Survival analysis with measurement error in a cumulative exposure variable: radon progeny in relation to lung cancer mortality

Exposure variables in occupational and environmental epidemiology are usually measured with error. This error tends to flatten the estimated exposure-response relationship. Here, we extended the risk set regression calibration (RRC) method to obtain unbiased point and interval estimates of relative risks corrected for exposure measurement error in Cox models to be able to analyze cumulative exposure variables. We show that the RRC methodology originally developed for use with an external validation study can also be applied to internal validation study designs. We then analyzed the 3,469 New Mexico uranium miners cohort with follow-up extended from 1957 to 2012. The exposure data were collected using several different methods of measurement, some of which had a substantial amount of error. We compare results from the standard analysis of the effect of cumulative radon exposure on lung cancer mortality to measurement error corrected results in a subset of 2337 miners observed during the time period when exposure was measured by work area samples and/or personal exposure estimates provided by the mining companies (the gold standard). The correlation these two methods of measurements was 0.33. After adjusting for bias due to exposure measurement error, the multivariate- adjusted hazard ratio for lung cancer mortality in relation to cumulative radon exposure was estimated to be 4.69 ( 95%CI 2.21-9.95), substantially higher than the estimate obtained from the standard analysis ignoring measurement error (HR=1.35, 95%CI 1.21-1.50). Publicly available user-friendly software is available that supports the new methodology.