International Biometric Society Efficiency of two-phase designs to correct for measurement error in regression

Measurement error can lead to substantial bias in regression problems but can be overcome if replicate measures are available; however replication may be expensive. Although there is a substantial literature on use of 2-phase case control studies to address measurement error problems (eg McNamee 2005), less attention has been paid to 2-phase designs for estimation of β in the Normal regression model E[Y]=α+βX where Y and X are continuous and X can only be measured with error by W. Here we consider the efficiency of four 2-phase designs for this problem. In design A, both Y and W1=X+ε1 –where ε1 denotes random error are measured on n 1 phase subjects and W2=X+ε2 on a fraction p of these in the 2 phase. In design B, W1 alone is measured for n 1st phase subjects and Y and W2 in the second phase fraction. Variants of A and B allow 2nd phase subjects to be chosen randomly or from the extremes of the 1st phase W1 distribution (‘extreme sampling’). Berglund et al (2005) showed that, for design A, extreme sampling is more efficient than random sampling, but the overall efficiency of these 2-phase designs compared to usual, ‘single-phase’ designs has not been evaluated previously. Therefore it is not clear whether 2-phase designs should be recommended over usual practice.