Positive predictive value

A positive predictive value (ようせいてきちゅうりつ) is a value defined for "the probability that is true positive when it is judged to be positive" in a certain inspection in one of the subsequent probability in the clinical inspection.

Table of contents

Synonym

Positive predictive value, positive proper middle degree, positive-predictive value, positive predictive value, positive reaction predictive value, positive reaction proper middle degree, positive reaction hitting ratio, positive-predictive value,

Examine a positive predictive rate, positive pre-gauging, positive predictive value, existence sign plus; a rate

Summary

I mean, "the probability that is true positive when it is determined that a test result is positive (patient) is high" saying "a positive predictive value is high".

Expression to make a pair includes a negative predictive value and is "the probability that is true negative when it is judged to be negative" in a certain inspection.

A positive predictive value is conditional probability when the judgment that a test result is with positive was got whereas the prior probability that is a patient is prevalence and is subsequent probability.

The positive predictive value PPV catches not only sensitivity Se and specific degree Sp but also the influence of prevalence a.

${\displaystyle PPV={\cfrac {Se\times a}{Se\times a+(1-Sp)(1-a)}}={\cfrac {1}{1+{\cfrac {(1-Sp)(1-a)}{Se\times a}}}}={\cfrac {1}{1+{\cfrac {1}{\cfrac {Se\times a}{(1-Sp)(1-a)}}}}}={\cfrac {1}{1+{\cfrac {1}{Odds}}}}}$ 

${\displaystyle PPV={\cfrac {Se\times a}{Se\times a+(1-Sp)(1-a)}}={\cfrac {\cfrac {Se\times a}{(1-Sp)(1-a)}}{{\cfrac {Se\times a}{(1-Sp)(1-a)}}+1}}={\cfrac {Odds}{Odds+1}}}$ 

${\displaystyle {\cfrac {PPV}{(1-PPV)}}={\cfrac {Se}{(1-Sp)}}\times {\cfrac {a}{1-a}}=Odds}$ 

In other words, the odds (= follow-up odds) of the positive predictive value PPV which is subsequent probability becomes odds (= prior odds) of prevalence a which is prior probability and the product of the likelihood ratio (= sensitivity and the ratio of (1-specific degree)).

Generally, if a specific degree is high, a positive predictive value rises and is useful for a definitive diagnosis.

Reference

About sensitivity, a specific degree, positive predictive value, the negative predictive value, the following tables want to be referred to.

		True state (the result of the examination for details such as the biopsy determines it)
		Positive	Negative
Inspection Result	Positive	Truth positive	False-positive (blunder of the first kind)	Positive predictive value = Truth-positive number 　  Inspection-positive number
	Negative	False-negative (blunder of the second kind)	Truth negative	Negative predictive value = Truth-negative number  Inspection-negative number
		Sensitivity = Truth-positive number Truth-positive + false-negative	Specific degree = Truth-negative number False-positive + truth negative

Allied item

• Epidemiology
• Clause 2 classification
• A first-class blunder and the second kind blunder
• Sensitivity
• Specific degree
• Negative predictive value
• Likelihood ratio
• Negative likelihood ratio
• Positive likelihood ratio

References

• For written by Koichi Nakamura "pleasant epidemiology" (the third edition) medicine study, 2,013 years, it is P130-134, ISBN 978-4-260-01669-8

• For written by Koichi Nakamura "plain statistics" (the revision second edition) diagnosis and treatment company, 2,012 years, it is P165-173, ISBN 978-4-7878-1794-5

• For written by Chieko Okuda "statistics (the revision second edition) as the tool" 金芳堂, 2,011 years, it is P171-172, ISBN 978-4-7653-1501-2

• For written by Chieko Okuda "how to choose statistics technique 金芳堂 to the study design for pharmaceutical researchers", 2,009 years, it is P70-72, ISBN 978-4-7653-1376-6

• For Hideki Nomura / Satoru Matsukura fine weather work "actually plain clinical statistics Nakayama Bookstore for clinicians by the clinicians", 2,005 years, it is P154-156, ISBN 978-4-521-01901-7

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This article is taken from the Japanese Wikipedia Positive predictive value

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