Decision threshold and detection capability

1. Decision threshold anddetection capability Ivo Leito ivo.leito@ut.ee http://www.ut.ee/ams/ http://www.ut.ee/ams/

2. Decision threshold (limit) anddetection capability • Recently these have become increasingly important • Often required by legislation • E.g. European Commission decision 2002/657/EC concerning the performance of analytical methods and the interpretation of results http://www.ut.ee/ams/

3. a and b error: fire alarm http://www.ut.ee/ams/

4. a and b error: contamination detection Falsepositive False negative http://www.ut.ee/ams/

5. Decision threshold (limit), CCa • Answers the question: Starting from which analyte concentration it is possible to state that the probability of false positive is a or lower? or Starting from which analyte concentration it is possible lates millisest tulemuse väärtusest võime öelda, et proovi nõuetele mittevastavuse tõenäosus on üle 1-a? • According to legislation the a probabilities are normally 0.01 or 0.05 depending on analyte http://www.ut.ee/ams/

6. Detection capability, CCb • Answers the question: Starting from which analyte content we can say the probability of a false negative is b or less? or Starting from which analyte content we can say that the probability of analyte detection is above 1-b? • According to legislation the b probability is 0.05 • That is 1 - b = 0.95 (or 95%) http://www.ut.ee/ams/

7. Normal Distribution • When we find U then we use for ktwo-tailed quantiles • k = 1 (68%), 2 (95.5%), 3 (99.7%) 68% 95.5% 99.7% http://www.ut.ee/ams/

8. NormalDistribution • Here we use as ksingle-tailed quantiles: • k = 1.64 (a = 0.05), 2.33 (a = 0.01) a = 0.05 (5%) 1 - a = 0.95 a = 0.01 (1%) 1 – a = 0.99 http://www.ut.ee/ams/

9. Decision threshold, if there is no maximum permissible limit Distribution function of a blank Repeatability s of blank Average concentration found for blanks If the result is beyond 2.33s level then the probability of the analyte not being present in the sample is less than 1% http://www.ut.ee/ams/

10. Decision threshold if there is a legal upper limit Distribution function of analyte determination in sample contaminated at the legal limit Standard deviation of sample contaminated at the legal limit Average analyte content found in samples contami-nated at the legal limit If the result is beyond the 2.33s level then the probability that the content is not above the limit is less than 1% http://www.ut.ee/ams/ CCa CCa

11. Detection capability Distribution function of a sample contaminated at detection capability level Repeatability s of a sample contaminated at the level of decision threshold If the result is below CCa then the sample is considered not contaminated. The probability of contamination is 5%. Decision threshold CCa CCb http://www.ut.ee/ams/ CCa = CCb – 1.64 ss

12. Assumptions • The measurand is Normally distributed • This means that a sufficient number of parallel measurements must be made • Repeatability is the same at CCa and CCb levels • Repeatability must be determined under constant analyte content • Systematic effects have been taken into account http://www.ut.ee/ams/