title: Regression analysis with categorized regression calibrated exposure: some interesting findings.
abstract: BACKGROUND
  Regression calibration as a method for handling measurement error is becoming increasingly well-known and used in epidemiologic research. However, the standard version of the method is not appropriate for exposure analyzed on a categorical (e.g. quintile) scale, an approach commonly used in epidemiologic studies. A tempting solution could then be to use the predicted continuous exposure obtained through the regression calibration method and treat it as an approximation to the true exposure, that is, include the categorized calibrated exposure in the main regression analysis.
  
  
  METHODS
  We use semi-analytical calculations and simulations to evaluate the performance of the proposed approach compared to the naive approach of not correcting for measurement error, in situations where analyses are performed on quintile scale and when incorporating the original scale into the categorical variables, respectively. We also present analyses of real data, containing measures of folate intake and depression, from the Norwegian Women and Cancer study (NOWAC).
  
  
  RESULTS
  In cases where extra information is available through replicated measurements and not validation data, regression calibration does not maintain important qualities of the true exposure distribution, thus estimates of variance and percentiles can be severely biased. We show that the outlined approach maintains much, in some cases all, of the misclassification found in the observed exposure. For that reason, regression analysis with the corrected variable included on a categorical scale is still biased. In some cases the corrected estimates are analytically equal to those obtained by the naive approach. Regression calibration is however vastly superior to the naive method when applying the medians of each category in the analysis.
  
  
  CONCLUSIONS
  Regression calibration in its most well-known form is not appropriate for measurement error correction when the exposure is analyzed on a percentile scale. Relating back to the original scale of the exposure solves the problem. The conclusion regards all regression models.
authors.affiliation: lnstitute of Basic Medical Sciences, Department of Biostatistics, University of Oslo, P,O, Box 1122, Blindern, 0317 Oslo, Norway. ingvild.dalen@medisin.uio.no
authors.forename: Ingvild
authors.initials: I
authors.lastname: Dalen
authors.forename: John P
authors.initials: JP
authors.lastname: Buonaccorsi
authors.forename: Petter
authors.initials: P
authors.lastname: Laake
authors.forename: Anette
authors.initials: A
authors.lastname: Hjartåker
authors.forename: Magne
authors.initials: M
authors.lastname: Thoresen