The accuracy of diagnostic tests

Every disease has a rate of prevalence and incidence within both the general population and specific populations. The term 'prevalence' is a statistic based upon a particular point in time. It refers to the number of cases of a particular disease divided by the total number of people within the population and is usually represented as a percentage. 'Lifetime prevalence' is the number of people within a population who may have a particular disease at some time in their life, expressed as a percentage of the total population. The term 'incidence' refers to the number of new cases of a disease occurring over a specified period of time. The two terms are useful for different kinds of disease. The prevalence of a disease is often useful for more chronic diseases - those diseases which people rarely recover from, but also rarely cause death. A useful example is an estimate of the lifetime prevalence of peanut allergy within a given population. Diseases with high recovery rates or with high mortality rates are more usefully explored using the concept of 'incidence'. These include childhood infectious diseases. They also include food allergies that commonly occur in infancy and are known to have a high rate of resolution, such as milk or egg allergy.1

Obtaining accurate estimates of incidence and prevalence of diseases is not always simple. There are problems not only in defining true cases of the disease but also in making good estimates of the total population. From the available figures of incidence and prevalence, either formally or informally, the health professional develops an idea of the 'risk' that a particular patient has of a particular disease. This may simply be the risk derived from the general population's incidence or prevalence of the disease. If a chronic but not usually life-threatening disease has a prevalence of 1%, a particular patient has a risk of one in a 100 of having the disease. Further refining the prevalence from the patient's particular sub-population will modify each assessment of 'risk'. If the patient is female, and the disease has a 2% prevalence within the female population, her risk will increase to two in 100.

Each piece of new information, whether gleaned from the history, the examination, or subsequent diagnostic tests, progressively modifies the individual's risk of a given condition. Each individual can be thought of as having a prior or pre-test probability of the illness. Subsequent to a positive or negative result from a particular test, a posterior or post-test probability can be calculated. A positive diagnostic test will have different implications for an individual whose risk of food allergy has already been estimated as high from their history, compared to those for an individual drawn from the general population, with an unspecified but certainly lower risk. A patient who is seen in a non-specialist clinic is likely to have a lower risk than a patient seen by a specialist, as a filtering process will already have taken place. The impact that the test has on each individual's risk can be expressed statistically as a likelihood ratio.

The likelihood ratio can be calculated from the test's sensitivity and specificity.2 Consider a given disease in a population, such as peanut allergy. There will be people who definitely have this disease, who have immunolo-gically mediated reactions to peanut proteins. One needs to identify a 'gold standard' against which to measure the performance of other tests. This 'gold standard' is the best method available for estimating the prevalence of people who really have immunologically mediated reactions to peanut proteins. Let us consider the double-blind placebo-controlled challenge as our gold standard. At present within the field of food allergy it is probably the nearest we have to a 'gold standard'. If a patient has a clinically documented reaction by a blinded observer to hidden peanut protein, they are regarded as having the disease known as peanut allergy. We can then assess various tests against this 'gold standard' as to their efficacy at identifying true positives and true negatives.

How good is each test at correctly identifying those patients who truly have the disease, and at correctly identifying those who do not?

A highly sensitive test is one that is very good at identifying all cases of the disease while also including many of the normal population. A negative result is particularly useful, as the person showing that result is very unlikely to have the disease. Sensitivity can be expressed mathematically as a ratio, calculated thus:

true positives

true positives + false negatives

Specificity, however, is a measure of how important a positive result is. A positive result from a highly specific test is very likely to indicate that the individual showing that result has the disease, whereas a negative result does not so reliably rule out the condition. This can be expressed mathematically again as a ratio, calculated thus:

true negatives

true negatives + false positives

A test often forfeits specificity at the expense of sensitivity. The most desirable test is both highly specific and highly sensitive, but in different situations sensitivity might be more important than specificity, while others one may be more interested in the specificity of the test.

Recognizing and Dealing With Nut Allergies

Recognizing and Dealing With Nut Allergies

Protect your children, your family and your lives by reading this important book. Recognizing And Dealing With Nut Allergies There are dozens of different nut allergies that exist and each allergy requires different methods to treat it. Don't assume that your doctors will tell you if there's something wrong, you need to learn for yourself what the warning signs are, what the symptoms are and how to treat the allergy if in fact you or someone in your family has it.

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