Bias corrected estimation for generalized probit regression with covariate measurement error and censored responses

• Published in: Journal of statistical planning and inference Vol. 142; no. 1; pp. 221 - 231
• Main Authors: Wu, Yueqin, Gu, Minggao
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 2012; Elsevier
• Subjects: Corrected score; Distribution theory; Exact sciences and technology; General topics; Generalized probit regression; Interval censoring; Linear inference, regression; Marginal likelihood; Mathematics; Measurement error; Nonparametric inference; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Statistics; Corrected score; Interval censoring; Measurement error; Marginal likelihood; Generalized probit regression; Statistical distribution; Variance estimation; Bias; Generalized function; Censored sample; Probit model; Covariate; Distribution function; Approximation theory; Censored data; Statistical moment; Statistical decision; Statistical method; Statistical regression; Regression coefficient; Cox model; Simulation; Regression model; Relative error; Biased estimation
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/j.jspi.2011.07.011

In this paper, we propose a bias corrected estimate of the regression coefficient for the generalized probit regression model when the covariates are subject to measurement error and the responses are subject to interval censoring. The main improvement of our method is that it reduces most of the bias that the naive estimates have. The great advantage of our method is that it is baseline and censoring distribution free, in a sense that the investigator does not need to calculate the baseline or the censoring distribution to obtain the estimator of the regression coefficient, an important property of Cox regression model. A sandwich estimator for the variance is also proposed. Our procedure can be generalized to general measurement error distribution as long as the first four moments of the measurement error are known. The results of extensive simulations show that our approach is very effective in eliminating the bias when the measurement error is not too large relative to the error term of the regression model. ► We study the generalized probit model with covariate measurement error. ► A bias corrected estimation for the regression coefficient is proposed. ► A sandwich estimator for the variance is also proposed. ► Our approach is baseline and censoring distribution free. ► Our procedure only needs to know the first four moments of the measurement error.