Sensitivity

Calculating Sensitivity Scores

Sensitivity is calculated based on the relationship of the following two types of dichotomous outcomes: (1) the outcome of the test, instrument, or battery of procedures and (2) the true state of affairs. The outcome of the test is typically referred to as being positive (indicating the condition is present) or negative (the condition is not present). The true state of affairs is typically defined either by assignment of some experimental condition or classification based on some known gold standard test. Based on these two types of dichotomous outcomes, there are four possible outcome variables, which are defined as follows:

Table 1 shows each of these four variables and the statistics generated from them. Sensitivity is based on the variables in the Does Have the Condition column and is calculated as the number of True Positives divided by the number of True Positives plus the number of False Negatives.

When a test is measuring some characteristic on a continuous scale, the sensitivity might be changed depending on the cutoff used to define a positive test. To demonstrate this, consider an example in which 5a-dihydrotestosterone (DHT) levels were measured from 100 athletes, 50 of which were administered a dose of anabolic steroid prior to their test. Table 2 shows, from left to right, simulated data showing DHT levels and the corresponding number of athletes receiving [Page 1338]steroids who have that level of DHT. If a positive test is defined as being any athlete with a DHT level of at least 10-12 mol/l, then 49 of the 50 steroid-administered athletes would have a positive test outcome (sample size from the 10-12, 10-11, and 10-10 groups). Given this cutoff then, the sensitivity of the procedure would be calculated as: [49 (true positives) ÷ [49 (true positive) + 1 (false negative)]] = 98%. In contrast, if a positive test is defined as a DHT level of at least 10-10, then 30 of the 50 steroid-administered athletes would have a positive test outcome resulting in a sensitivity of 60% (30÷ [30 + 20]).

The athletes who did not receive the drug are not listed in Table 2 because they would by definition either be “True Negative” or “False Positive” cases, which are not part of the sensitivity calculation. They would instead be pertinent to the calculation of specificity. This example demonstrates how, because sensitivity and specificity are calculated on two different samples of individuals, both of these statistics are free to vary from one another independently.

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