Odds-Likelihood Ratios

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Another way to calculate the posttest probability of disease is to use the odds-likelihood (or odds-probability) approach. Sensitivity and specificity are combined into one entity called the likelihood ratio (LR):

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When test results are dichotomized, every test has two likelihood ratios, one corresponding to a positive test (LR+) and one corresponding to a negative test (LR):

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For continuous measures, multiple likelihood ratios can be defined to correspond to ranges or intervals of test results. (See Table e3–5 for an example.)

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Table e3–5. Likelihood ratios of serum ferritin in the diagnosis of iron deficiency anemia. 
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Likelihood ratios can be calculated using the above formulas. They can also be found in some textbooks, journal articles, and online programs (see Table e3–6 for sample values). Likelihood ratios provide an estimation of whether there will be significant change in pretest to posttest probability of a disease given the test result, and thus can be used to make quick estimates of the usefulness of contemplated diagnostic tests in particular situations. A likelihood ratio of 1 implies that there will be no difference between pretest and posttest probabilities. Likelihood ratios of > 10 or < 0.1 indicate large, often clinically significant differences. Likelihood ratios between 1 and 2 and between 0.5 and 1 indicate small differences (rarely clinically significant).

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Table e3–6. Examples of likelihood ratios (LR). 
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The simplest method for calculating posttest probability from pretest probability and likelihood ratios is to use a nomogram (Figure e3–7). The clinician places a straightedge through the points that represent the pretest probability and the likelihood ratio and then reads the posttest probability where the straightedge crosses the posttest probability line.

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Figure e3–7.
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Nomogram for determining posttest probability from pretest probability and likelihood ratios. To figure the posttest probability, place a straightedge between the pretest probability and the likelihood ratio for the particular test. The posttest probability will be where the straightedge crosses the posttest probability line. (Adapted and reproduced, with permission, from Fagan TJ. Nomogram for Bayes theorem. [Letter.] N Engl J Med. 1975 Jul 31;293(5):257.)

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A more formal way of calculating posttest probabilities uses the likelihood ratio as follows:

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To use this formulation, probabilities must be converted to odds, where the odds of having a disease are expressed as the chance of having the disease divided by the chance of not having the disease. For instance, a probability of 0.75 is the same as 3:1 odds (Figure e3–8).

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Figure e3–8.
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Formulas for converting between probability and odds. (Reproduced, with permission, from Nicoll D et al. Pocket Guide to Diagnostic Tests, 6th ed. McGraw-Hill, 2012.)

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To estimate the potential benefit of a diagnostic test, the clinician first estimates the pretest odds of disease given all available clinical information and then multiplies the pretest odds by the positive and negative likelihood ratios. The results are the posttest odds, or the odds that the patient has the disease if the test is positive or negative. To obtain the posttest probability, the odds are converted to a probability (Figure e3–8).

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For example, if the clinician believes that the patient has a 60% chance of having a myocardial infarction (pretest odds of 3:2) and the troponin I test is positive (LR+= 24), then the posttest odds of having a myocardial infarction are

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If the troponin I test is negative (LR= 0.01), then the posttest odds of having a myocardial infarction are

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Sequential Testing

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To this point, the impact of only one test on the probability of disease has been discussed, whereas during most diagnostic workups, clinicians obtain clinical information in a sequential fashion. To calculate the posttest odds after three tests, for example, the clinician might estimate the pretest odds and use the appropriate likelihood ratio for each test:

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When using this approach, however, the clinician should be aware of a major assumption: the chosen tests or findings must be conditionally independent. For instance, with liver cell damage, the aspartate aminotransferase (AST) and alanine aminotransferase (ALT) enzymes may be released by the same process and are thus not conditionally independent. If conditionally dependent tests are used in this sequential approach, an inaccurate posttest probability will result.

Linnet K et al. Quantifying the accuracy of a diagnostic test or marker. Clin Chem. 2012 Sep;58(9):1292–301.   [PubMed: 22829313]

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Threshold Approach to Decision Making

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A key aspect of medical decision making is the selection of a treatment threshold, ie, the probability of disease at which treatment is indicated. The treatment threshold is determined by the relative consequences of different actions: treating when the disease is present; not treating when the disease is absent; treating when the disease is actually absent; or failing to treat when the disease is actually present. Figure e3–9 shows a possible way of identifying a treatment threshold by considering the value (utility) of these four possible outcomes.

