Bias and efficiency loss due to misclassified responses in binary regression

Methods that ignore errors in binary responses yield biased estimators of the associations of covariates with response. This paper derives general expressions for the magnitude of the bias due to errors in the response and shows that, unless both the sensitivity and specificity are very high, ignoring errors in the responses will yield highly biased covariate effect estimators. When the true, error-free response follows a generalised linear model and misclassification probabilities are known and independent of covariate values, responses observed with error also follow such a model with a modified link function. We describe a simple method to obtain consistent estimators of covariate effects and associated errors in this case, and derive an expression for the asymptotic relative efficiency of covariate effect estimators from the correct likelihood for the responses with errors with respect to estimates based on the true, error-free responses. This expression shows that errors in the response can lead to substantial losses of information about covariate effects. Data from a study on infection with human papilloma virus among women and simulation studies motivate this work and illustrate the findings.