In a simple case-control study to investigate the effect of exposure v or non-exposure v∗ to a chemical on the possibility of developing (u)

or not developing (u∗) a certain disease, a random sample of patients suffering from the disease and another random sample of individuals not suffering from the disease were selected and for each case it was determined whether the individual had been exposed to the chemical or not. Use the technique of the background population – with joint probability density function π(u, v), selection into the study by factors s(u), s(u∗) and referral of a generic ‘new patient’ R by factors r(v), r(v∗) – to show that it is possible to assess the

‘odds ratio’

without knowledge of s(u), s(u∗), r(v), r(v∗). Consider how you might explain the use of this odds ratio to a clinician.