Statistics Meeting Book (May 15, 2019)

ANNEX C Calculation of POD and dPOD Values from Qualitative Method Single Laboratory Data In general, four different probabilities detected (PODs) are to be calculated: POD R (for the reference method), POD C (for the confirmed candidate method), POD CP (for the candidate presumptive method), and POD CC (for the candidate confirmation method). For each of these four cases, calculate the POD as the ratio of the number positive ( x ) to total number tested ( N ): POD = x / N

where POD is POD C , POD R , etc. The POD estimates and 95% confidence interval (LCL, UCL) estimates are given by: ( 1 ) For the case where x = 0 . POD =0

LCL = 0

UCL= 3.8415/( N + 3.8415)

( 2 ) For the case where x = N .

POD =1

LCL = N /( N + 3.8415)

UCL = 1

( 3 ) For the case where 0 < x < N .

POD = x / N

XXX

XXX

where 1.9600 = z, the Gaussian quantile for probability 0.975, 1.9207 = z 2 /2, 0.9604 = z 2 /4 and 3.8415 = z 2 . Finally, if x ” 1, set LCL = 0. If x • N-1, set UCL = 1. The confidence interval corresponds to the uncorrected Wilson-score method, modified for x = 1 and x = N–1 to improve coverage accuracy on the boundary. dPOD for Unpaired Studies The differences in proportions detected are estimated by: dPOD C = POD C – POD R

dPOD CP = POD CP – POD CC

If the replicates tested by the candidate and reference methods are unpaired (i.e., the enrichment conditions differ between the methods, thus the methods require analysis of distinct test portions), the associated 95% confidence interval (LCL, UCL) for the expected value of dPOD = POD 1 – POD 2 is estimated by: XXX XXX where (LCL 1 , UCL 1 ) is a 95% confidence interval for POD 1 and (LCL 2 , UCL 2 ) is a 95% confidence interval for POD 2 , as determined above. dPOD for Paired Studies If the replicates tested by the candidate and reference methods are paired (i.e., the enrichment conditions are the same, thus common test portions are analyzed by both methods), the associated 95% confidence interval (LCL, UCL) for the expected value of dPOD = POD 1 – POD 2 is estimated by the following: For the single lab situation where a sample is tested N times in a paired study, the paired test portions will receive a positive or negative result for the two methods. The methods may be candidate and reference method, or they may be presumptive and confirmed results. The following tables are labeled “Candidate” and “Reference” but can be generalized to any two methods being compared. For the sake of convention, in this case dPOD = POD(c) – POD(r).

Reference Method Positive

Reference Method Negative

Candidate Method Positive

A

B

Candidate Method Negative

C

D

Let: A = number of pairs with positive results by both methods

B = number of pairs with positive result by candidate and negative result by reference C = number of pairs with negative result by candidate and positive result by reference D = number of pairs with negative results by both methods N = A+B+C+D