In a physical activity study, the 7-day physical activity log viewed as an alloyed gold standard was used to correct the measurement error in the physical activity questionnaire. Due to correlations between the errors in the two measurements, the usual regression calibration may result to a biased estimate of the calibration factor. We propose a method of removing the correlation through orthogonal decomposition of the errors, then the usual regression calibration can be applied. Simulation studies show that our method can effectively correct the bias.
Keywords: adjusted regression calibration; correlated measurement errors; orthogonal decomposition; physical activity.