# Adjustment of a Prevalence Estimate for Selection Bias

Denote those who truly have the disease in the population as 'A',
those who do not have the disease in the population as 'B'.
Subjects with the disease who are selected into the study sample as,
'a' and those selected who do not have the disease as 'b'.
Based on the above, we can say that:

a = A * (selection probability for the diseased)

similarly,

b = B * (selection probability for the non-diseased)

If the selection probabilities are known, then each observed value; 'a' and
'b' can be divided by these probabilities to estimate the number of
diseased and non-diseased within the population. Converting this into a
proportion leads to an adjusted prevalence estimate.

Alternatively, you can take the observed odds of disease and multiply
this by the inverse of the selection odds (the ratio of selection
probabilities for the diseased and non-diseased) to produce an adjusted
odds of disease. This can be converted back to a proportion, if you
wish.

## Explore the Impact of Selection Bias by Putting
Some Values into this Calculator