Parnchit Wattanasaruch, Veeranun Pongsapukdee, Pairoj Khawsithiwong, and Anothai Wingsanoi

pp. 467 - 474

Abstract

The analyses of clinical and epidemiologic studies are often based on some kind of regression analysis, mainly linear
regression and logistic models. These analyses are often affected by the fact that one or more of the predictors are measured
with error. The error in the predictors is also known to bias the estimates and hypothesis testing results. One of the procedures
frequently used to handle such problem in order to reduce the measurement errors is the method of regression calibration for
predicting the continuous covariate. The idea is to predict the true value of error-prone predictor from the observed data, then
to 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. The
processes give the predicted true values of a binary explanatory variable using the calibration techniques then use these
predicted values to fit the three models such that the probit, the complementary log-log, and the logit models under the binary
response. All of which are investigated by considering the mean square error (MSE) in 1,000 simulation studies in each case
of the known parameters and conditions. The results show that the proposed working calibration techniques that can perform
adequately well are the probit, logistic, and logit calibration procedures. Both the probit calibration procedure and the probit
model are superior to the logistic and logit calibrations due to the smallest MSE. Furthermore, the probit model-parameter
estimates also improve the effects of the misclassification explanatory variable. Only the complementary log-log model and
its calibration technique are appropriate when measurement error is moderate and sample size is high.