Past exam of the mathematics course of the University of Cambridge / 2003 / iii / Paper 40 / 4 / c / Solution

Assume individuals who immediately sell the intervention retain the untreated risk $0.005$, while those who keep it have the posited halved risk $0.0025$. The law of total expectation gives the expected count per thousand assigned to treatment:The assignment risk is therefore $0.003$. This is an intention-to-treat mixture under the stated adherence-specific risks, not an assertion that receipt or sale is randomized. It also assumes that selling does not itself change the seller's baseline risk and that effects on recipients outside this group do not alter this calculation.