## Individualizing the results

When satisfied that biologic and socioeconomic differences do not compromise the applicability of a test in your setting, the next step is to determine the impact that the test (and its results) might have on your specific patient's probability of having a disease. While studies of diagnosis report the average effect of a test on probability of disease, the effect may vary greatly from patient to patient. The main source of this variation is the individual's baseline probability of disease, also known as the pre-test probability.

A variation in pre-test probability is common. Based on history and physical examination, individuals may have little or no signs of disease in which case disease probability is very low. Other individuals may have florid signs of disease, in which case the pre-test probability is very high. Take, for example, a 24-year old female consulting for fleeting chest pain. Her history reveals occasional pricking pain on the anterior chest wall not related to effort. Her physical findings are unremarkable. The probability that this particular individual is having a heart attack is quite low, i.e. you assess her pre-test probability for a heart attack to be around 0.1%. Contrast this with a 60-year hypertensive male smoker with a chronic history of chest discomfort during physical exertion. He presents at the emergency room with acute, severe chest pain. On physical examination, he is hypotensive with a BP of 80/60, tachycardic with a heart rate of 110 and has cold clammy perspiration. The probability of this man having a heart attack is high, i.e. the pre-test probability of a heart attack may

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threshold a threshold

Disease probability

100%

Figure 3.1 Disease probability and thresholds of management be more than 90%. Figure 3.1 above illustrates the probability of disease, and shows us some conceptual thresholds in the management of disease.

Figure 3.1 depicts the two threshold regions at the upper and lower levels of probability: the therapeutic threshold is the probability of disease above which we are willing to stop testing and just get on with therapy and the diagnostic threshold is the probability of disease below which we are willing to stop testing and just reassure the patient. Between these two thresholds, the clinician is more uncertain and so further tests are required. Tests are useful when they can move us out of the testing range to somewhere beyond the treatment threshold (so we can commence treatment), or below the diagnostic threshold (so we can just reassure the patient or consider other diseases). How do the results of a test change disease probability i.e. how do we estimate the post-test probability? Tackle Box 3.3 illustrates a strategy for those who are up to the challenge of manual computation. Tackle Box 3.4 illustrates a strategy for those of us afraid of numbers.

After arriving at a post-test probability of disease, you may now make a clinical decision, i.e. to treat, reassure, or carry out more tests (depending on whether you land above the treatment threshold, below the diagnostic threshold or in-between).

While this discussion focuses on use of likelihood ratios to interpret test results when they arrive, we can also use these calculations to decide if the tests should be done at all for a particular patient. Consider the following when you contemplate requesting a test.

1. When the test result will not lead to important changes in probability, we should think twice about doing the test at all. Remember that the change in probability is not just a function of the LRs of a test, it is also a function of the pre-test probability. When the pre-test probability is close to 50% (as uncertain as it can get), the changes in probability tend to be great and the tests become much more useful. When the pretest probability is already close to 0% or 100%, the changes in probability tend to be very small and testing is of less value.

2. When effective treatment is unavailable for the disease you are detecting, either because it is difficult to treat or the patient cannot afford the treatment, testing may not be useful.

3. The cost of the test should always be considered, especially in places where medical care is mainly an out-of-pocket expense. When we talk of cost, it is not just the immediate cost of the test but also the cost of the subsequent tests, as well as subsequent medical or surgical interventions.

4. Safety is an issue for some tests, especially invasive procedures.

5. Just as we should involve the patient when deciding on a therapeutic intervention, the patient should make informed choices about diagnostic tests to be performed.

Tackle Box 3.3 Computing for post-test probability of disease given a test result Instructions: Results of a test change the probability of disease. This tackle box discusses the math involved. If you're numero-phobic, skip this tackle box and proceed directly to Tackle Box 3.4. | ||

How to do this |
Need an equation? | |

Step 1: Estimate the pre-test probability in percent. |
Interview the patient and carry out a good physical examination. Based on your findings, your clinical experience will give you a good estimate of the probability of disease. If the case is difficult, an expert might be in a better position to estimate what the probability of the disease might be. Exercise (1): Ms X, a 25-year old sexually active female presents with a 3-day history of burning sensation on urination. Physical exam was unremarkable. Estimate the pre-test probability that she has a urinary tract infection (UTI). |
There isn't any... what you need are good skills in history and physical examination. |

