Guide to Statistics: "Supporting Statistics in Medicine;"

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7 Screening and diagnostic tests

Studies which evaluate diagnostic tests aim to compare their performance against a 'gold standard’. The gold standard is regarded as the true diagnosis of a condition. However it may not always be possible to know absolutely the true diagnosis and in this case the gold standard represents diagnosis using the best currently available method. Figure 5 shows the four possible outcomes when performing a diagnostic test:

Figure 5: Possible outcomes from a diagnostic test

and these may be organised in a table as follows:

Table 7:  Relationship between gold standard diagnosis and the results of a diagnostic test
	Gold standard diagnosis:
Test:	Disease present	Disease absent
Disease present	a	b	a+b
Disease absent	c	d	c+d
	a+c	b+d	a+b+c+d=n

Tests are usually evaluated using the following statistical measures:
Sensitivity: the proportion of people with disease who have a positive test.  In the 2$$\times$$2 table, calculate as: $$ a/(a + c).$$
Specificity: the proportion of people free of disease who have a negative test. In the 2$$\times$$2 table, calculate as:  $$d/(b + d).$$
Positive predictive value: the proportion of patients who test positive who actually have the disease. $$a/(a + b).$$
Negative predictive value: the proportion of patients who test negative who genuinely don't have the disease.  $$d/(c + d).$$
The Sensitivity and Specificity are useful for developing a test and explain the relative performance of the test. Theoretically they are not affected by the disease prevalence. The positive and negative predictive values are useful to a clinician and a patient using the new test in practice. They are affected by the prevalence of the disease in the population of interest and are therefore only applicable to the population for which the values were calculated.
A statistic that combines the extra information provided by the test result is the likelihood ratio.
Likelihood ratio: the ratio of the probability that a given test result would occur in a patient with the disease to the probability that the same result would occur in a patient without the disease.
For a positive test result:
LR(+) = Sensitivity/(1- Specificity) $$ = a/(a + c) / b/(b + d).$$
For a negative test result:
LR(-) = (1- Sensitivity)/ Specificity $$ =c/(a + c) / d/(b + d).$$
Clinical example:
Children with suspected measles were screened using a new laboratory test which was compared against the existing test (Gold Standard). In this study, the authors recruited children from primary care who were suspected of having measles.

Table 8:
	RT-PCR:			Sensitivity $$ =43/(43+59)  =0.42$$
New laboratory test:	Positive	Negative		Specificity $$ =190/(190+8)    =0.96$$
Positive	43	8		PPV        $$ =43/(43+8)    =0.84$$ NPV        $$ = 190/(190+59) = 0.76$$
Negative	59	190		LR (+)     $$ = 0.42/0.04    = 10.5$$
				LR (-)      $$ =0.58/0.96     = 0.604$$

This test has a high specificity; i.e. there are very few false positive results. The test would therefore be useful to “rule in” the disease, if a positive result is found. The following mnemonics have been suggested:
$$S_{p}$$ Pin: for a test with high specificity $$(S_{p})$$ a Positive test rules the disease in.
$$S_{n}$$ Nout: for a test with high sensitivity $$(S_{n})$$ a Negative result rules the disease out.

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