We have studied the influence of measurement error in a typical analysis of high-dimensional data (Hellton and Thoresen 2014a, Sørensen, Frigessi and Thoresen 2015), and we have developed correction methods for measurement error in high-dimensional regression (Sørensen, Frigessi and Thoresen 2014, 2015). Further, we have studied the high-dimensional behavior of PCA, with focus on component scores (Hellton and Thoresen 2014b)
Earlier, we have in several papers investigated the behavior of the most well-known correction method for measurement error in regression, the so-called regression calibration method (Thoresen and Laake 2000, 2007, Thoresen 2006). We have done this in comparison with other methods, and under non-standard conditions. This work has contributed to a better understanding of the qualities of this method. The method is also applied in a study in nutritional epidemiology (Hjartåker et al. 2010).
Further, we have studied one specific, often overlooked, measurement error problem; the problem with errors in both exposure and outcome where these errors are correlated (Thoresen and Laake 2007, Thoresen 2007). We have described a method to correct for such errors, given that the necessary information is available.
Next, we have studied the effect of measurement error in continuous exposure variables that are categorized before entered into a regression model. We have investigated the behavior of different standard correction methods in this situation, and also suggested a new method that seems to work satisfactory in specific situations (Dalen et al. 2006, 2009).