Constrained four parameter logistic model.

The constrained four parameter logistic model has found wide application in describing dose response relationships across many assay systems. This discussion examines the basic model and its practical application to potency testing in the context of the 96 well plate. A two step procedure is recommended for the analysis: (i) the constrained logistic model to generate potency estimates, (ii) a linear mixed-effects model to account for within-plate and between plate variability for producing the final combined estimate of potency. The method is outlined in a case study. Design issues related to possible location effects on the plate may be ameliorated by use of a Latin square design.

Optimal designs for the individual and joint exposure general logistic regression models.

Interest in administering compounds in combination lies both in enhancing efficacious effects and in limiting adverse effects. Although much statistical work has focused on developing mathematical functions to model the joint dose-response curves, relatively little work exists in regard to designing experiments for assessing joint action. A variety of parametric dose-response models based on either the normal or logistic probability distribution have been proposed in the literature. These models are typically nonlinear in the parameters, and as such, a nonlinear weighted least squares approach can be employed for the purpose of designing experiments. The approach is applicable across a wide variety of settings commonly associated with joint action data, including continuous and discrete responses, alternative error structures, and nonzero background response. Further, designs can be expressed in terms of proportionate responses associated with the individual compounds rather than dose levels, thereby providing for results that are applicable across compounds. As a precursor to this effort, optimal and minimal experimental designs for the case in which a single compound is administered have also been developed. Although the proposed methodology for deriving experimental designs can be applied to any nonlinear regression model, primary focus is given to the additive and nonadditive independent joint action (IJA) models for individual and combined exposures proposed by Barton, Braunberg, and Friedman (1).

Comparison of bracketing and matrixing designs for a two-year stability study.

In the U.S. Food and Drug Administration (FDA) guidelines for stability testing of new drug products, both bracketing and matrixing designs were suggested as the statistical designs. More recently, they have increasing attention from pharmaceutical companies, because both designs reduce the cost of stability studies. The purpose of this paper is to investigate both designs in terms of the power of detection of significant difference between slopes, and use the mean square error to evaluate the precision of estimated drug shelf life. Additionally, the distributions of both designs are compared by using 1000 simulations.

Designs for testing lack of fit for a nonlinear dose-response curve model.

We would like to estimate the parameters of a dose-response function with the greatest precision as possible. For a two-parameter model, this is equivalent to minimizing the area of the confidence ellipsoid, i.e., a D-optimal design. Previous work on this particular model has included minimal designs. These designs are unable to determine lack of fit. We introduce a distinct dose level to the design to be able to estimate the lack of fit. The minimal and new designs will be compared, and the sample size needed to achieve adequate power for the lack-of-fit test will be derived.

Effect of investigator bias on the significance level of the Wilcoxon rank-sum test.

When using subjective ordered categorical variables to measure the efficacy of an active treatment versus placebo in a double-blind clinical trial setting, bias may be introduced into the response variables when investigators become partially or totally unblinded to treatment assignment due to characteristic side effects. The investigators may alter the classification of a patient's response to treatment based on perceived treatment assignment. The introduction of bias leads to a considerable increase in the actual significance level of the Wilcoxon rank-sum test.

Effect of investigator bias on the power and level of the two-sample Z-test.

The use of subjective measures in the evaluation of treatment efficacy in clinical trials may introduce bias into the response variables of interest when investigators attempt to guess the treatment that patients are receiving. The bias may be introduced even in the setting of double-blind clinical trials due to the presence of characteristic side effects. The introduction of bias leads to an increase in the power of the statistical test. However, this increase in power is achieved at a considerable increase in the actual level of the statistical test.

Some optimal matrix designs in stability studies.

As part of an application for licensure of a new drug, it is necessary to provide data on the stability of the product over time under various conditions. If every combination of conditions is studied at every sampling time, the cost of the study can be substantial. To minimize expense, matrix designs are discussed, whereby only a fraction of the various design combinations of interest are tested at any specified sampling time. A method for choosing the time vectors such that the design is optimal in terms of maximum information per unit cost is proposed.