Quantify the risk of wrong diagnosis of a disease

Population is unknown and population parameters are also unknown. Biophysics of human body is a complex system that can be related to an unknown population. Knowing the values of population parameters is normally beyond the scope of medical examination of a patient. Limited time and money compels the examiner and the patient to make valid and correct conclusions from a sample. Blood sample, urine sample and stool sample are taken in addition to several scans conducted by advanced medical equipment. Although these tests and equipments are very advanced and correct, risk of a wrong diagnosis always remains. The quantification of this risk of wrong diagnosis can be done by probability as illustrated by the example below.

Example: The incidence of a rare disease (X) is only 4% in the entire population and is illustrated by a tree diagram. Hospital records have shown that there is a chance of 4 in 100 that a person with disease is wrongly diagnosed and that there is a chance of 1 in 100 that a healthy person is wrongly diagnosed. This information is exhibited by the diagram above.

P( wrong diagnosis) = (0.04)(0.04)+(0.96)(0.01) = 0.0112

So the risk of a wrong diagnosis is 1.12 %