Rule of three (medicine)

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The rule of three states that, if no major adverse events occurred in a clinical trial of a drug, then there can be 95% confidence that major adverse events do not happen more often than one in n/3 people, where n is the number of people in the study. This is based on an asymptotic result of risk estimation, and is valid where n>30.

For example, in a trial of a drug for pain relief in 1500 people, none have a major adverse event. The rule of three says we should have 95% confidence that the rate of adverse events is no more frequent than 1 in 500.

This rule is useful in the interpretation of drug trials, particularly in phase 2 and phase 3, which frequently do not have the statistical power or duration to find the relationship between the intervention and adverse events. They are designed to test the effectiveness of a drug, and often the discovery of adverse events is not in the interests of the sponsors.

Eypasch, Ernst; Rolf Lefering, C K Kum, Hans Troidl (1995-09-02). "Probability of adverse events that have not yet occurred: a statistical reminder". BMJ 311 (7005): 619-620. 

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