Step 2: Convert pre-test probability to odds. |
There are two ways of expressing the possibility of disease: as odds or as probabilities. Probabilities are a portion of the whole, while odds are the ratio of portions. To convert from probability to odds, we simply reduce the denominator by subtracting the numerator from it. For example: 25/100 (probability) becomes 25/75 (odds), and 90/100 (probability) becomes 90/10 (odds). If you are not yet comfortable with probabilities and odds, return to Tackle Box 3.2 (review the concept of the pie)! Exercise [2]: If you set the pre-test probability of UTI in exercise [1] at 80%, what would the pre-test odds be? |
Odds = Probability 100 - Probability |

Step 3: Multiply pre-test odds by the Likelihood Ratio of the test result to get the post-test odds. |
The pre-test odds were estimated in step 2. The study you read should tell you the LR of the test result you obtained. Remember, LR varies according to the result. A positive test will probably have an LR > 1.0, a negative test an LR < 1.0 while an equivocal test an LR that is close to 1.0. Exercise (3): Continuing the scenario in exercise (2), estimate the post-test odds of UTI in the following scenarios: (a) her urine dipstick nitrite is positive; (b) her urine dipstick is negative. Note: Study shows that urine dipstick nitrite has an LR(+) = 3.0 and an LR(-) = 0.518. |
Post-test Odds = Pre-test Odds xLR |

Step 4: Convert post-test odds back to post-test probability in percent. |
Simple. Just increase the denominator by adding the numerator back to it. Thus, odds of 1/3 become a probability of 1/4 (or 25%); and odds of 1/1 become a probability of 1/2 (or 50%). You can also use the formula in the next column. Exercise (4): Convert the post-test odds back to (post-test) probability in the two scenarios in exercise (3). |
; 1 + Odds |

Notes: 1. In these equations, probability is expressed as a percentage. 2. Usually a sequence of tests is necessary to confirm disease or rule it out. In this case, the post-test probability of one test becomes the pre-test probability for the next test and so forth. This only works in non-emergency cases. When confronted with an emergency, forget sequential tests; do everything at the same time! Answers: Exercise (1): Depending on the details of the history, estimates of the probability of UTI may vary. A reasonable estimate might be around 80%. Exercise (2): If you set the pre-test probability at 80%, pre-test odds will be 80/20 or 4/1. Exercise (3): For scenario (a) with urine dipstick result positive, post-test odds = 4.0 x 3.0 = 12. For scenario (b) with urine dipstick result negative, post-test odds = 4.0 x 0.5 = 2. Exercise (4): For scenario (a), post-test probability will be [12/(1+12)] x 100 = 92%. For scenario (b), post-test probability will be [2/(1 + 2)] x 100 = 67%. |

Tackle Box 3.4 Estimating post-test probability of disease given test results (using nomogram [18]) Instructions: If you are uncomfortable with manual computations for post-test probability as described in tackle box 3.3, go through the nomogram shown in Figure 3.2 to learn an easier way to do it. | |

Step 1: Estimate the pre-test probability based on your history or physical examination, i.e. clinical intuition. You can also derive this estimate from the results of surveys. Plot this on the left-most vertical axis. Exercise: Ms X, a 25-year old sexually active female presents with a three day history of a burning sensation on urination. Physical exam was unremarkable. Estimate the pre-test probability that she has a urinary tract infection (UTI). Step 2: Determine the likelihood ratio of the test result from the results of the study you reviewed. Remember, the LR varies depending on the test result. Plot this on the middle vertical axis. Exercise: Study shows that urine dipstick nitrite has an LR(+) = 3.0 and LR(-) = 0.5[19]. Look for these points along the middle axis. Step 3: Connect the two points in steps 1 and 2, and extend the line to the rightmost vertical axis. The point of intersection is the probability of disease after the test (the post-test probability). Exercise: What would the post-test probabilities be if (a) her dipstick nitrite is positive; (b) her dipstick nitrite is negative? | |

Note: Sometimes, a sequence of tests is necessary to confirm disease or rule it out. In this case, the post-test probability of the earlier test becomes the pre-test probability for the next test and so forth and so on. This only works in non-emergency cases. When confronted with an emergency, forget about sequential testing, do everything at the same time! Answers: If you set the pre-test probability at 80%, if the urine dipstick result is positive, post-test probability will be around 95% and when negative, the post-test probability will be around 65%. These numbers just approximate the exact answers for Tackle Box 3.3. |
90 95 1000 200 100 50 0.002 0.001 Pre-test probability Likelihood ratio 95 90 80 70 60 50 40 30 20 10 5 Post-test probability Figure 3.2 Bayes nomogram for estimating post-test probability* * Reproduced with permission'18' |

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