Correction for regression dilution bias using replicates from subjects with extreme first measurements

The least squares estimator of the slope in a simple linear regression model will be biased towards zero when the predictor is measured with random error, i.e. intra-individual variation or technical measurement error. A correction factor can be estimated from a reliability study where one replicate is available on a subset of subjects from the main study. Previous work in this field has assumed that the reliability study constitutes a random subsample from the main study. We propose that a more efficient design is to collect replicates for subjects with extreme values on their first measurement. A variance formula for this estimator of the correction factor is presented. The variance for the corrected estimated regression coefficient for the extreme selection technique is also derived and compared with random subsampling. Results show that variances for corrected regression coefficients can be markedly reduced with extreme selection. The variance gain can be estimated from the main study data. The results are illustrated using Monte Carlo simulations and an application on the relation between insulin sensitivity and fasting insulin using data from the population-based ULSAM study. In conclusion, an investigator faced with the planning of a reliability study may wish to consider an extreme selection design in order to improve precision at a given number of subjects or alternatively decrease the number of subjects at a given precision.