  The association between multidimensional exposure patterns and outcomes is
commonly investigated by first applying cluster analysis algorithms to derive
patterns and then estimating the associations. However, errors in the
underlying continuous, possibly skewed, exposure variables lead to
misclassified exposure patterns and therefore to biased effect estimates. This
is often the case for lifestyle exposures in epidemiology, e.g. for dietary
variables measured on daily basis. We introduce three new algorithms for
correcting the biased effect estimates, which are based on regression
calibration (RC), simulation extrapolation (SIMEX) and multiple imputation
(MI). In addition, the naive method ignoring the measurement error structure is
considered for comparison. These methods are combined with the k-means cluster
algorithm and the Gaussian mixture model to derive exposure patterns. The
performance of the correction methods is compared in a simulation study
regarding absolute, maximum and relative bias. The simulated data mimic a
typical situation in nutritional epidemiology when diet is assessed using
repeated 24-hour dietary recalls. Continuous and binary outcomes are
considered. Simulation results show, that the correction method based on RC and
MI perform better than the naive and the SIMEX-based method. Furthermore, the
MI-based approach, which can use outcome information in the error model, is
superior to the RC-based approach in most scenarios. Therefore, we recommend
using the MI-based approach.
