Description of terms used to describe test effectiveness

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.