling rule. The tool does not automatically choose a preferred method, perform a hypothesis test, or determine clinical significance.
Examples
Example) Four responses among 20 at two-sided 90% gives an observed rate of 20%. The Clopper–Pearson exact CI is approximately 7.1354%–40.1029%, and the Wilson CI is shown alongside it. Exact and Wilson results remain available at boundaries such as 0/10 or 10/10.