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Thread: Likelihood Ratios

  1. #1

    Default Likelihood Ratios

    The likelihood ratio (LR) is a test performance characteristic that circumvents the vulnerabilities of predictive values. The LR also reflects the perspective of the clinician receiving a test result, but is independent of disease prevalence. LRs are "the doctor's friend" because they help us make sense out of test results we encounter in clinical practice.

    The LR is merely a ratio of likelihoods (LR = L1/L2), comparing how likely a given test result is t occur in patients with disease relative to those without disease. Because we regard clinical findings as test results, we can calculate LRs using the formula:

    LR = Likelihood of a clinical finding in patients with disease/Likelihood of the same clinical findings in patients without disease

    When LRs are greater than 1, the numerator is large, meaning the test result occurs more frequently in patients with disease than in those without disease (thus, increasing the probability of disease). When LRs are less than 1, the denominator is larger, meaning the test result occur more frequently in patients without disease (thus decreasing the probability of disease). An LR near 1 has no diagnostic utility, because the test result is equally likely to occur in diseased and nondiseased individuals.

    When considering dichotomous outcome from a 2 x 2 table, we refer to a LR for a positive clinical finding or test result (LR+) and a LR for a negative test (LR-). LRs can easily be calculated from the classic test performance characteristics of sensitivity and specificity:

    Likelihood Ratios-screen-shot-2016-07-15-at-10-13-30-am-png

    How Likelihood Ratios Affect Pretest Probability
    Likelihood Ratios-screen-shot-2016-12-17-at-3-57-33-pm-png

    Likelihood Ratios and Beside Estimates
    Likelihood Ratios-screen-shot-2016-12-17-at-4-57-25-pm-png

    Calculating Probability
    Likelihood Ratios-screen-shot-2016-12-19-at-8-30-41-pm-pngLikelihood Ratios-screen-shot-2016-12-19-at-8-31-01-pm-pngLikelihood Ratios-screen-shot-2016-12-19-at-8-30-54-pm-png

    PS: See Calculator in the attachment
    Attached Files Attached Files
    Last edited by admin; Mon 19th December '16 at 8:47pm.
    Clinical Pharmacy Specialist - Infectious Diseases

  2. #2
    PharmD Year 1 TomHsiung's Avatar
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    Default Re: Likelihood Ratios

    Advantages of Likelihood Ratios

    In a single number, the LR conveys to clinicians how convincingly a physical sign argues for or against disease. If the LR of a finding is large, disease is likely, and if the LR of a finding is close to zero, disease is doubtful. This advantage allows clinicians to quickly compare different diagnostic strategies and thus refine clinical judgment.

    Using LRs to describe diagnostic accuracy is superior to using sensitivity and specificity because the earlier described mnemonics, SpPin and SnNout, are sometimes misleading. For example, according to the mnemonic SpPin, a finding with a specificity of 95% should argue conclusively for disease, but it does so only if the positive LR for the finding is a high number. If the finding's sensitivity is 60% (high false negative), the positive LR is 12 and the finding does argue convincingly for disease (i.e., consistent with the SpPin mnemonic); if the finding's sensitivity is only 10%, however, the positive LR is 2 and post-test probability changes only slightly (i.e., inconsistent with the SpPin mnemonic). Similarly, a highly sensitive finding argues convincingly against disease (i.e., SnNout) only when its calculated negative LR is a number close to zero.

    3.Levels of Findings
    Another advantage of LRs is that a physical sign measured on an ordinal scale (e.g., 0, 1+, 2+, 3+) or a continuous scale (e.g., blood pressure) can be categorized into different levels to determine the LR for each level, thereby increasing the accuracy of the finding. Other examples include continuous findings such as heart rate, respiratory rate, temperature, and percussed span of the liver, and ordinary findings such as intensity of murmurs and degree of edema.

    PS: SpPin, a Specific test, when Positive, rules in disease; SnNout, a Sensitive test, when Negative, rules out disease.

