Quantitative high throughput screening (qHTS) assays use cells or tissues to screen thousands of compounds in a short period of time. Data generated from qHTS assays are then evaluated using nonlinear regression models, such as the Hill model, and decisions regarding toxicity are made using the estimates of the parameters of the model. For any given compound, the variability in the observed response may either be constant across dose groups (homoscedasticity) or vary with dose (heteroscedasticity). Since thousands of compounds are simultaneously evaluated in a qHTS assay, it is not practically feasible for an investigator to perform residual analysis to determine the variance structure before performing statistical inferences on each compound. Since it is well-known that the variance structure plays an important role in the analysis of linear and nonlinear regression models it is therefore important to have practically useful and easy to interpret methodology which is robust to the variance structure. Furthermore, given the number of chemicals that are investigated in the qHTS assay, outliers and influential observations are not uncommon. In this article we describe preliminary test estimation (PTE) based methodology which is robust to the variance structure as well as any potential outliers and influential observations. Performance of the proposed methodology is evaluated in terms of false discovery rate (FDR) and power using a simulation study mimicking a real qHTS data. Of the two methods currently in use, our simulations studies suggest that one is extremely conservative with very small power in comparison to the proposed PTE based method whereas the other method is very liberal. In contrast, the proposed PTE based methodology achieves a better control of FDR while maintaining good power. The proposed methodology is illustrated using a data set obtained from the National Toxicology Program (NTP). Additional information, simulation results, data and computer code are available online as supplementary materials.