J Martin Bland

The simplest diagnostic test is one where the results of an investigation, such as an x ray examination or biopsy, are used to classify patients into two groups according to the presence or absence of a symptom or sign. For example, the table shows the relation between the results of a test, a liver scan, and the correct diagnosis based on either necropsy, …

The whole point of a diagnostic test is to use it to make a diagnosis, so we need to know the probability that the test will give the correct diagnosis. The sensitivity and specificity1 do not give us this information. Instead we must approach the data from the direction of the test results, using predictive values. Positive predictive value is the proportion of patients with positive test results who are correctly diagnosed. Negative predictive value is the proportion of patients with negative test results who are correctly diagnosed. Using the same data as in the previous note,1 we know that 231 of 263 patients with abnormal liver scans had abnormal pathology, giving the proportion of correct diagnoses as 231/263 = 0.88. …

In recent years odds ratios have become widely used in medical reports—almost certainly some will appear in today's BMJ . There are three reasons for this. Firstly, they provide an estimate (with confidence interval) for the relationship between two binary (“yes or no”) variables. Secondly, they enable us to examine the effects of other variables on that relationship, using logistic regression. Thirdly, they have a special and very convenient interpretation in case-control studies (dealt with in a future note). The odds are a way of representing probability, especially familiar for betting. For example, the odds that a single throw of a die will produce a six are 1 to 5, or 1/5. The odds is the ratio of the probability that the event of interest occurs to the probability that it does not. This is often estimated by the ratio of the number of times that the event of interest occurs to …

In earlier Statistics Notes1 2 we commented on the analysis of paired data where there is more than one observation per subject. It can be highly misleading to analyse such data by combining repeated observations from several subjects and then calculating the correlation coefficient as if the data were a simple sample.1 The appropriate analysis depends on the question we wish to answer. If we want to know whether an increase in one variable within the individual is associated with an increase in the other we can calculate the correlation coefficient within subjects.2 If we want to know whether subjects with high values of one variable also tend to have …