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Figure e3–9.
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The “treat/don’t treat” threshold. A: Patient does not have disease and is not treated (highest utility). B: Patient does not have disease and is treated (lower utility than A). C: Patient has disease and is treated (lower utility than A). D: Patient has disease and is not treated (lower utility than C). (Reproduced, with permission, from Nicoll D et al. Pocket Guide to Diagnostic Tests, 6th ed. McGraw-Hill, 2012.)

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Use of a diagnostic test is warranted when its result could shift the probability of disease across the treatment threshold. For example, a clinician might decide to treat with antibiotics if the probability of streptococcal pharyngitis in a patient with a sore throat is > 25% (Figure e3–10A).

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Figure e3–10.
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Threshold approach applied to test ordering. If the contemplated test will not change patient management, the test should not be ordered. (See text for explanation.) (Reproduced, with permission, from Nicoll D et al. Pocket Guide to Diagnostic Tests, 6th ed. McGraw-Hill, 2012.)

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If, after reviewing evidence from the history and physical examination, the clinician estimates the pretest probability of strep throat to be 15%, then a diagnostic test such as throat culture (LR+ = 7) would be useful only if a positive test would shift the posttest probability above 25%. Use of the nomogram shown in Figure e3–7 indicates that the posttest probability would be 55% (Figure e3–10B); thus, ordering the test would be justified since it affects patient management. On the other hand, if the history and physical examination had suggested that the pretest probability of strep throat was 60%, the throat culture (LR= 0.33) would be indicated only if a negative test would lower the posttest probability below 25%. Using the same nomogram, the posttest probability after a negative test would be 33% (Figure e3–10C). Therefore, ordering the throat culture would not be justified because it does not affect patient management.

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This approach to decision making is now being applied in the clinical literature.

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Decision Analysis

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Up to this point, the discussion of diagnostic testing has focused on test characteristics and methods for using these characteristics to calculate the probability of disease in different clinical situations. Although useful, these methods are limited because they do not incorporate the many outcomes that may occur in clinical medicine or the values that patients and clinicians place on those outcomes. To incorporate outcomes and values with characteristics of tests, decision analysis can be used.

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Decision analysis is a quantitative evaluation of the outcomes that result from a set of choices in a specific clinical situation. Although it is infrequently used in routine clinical practice, the decision analysis approach can be helpful to address questions relating to clinical decisions that cannot easily be answered through clinical trials.

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The basic idea of decision analysis is to model the options in a medical decision, assign probabilities to the alternative actions, assign values (utilities) (eg, survival rates, quality-adjusted life years, or costs) to the various outcomes, and then calculate which decision gives the greatest expected value (expected utility). To complete a decision analysis, the clinician would proceed as follows: (1) Draw a decision tree showing the elements of the medical decision; (2) Assign probabilities to the various branches; (3) Assign values (utilities) to the outcomes; (4) Determine the expected value (expected utility) (the product of probability and value [utility]) of each branch; (5) Select the decision with the highest expected value (expected utility). The results obtained from a decision analysis depend on the accuracy of the data used to estimate the probabilities and values of outcomes.

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Figure e3–11 shows a decision tree in which the decision to be made is whether to treat without testing, perform a test and then treat based on the test result, or perform no tests and give no treatment. The clinician begins the analysis by building a decision tree showing the important elements of the decision. Once the tree is built, the clinician assigns probabilities to all the branches. In this case, all the branch probabilities can be calculated from: (1) the probability of disease before the test (pretest probability), (2) the chance of a positive test result if the disease is present (sensitivity), and (3) the chance of a negative test result if the disease is absent (specificity). Next, the clinician assigns value (utility) to each of the outcomes.

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Figure e3–11.
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Generic tree for a clinical decision where the choices are: (1) to treat the patient empirically, (2) to do the test and then treat only if the test is positive, or (3) to withhold therapy. The square node is called a decision node, and the circular nodes are called chance nodes. p, pretest probability of disease; Sens, sensitivity; Spec, specificity. (Reproduced, with permission, from Nicoll D et al. Pocket Guide to Diagnostic Tests, 6th ed. McGraw-Hill, 2012.)