    For example, in patients with COPD, breath sounds are typically faint. If the clinician grades the intensity of breath sounds on a scale from 0 (absent) to 24 (very loud), he or she can classify the patient's breath sounds into one of four groups (discussed detail elsewhere): scores of 9 or less (very faint), 10 to 12, 13 to 15, or greater than 15 (loud). Each category then has its own LR: scores of 9 or less significantly increase the probability of obstructive disease (LR = 10.2), whereas scores greater than 15 significantly decrease it (LR = 0.1). Scores from 10 to 12 argue somewhat for disease (LR = 3.6), and scores from 13 to 15 provide no diagnostic information (LR not significantly different from 1). If the clinician had instead identified breath sounds as simply "faint" or "normal/increased" (i.e., the traditional positive or negative finding), the finding may still discriminate between patients with and without obstructive disease, but it misses the point that the discriminatory power of the sign resides mostly with scores less than 10 and greater than 15.

    When findings are categorized into levels, the term specificity becomes meaningless. For example, the specificity of a breath sound score of 13 to 15 is 80%, which means that 80% of patients without chronic airflow limitation have values other than 13 to 15, though the "80%" does not convey whether most of these other values are greater than 15 or less than 13. Similarly, when findings are put into more than two categories, the LR descriptor negative is no longer necessary, because all LRs are positive ones for their respective category.

    4.Combining Findings
    A final advantage of LRs is that clinicians can use them to combine findings, which is particularly important for those physical signs with LRs between 0.5 and 2, signs that by themselves change probability little but when combined change probability a greater amount. Individual LRs can be combined, however, only if the findings are "independent."

    a.Independent of Findings
    Independence means that the LR for the second finding does not change once the clinician determines whether the first finding is present or absent. For a few diagnostic problems, investigators have identified which findings are independent of each other. These findings appear as components of "diagnostic scoring schemes" in the tables commonly used as diagnostic score systems. For most physical findings, however, very little information is available about independence, and the clinician must judge whether combining findings is appropriate.

    One important clue is that most independent findings have a unique pathophysiologic basis. For example, when considering pneumonia in patients with cough and fever, the clinician should combine the findings of abnormal mental status and diminished breath sounds, using the individual LRs of each findings, because abnormal mental status and diminished breath sounds probably have separate pathophysiologic bases. Similarly, when considering hear failure in patients with dyspnea, the clinician could combine the findings of elevated neck veins and third heart sound because these findings also have different pathophysiologic bases.

    Examples of findings whose individual LRs should not be combined (because the findings share the same pathophysiologic basis) are flank dullness and shifting dullness in the diagnosis of ascites (both depend on intra-abdominal contents dampening the vibrations of the abdominal wall during percussion), neck stiffness and Kerning sign in the diagnosis of meningitis (both are caused by meningeal irritation), and edema and elevated neck veins in the diagnosis of heart failure (both depend on elevated right atrial pressure).

    Until more information is available, the safest policy for the clinician to follow, when combining LRs of individual findings, is to combine no more than three findings, all of which have a distinct pathophysiologic basis.

    b.How to Combine Findings
    The clinician can use any of the methods previously described to combine findings, simply by making the post-test probability from the first finding the pretest probability for the second finding. For example, a hypothetical patient with acute fever and cough has two positive findings that we believe have separate pathophysiologic bases and therefore are independent: abnormal mental status (LR = 1.9 for pneumonia) and diminished breath sounds (LR = 2.3 for pneumonia). The pretest probability of pneumonia, derived from published estimates and clinical experience, is estimated to be 20%. Using the graph, the finding of abnormal mental status increases the probability from 20% to 32%; this post-test probability then becomes the pretest probability for the second findings, diminished breath sounds, which increases the probability from 32% to 52% - the overall probability after application of the two findings. Using the approximating rules, both findings (LRs =~2) increases the probability about 15%; the post-test probability is thus 20% + 15% + 15% = 50% (an error of only 2%). Using formulas to calculate probability, the LRs of the separate findings are multiplied together, and the product is used to convert pretest into post-test odds. The product of the two LRs is 4.4 (1.9 x 2.3); the pretest odds are 0.2/0.8 = 0.25; and the post-test odds are 0.25 x 4.4 = 1.1, which equals a probability of 1.1 / 2.1 = 52%.
    Last edited by TomHsiung; Mon 19th December '16 at 8:18pm.
    B.S. Pharm, West China School of Pharmacy, Class of 2007, Health System Pharmacist, RPh. Hematology, Infectious Disease.

