Probability or specificity – evaluating the evidence

While the probability of infection is obviously proportional to the specificity of the test, it is important to understand the influence of incidence (pre-test probability).

Incidence will not affect the specificity, but it will influence the positive predictive value (post-test probability) of a test, particularly if the disease being diagnosed by the test is of low incidence (<10%), which is typically the case for invasive fungal disease (IFD).

For an infection such as invasive aspergillosis (IA), an incidence of 5-10% is typical, in high-risk haematology patients, so prior to performing any test the probability of IA could be as low as 5%. Conversely, the probability of a patient not having IA is 95%. It is therefore difficult to gain a post-test probability >50%, irrespective of test specificity. Obviously, a test with 100% specificity confirms IFD/IA, irrespective of incidence, but such tests rarely exist in mycology due to the ubiquitous nature of fungi.

At an incidence of 5%, a test requires a specificity of >95% before the post probability of IFD associated with a positive test result exceeds 50% (Table 1) and if the sensitivity of such test were to drop below 76%, then the post-test probability would drop below 50%. For incidences <5%, exceptional test specificity (>99%) is required to provide a post-test probability to base confident administration of antifungal treatment.

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This raises the question of when to treat a patient at high-risk of IFD (albeit with a likely low incidence) with a positive mycology result. One strategy is to rely on the use of combination testing, where multiple positive results from different tests significantly improve specificity. In the previous section 1.9, combining galactomannan ELISA testing with Aspergillus PCR to aid in the diagnosis of IA generated a specificity of 98%, when both tests were positive, and at incidence of 5% provided a post test-probability of IA of 72%.

From a statistical perspective, using the positive likelihood ratio (LR +tive) may be a useful parameter for determining the significance of a positive result. While likelihood ratios are used to calculate the post-test probability of IFD, based on the initial incidence and using Fagan’s nomogram, their values are less affected by incidence (Table 2).

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A positive result from a test with a LR +tive threshold of 10 (i.e. 10 times more likely to see a positive result in a patient with IFD than without IFD) is a widely accepted as a good indication of disease, and a test with >90% specificity would provide this performance irrespective of incidence (Table 2).

For IFD, where the incidence (pre-test probability) is usually low (<10%) even in high-risk populations, it is far easier to exclude IFD on the basis of high negative predictive values. As the probability of the patient not having IFD prior to testing is >90%, it is far easier to improve this probability and negative results from tests with a moderate sensitivity (75%) increase the probability of the patient not having IFD to 99%.

Conversely, specificities of >99% are required to provide comparable post-test probabilities confirming a diagnosis. However, we should not overlook the significant achievement in increasing pre-test probability from 5% to a post-test probability 50%, basing treatment decisions on these values represents an improvement in accuracy over empirical antifungal therapy. In clinical practice, positivity in tests with specificity >90% (and certainly >95%) provide a significant probability of infection and treatment is warranted.