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Tests are routinely used in medicine to screen for, diagnose, grade, and monitor the progression of disease. Diagnostic information is obtained from a multitude of sources, including imaging and biochemical technologies, pathological and psychological investigations, and signs and symptoms elicited during history taking and clinical examinations.1 Each of these items of information can be regarded as a result of a separate diagnostic or screening “test.” Systematic reviews of evaluations of tests are undertaken for the same reasons as systematic reviews of treatment interventions: to produce estimates of test performance and impact based on all available evidence, to evaluate the quality of published studies, and to account for variation in findings between studies.2–5 Reviews of studies of diagnostic accuracy involve the same key stages of defining questions, searching the literature, evaluating studies for eligibility and quality, and extracting and synthesising data. However, studies that evaluate the accuracy of tests have a unique design requiring different criteria to appropriately assess the quality of studies and the potential for bias. Additionally, each study reports a pair of related summary statistics (for example, sensitivity and specificity) rather than a single statistic (such as a risk ratio) and hence requires different statistical methods to pool the results of the studies. This article concentrates on the dimensions of study quality and the advantages and disadvantages of different summary statistics for combining studies in meta-analysis. Other aspects, including searching the literature and further technical details, are discussed elsewhere.6
Studies of test performance (or accuracy) compare test results between groups of patients with and without the target disease, each of whom undergoes the experimental test as well as a “gold standard” diagnostic investigation to ascertain disease status. The relation between the test results and disease status is described using probabilistic measures, such as sensitivity, specificity, likelihood ratios, diagnostic odds ratios (box), and receiver operating characteristic curves (box).
Sensitivities and specificities
The rates of correct identification of patients with and without the disease are known as test sensitivity and test specificity, respectively.7 For a test to be useful at ruling out a disease it must have high sensitivity, and for it to be useful at confirming a disease it must have high specificity
Positive and negative likelihood ratios describe the discriminatory properties of positive and negative test results, respectively.8 Likelihood ratios state how many times more likely particular test results are in patients with disease than in those without disease. Positive likelihood ratios above 10 and negative likelihood ratios below 0.1 have been noted as providing convincing diagnostic evidence, whereas those above 5 and below 0.2 give strong diagnostic evidence.9 Likelihood ratios can be directly applied to give probabilistic statements concerning the likelihood of disease in an individual (box)
Diagnostic odds ratios
The diagnostic odds ratio is a convenient measure when combining studies in a systematic review (it is often reasonably constant regardless of the diagnostic threshold) but is difficult to apply directly to clinical practice. The diagnostic odds ratio describes the odds of positive test results in participants with disease compared with the odds of positive test results in those without disease. A single diagnostic odds ratio corresponds to a set of sensitivities and specificities depicted by a receiver operating characteristic curve
Receiver operating characteristic curves are used in studies of diagnostic accuracy to depict the pattern of sensitivities and specificities observed when the performance of the test is evaluated at several different diagnostic thresholds. Figure Figure11 is a receiver operating characteristic curve from a study of the detection of endometrial cancer by endovaginal ultrasonography.8 Women with endometrial cancer are likely to have increased endometrial thicknesses: few women who do not have cancer will have thicknesses above a high threshold whereas few women with endometrial cancer will have thicknesses below a low threshold. This pattern of results is seen in figure figure11 , with the 5 mm threshold showing high sensitivity (0.98) but poor specificity (0.59) and the 25 mm threshold showing poor sensitivity (0.24) but high specificity (0.98).
The overall diagnostic performance of a test can be judged by the position of the receiver operating characteristic line. Poor tests have lines close to the rising diagonal, whereas the lines for perfect tests would rise steeply and pass close to the top left hand corner, where both the sensitivity and specificity are 1. Receiver operating characteristic plots are used in systematic reviews to display the results of a set of studies, the sensitivity and specificity from each study being plotted as a separate point in the receiver operating characteristic space
The quality of a study relates to aspects of the study's design, methods of sample recruitment, the execution of the tests, and the completeness of the study report, as summarised in table table11.4–6,10–12
To be reliable a systematic review should aim to include only studies of the highest quality. Systematic reviews may either exclude studies that do not meet these criteria and are susceptible to bias or include studies with a mixture of quality characteristics and explore the differences.3,5 Whichever approach is adopted, it is essential that the quality of the studies included in the review is assessed and reported, so that appropriately cautious inferences can be drawn.
A recent empirical study evaluated which aspects of design and execution listed in table table11 are of most importance.13 The most notable finding related to the design of the study. Studies that recruited participants with disease separately from those without disease (for example, by comparing a group known to have the disease with a group of healthy controls) overestimated diagnostic accuracy when compared with studies that recruited a cohort of patients unselected by disease status and representative of the clinical population in which the test was used. Studies that used different reference tests according to the results of the experimental test also overestimated diagnostic performance, as did unblinded studies. Omission of specific details from the report of the study was also associated with systematic differences in results.
Meta-analysis is a two stage process involving derivation of summary statistics for each study and computation of a weighted average of the summary statistics across the studies.14 I illustrate the application of three commonly used methods for pooling different summaries of diagnostic accuracy with a case study.
