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Literature review > Issue_5 > Review on Zenilman et al. |
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The stated objective of this study was to estimate the positive predictive value (PPV) of a single LCR test for C. trachomatis and N. gonorrhoeae by retesting positive specimens. However, it really only addresses the reproducibility (R) of a positive test, and not its predictive value. To be precise, PPV is defined as. PPV = The probability that a test-positive specimen is from an infected subject Whereas they estimate reproducibility as: R = The probability that an initially positive specimen retests as positive]. The entities R and PPV can therefore differ substantially. In particular, in a low prevalence population many of the positive results may be false positive, which may result in a low PPV. Yet, the reproducibility of positive tests (true and false) could still be high. To illustrate numerically, suppose that the prevalence of C. trachomatis in a population is 1.0%. Since 3.5% of subjects initially tested positive with LCR, at most 1% are true positive, and at least 2.5% are false positive. The PPV is the fraction of the total number of positive tests that are true positive. Therefore, PPV < 1% / 3.5% = 28.6% However, the reproducibility (R) of positive tests could be very high. Indeed, if most of the false positive results are due to contamination or cross-reactivity, and assuming that the sensitivity of the LCR test is 89%, then one would expect that R would be at least 89%, a number very different from the PPV of 28.6%. Since it is tenable that R is very different from PPV, R should not pose as a valid estimate of PPV. To the authors' credit, the potential for R to overestimate PPV is acknowledged as a limitation of their study. However, the potential extent of the over estimation is not reported and in my mind invalidates the paper as yielding an estimate of the PPV of the LCR test for chlamydia or gonorrhea. Rather, the study yields an estimate of reproducibility, which is an entity that may be of interest in its own right, but the paper is not at all clear on this point. The second set of calculations provided in the paper explore how sensitivity, specificity, and prevalence influence the PPV of a test using a mathematical formula called Bayes' theorem. As noted in the summary, assumed values for sensitivity and specificity of 0.95 and 0.99 yield a PPV = 66% when prevalence = 2%, while PPV = 32% when prevalence = 0.5%. This is a very wide range for the PPV and indicates how lack of knowledge about the prevalence of disease implies lack of knowledge about how to interpret the test result in practice. The authors note that the assumed value for specificity is much more influential on the PPV calculation than is sensitivity. This is a well-known phenomenon that is more easily seen from the following reformulation of Bayes' theorem:
The term sensitivity/(1-specificity) = DLR is called the positive DLR, or diagnostic likelihood ratio [1], and is interpreted as the factor to update the probability that the subject has disease (from the pretest probability or prevalence) given a positive test result. If specificity is close to 100%, small changes in the specificity can yield large changes in 1/(1-specificity) and hence in the PPV. As an example, assuming a sensitivity of 0.9 and say, a specificity = 0.99, yields a DLR factor of 0.9/(1-0.99) = 90, while a slightly higher specificity = 0.995 yields a DLR factor of 0.9/(1-0.995) = 180. The fact that the PPV changes so much with small changes in assumptions about specificity, and that, in practice, specificity will not be known with certainty, suggests that one should be very cautious about making these PPV calculations. The authors' conclusions that repeat testing of positive samples from a low prevalence population will increase specificity and reduce incidence of false positive results may in fact be true, but it is not addressed by this study. What is shown in the study is simply that the reproducibility of a positive LCR test is fairly high, 89.5% (lower confidence limit=78.3%) for chlamydia and 83.3% (lower confidence limit=73.5%) for gonorrhea. In summary, I don't think that we can learn very much about the PPV of the LCR test from this paper. Instead, we learn something about the reproducibility of a positive LCR test, another result that is interesting, but whose implications are not as far reaching as it first appears. It is also fair to note that this study is now largely of academic interest since the Abbott LCR test kit was withdrawn from the market in 2003. References: 1. Pepe MS. The Statistical Evaluation of Medical Tests for Classification and Prediction. Oxford University Press. 2003, pp 17-21.. |
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