A simple way to correctly interpret results of medical diagnostic tests or procedures

In the previous posts we considered the topic of medical errors (see [1-8]). In many cases medical errors start from errors in medical diagnoses (see [7]).


“The death toll from health care screwups adds up to at least 500,000 Americans annually. That is the equivalent of more than three jumbo jets crashing every day of the year (or over 1,000 jets annually). Because these individuals are dying at home, in hospitals, or in nursing homes, no one is counting the bodies. There is no outrage, no plan to change a system that allows too many to die unnecessarily. The medical profession seems largely immune to the consequences of its errors.” See [1] p. 7.

Imagine that you had been diagnosed with a cancer. You took radiation treatments (which is equivalent to an exposure to a nuclear bomb explosion), then you took chemotherapy for many months (or maybe years). You had destroyed your health to such degree that you have only several months till the death. And at this time you learned that the diagnosis was wrong, you were a healthy person at the time of the diagnosis.

The sad fact is, that for many people this imaginary nightmare situation was real. Many had died or committed suicide due to a misdiagnosis or diagnostic errors. Many healthy babies were killed due to medical diagnostic errors (see [7]). In this post, we consider a simple way to correctly interpret results of diagnostic medical tests or procedures to reduce your chances to become a victim of such medical diagnostic errors.

Let us consider an example. Ms. X had a mammogram for screening breast cancer. The result was positive for breast cancer. The doctor told to Ms. X that accuracy of the test is 80%. Now, the question to you is: What is a probability that Ms. X has breast cancer?

Which answer you select from these three:

a) a high probability (over 70%);

b) in the range of 30-60%;

c) a low probability (<20%)?


The correct answer is the answer c). If your answer is different then you have a high chance to become a victim of misdiagnosis errors.

Let us consider the second example. Mr. Y had unprotected classical sex with unknown woman, when he was drunk. Next day, when clarity of mind was restored, Mr. Y took three tests for HIV (human immunodeficiency virus). Two tests from three were positive. What is a probability that Mr. Y contracted HIV?

Which answer you select from these three:

a) a high probability (over 80%);

b) in the range of 20-70%;

c) a low probability (<10%)?


The correct answer is the answer c). If your answer is different then you have a very high chance to become a victim of misdiagnosis errors.

To correctly interpret results of a medical diagnostic test or procedure we need at least two parameters: prevalence of a condition/disease among general population in your region and accuracy of the test/procedure.

By definition, prevalence is the proportion of a population who have a specific characteristic (condition/disease) in a given time period. It can be interpreted as a probability for a given person to have a condition/disease in a given time period. This number can be found in governments medical or statistical data. This probability often is called apriory probability to have a condition/disease.

If you do not trust government data then you can use the sampling method. You should count a number of people in your neighborhood, let it be -n, and a number of persons who was infected with a virus in a given year, let it be -k. Then the apriory probability to be infected with this virus, in the given year, in your neighborhood, is equal to k/n.

To find accuracy of a medical test or procedure we should look into the description of the test or procedure. Accuracy (% of correct) on persons who have a condition/disease is called a sensitivity or a true positive rate. Accuracy on persons who do not have a condition/disease is called specificity or true negative rate. We define a test/procedure’s accuracy as the minimum from sensitivity and specificity.

If you can not find such information or you do not trust information provided by manufacturers of the diagnostic tests, you can use the experimental method. Let -k is a number of positive tests from the total number -n of tests on people, who has a condition/disease. Then, the sensitivity (true positive rate) estimation is the ratio k/n. In the same way, if k is a number of negative tests from the total number of -n tests on healthy people, then the specificity (true negative rate) is estimated as k/n.

Now, let us return to the first example. When we look into breast cancer statistics for women with age of Ms. X we find that the prevalence/probability is about 5%. If we believe the doctor, then the accuracy of the mammogram screening test is 80%.

Now, we go to the URL https://www.ispreport.xyz/utools/mtest/basic/mcb.html and enter these numbers into the fields: “Apriory probability” and “Accuracy of the test”.


When we click on the button “Calculate” we get the result.


As we can see, the probability that Ms. X has breast cancer (under the condition of the positive test) is only 17.39%. This probability often called aposteriory probability.

Now, let us consider the second example. The Center for Disease Control and Prevention (CDC) provides the following risk estimate for infection of HIV, via a classical intercourse: 0.04%. The accuracy of HIV test is 99% (if we believe manufacturers of such tests).

Now, we go to the URL https://www.ispreport.xyz/utools/mtest/advanced/mca.html and enter these numbers into the input fields.


When we click on the button “Calculate” we get the result.


As we can see the aposteriory probability that Mr. Y has HIV (based on 2 positive tests from 3) is 3.81%.


Here is the list of questions to ask your doctor to reduce chances to become a victim of diagnostic disasters (from [1]).

1. What are my primary concerns and symptoms?

2. How confident are you about this diagnosis?

3. What further tests might be helpful to improve your confidence?

4. Will the tests you are proposing change the treatment plan in any way?

5. Are there any finding or symptoms that don’t fit your diagnosis or contradict it?

6. What else could it be?

7. Can you facilitate a second opinion by providing me my medical records?

8. When should I expect to see my test results?

9. What resources can you recommend for me to learn more about my diagnosis?

10. May I contact you by e-mail if my symptoms change or if I have an important question? If so, what is your e-mail address?


If you need a motivational story, then read [2]. The story is about the author -Judy Berger, the award-winning journalist and marathoner, who sees a doctor about a minor tingling sensation in her hands and feet. One MRI later, she is diagnosed with multiple sclerosis and told to pick a drug and accept her fate.

Instead of passively accepting such fate, she starts to use her professional skills of a journalist, asks questions and frees herself from the fate to become a new victim of medical diagnostic errors.


P.S. The tools used to calculate aposteriory probabilities are not free.


In the next post we consider a simple betting strategy in American football (NFL).



[1] Top Screwups Doctors Make and How to Avoid Them, Joe Graedon, MS, and Teresa Graedon, PhD, Graedon Enterprises, Inc., 2011.

[2] Misdiagnosed: One Woman’s Tour of and Escape from Healthcareland, Jody Berger, Published by Sourcebook, Inc., 2014

[3] When We Do Harm: A Doctor Confronts Medical Error, Danielle Orfi, MD, Beacon Press, 2020.

[4] Epidemic of Medical Errors and Hospital-Acquired Infections: Systemic and Social Causes, Ed. By William Charney, CRC Press, Taylor & Francis Group, 2013.

[5] Catastrophic Care: Why Everything We Think We Know About Health Care is Wrong, David Goldhill, Vintage Books (a division of Random House LLC), 2013.

[6] Medical Catastrophe: Confessions of an Anesthesiologist, Ronald W. Dworkin, MD, Rowman & Littlefield, 2017.

[7] FDA issues warning as women abort healthy babies due to false positives on prenatal genetic screening tests


[8] Why Getting Medically Misdiagnosed Is More Common Than You May Think








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I_g_o_r is an author of several books available on amazon.com

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