Abstract by Prof. Paul Rathouz

Information from Separate Sources using Berkson and Classical Measurement Error Models.

This work is motivated by a problem in occupational epidemiology of linking data sets via a common indicator, e.g. occupational code I. The primary data set (DS1) contains I and health outcome y. Interest is on regression of y on psychosocial variable x, and covariates w. Unfortunately, x is unobserved in the primary data set. An auxiliary data set (DS2) containing x and I provides estimates of the mean of x for the I-th stratum, which are then used to fit the regression model. While this approach is a simple one, there are problems in using it for inference. These problems are formulated in terms of both Berkson and classical measurement error (Carroll and Stefanski, 1990, JASA, 85, 652-663), illuminating the issues of bias and standard error estimation for the regression of interest. The Berkson error is addressed via approximate quasi-likelihood for the observed data, which include y and w (from DS1), and the mean of x for stratum I (from DS2). However, the x means are subject to classical measurement error (see, e.g. Stefanski and Carroll, 1987, Biometrika, 74, 703-716). A projected quasi-score method (Waterman and Lindsay, 1996, Biometrika, 83, 1-13) is developed to address this second source of error, treating the x-means as nuisance parameters. Estimation of the x-means for stratum I is accomplished via either the data for stratum I or via an empirical Bayes strategy which borrows information from neighboring strata. The result is an inferentially correct and nearly efficient estimation method for the regression model. The approach brings up theoretical issues regarding (1) the extension of the projection methods to quasi-likelihood, and (2) benefits accrued in using empirical Bayes strategies for estimation of many nuisance parameters. We illustrate our method with an application to data on Swedish workers.

Monday - February 3, 1997.
4:00 PM - 2 Illini Hall - PROBABILITY & STATISTICS SEMINAR