In epidemiological studies of an exposure-response association, often only a mismeasured exposure is taken on each individual of the population under study. If ignored, exposure measurement error can bias the estimated exposure-response association in question. A reliability study may be carried out to estimate the relation between the mismeasured and true exposure, which could then be used to adjust for measurement error in the attenuated exposure-response relationship. However, taking repeated exposure measurements may be expensive. Given a fixed total study cost, a two-stage design may be a more efficient approach for regression parameter estimation compared to the traditional single-stage design since, in the second-stage, repeated measurement is restricted to a sample of first-stage subjects. Sampling the extremes of the first-stage exposure distribution has been shown to be more efficient than random sampling.