As with systematic reviews of randomised controlled trials, meta-analysis should be considered only when the studies have recruited from similar patient populations (it is problematic to combine studies from general practice with studies from tertiary care), have used comparable experimental and reference tests, and are unlikely to be biased. Even when these criteria are met there may still be such gross heterogeneity between the results of the studies that it is inappropriate to summarise the performance of a test as a single number.
Smith-Bindman et al published a systematic review of 35 studies evaluating the diagnostic accuracy of endovaginal ultrasonography for detecting endometrial cancer and other endometrial disorders.15 All studies included in the review were of prospective cohort designs and used the results of endometrial biopsy, dilation and curettage, or hysterectomy as a reference standard. Most of the studies presented sensitivities and specificities at several endometrial thicknesses detected by endovaginal ultrasonography (the receiver operating characteristic curve in figure figure11 is from one of these studies). The case study is based on the subset of 20 studies from this review that considered the diagnostic accuracy of endovaginal ultrasonography in ruling out endometrial cancer with endometrial thicknesses of 5 mm or less. Figure Figure22 shows the sensitivities and specificities for the 20 studies.
The choice of meta-analytical method depends in part on the pattern of variability (heterogeneity) observed in the results. Heterogeneity can be considered graphically by plotting sensitivities and specificities from the studies as points on a receiver operating characteristic plot (fig (fig3).3). Some divergence of the results around a central point is to be expected by chance, but variation in other factors, such as patient selection and features of the study's design, may increase the observed variability.16
One important extra source of heterogeneity is variation introduced by changes in diagnostic threshold. Studies may use different thresholds to define positive and negative test results. Some may have done this explicitly—for example, by varying numerical cut-off points used to classify a biochemical measurement as positive or negative, whereas for others there may be naturally occurring variations in diagnostic thresholds between observers, laboratories, or machines. The choice of a threshold may also vary according to the prevalence of the disease—when the disease is rare a more extreme threshold may have been used to avoid large numbers of false positive diagnoses. Unlike other sources of variability, variation of the diagnostic threshold introduces a particular pattern into the receiver operating characteristic plot of study results, such that the points show curvature (fig (fig11).
If there is no heterogeneity between the studies, the best summary estimate of test performance should be a single point on the receiver operating characteristic graph. The first two methods estimate such a summary, first by pooling sensitivities and specificities then by pooling positive and negative likelihood ratios. The third method is more complex and pools diagnostic odds ratios to take account of possible heterogeneity in diagnostic threshold.
The pooled estimate of sensitivity is 0.96 (95% confidence interval 0.93 to 0.99) and is depicted by the horizontal line on the receiver operating characteristic plot in figure figure33 (left). The overall estimate of mean specificity is lower: 0.61 (0.55 to 0.66).
Heterogeneity is, however, clearly evident in figure figure33 (left): although the study points lie reasonably close to the summary sensitivity (test for heterogeneity, P=0.04), the results of many studies lie some distance from the summary specificity (test for heterogeneity, P<0.001).
Regardless of the causes of the heterogeneity, the overall high estimate and relative consistency of the sensitivity results does suggest that a negative test result could be of potential clinical use in ruling out endometrial cancer. As there is heterogeneity between specificities, however, it is more appropriate to note the range of specificities (0.27 to 0.88) rather than to quote the average value of 0.61. It is difficult to draw a conclusion about test specificity: the observed values vary considerably and there is no understanding from this analysis as to the reasons for the variation.
Assuming that the study samples are representative, an estimate of the pretest odds can be calculated from the prevalence of endometrial cancer across the studies (13%)
Applying Bayes' theorem to the summary negative likelihood ratio:
and converting the post-test odds to a probability:
we estimate that only 1.3% of women with an endometrial thickness of 5 mm or less measured by endovaginal ultrasonography will have endometrial cancer. Knowledge of other characteristics of a particular patient that either increase or decrease their prior probability of endometrial cancer can be incorporated into the calculation by adjusting the pretest probability accordingly1
For the case study the pooled estimate of the positive likelihood ratio was not particularly high (2.54, 2.16 to 2.98), and the values varied significantly between the studies (test for heterogeneity, P<0.001). In figure figure33 (centre) it is clear that the summary positive likelihood ratio lies some distance from many of the values. Again it is debatable whether reporting the average value of such heterogeneous results is sensible, but it is unlikely that a positive test result could provide convincing evidence of the presence of endometrial cancer as the positive likelihood ratios are all below 10 (data not shown).
The negative likelihood ratios show no evidence of significant heterogeneity (test for heterogeneity, P=0.09), the pooled estimate being 0.09 (0.06 to 0.13), with the summary line on the receiver operating characteristic plot in figure figure33 (centre) lying close to the results of most of the studies. This finding again shows that a measurement of an endometrial thickness of 5mm or less made by endovaginal ultrasonography can provide reasonably convincing evidence to rule out endometrial cancer.
Although these conclusions concerning potential diagnostic use are similar to those obtained by pooling sensitivities and specificities, the summaries obtained by pooling likelihood ratios can be more easily interpreted and applied to clinical practice. The box describes how the summary negative likelihood ratio can be applied to estimate the probability of endometrial cancer in a woman with a negative test result.
