Rule of three (medicine)
Encyclopedia
In the statistical analysis of clinical trials, the rule of three states that if no major adverse event
s occurred in a group of n people, there can be 95% confidence that the chance of major adverse events is less than one in n / 3 (or equivalently, less than 3 in n). This is an approximate result, but is a very good approximation when 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 efficacy
of a drug, and often the discovery of adverse events is not in the interests of the sponsors.
It should also be noted that this rule applies equally well to any trial done n times. It need not refer to medical or clinical settings. For example, if testing parachutes from the same batch, you test 300 and they all open successfully, the chance of another parachute from the same batch failing to open is likely to be less than 3/300, i.e. less than 1 in 100.
for the probability p of an event occurring, given that it has not been observed to occur in n Bernoulli trial
s. Denoting the number of events by X, we therefore wish to find the values of the parameter p of a binomial distribution that give Pr(X = 0) ≥ 0.05. The rule can then be derived either from the Poisson approximation to the binomial distribution, or from the formula (1-p)n for the probability of zero events in the binomial distribution by taking logarithms and keeping only the first term of a series expansion of the natural logarithm. In either case, the factor of three arises from –ln
(0.05) = ln(20) = 2.9957 ≈ 3.
Adverse event
An adverse event is any adverse change in health or side effect that occurs in a person who participates in a clinical trial while the patient is receiving the treatment or within a previously specified period of time after the treatment has been completed.AEs in patients participating in...
s occurred in a group of n people, there can be 95% confidence that the chance of major adverse events is less than one in n / 3 (or equivalently, less than 3 in n). This is an approximate result, but is a very good approximation when 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
PHASE 2
PHASE 2 is one of the most influential and well known New York City aerosol artist. Mostly active in the 1970s, Phase 2 is generally credited with originating the "bubble letter" style of aerosol writing, also known as "softies"...
and phase 3, which frequently do not have the statistical power
Statistical power
The power of a statistical test is the probability that the test will reject the null hypothesis when the null hypothesis is actually false . The power is in general a function of the possible distributions, often determined by a parameter, under the alternative hypothesis...
or duration to find the relationship between the intervention and adverse events. They are designed to test the efficacy
Efficacy
Efficacy is the capacity to produce an effect. It has different specific meanings in different fields. In medicine, it is the ability of an intervention or drug to reproduce a desired effect in expert hands and under ideal circumstances.- Healthcare :...
of a drug, and often the discovery of adverse events is not in the interests of the sponsors.
It should also be noted that this rule applies equally well to any trial done n times. It need not refer to medical or clinical settings. For example, if testing parachutes from the same batch, you test 300 and they all open successfully, the chance of another parachute from the same batch failing to open is likely to be less than 3/300, i.e. less than 1 in 100.
Outline of derivation
We seek a 95% confidence intervalConfidence interval
In statistics, a confidence interval is a particular kind of interval estimate of a population parameter and is used to indicate the reliability of an estimate. It is an observed interval , in principle different from sample to sample, that frequently includes the parameter of interest, if the...
for the probability p of an event occurring, given that it has not been observed to occur in n Bernoulli trial
Bernoulli trial
In the theory of probability and statistics, a Bernoulli trial is an experiment whose outcome is random and can be either of two possible outcomes, "success" and "failure"....
s. Denoting the number of events by X, we therefore wish to find the values of the parameter p of a binomial distribution that give Pr(X = 0) ≥ 0.05. The rule can then be derived either from the Poisson approximation to the binomial distribution, or from the formula (1-p)n for the probability of zero events in the binomial distribution by taking logarithms and keeping only the first term of a series expansion of the natural logarithm. In either case, the factor of three arises from –ln
Natural logarithm
The natural logarithm is the logarithm to the base e, where e is an irrational and transcendental constant approximately equal to 2.718281828...
(0.05) = ln(20) = 2.9957 ≈ 3.