  3. #3
    PharmD Year 1 TomHsiung's Avatar
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    Default Re: Likelihood Ratios


    Negative predictive value = TN / (FN + TN)
    Positive predictive value = TP / (FP + TP)

    Sensitivity = TP / (FN + TP)
    Specificity = TN / (FP + TN)

    Positive likelihood ratio = sensitivity / (1 - specificity)

    Likelihood Ratios-screen-shot-2017-03-27-at-8-43-55-pm-png

    Positive LRs that are significantly above 1 indicate that a true-positive is much more likely than a false-positive, pushing you across the treatment threshold. An LR+ >10 causes a large shift in disease probability; in general, tests with LR+ >10 are very useful for ruling in disease. An LR+ between 5 and 10 causes a moderate shift in probability, and tests with these LRs are somewhat useful. "Fringerprints," findings that often rule in a disease, have very high positive LRs.

    Negative likelihood ratio = (1 - sensitivity) / specificity

    Likelihood Ratios-screen-shot-2017-03-27-at-8-44-03-pm-png

    Negative LRs that are significantly less than 1 indicate that a false-negative is much less likely than a true-negative, pushing you below the test threshold. An LR- less than 0.1 causes a large shift in disease probability; in general, tests with LR- less than 0.1 are very useful for ruling out disease. An LR- between 0.1 and 0.5 causes a moderate shift in probability, and tests with these LRs are somewhat useful.


    When you have a specific pretest probability, you can use the LR to calculate an exact posttest probability, like shown in Figure 1-9. If you are using descriptive pretest probability terms such as low, moderate, and high, you can use LRs as follows:
    • A test with an LR- of 0.1 or less will rule out a disease of low or moderate pretest probability
    • A test with an LR+ of 10 or greater will rule in a disease of moderate or high probability
    • Beware if the test result is the opposite of what you expected!
      • If your pretest probability is high, a negative test rarely rules out the disease, no matter what the LR- is
      • If your pretest probability is low, a positive test rarely rules in the disease, no matter what the LR+ is
      • In these situations, you need to perform another test

    Likelihood Ratios-clinical-skills-to-estimate-protest-probability-png

    (The End)
    Last edited by admin; Sun 25th June '17 at 4:15pm.
    B.S. Pharm, West China School of Pharmacy, Class of 2007, Health System Pharmacist, RPh. Hematology, Infectious Disease.

  4. #4
    Administrator admin's Avatar
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    Default Re: Likelihood Ratios

    Testing Principles

    Bayes' rule combines data on sensitivity and specificity of tests with prior probabilities, yielding a probabilistic view of various diagnoses that incorporates the test results. The application of Bayes' rule to diagnostic testing yields important testing principles: The specificity of a test is critical for case finding, especially when screening asymptomatic patients, because the higher the specificity, the lower is the false-positive rate. In populations in which disease prevalence is low, most positive tests will be false positives unless a test is exceptionally specific so that almost all patients without disease have a negative test. Indeed, if the disease prevalence is extremely low, a test (if it is the only one available) should not be done unless it is nearly perfectly specific. Thus, when a test is highly specific, a positive test result helps "rule in" a disease.

    Tests that are not highly specific are most useful for screening if they are applied in populations with a high disease prevalence. When other confirmatory tests are available, a test with only a moderately high specificity may be worth using as an initial screening test if it has high sensitivity.

    When a test is highly sensitive, a negative test result helps "rule out" a disease.
    B.S. Pharm, West China School of Pharmacy, Class of 2007, Health System Pharmacist, RPh. Hematology, Infectious Disease. Chengdu, Sichuan, China.

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