SIMEX for correction of dietary exposure effects with Box-Cox transformed data

Modelling dietary data, and especially 24-hr dietary recall (24HDR) data, is a challenge. Ignoring the inherent measurement error (ME) leads to biased effect estimates when the association between an exposure and an outcome is investigated. We propose an adapted simulation extrapolation (SIMEX) algorithm for modelling dietary exposures. For this purpose, we exploit the ME model of the NCI method where we assume the assumption of normally distributed errors of the reported intake on the Box-Cox transformed scale and of unbiased recalls on the original scale. According to the SIMEX algorithm, remeasurements of the observed data with additional ME are generated in order to estimate the association between the level of ME and the resulting effect estimate. Subsequently, this association is extrapolated to the case of zero ME to obtain the corrected estimate. We show that the proposed method fulfils the key property of the SIMEX approach, that is, that the MSE of the generated data will converge to zero if the ME variance converges to zero. Furthermore, the method is applied to real 24HDR data of the I.Family study to correct the effects of salt and alcohol intake on blood pressure. In a simulation study, the method is compared with the NCI method resulting in effect estimates with either smaller MSE or smaller bias in certain situations. In addition, we found our method to be more informative and easier to implement. Therefore, we conclude that the proposed method is useful to promote the dissemination of ME correction methods in nutritional epidemiology.