Group testing has long been used as a cost-effective procedure in biomedical applications for the screening and surveillance of infectious diseases. In such settings, a set of individual samples, such as blood and urine, are pooled together and tested simultaneously to yield a positive or negative result. Ideally, a pool tests negative when all individuals in the pool are truly negative, and a pool tests positive when at least one individual in the pool is truly positive. However, testing results can be misclassified due to diagnostic errors. Consequently, group testing models that use misclassified responses without an adjustment for test errors can lead to severely biased estimates. In this article, we study the asymptotic properties of disease prevalence estimators based on pooled sample models. We examine the bias, efficiency, and cost efficiency of an estimator as a function of many factors including test errors and pool sizes. We demonstrate that the adverse effects of testing errors can be greatly minimized through pooling. Also, our optimality shows that nearly unbiased estimates of the disease prevalence can be enjoyed even though test errors are completely ignored.