Determination of Offset Values in Binary Regression Models to Adjust for Misclassification Errors

In randomized clinical trials and observational studies alike, it is difficult and challenging to collect gold-standard outcome measures for all participants. Although it would be ideal to use gold-standard measures, the costs and logistics of collecting them are often prohibitive. Therefore, surrogate or proxy measures or screening survey instruments are more often used to mitigate such difficulties, yet at the expense of misclassification errors and consequent biased statistical inferences. In this paper, when misclassification errors of proxy measures in comparison to a gold-standard measure are available through external or internal validation samples, we determined appropriate offset values in generalized binary regression models as a function of the proxy measure to eliminate biases of estimated effects in terms of risk difference, relative risk, and odds ratio that are incurred due to misclassification errors. Simulation studies were conducted to empirically demonstrate and verify the approach using appropriate offset values specific to each binary effect measure for estimating unbiased effects. Both point estimates of all effect measures and standard errors of regression coefficients obtained from the proposed offset-adjusted binary models were shown to be unbiased.