Conditional-Cumulant-of-Exposure Method in Logistic Missing Covariate Regression
Article first published online: 25 MAY 2004
Volume 56, Issue 1, pages 98–105, March 2000
How to Cite
Wang, C. Y. and Huang, W.-T. (2000), Conditional-Cumulant-of-Exposure Method in Logistic Missing Covariate Regression. Biometrics, 56: 98–105. doi: 10.1111/j.0006-341X.2000.00098.x
- Issue published online: 25 MAY 2004
- Article first published online: 25 MAY 2004
- Received May 1998. Revised November 1998. Accepted April 1999.
- Cumulant-generating function;
- Measurement error;
- Missing data
Summary. We consider estimation in logistic regression where some covariate variables may be missing at random. Satten and Kupper (1993, Journal of the American Statistical Association88, 200–208) proposed estimating odds ratio parameters using methods based on the probability of exposure. By approximating a partial likelihood, we extend their idea and propose a method that estimates the cumulant-generating function of the missing covariate given observed covariates and surrogates in the controls. Our proposed method first estimates some lower order cumulants of the conditional distribution of the unobserved data and then solves a resulting estimating equation for the logistic regression parameter. A simple version of the proposed method is to replace a missing covariate by the summation of its conditional mean and conditional variance given observed data in the controls. We note that one important property of the proposed method is that, when the validation is only on controls, a class of inverse selection probability weighted semiparametric estimators cannot be applied because selection probabilities on cases are zeros. The proposed estimator performs well unless the relative risk parameters are large, even though it is technically inconsistent. Small-sample simulations are conducted. We illustrate the method by an example of real data analysis.