If the observed heterogeneity between the studies arises due to variation in the diagnostic threshold, estimates of summary sensitivity and specificity or summary positive and negative likelihood ratios will underestimate diagnostic performance.18 In this situation the appropriate meta-analytical summary is not a single point in the receiver operating characteristic space but the receiver operating characteristic curve itself. Methods of deriving the best fitting summary receiver operating characteristic curve are necessarily more complex.2–5,18–21
How is a summary receiver operating characteristic curve estimated? The simplest approach involves calculating a single summary statistic for each study—the diagnostic odds ratio (box). Each diagnostic odds ratio corresponds to a particular receiver operating characteristic curve. If the studies in a review all relate to the same curve they may have consistent diagnostic odds ratios even if they have variable sensitivities and specificities. Table Table22 gives examples of diagnostic odds ratios corresponding to particular sensitivities, specificities, and positive and negative likelihood ratios.
In the case study it is possible that some of the observed heterogeneity could be explained by a threshold effect, perhaps due to differences in calibration of the ultrasound machines. The estimate of the summary diagnostic odds ratio is 28.0 (18.2 to 43.2) and is reasonably consistent across the studies (test for heterogeneity, P=0.3), suggesting that the points indeed could have originated from the same receiver operating characteristic curve. The summary diagnostic odds ratio can be interpreted in terms of sensitivities and specificities by consulting table table22 (for example, a diagnostic odds ratio of 29 corresponds to a sensitivity of 0.95 and a specificity of 0.60 and to a sensitivity of 0.60 and specificity of 0.95) or by plotting the corresponding summary receiver operating characteristic curve (fig (fig33 (right)). This method does not yield a unique joint summary estimate of sensitivity and specificity: it is only possible to obtain a summary estimate of one value by specifying the value of the other. This greatly limits its clinical application.
Systematic reviews of diagnostic accuracy have not, as yet, made the same impression on the practice of evidence based health care as have systematic reviews of randomised controlled trials. Reasons relate to reliability, heterogeneity, and clinical relevance.
Many meta-analyses of the accuracy of diagnostic tests are hindered by the poor quality of the primary studies: most published evaluations of the accuracy of diagnostic tests having at least one flaw.12 Headway has been made in understanding the importance of particular features of a study's design and in improving quality, but for many diagnostic tests few high quality studies have been undertaken and published.13
The reliability of a review also depends crucially on whether the included studies are an unbiased selection. As with all reviews, systematic reviews of diagnostic tests are susceptible to publication bias, and this may be a greater problem than for randomised controlled trials.2,3 No investigations, however, have been conducted to estimate rates of publication bias for studies of diagnostic accuracy.
Heterogeneity of the results of studies of diagnostic accuracy is common but in itself does not prevent conclusions of clinical value from being drawn.22 Despite heterogeneity being observed in the case study, it was still possible to draw a conclusion of clinical value—that an endometrial thickness of 5 mm or less can rule out endometrial cancer.
Diagnostic odds ratios and summary receiver operating characteristic curves are, however, often promoted as the most statistically valid method for combining test results when there is heterogeneity between studies, and they are commonly used in systematic reviews of diagnostic accuracy.2–4 Unfortunately summary curves are of little use to practising healthcare professionals: they can identify whether a test has potential clinical value, but they cannot be used to compute the probability of disease associated with specific test outcomes. Their use is also based on a potentially inappropriate and untested assumption that observed heterogeneity has arisen through variation in diagnostic threshold. In the case study, whereas the diagnostic odds ratio was a reasonably consistent summary statistic across the studies, there was no evidence to suggest that the observed heterogeneity arose through variations in diagnostic threshold (all included studies had a 5 mm threshold for endometrial thickness). Variation in referral patterns, sample selection, and study methods may be more likely explanations for the heterogeneity. There is no clear statistical advantage in using a summary receiver operating characteristic approach to synthesise the results over pooling sensitivity and specificity or likelihood ratios unless there is a threshold effect. Empirical research is urgently required to find out whether the simpler methods for pooling sensitivities, specificities, and likelihood ratios are likely to be seriously misleading in practice and whether apparent threshold effects are really due to variations in diagnostic threshold rather than alternative sources of heterogeneity.
Systematic reviews of the accuracy of tests do not always answer the most clinically relevant question. New tests are often evaluated for their ability to replace or be used alongside existing tests. The important issues are comparisons of tests or comparisons of testing algorithms: these would be best addressed in properly designed comparative studies, rather than by synthesising studies of diagnostic accuracy separately for each test.
The evaluation of the diagnostic accuracy of a test is also only one component of assessing whether it is of clinical value.23,24 Treatment interventions are recommended for use in health care only if they are shown on average to be of benefit to patients: the same criterion should also be applied for the use of a diagnostic test, and even the most accurate of tests can be clinically useless or do more harm than good. It should always be considered whether undertaking a systematic review of studies of diagnostic accuracy is likely to provide the most useful evidence of the value of a diagnostic intervention.
I thank Rebecca Smith-Bindman for providing the data for the case study.
This is the third in a series of four articles