Pooling biological specimens prior to performing expensive laboratory assays has been shown to be a cost effective approach for estimating parameters of interest. In addition to requiring specialized statistical techniques, however, the pooling of samples can introduce assay errors due to processing, possibly in addition to measurement error that may be present when the assay is applied to individual samples. Failure to account for these sources of error can result in biased parameter estimates and ultimately faulty inference. Prior research addressing biomarker mean and variance estimation advocates hybrid designs consisting of individual as well as pooled samples to account for measurement and processing (or pooling) error. We consider adapting this approach to the problem of estimating a covariate-adjusted odds ratio (OR) relating a binary outcome to a continuous exposure or biomarker level assessed in pools. In particular, we explore the applicability of a discriminant function-based analysis that assumes normal residual, processing, and measurement errors. A potential advantage of this method is that maximum likelihood estimation of the desired adjusted log OR is straightforward and computationally convenient. Moreover, in the absence of measurement and processing error, the method yields an efficient unbiased estimator for the parameter of interest assuming normal residual errors. We illustrate the approach using real data from an ancillary study of the Collaborative Perinatal Project, and we use simulations to demonstrate the ability of the proposed estimators to alleviate bias due to measurement and processing error.