Objective: To explore the impact of measurement error on the associated effects under the incorrectly-measured variables when mixed with precisely measured variables.
Methods: Based on the functions of measurement error, correlation of incorrectly-measured predictors and precisely measured explanatory variables, number of precisely measured explanatory variables and associated effect, the 'R Project for Statistical Computing' method is used to analyze the impact of measurement on the validity of a study.
Results: Under the scenario that the continuous response Y and the continuous explanatory Z are precisely measured but the continuous predictor X is incorrectly-measured, when focusing on inference about the effect of X on Y, the non-differential measurement error always makes the value of estimated effect less than the actual value, and the attenuation effect of measurement error more closely worsens the correlation of X and Z. Under a misclassification dichotomous predictor X with an additional precisely measured explanatory variable Z and focusing on inference about the effect of X on Y, the misclassification bias is not only related to the sensitivity and specificity of exposure measurement, but also to the correlation between X and Z and exposure proportion of X. The attenuation factor (AF) decreases gradually with the increasing correlation between X and Z. For instance, in the p = 0.5 scenario, AF is 1.419, and the estimated effect of dichotomous predictor X on continuous response Y is more than the actual effect. When it increases to 0.9, AF is 0.474, the estimated effect becomes less than the true effect.
Conclusion: In the studies of the impact of measurement error in linear regression with additional precisely measured explanatory variables, the impact of measurement error on the associated effect is relatively complex, suggesting that it is necessary to control and to assess the measurement error bias in order to correctly interpret the results of a study.