Accuracy of an Exam
  1. When ever a patient undergoes a medical exam, there are probabilities associated with the accuracy of its diagnosis. If an exam is very accurate and its results are positive or negative, then with a high degree of confidence you are assured that the results are correct. However, this is not always the case, so let us explore this realm of exam accuracy.

  2. Basic terms
    1. If the exam does not show disease it is considered negative
    2. If the exam does show the disease then it is positive
    3. With the two basic terms there are four possible outcomes/variables and they are:
      1. True positive (TP) occurs when the positive exam really is positive
      2. False positive (FP) exam occurs when positive exam is really negative
      3. True negative (TN) is an exam that is truly negative
      4. False negative (FN) occurs when the negative exam is actually positive
  3. So let us look at an example on how this works .. What if a patient has a bone scan for the diagnosis of metastatic disease. Once the results of the bone scan is know there are for possible outcomes: TP, FP, TN, or FN.

  4. Now let us assume that there is a population of 110 patients have underwent a whole body bone scan for the assessment of metastatic cancer:

    1. From the 110 patients the results indicate that all is not black and white. In the mix of positive and negatives values of the four variables mentioned earlier. The question that now has to be asked is how does one report the above data? There are several factors to look at and there are discussed below

    2. Sensitivity is considered the true positive (TP) fraction in the study of 110 patients. To calculate the % of TP apply the above formula. Under this discussion the value is 87%. We call this sensitivity. Another way to state sensitivity is to say that this test identifies TP 87% of the time (87 out of 100 patients) correctly diagnosing disease

    3. Specificity, also known as the true negative fraction (TN) and in this example it states that 89% of the patients are truly negative of disease. Therefore specificity states (1) the amount of people that do not have the disease and (2) identified as disease free

    4. Accuracy is the yet another term used to describe our diagnostic evaluation of 110 patient and is expressed in the above formula. This term combines specificity and sensitivity or another way to state this is the total number of correct diagnosis divide by the entire population

    5. PPV or positive predictive value is expressed above. In this case the sensitivity in the population is 87%. The PPV is the odds of a person having the disease if the results are positive, which in this case is 92%.

    6. NPV or negative predictive value is expressed above. In this case the specificity in this population is 89%. The NVP is the odds of a person NOT having disease is truly negative and in this case it is 80%.

    7. Further explanation can be given seen when you graph the four values of TN, TP, FN, and FP
    8. I do have to admit that the terms sensitivity and PPV are a little confusing. To make more sense of it look at the denominators of both formulas. This might help explain the difference. The same thing can be said with specificities and NPV.
    9. Another point - when research is done on any radiopharmaceutical, statistical data is collected to determine the ability to diagnosing disease
  1. Bayes' theorem is another concept that actually affects the probable outcome of a study. Let's apply this application to nuclear cardiology
    1. Two questions must first be considered when attempting to diagnose disease
      1. What is the probability of the patient having disease if the results are positive?
      2. What is the probability of the patient not having disease if the results are negative?
    2. First, always, determine the pretest likelihood of disease, so let us setup the parameters
      1. Asymptomatic
      2. Chest pain (three possible results might cause this) = sub-sternal location, provoked by exercise, and pain relief via nitroglycerin
        1. Typical angina = all the
        2. Atypical angina = two of three
        3. Non-angina = one of three
    3. Pretest likelihood of disease affects the post-test likelihood of disease
      1. In an asymptomatic patient, pretest probability of having diseases is 5%. The results then indicate only 20% that have a positive stress test are truly positive, while less than 1% of the negatives are false negative
      2. In classifying those patients with an intermediate likelihood of CAD the pretest probability is 50%. [post test] Of those patients that have a positive test, 90% will be true positives, while those that are negative have less than 10% of being false negative
      3. High pretest likelihood (typical angina) of CAD has a 90% likelihood of disease. [post test] Of those that are positive 99% are true positive, while of those that have a negative scan, 75% are false negative
      4. Conclusion:
        1. Does a nuclear cardiology exam benefit patients with low probability of disease?
        2. When should nuclear cardiology be ordered on a patient?
        3. Of the classifications above, which group of patients receives the most benefit when Bayes' theorem is applied?
        4. What is the value of taking a patient's history?

Return to the top of the Page
Return to the Home Page

1/22