Least-MSE calibration procedures for corrections of measurement and misclassification errors in generalized linear models

The analyses of clinical and epidemiologic studies are often based on some kind of regression analysis, mainly linearregression and logistic models. These analyses are often affected by the fact that one or more of the predictors are measuredwith error. The error in the predictors is also known to bias the estimates and hypothesis testing results. One of the proceduresfrequently used to handle such problem in order to reduce the measurement errors is the method of regression calibration forpredicting the continuous covariate. The idea is to predict the true value of error-prone predictor from the observed data, thento use the predicted value for the analyses. In this research we develop four calibration procedures, namely probit, complementary log-log, logit, and logistic calibration procedures for corrections of the measurement error and/or the misclassification error to predict the true values for the misclassification explanatory variables used in generalized linear models. Theprocesses give the predicted true values of a binary explanatory variable using the calibration techniques then use thesepredicted values to fit the three models such that the probit, the complementary log-log, and the logit models under the binaryresponse. All of which are investigated by considering the mean square error (MSE) in 1,000 simulation studies in each caseof the known parameters and conditions. The results show that the proposed working calibration techniques that can performadequately well are the probit, logistic, and logit calibration procedures. Both the probit calibration procedure and the probitmodel are superior to the logistic and logit calibrations due to the smallest MSE. Furthermore, the probit model-parameterestimates also improve the effects of the misclassification explanatory variable. Only the complementary log-log model andits calibration technique are appropriate when measurement error is moderate and sample size is high.