The research focuses on the analysis of generalized linear models when predictors are measured with error. We are concerned with two general forms for error, the measurement error model and the Berkson (instrumental variable) model. We describe examples of such models taken from the October 1987 National Cancer Institute Workshop on Errors-in-Variables in Epidemiology. Research will be performed in the following areas: (1) Testing for the effect of a predictor measured with error. In some instances the usual test ignoring error is valid (correct type 1 error asymptotically), but it is also known to be inefficient and nonrobust, sometimes badly so. We will define efficient tests and robust test, and categorize those cases in which the usual test ignoring error is valid. (2) In randomized generalized linear model covariance studies, testing for a treatment effect is important. We will investigate the validity (see above) of the usual tests which ignore measurement error. In those cases that the usual test is invalid, we will correct it to have specified asymptotic level. The usual tests are inefficient and nonrobust; we will define robust tests and efficient tests. (3) In many cases, ignoring error in predictors can lead to incorrect inference. This happens in nonrandomized covariance studies or in studies for which more than one predictor is measured with error and the errors are correlated. Examples are given in the proposal. Good estimates of parameters and inference for them are required which make few assumptions. Most methods available yield good estimates but poor and unrealistic inference. In the measurement error model, we will improve upon inference by defining better standard errors. In the Berkson model, we will use a semiparametric approach.
| Freedman, L S; Carroll, R J; Wax, Y (1991) Estimating the relation between dietary intake obtained from a food frequency questionnaire and true average intake. Am J Epidemiol 134:310-20 |
