A fourth set of measures of diagnostic performance, predictive values, describe the probabilities that positive or negative test results are correct, and are calculated as indicated in Box 14.3. Note that in contrast to the calculations in Box 14.1, the calculations of predictive values are undertaken on the rows of the 2X2 table, and therefore do depend on the prevalence of the disease in the study sample. The more common a disease is, the more likely it is that a positive result is right and a negative result is wrong. Whilst clinicians often consider predictive values to be the most useful measures of diagnostic performance when interpreting the test results of a single patient, they are rarely used in systematic reviews. Disease prevalence is rarely constant across studies included in a systematic review, so there is often an unacceptably high level of heterogeneity among positive and negative predictive values, making them unsuitable choices of effect measures. There is an analogy here with the estimation of risk differences in systematic reviews of RCTs (Chapter 16), which are the easiest summary statistics to understand and apply, but are rarely the summary of choice for a meta-analysis as they are commonly heterogeneous across trials.
However, predictive values can be estimated indirectly from the results of systematic reviews. The predictive values of a test can be thought of as post-test probabilities, and hence estimated from summary likelihood ratios by application of Bayes' Theorem11 as described previously. In this situation the pre-test probability is estimated by the population prevalence: application of the positive likelihood ratio yields the positive predictive value. The negative predictive value can be calculated by application of the negative likelihood ratio, and subtracting the resulting post-test probability from one.
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