Statistical Methods for Dose-Response Assays
Dose-response assays are a common and increasingly high throughput method of assessing the toxicity of potential drug targets on test populations of cells. Such assays typically involve serial dilutions of the compounds in question applied to cell samples to determine the level of cell activity across a broad range of concentrations. Another factor in such experiments may be the change in activity under different enzyme combinations and the use of controls to adjust for interassay variations. Typically, the decreasing number in the population of cells due to increasing concentrations of the drug can be modeled with a logistic curve. Since the appropriate range of concentrations of the drug to test in order to see these reactions cannot be predetermined fully, frequently the data available for a given experimental unit may not be enough to fit such curves on their own successfully. Instead, the assay data as a whole can be successfully analyzed with methods such as constrained fitting and mixed effects models, where each set can borrow strength from each other in order to be fitted while still taking into account individual significances of the specific experiment.
This dissertation illustrates variations of such methods on three major datasets from the Joe Gray lab at Lawrence Berkeley National Laboratory, the Douglas Clark lab at the Department of Chemical Engineering at UC Berkeley, and Bionovo, Inc. of Emeryville, California. The first dataset from breast cancer cell line testing involves the estimation of the National Cancer Institute concentration parameter called GI50, the concentration of the drug at which it inhibits the growth of the population of cells by half. We develop a method utilizing replicate data to estimate this parameter. The second dataset involves the estimation of a more commonly used concentration parameter called the IC50, which doesn't take into account the initial cell population, on special assays that mimic the liver metabolism in the body. The methods involve mixed effects models that incorporate the specific enzyme conditions and types of cells important to the experiment. The third dataset, involving different effects of plant compounds on an osteosarcoma cell line, illustrates the usage of negative and positive controls to appropriately adjust the observations for interassay variation.