Screening for alcohol problems: what makes a test effective?

Alcohol Research & Health, Wntr, 2004 by Scott H. Stewart, Gerard J. Connors

Positive Likelihood Ratio. The positive likelihood ratio in the AUDIT example used earlier (Volk et al. 1997) is the probability that an at-risk drinker has a positive test result divided by the probability that a nonrisk drinker has a positive test result. It represents the ratio of true positives to false positives. Mathematically, it is calculated as the ratio of sensitivity over [1-specificity] (see figure 1). In the AUDIT example with a cutoff of 4 (i.e., with a sensitivity of 85 percent and a specificity of 84 percent), the positive likelihood ratio would be calculated as 0.85 / [1 - 0.84] = 5.3. Thus, the positive likelihood ratio (like the negative likelihood ratio) is a factor that is inherent in a given test--if one knows the sensitivity and specificity of a test, one can calculate the test's likelihood ratios.

This positive likelihood ratio, together with information on other risk factors for at-risk drinking in a given patient, can be used to calculate that patient's odds or probability (3) of being an at-risk drinker. To illustrate this process, imagine the following example: A primary care physician has two 40-year-old male patients who are being treated for high blood pressure. Patient 1 was divorced about 1 year ago, seems depressed, and has poorly controlled blood pressure and slightly abnormal levels of certain liver enzymes. Based only on his history, the physician estimates this patient's probability of being an at-risk drinker to be 40 percent. Patient 2 appears well and has excellent blood pressure control. The physician estimates his probability of being an at-risk drinker to be 20 percent (equal to the prevalence of at-risk drinking in the local population). Both of these patients have AUDIT results above the cutoff score of 4 chosen by the physician. Through some mathematical calculations based on the estimates of the patients' individual probabilities of being at-risk drinkers and the AUDIT's positive likelihood ratio of 5.3 (when using a cutoff score of 4), the physician estimates the posttest probability of Patient 1 being an at-risk drinker to be 0.78 (or 78 percent). In contrast, the post-test probability of Patient 2 is calculated to be 0.56 (or 56 percent). (4)

This example illustrates how a clinician can estimate a specific patient's probability for being an at-risk drinker following a positive screening test. Similar calculations can be performed based on negative screening results, as described in the next section.

Negative Likelihood Ratio. The negative likelihood ratio is the probability that a person with a disorder, such as at-risk drinking, has a negative test result (e.g., on the AUDIT) divided by the probability that a person without the disorder has a negative test result. It represents the ratio of false negatives to true negatives and is calculated as the ratio of [1-sensitivity] over specificity (see figure 1). For example, for the AUDIT with a cutoff score of 4, the negative likelihood ratio is [1 - 0.85] / 0.84 = 0.18.