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The dose-dependent bioactivity of small molecules on cells is a crucial factor in drug discovery and personalized medicine. Although small-molecule microarrays are a promising platform for miniaturized screening, it has been a challenge to use them to obtain quantitative dose-response curves in vitro, especially for lipophilic compounds. Here we establish a small-molecule microarray assay capable of controlling the dosage of small lipophilic molecules delivered to cells by varying the sub-cellular volumes of surface supported lipid micro- and nanostructure arrays fabricated with nanointaglio. Features with sub-cellular lateral dimensions were found necessary to obtain normal cell adhesion with HeLa cells. The volumes of the lipophilic drug-containing nanostructures were determined using a fluorescence microscope calibrated by atomic-force microscopy. We used the surface supported lipid volume information to obtain EC-50 values for the response of HeLa cells to three FDA-approved lipophilic anticancer drugs, docetaxel, imiquimod and triethylenemelamine, which were found to be significantly different from neat lipid controls. No significant toxicity was observed on the control cells surrounding the drug/lipid patterns, indicating lack of interference or leakage from the arrays. Comparison of the microarray data to dose-response curves for the same drugs delivered liposomally from solution revealed quantitative differences in the efficacy values, which we explain in terms of cell-adhesion playing a more important role in the surface-based assay. The assay should be scalable to a density of at least 10,000 dose response curves on the area of a standard microtiter plate.