Inference on regression model with misclassified binary response

Misclassification of binary responses, if ignored, may severely bias the maximum likelihood estimators (MLEs) of regression parameters. For such data, a binary regression model incorporating non-differential classification errors is extensively used by researchers in different application contexts. We strongly caution against indiscriminate use of this model considering the fact that it suffers from a serious estimation problem due to confounding of the unknown misclassification probabilities with the regression parameters, and thus, may lead to a highly biased estimate. To overcome this problem, we propose here the use of an internal validation sample in addition to the main sample. Assuming differential classification errors, we consider MLEs of the regression parameters based on the joint likelihood of the main sample and the internal validation sample. We then develop a rigorous asymptotic theory for the joint MLEs under standard assumptions. To facilitate its easy implementation for inference, we propose a bootstrap approximation to the asymptotic distribution and prove its consistency. The results of the simulation studies suggest that even an extremely small validation sample may lead to a vastly improved inference. Finally, the methodology is illustrated with a real-life survey data.