Diagnostic Effectiveness.

True positives, false positives, true negatives, false negatives. Note that the perspective of the test is taken, not the perspective of the (outcome) standard. Positive means that the test result indicates that a problem (disease) is present but that doesn't have to be necessarily true. A false positive for example is someone who tested positive but who is in fact problem free. Presented are respectively the numbers in this particular table and the proportions for each of the cells relative to the complete table.

Accuracy, number and proportion of all the observations in the table which have been classified correctly by the test.

Kappa is a measure of agreement and takes on the value zero if there is no more agreement between test and outcome then can be expected on the basis of chance. Kappa takes on the value 1 if there is perfect agreement; i.e. the test always correctly predicts the outcome. It is considered that Kappa values lower than 0.4 represent poor agreement, values between 0.4 and 0.75 fair to good agreement, and values higher than 0.75 excellent agreement. Negative Kappa indicates a problem in the application of the test. Kappa is dependent not only on the quality of the test, i.e., the inside of the table, but also on the prevalence of the disease in the population in which the test is applied, kappa is also sensitive to the distribution of cases in the table margin. Basically what Kappa shows is that for the same sensitivity and specificity the agreement between test and outcome will decrease with a decreasing prevalence. In Kappa terms a test will perform wearse in low prevalence populations.

Sensitivity. The probability that an individual which is diseased is indeed tested as diseased. You would want the sensitivity of a test to be high if having the "disease" is relatively serious and the "cure" is relatively inexpensive and easily available. One would expect the sensitivity to be larger as 0.5.

Specificity. The probability that an individual which is not diseased is tested as not diseased. You would want the specificity to be high if having the disease is not so serious and the "cure" is relatively expensive in money and other terms. Note that there is a tradeoff between specificity and sensitivity, high specificity mostly means low sensitivity, and vice versa. For example, a diagnostic instrument is based on some type of blood count and treatment is given if the blood count is below a certain level. If you give treatment at a relatively high blood-count and thus give relatively many patients treatment (high sensitivity, low specificity) people who do not need it will get unnecessary treatment. If you are conservative and set blood count level for inclusion in treatment low (low sensitivity, high specificity) people who require treatment will be missed. One would expect the specificity to be larger as 0.5.

Negative likelihood. Indicates how much more likely it is to get a negative test in the non-diseased as opposed to the diseased group.

Diagnostic Odds Ratio. Often used as a measure of the discriminative power of the test. Has the value one if the test does not discriminate between diseased and not diseased. Very high values above one means that a test discriminates well. Values lower than one mean that there is something wrong in the application of the test.

Error Odds Ratio. Indicates if the probability of being wrongly classified is highest in the diseased or in the non-diseased group. If the error odds is higher than one the probability is highest in the diseased group (and the specificity of the test is better than the sensitivity), if the value is lower than one the probability of an incorrect classification is highest in the non-diseased group (and the sensitivity of the test is better than the specificity).

Youden's J. Is used to study the overall performance of a test. The J takes on the value 1 if a diagnostic test discriminates perfectly and without making any mistakes. If you want to minimize the probability of making an error you should maximize the Youden's J. That, of course, is of only theoretical importance, such decisions should be taken on the basis of a cost-benefit analysis of treatment as opposed to no treatment.

Positive predictive accuracy. In a table representative of the population it gives: 1) the post-test probability, the probability for an individual in the population who tested positive of having the disease; 2) of those who tested positive the fractions who were correctly and who were not-correctly classified.

Negative predictive accuracy. In a table representative of the population it gives: 1) the post-test probability, the probability for an individual in the population who tested negative of not having the disease; 2) of those who tested negative the fractions who were correctly and who were not-correctly classified.

Pearson's Correlation. Much the same story as for the Kappa.

Bayesian approach. Diagnostic tests are often first developed in research (hospital) settings. Sometimes an experimental group is formed of available patients to be compared with a control group from the general population. These controls are often selected on the basis that it is unlikely that they have been exposed to the disease. For example, in developing a test for syphilis the outcome of the test in a group of people who show all the clinical manifestations of syphilis is compared with the outcome of the test in a group of nuns. Some kind of procedure will be applied to minimize error rates in both groups. However, in practice tests are often used in primary care or general screening environments. The prevalence of the disease in these circumstances will be very much lower as was the case in the experimental situation. Sensitivity and specificity of tests tend to be quite robust under these circumstances and to change little between high and low prevalence populations. However, positive and negative predictive accuracy particularly are very sensitive to the prevalence of the disease in the population in which the test is applied. Therefore an approach has been developed on the basis of Bayes theorem which makes it possible to enter the prevalence of the disease as a piece of prior knowledge in the equation. Corrected positive and negative predictive accuracies can then be calculated for different populations. To do this in SISA you need to enter a proportion, between zero and one, in the 'prevalence' box. Note that a test requires to be optimized for the population in which it is applied and that practical and financial reasons will have to play a role besides clinical considerations. The Bayesian approach can be valuable to model the various practical options.