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After the expected value (expected utility) is calculated for each branch of the decision tree, by multiplying the value (utility) of the outcome by the probability of the outcome, the clinician can identify the alternative with the highest expected value (expected utility). When costs are included, it is possible to determine the cost per unit of health gained for one approach compared with an alternative (cost-effectiveness analysis). This information can help evaluate the efficiency of different testing or treatment strategies.

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Although time-consuming, decision analysis can help structure complex clinical problems and assist in difficult clinical decision-making.

Aleem IS et al. Clinical decision analysis: incorporating the evidence with patient preferences. Patient Prefer Adherence. 2009 Nov 3;3:21–4.   [PubMed: 19936141]
Lennon S et al. Utility of serum HER2 extracellular domain assessment in clinical decision making: pooled analysis of four trials of trastuzumab in metastatic breast cancer. J Clin Oncol. 2009 Apr;27(10):1685–93.  [PubMed: 19255335]
Peyrade F et al. Treatment decisions for elderly patients with haematological malignancies: a dilemma. Lancet Oncol. 2012 Aug;13(8):e344–52.   [PubMed: 22846839]

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Evidence-Based Medicine

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Vast resources are being spent on diagnostic testing. New laboratory tests are being developed and marketed all the time. Clinicians need to know how to appraise published studies on new diagnostic tests (eg, performance characteristics) and how to determine whether a new test is superior to existing test(s) in terms of clinical utility and cost-effectiveness. Careful examination of the best available evidence is essential.

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Evidence-based medicine is the care of patients using the best available research evidence to guide clinical decision making. It relies on the identification of methodologically sound evidence, critical appraisal of research studies, for both internal validity (freedom from bias) and external validity (applicability and generalizability), and the dissemination of accurate and useful summaries of evidence to inform clinical decision making. Systematic reviews can be used to summarize evidence for dissemination, as can evidence-based synopses of current research. Systematic reviews often use meta-analysis: statistical techniques to combine evidence from different studies to produce a more precise estimate of the effect of an intervention or the accuracy of a test. The concept of evidence-based medicine can be readily applied to diagnostic testing, since appropriate use of a diagnostic test is part of the decision-making process.

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Clinical practice guidelines are systematically developed statements intended to assist practitioners in making decisions about health care. Clinical algorithms and practice guidelines are now ubiquitous in medicine, developed by various professional societies or independent expert panels. Diagnostic testing is an integral part of such algorithms and guidelines. Their utility and validity depend on the quality of the evidence that shaped the recommendations, on their being kept current, and on their acceptance and appropriate application by clinicians. Although some clinicians are concerned about the effect of guidelines on professional autonomy and individual decision making, many organizations are trying to use compliance with practice guidelines as a measure of quality of care. It is important to note, however, that evidence-based guidelines are used to complement, not replace, clinical judgment tailored to individual patients.

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Computerized information technology provides clinicians with information from laboratory, imaging, physiologic monitoring systems, and many other sources. Computerized clinical decision support systems, along with test order communication systems, have been increasingly used to develop, implement, and refine computerized protocols for specific processes of care derived from evidence-based practice guidelines. It is important that clinicians use modern information technology to deliver standard medical care in their practice.

Bright TJ et al. Effect of clinical decision-support systems: a systematic review. Ann Intern Med. 2012 Jul;157(1):29–43.   [PubMed: 22751758]
Charles C et al. The evidence-based medicine model of clinical practice: scientific teaching or belief-based preaching? J Eval Clin Pract. 2011 Aug;17(4):597–605.   [PubMed: 21087367] [[XSLOpenURL/ 21087367]]
Fiks AG. Designing computerized decision support that works for clinicians and families. Curr Probl Pediatr Adolesc Health Care. 2011 Mar;41(3):60–88.   [PubMed: 21315295]
Main C et al. Computerized decision support systems in order communication for diagnostic, screening or monitoring test ordering: systematic reviews of the effects and cost-effectiveness of systems. Health Technol Assess. 2010 Oct;14(48):1–227.   [PubMed: 21034668]
Sacks DB et al. Guidelines and recommendations for laboratory analysis in the diagnosis and management of diabetes mellitus. Diabetes Care. 2011 Jun;34(6):e61–99.   [PubMed: 21617108]

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