Identification of the minimum effective dose based on weighted Kaplan–Meier statistics

Testing procedures are considered for identifying the minimum effective dose (MED) in a dose–response study with randomly right-censored survival data, where the MED is defined to be the smallest dose level under study that has survival advantage over the zero dose control. The proposed testing procedures are implemented in a step-down manner together with three different types of weighted Kaplan–Meier statistics. Comparative results of a Monte Carlo error rate and power/bias study for a variety of survival and censoring distributions are then presented and discussed. The application of the proposed procedures is finally illustrated for identifying the MED of the diethylstilbestrol in the treatment of prostate cancer.     

Impact of Acquired Immunity and Dose‐Dependent Probability of Illness on Quantitative Microbial Risk Assessment

Dose‐response models in microbial risk assessment consider two steps in the process ultimately leading to illness: from exposure to (asymptomatic) infection, and from infection to (symptomatic) illness. Most data and theoretical approaches are available for the exposure‐infection step; the infection‐illness step has received less attention. Furthermore, current microbial risk assessment models do not account for acquired immunity. These limitations may lead to biased risk estimates. We consider effects of both dose dependency of the conditional probability of illness given infection, and acquired immunity to risk estimates, and demonstrate their effects in a case study on exposure to Campylobacter jejuni. To account for acquired immunity in risk estimates, an inflation factor is proposed. The inflation factor depends on the relative rates of loss of protection over exposure. The conditional probability of illness given infection is based on a previously published model, accounting for the within‐host dynamics of illness. We find that at low (average) doses, the infection‐illness model has the greatest impact on risk estimates, whereas at higher (average) doses and/or increased exposure frequencies, the acquired immunity model has the greatest impact. The proposed models are strongly nonlinear, and reducing exposure is not expected to lead to a proportional decrease in risk and, under certain conditions, may even lead to an increase in risk. The impact of different dose‐response models on risk estimates is particularly pronounced when introducing heterogeneity in the population exposure distribution.     

Testing drug additivity based on monotherapies

Under the Loewe additivity, constant relative potency between two drugs is a sufficient condition for the two drugs to be additive. Implicit in this condition is that one drug acts like a dilution of the other. Geometrically, it means that the dose‐response curve of one drug is a copy of another that is shifted horizontally by a constant over the log‐dose axis. Such phenomenon is often referred to as parallelism. Thus, testing drug additivity is equivalent to the demonstration of parallelism between two dose‐response curves. Current methods used for testing parallelism are usually based on significance tests for differences between parameters in the dose‐response curves of the monotherapies. A p‐value of less than 0.05 is indicative of non‐parallelism. The p‐value‐based methods, however, may be fundamentally flawed because an increase in either sample size or precision of the assay used to measure drug effect may result in more frequent rejection of parallel lines for a trivial difference. Moreover, similarity (difference) between model parameters does not necessarily translate into the similarity (difference) between the two response curves. As a result, a test may conclude that the model parameters are similar (different), yet there is little assurance on the similarity between the two dose‐response curves. In this paper, we introduce a Bayesian approach to directly test the hypothesis that the two drugs have a constant relative potency. An important utility of our proposed method is in aiding go/no‐go decisions concerning two drug combination studies. It is illustrated with both a simulated example and a real‐life example. Copyright © 2015 John Wiley & Sons, Ltd.     

Adaptive designs for selecting drug combinations based on efficacy–toxicity response

We propose a new adaptive procedure for dose-finding in clinical trials with combination of two drugs when both efficacy and toxicity responses are available. We model the distribution of this bivariate binary endpoint using the bivariate probit model. The analytic formulae for the Fisher information matrix are obtained, that form the basis for derivation of the locally optimal, minimax, Bayesian, and adaptive designs in the framework of optimal design theory.     

