Statistics Meeting Book (February 20, 2019)

INTRODUCTION

Suppose two qualitative methods A and B are available to test for the presence of analyte in a particular test portion. Of interest is the degree of agreement of the two methods in detecting the analyte. If the two methods agree more often than not, then a ‘paired’ or ‘matched’ experimental study gives the most accurate measures of agreement. The terms ‘paired on test portion’ or ‘matched on test portion’ mean that the two methods are applied to the same test portion or its laboratory derivative. This occurs frequently for microbial analytes when the test portion’s incubated enrichment broth is tested by both methods. ‘Presumptive’ and ‘Confirmatory’ methods typically satisfy this requirement.

Paired data are most conveniently summarized by the two-way outcome classification table

Table 1. Cross-classification for paired data results B B + -

Total a + b c + d

A A

+

a c

b d

-

Total

a + c

b + d

n = a + b + c + d

where ‘n’ is the total number of test portions tested, ‘a’ is the number of test portions for which both methods gave a positive result, etc.

The difference in proportion detected for the two methods A and B is given by

dPOD(A,B) = POD(A) – POD(B)

(1)

For Table 1, this difference is estimated (maximum likelihood, unbiased) by

dPOD(A,B) =

(a + b) / n (b – c) / n

-

(a + c) / n

(2a) (2b)

=

In TR342, a number of possible confidence intervals were suggested which dealt with the problem of degeneracy when dPOD = 0 or dPOD =1. In subsequent events, the choice was down-selected to the large-sample continuity-corrected estimate

√{ [ (b + c + 2) / (n + 2) – ((b – c) / (n + 2)) 2 ] / n }

SE(dPOD)

=

(3)

An approximate 95% confidence interval for dPOD is then given by

dPOD

+

z 0.975

SE(dPOD)

(4)

2