Where, a are true positive, b are false positive, c are false negative and d are true negative

Sensitivity = a/(a+c)

Specificity = d/(b+d)

PPV = a/(a+b)

“True” in true positive, is an abstract concept because in practice a reference standard must be adopted.
For colorectal cancer screening, true is usually defined by the outcome of total colonoscopy, the
best practical diagnostic procedure we have though it does not have a sensitivity of 100%. In a clinical
setting it is not always possible to perform a total colonoscopy on all subjects who have negative
screening tests, so it is difficult to estimate the number of false negatives (c) and true negatives (d).
The difficulty of estimating false negative has a great impact on sensitivity but much less so on specificity.
In fact (c) is a number much lower than (d), so that the sum c+d (i.e. the number of negatives
to the test) is a small overestimate of d.

For sensitivity, (c) is a significant proportion of (a+c), so that it is necessary to have a direct estimate
of the number of false negatives. Very often this estimate is obtained by measurement of the interval
cancers (i.e. the number of colorectal cancers that are diagnosed in subjects negative to the test during
defined interval of time). Clearly the reliability of the estimated number of false negatives will
depend on the time interval, and that will increase as time elapses. It is therefore important when
comparing estimates of sensitivity obtained in this way to verify that the time interval used is the
same.

The ideal theoretical approach to estimating cancer-screening performance would be to obtain the
disease status using a “gold-standard” method that is independent of the screening method. For colorectal
cancer, the disease status is usually determined from a histological examination of biopsy specimens
of those with positive test results, because it is not ethically acceptable to collect biopsies from
all individuals undertaking a screening test. The sensitivity and specificity of screening test are therefore
usually estimated using interval cancers. As initially described by Day (1985) interval cancers will
not include slow-growing cancers missed by the test and not evident between two screening events
(therefore clinical sensitivity will be overestimated). Conversely, interval cancers will include fastgrowing
cancers not present at the time of the screening test, but developing during the interval
period (thus underestimating clinical sensitivity). This limitation is common to all screening procedure
evaluations.

Programme sensitivity is an estimate of sensitivity (i.e. the number of CRC detected/the number of
cancers detected plus the number of interval cancers occurring in a certain interval of time) and is
biased toward overdiagnosis of CRC (i.e. it estimates diagnosis of CRC that would never occur
clinically). For this reason it is sometime preferable to give an estimate of sensitivity based on the
ratio between interval cancers (in a defined time period) and the number of cancers expected in the
same period (more precisely, 1- (interval cancers occurred in x years/expected cancers in x years)).
This estimate gives an idea of cancers anticipated by screening, and it is not affected by overdiagnosis.

It is also worth noting that from a practical point of view, the choice of the test (or combination of
tests) is not based on clinical sensitivity and specificity but on the determination of detection rate (for
cancer or adenomas) and its correlation with positivity being first correlated to sensitivity and latter to
specificity.

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