Quantal resp0nse assays by inverse regression

A general inverse regression procedure for estimating dose-response curves in quanta1 response assays is presented. Asymptotic distributional properties are developed. The special case is given, where after suitable transformation, the -dose response curve is linear. The inverse method has a decided advantage over the more classical methods in this case, both inflexibility and in ease of application. The procedure will be shown to be fully efficient, in the asymptotic context*     

Hormesis: A Highly Generalizable and Reproducible Phenomenon With Important Implications for Risk Assessment

From a comprehensive search of the literature, the hormesis phenomenon was found to occur over a wide range of chemicals, taxonomic groups, and endpoints. By use of computer searches and extensive cross-referencing, nearly 3000 potentially relevant articles were identified. Evidence of chemical and radiation hormesis was judged to have occurred in approximately 1000 of these by use of a priori criteria. These criteria included study design features (e.g., number of doses, dose range), dose–response relationship, statistical analysis, and reproducibility of results. Numerous biological endpoints were assessed, with growth responses the most prevalent, followed by metabolic effects, reproductive responses, longevity, and cancer. Hormetic responses were generally observed to be of limited magnitude with an average maximum stimulation of 30 to 60 percent over that of the controls. This maximum usually occurred 4- to 5-fold below the NOAEL for a particular endpoint. The present analysis suggests that hormesis is a reproducible and generalizable biological phenomenon and is a fundamental component of many, if not most, dose–response relationships. The relatively infrequent observation of hormesis in the literature is believed to be due primarily to experimental design considerations, especially with respect to the number and range of doses and endpoint selection. Because of regulatory considerations, most toxicologic studies have been carried out at high doses above the low-dose region where the hormesis phenomenon occurs.     

Upper Confidence Limits on Excess Risk for Quantitative Responses

The definition and observation of clear-cut adverse health effects for continuous (quantitative) responses, such as altered body weights or organ weights, are difficult propositions. Thus, methods of risk assessment commonly used for binary (quantal) toxic responses such as cancer are not directly applicable. In this paper, two methods for calculating upper confidence limits on excess risk for quantitative toxic effects are proposed, based on a particular definition of an adverse quantitative response. The methods are illustrated with data from a dose-response study, and their performance is evaluated with a Monte Carlo simulation study.     

Experimental Design of Bioassays for Screening and Low Dose Extrapolation

Relatively high doses of chemicals generally are employed in animal bioassays to detect potential carcinogens with relatively small numbers of animals. The problem investigated here is the development of experimental designs which are effective for high to low dose extrapolation for tumor incidence as well as for screening (detecting) carcinogens. Several experimental designs are compared over a wide range of different dose response curves. Linear extrapolation is used below the experimental data range to establish an upper bound on carcinogenic risk at low doses. The goal is to find experimental designs which minimize the upper bound on low dose risk estimates (i.e., maximize the allowable dose for a given level of risk). The maximum tolerated dose (MTD) is employed for screening purposes. Among the designs investigated, experiments with doses at the MTD, 1/2 MTD, 1/4 MTD, and controls generally provide relatively good data for low dose extrapolation with relatively good power for detecting carcinogens. For this design, equal numbers of animals per dose level perform as well as unequal allocations.     

The treatment versus experimentation dilemma in dose finding studies

Phase I clinical trials are conducted in order to find the maximum tolerated dose (MTD) of a given drug from a finite set of doses. For ethical reasons, these studies are usually sequential, treating patients or groups of patients with the optimal dose according to the current knowledge, with the hope that this will lead to using the true MTD from some time on. However, the first result proved here is that this goal is infeasible, and that such designs, and, more generally, designs that concentrate on one dose from some time on, cannot provide consistent estimators for the MTD unless very strong parametric assumptions hold. Allowing some non-MTD treatment, we construct a randomized design that assigns the MTD with probability that approaches one as the size of the experiment goes to infinity and estimates the MTD consistently. We compare the suggested design with several methods by simulations, studying their performances in terms of correct estimation of the MTD and the proportion of individuals treated with the MTD.     

Assessing departure from dose linearity under a repeated measures incomplete block design

Dose proportionality/linearity is a desirable property in pharmacokinetic studies. Various methods have been proposed for its assessment. When dose proportionality is not established, it is of interest to evaluate the degree of departure from dose linearity. In this paper, we propose a measure of departure from dose linearity and derive an asymptotic test under a repeated measures incomplete block design using a slope approach. Simulation studies show that the proposed method has a satisfactory small sample performance in terms of size and power.