Question

The prevalence of a disease is the fraction of individuals who are afflicted, i.e., the ratio of the number of cases to the whole population. The incidence of a disease is the fraction of individuals who become infected in one time period, usually one year. This terminology is usually reserved for chronic diseases such as diabetes or AIDS or cardiovascular disease, not for seasonal flu or coronavirus. The prevalence is equal to the incidence times the mean survival time. Thus a disease that is immediately and always fatal has zero prevalence. '

A biochemical test designed to detect a specific genetic mutation has a sensitivity of 95% and a specificity of 90%. A sensitivity of 95% means that an individual who has the defect (a carrier) will test positive with probability 0.95, and negative with probability 0.05. A specificity of 90% means that a non-carrier will test negative with probability 0.90, and positive with probability 0.10. The prevalence of the defect in the population is 1%.

Part a: Ten thousand individuals randomly selected from this population are tested. Calculate the expected number of individuals in each cell of the following table.

xxxxxx Carrier xxxx  Non-carrier xxxxx Total

Test +

Test −

Total xxxxxxxxxxxxxxxxxxxxxx 10000

Part b: An individual from this population tests positive. What is the probability that he/she is a carrier?

Part c: An individual from this population tests negative. What is the probability that he/she is a non-carrier?

Answer 1

From the given information , first we can draw the tree diagram as follows :

Table :

Part b: An individual from this population tests positive. What is the probability that he/she is a carrier?

P( Carrier | Test + ) =   = 95 / 1085

P( Carrier | Test + ) = 0.0876

Part c: An individual from this population tests negative. What is the probability that he/she is a non-carrier?

P( Non carrier | Test - ) = = 8910/8915

P( Non carrier | Test - ) = 0.9994