Regression calibration when foods (measured with error) are the variables of interest: Markedly non-gaussian data with many zeroes

Regression calibration has been described as a means of correcting effects of measurement error for normally distributed dietary variables. When foods are the items of interest, true distributions of intake are often positively skewed, may contain many zeroes, and are usually not described by well-known statistical distributions. The authors considered the validity of regression calibration assumptions where data are non-Gaussian. Such data (including many zeroes) were simulated, and use of the regression calibration algorithm was evaluated. An example used data from Adventist Health Study 2 (2002-2008). In this special situation, a linear calibration model does (as usual) at least approximately correct the parameter that captures the exposure-disease association in the "disease" model. Poor fit in the calibration model does not produce biased calibrated estimates when the "disease" model is linear, and it produces little bias in a nonlinear "disease" model if the model is approximately linear. Poor fit will adversely affect statistical power, but more complex linear calibration models can help here. The authors conclude that non-Gaussian data with many zeroes do not invalidate regression calibration. Irrespective of fit, linear regression calibration in this situation at least approximately corrects bias. More complex linear calibration equations that improve fit may increase power over that of uncalibrated regressions.