Correcting for measurement error in binary and continuous variables using replicates

Measurement error in exposures and confounders leads to bias in regression coefficients. It is possible to adjust for this bias if true values or independent replicates are observed on a subsample. We extend a method suitable for quantitative variables to the situation where both binary and quantitative variables are present. Binary variables with independent replicates introduce two extra problems: (i) the error is correlated with the true value, and (ii) the measurement error probabilities are unidentified if only two replicates are available. We show that - under plausible assumptions - adjustment for error in binary confounders does not need to address these problems. The regression coefficient for a binary exposure is overadjusted if methods for continuous variables are used. Correct adjustment is possible either if three replicates are available, or if further assumptions can be made; otherwise, bounds can be put on the correctly adjusted value, and these bounds are reasonably close together if the exposure has prevalence near 0.5.