Statistics
The False-Positive paradox explained in an easy way
The concept of false-positive paradox highlights the misleading nature of a diagnostic test that exhibits high sensitivity and specificity, particularly for low prevalence conditions. For instance, if we were to conduct genetic screening for hypertrophic cardiomyopathy (HCM) among all individuals in the United States — approximately 330 million people — with a prevalence rate of about 1:500, an algorithm analyzing their ECGs could demonstrate a sensitivity and specificity score of 98% and 99%, respectively. However, despite the impressively high predictive value of this screening test, a positive result for any individual does not confirm the likelihood that they are affected by HCM. In fact, due to the large population size and low prevalence rate of HCM, a false-positive result is more likely than a true positive.
Out of the 330 million electrocardiograms (ECGs) analyzed, it can be found through statistical analysis that approximately 660,000 individuals would be affected by hypertrophic cardiomyopathy (HCM). The test utilized in this fictive study would manage to detect HCM in about 646,800 cases. However, a small percentage comprising 13,200 people remained undetected. Though this is an unfortunate reality for those few who remain unrecognized and untreated; when considering that such a large population has been screened across United States territories- the numbers are relatively low.
Upon further examination in this fictive study, it was discovered that among the 329.34 million ECGs analyzed in the non-HCM affected group, approximately 1% or roughly 3,293,400 individuals have received false positive results suggesting an ailment. Such erroneous outcomes can cause unwarranted distress and apprehension among those concerned without proper medical validation. This occurrence highlights a perplexing issue of misleading outcomes, even when high-precision diagnostic tests are utilized on a large population with minimal instances of the ailment in question. It is crucial to recognize this problem and take necessary precautions to prevent misdiagnosis or unnecessary treatment.
