![]() | This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||||||||||||||||||||||||||||||||
|
The result of the move request was: moved per request. Favonian ( talk) 22:07, 4 January 2013 (UTC)
Rule of three (medicine) → Rule of three (statistics) – to be more accurately descriptive of content and less restrictive on the scope of the article 75.172.49.186 ( talk) 16:49, 28 December 2012 (UTC)
There are very many errors, bad links, and confusions generally in the lead:
In the statistical analysis of clinical trials, the rule of three states that if no major adverse events occurred in a group of n people, then the interval from 0 to 3/n can be used as a 95% Confidence interval that for the probability that a corresponding major event will arise for a single new individual. This is an approximate result, but is a very good approximation when n is greater than 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 that 0 to 1 in 500 people is a 95% confidence interval for the rate of adverse events.
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.
I propose this improvement:
In the statistical analysis of clinical trials, the rule of three states that if a certain event did not occur in n subjects, 0 to 3/n is a 95% confidence interval for the probability that
no such eventsuch an event will occur in some randomly chosen new subject. When n is greater than 30, this is a good approximation to results from more sensitive tests.For example, in a trial of a pharmaceutical drug for pain relief in 1500 people, there is no adverse event for any subject. From the rule of three, it can be concluded with 95% confidence that there is less than 1 chance in 500 that any given person will experience an adverse event (or equivalently, that fewer than 1 person in 500 will experience an adverse event).
The rule is useful in the interpretation of drug trials, particularly in phase II and phase III where statistical power and duration are sometimes less than ideal. The rule of three applies beyond medical research, to any trial done n times. If 300 parachutes from the same batch are randomly tested and all open successfully, then it is concluded with 95% confidence that the probability of failure in any other given parachute from the same batch is less than 3/300 (less than 1 in 100).
I'm 99% confident that this is indeed an improvement, but also that it needs more work. These are highly technical concepts, and great precision is needed. Advice would be welcome, from someone closer to their detailed application.
Please do not alter my proposed text above, but show suggestions in a new draft.
Noetica Tea? 23:31, 29 December 2012 (UTC)
In the statistical analysis of clinical trials, the rule of three states that if a certain event did not occur in n subjects, 0 to 3/n is a 95% confidence interval for assignment of a probability, for any single new subject, that such an event will occur.
fewer than 1 person in 500 will experience an adverse event
there is less than 1 chance in 500 that any given person will experience an adverse event
the probability that such an event will occur in each randomly chosen new subject
the probability for each randomly chosen new subject that such an event will occur
While the above is an improvement, I think we need something dead simple for the lead that can be understood by non-statiticians. This description I think provides a good model. For example, if 100 hundred individuals are tested and no adverse event are found, there is less than 3/100 (3%) probability than an adverse event will be found if a larger group of individuals are tested. A more precise and detailed description can then be included later in the article. Boghog ( talk) 10:40, 31 December 2012 (UTC)
It says that if you’ve tested N cases and haven’t found what you’re looking for, a reasonable estimate is that the probability is less than 3/N. So in our proofreading example, if you haven’t found any typos in 20 pages, you could estimate that the probability of a page having a typo is less than 15%. In the perfect pitch example, you could conclude that fewer than 3% of children have perfect pitch.
My thanks to Dicklyon and Boghog. I am about to replace the present lead with this very careful version:
In statistical analysis, the rule of three states that if a certain event did not occur in a sample with n subjects, 0 to 3/n is a 95% confidence interval for the rate of occurrences in the population. When n is greater than 30, this is a good approximation to results from more sensitive tests.
For example, a pain-relief drug is tested on 1500 human subjects, and no adverse event is recorded. From the rule of three, it can be concluded with 95% confidence that fewer than 1 person in 500 (or 3/1500) will experience an adverse event.
The rule is useful in the interpretation of clinical trials generally, particularly in phase II and phase III where often there are limitations in duration or statistical power. The rule of three applies well beyond medical research, to any trial done n times. If 300 parachutes are randomly tested and all open successfully, then it is concluded with 95% confidence that fewer than 1 in 100 parachutes of the exactly the same specifications (3/300) will fail.
All links have been considered and checked; and all expression has been made as reader-friendly as I could manage without compromising precision. In accord with the best sources, probability is now not mentioned at all.
Noetica Tea? 01:20, 1 January 2013 (UTC)
The figure suggests that the error in the approximation is small. That is done in words in the text.
After x=10^1 on the x-axis the lines are unable to be distinguished. This communicates no sense of the error - it is wasted space. This makes the right 75% of the figure non-informative.
