No abstract

Many drug concentration-effect relationships are described by nonlinear sigmoid models. The 4-parameter Hill model, which belongs to this class, is commonly used. An experimental design is essential to accurately estimate the parameters of the model. In this report we investigate properties of D-optimal designs. D-optimal designs minimize the volume of the confidence region for the parameter estimates or, equivalently, minimize the determinant of the variance-covariance matrix of the estimated parameters. It is assumed that the variance of the random error is proportional to some power of the response. To generate D-optimal designs one needs to assume the values of the parameters. Even when these preliminary guesses about the parameter values are appreciably different from the true values of the parameters, the D-optimal designs produce satisfactory results. This property of D-optimal designs is called robustness. It can be quantified by using D-efficiency. A five-point design consisting of four D-optimal points and an extra fifth point is introduced with the goals to increase robustness and to better characterize the middle part of the Hill curve. Four-point D-optimal designs are then compared to five-point designs and to log-spread designs, both theoretically and practically with laboratory experiments.D-optimal designs proved themselves to be practical and useful when the true underlying model is known, when good prior knowledge of parameters is available, and when experimental units are dear. The goal of this report is to give the practitioner a better understanding for D-optimal designs as a useful tool for the routine planning of laboratory experiments.

It appears unlikely that the good clinical efficacy of the combination is primarily caused by a synergistic interaction at the cellular level.

In preparing for the routine use of the ubiquitous in vitro cell growth inhibition assay for the study of anticancer agents, we characterized the statistical properties of the assay and found some surprising results. Parabolic well-to-well cell growth patterns were discovered, which could profoundly affect the results of routine growth inhibition studies of anticancer and other agents. Four human ovarian cell lines, A2780/WT, A2780/DX5, A2780/DX5B, and A121, and one human ileocecal adenocarcinoma cell line, HCT-8, were seeded into plastic 96-well plates with a 12-channel pipette, without drugs, and grown from 1-5 d. The wells were washed with a plate washer, cells stained with sulforhodamine B (SRB), and dye absorbance measured with a plate reader. Variance models were fit to the data from replicates to determine the nature of the heteroscedastic error structure. Exponential growth models were fit to data to estimate doubling times for each cell line. Polynomial models were fit to data from 10-plate stacks of 96-well plates to explore nonuniformity of cell growth in wells in different regions of the stacks. Each separate step in the assay was examined for precision, patterns, and underlying causes of variation. Differential evaporation of water from wells is likely a major, but not exclusive, contributor to the systematic well-to-well cell growth patterns. Because the fundamental underlying causes of the parabolic growth patterns were not conclusively found, a randomization step for the growth assay was developed.