A better figure would have absolute relative error, or its logarithm base-10, for the 95% confidence bound displayed on the y-axis. — Preceding unsigned comment added by 144.191.148.7 ( talk) 12:58, 13 July 2015 (UTC)
![]() | This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||||||||||||||||||||||||||||||||
|
The result of the move request was: moved per request. Favonian ( talk) 22:07, 4 January 2013 (UTC)
Rule of three (medicine) → Rule of three (statistics) – to be more accurately descriptive of content and less restrictive on the scope of the article 75.172.49.186 ( talk) 16:49, 28 December 2012 (UTC)
There are very many errors, bad links, and confusions generally in the lead:
In the statistical analysis of clinical trials, the rule of three states that if no major adverse events occurred in a group of n people, then the interval from 0 to 3/n can be used as a 95% Confidence interval that for the probability that a corresponding major event will arise for a single new individual. This is an approximate result, but is a very good approximation when n is greater than 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 that 0 to 1 in 500 people is a 95% confidence interval for the rate of adverse events.
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.
I propose this improvement:
In the statistical analysis of clinical trials, the rule of three states that if a certain event did not occur in n subjects, 0 to 3/n is a 95% confidence interval for the probability that
no such eventsuch an event will occur in some randomly chosen new subject. When n is greater than 30, this is a good approximation to results from more sensitive tests.For example, in a trial of a pharmaceutical drug for pain relief in 1500 people, there is no adverse event for any subject. From the rule of three, it can be concluded with 95% confidence that there is less than 1 chance in 500 that any given person will experience an adverse event (or equivalently, that fewer than 1 person in 500 will experience an adverse event).
The rule is useful in the interpretation of drug trials, particularly in phase II and phase III where statistical power and duration are sometimes less than ideal. The rule of three applies beyond medical research, to any trial done n times. If 300 parachutes from the same batch are randomly tested and all open successfully, then it is concluded with 95% confidence that the probability of failure in any other given parachute from the same batch is less than 3/300 (less than 1 in 100).
I'm 99% confident that this is indeed an improvement, but also that it needs more work. These are highly technical concepts, and great precision is needed. Advice would be welcome, from someone closer to their detailed application.
Please do not alter my proposed text above, but show suggestions in a new draft.
Noetica Tea? 23:31, 29 December 2012 (UTC)
In the statistical analysis of clinical trials, the rule of three states that if a certain event did not occur in n subjects, 0 to 3/n is a 95% confidence interval for assignment of a probability, for any single new subject, that such an event will occur.
fewer than 1 person in 500 will experience an adverse event
there is less than 1 chance in 500 that any given person will experience an adverse event
the probability that such an event will occur in each randomly chosen new subject
the probability for each randomly chosen new subject that such an event will occur
While the above is an improvement, I think we need something dead simple for the lead that can be understood by non-statiticians. This description I think provides a good model. For example, if 100 hundred individuals are tested and no adverse event are found, there is less than 3/100 (3%) probability than an adverse event will be found if a larger group of individuals are tested. A more precise and detailed description can then be included later in the article. Boghog ( talk) 10:40, 31 December 2012 (UTC)
It says that if you’ve tested N cases and haven’t found what you’re looking for, a reasonable estimate is that the probability is less than 3/N. So in our proofreading example, if you haven’t found any typos in 20 pages, you could estimate that the probability of a page having a typo is less than 15%. In the perfect pitch example, you could conclude that fewer than 3% of children have perfect pitch.
My thanks to Dicklyon and Boghog. I am about to replace the present lead with this very careful version:
In statistical analysis, the rule of three states that if a certain event did not occur in a sample with n subjects, 0 to 3/n is a 95% confidence interval for the rate of occurrences in the population. When n is greater than 30, this is a good approximation to results from more sensitive tests.
For example, a pain-relief drug is tested on 1500 human subjects, and no adverse event is recorded. From the rule of three, it can be concluded with 95% confidence that fewer than 1 person in 500 (or 3/1500) will experience an adverse event.
The rule is useful in the interpretation of clinical trials generally, particularly in phase II and phase III where often there are limitations in duration or statistical power. The rule of three applies well beyond medical research, to any trial done n times. If 300 parachutes are randomly tested and all open successfully, then it is concluded with 95% confidence that fewer than 1 in 100 parachutes of the exactly the same specifications (3/300) will fail.
All links have been considered and checked; and all expression has been made as reader-friendly as I could manage without compromising precision. In accord with the best sources, probability is now not mentioned at all.
Noetica Tea? 01:20, 1 January 2013 (UTC)
The figure suggests that the error in the approximation is small. That is done in words in the text.
After x=10^1 on the x-axis the lines are unable to be distinguished. This communicates no sense of the error - it is wasted space. This makes the right 75% of the figure non-informative.
A better figure would have absolute relative error, or its logarithm base-10, for the 95% confidence bound displayed on the y-axis. — Preceding unsigned comment added by 144.191.148.7 ( talk) 12:58, 13 July 2015 (UTC)