Estimation of the number of studies with positive trends when studies with negative trends are present

A two-point estimator is proposed for the proportion of studies with positive trends among a collection of studies, some of which may demonstrate negative trends. The proposed estimator is the y-intercept of the secant line joining the points (a, F?(a)) and (b, F?(b)), where F?(p) is the empirical distribution function of p-values from one-tailed tests for positive trend derived from the individual studies. Although this estimator is negatively biased for any choice of the points 0 ≤ a < b ≤ 1, the bias is less than that of the previously proposed one-point estimator defined by setting b = 1. The bias of the two-point estimator is smallest when a and b approach the inflection point of the true distribution function, E [F?(p)]. The utility of the two-point estimator is demonstrated by using it to estimate the number of male-mouse liver carcinogens among carcinogenicity studies conducted by the National Toxicology Program.     

On a confidence interval about a parameter estimated by a ratio of normal random variables

A confidence interval is geometrically constructed about a parameter estimated by the ratio of bivariate normal random variables. The resulting confidence interval is equivalent to that of Fieller's theorem. The geometric construction shown that such intervals are conservative. Bioassay examples are used to demonstrate the technique.     

Estimation of the mutagenic potency of environmental chemicals using short-term bioassay

The Ames Salmonella test is a widely used bioassay method for assessing the mutagenic potency of a potential carcinogen. The test is quick and reliable, and exploits the correlation that exists between mutagenic potential and carcinogenic potential. The data for this case study came from an international study involving 20 laboratories in nine countries. The laboratories participated in a designed experiment in which substances (complex chemical mixtures of the type encountered in the environment) were evaluated for mutagenicity using the Ames test. A stringent protocol was followed. The study's principal aim was to investigate intra- and inter-laboratory variation in test results. The data consist of counts of revertant Salmonella colonies at each of six dose levels of a substance. The data were obtained for each of five test substances from each participating laboratory. The bioassays were carried out according to a prescribed factorial experimental design. Three sets of analysts participated in this case study. They were asked to model the dose-response relationship for two substances, to develop an index of the strength of the relationship, and to assess intra- and inter-laboratory variation in bioassay results.     

Comparison of the Dependence of the TD50 on Maximum Tolerated Dose for Mutagens and Nonmutagens

The relationship between the minimum TD50 (i.e., the TD50 measured at the most sensitive site) and the maximum dose administered (maxD) in rodent carcinogenicity bioassays was investigated separately for mice and rats. The relationship between log(1/TD50) and log(1/maxD) was analyzed as a function of (1) mutagenicity and (2) the statistical significance cutoff for selecting the minimum TD50 values. For rat bioassays, the variance of log(1/TD50) is larger and the correlation of log(1/TD50) with log(1/maxD) is weaker for mutagens than for nonmutagens, suggesting that the relationship between minimum TD50 and MTD is, in general, stronger for nonmutagens than for mutagens. The difference in correlation does not depend on the TD50 statistical significance cutoff, but the difference in variance is not significant for the most stringently selected dataset. For mouse bioassays, no significant mutagen/nonmutagen differences in log(1/TD50) variance are found. A significantly weaker correlation of log(1/TD50) with log(1/maxD) for mutagens in comparison to nonmutagens occurs only for the dataset with minimum TD50 chosen at the least stringent level, suggesting that this difference may be due to chance variation. We also looked for changes in correlation and regression parameters as a function of mutagenic potency in Salmonella; the variance of log(1/TD50) and its correlation with log(1/maxD) are not found to vary in a consistent manner. Taken as a whole, our results indicate that (1) mutagenicity is a determinant of the TD50/maxD relationship in rats and (2) any effect that mutagenicity may exert on the TD50/maxD relationship in mice is unimportant.(ABSTRACT TRUNCATED AT 250 WORDS)     

Comparisons of outlier tests for potency bioassays

Potency bioassays are used to measure biological activity. Consequently, potency is considered a critical quality attribute in manufacturing. Relative potency is measured by comparing the concentration‐response curves of a manufactured test batch with that of a reference standard. If the curve shapes are deemed similar, the test batch is said to exhibit constant relative potency with the reference standard, a critical requirement for calibrating the potency of the final drug product. Outliers in bioassay potency data may result in the false acceptance/rejection of a bad/good sample and, if accepted, may yield a biased relative potency estimate. To avoid these issues, the USP<1032> recommends the screening of bioassay data for outliers prior to performing a relative potency analysis. In a recently published work, the effects of one or more outliers, outlier size, and outlier type on similarity testing and estimation of relative potency were thoroughly examined, confirming the USP<1032> outlier guidance. As a follow‐up, several outlier detection methods, including those proposed by the USP<1010>, are evaluated and compared in this work through computer simulation. Two novel outlier detection methods are also proposed. The effects of outlier removal on similarity testing and estimation of relative potency were evaluated, resulting in recommendations for best practice.     

Nonparametric estimators for shift in quantal bioassay

Let F(x) and F(x+θ) be log dose-response curves for a standard preparation and a test preparation, respectively, in a parallel quantal bioassay designed to test the relative potency of a drug, toxicant, or some other substance, and suppose the form of F is unknown. Several estimators of the shift parameter θ or relative potency, are compared, including some generalized and trimmed Spearman-Kärber estimators and a non parametric maximum likelihood estimator. Both point and interval estimation are discussed. Some recommendations concerning the choices of estimators are offered.     

Incorporation of historical controls using semiparametric mixed models

The analysis of animal carcinogenicity data is complicated by various statistical issues. A topic of recent debate is how to control for the effect of the animal's body weight on the outcome of interest, the onset of tumours. We propose a method which incorporates historical information from the control animals in previously conducted experiments. We allow non-linearity in the effects of body weight by modelling the relationship nonparametrically through a penalized spline. A simple extension of the penalized spline model allows the relationship between weight and the onset of tumour to vary from one experiment to another.     

A bayesian approach to bioassay. technical report m498

We describe the design and analysis for a simulation experiment to compare the mean-squared errors (MSE's) of two quantile estimators defined for random walk designs. The dependence of the easily computed MSE of the first estimator on the levels of five factors is examined via multiple regression. This information is used to plan a simulation to compute the MSE of the second estimator using a fraction of a 3³5²factorial allowing uncorrelated estimates for all main effects and the two-factor interactions of a specified factor. Efficient estimation of the MSE of the second estimator is attempted through antithetic and control variate techniques of variance reduction, with modest success.     

An Overview of the Report: Correlation Between Carcinogenic Potency and the Maximum Tolerated Dose: Implications for Risk Assessment

Current practice in carcinogen bioassay calls for exposure of experimental animals at doses up to and including the maximum tolerated dose (MTD). Such studies have been used to compute measures of carcinogenic potency such as the TD₅₀ as well as unit risk factors such as q ₁ * for predicting low-dose risks. Recent studies have indicated that these measures of carcinogenic potency are highly correlated with the MTD. Carcinogenic potency has also been shown to be correlated with indicators of mutagenicity and toxicity. Correlation of the MTDs for rats and mice implies a corresponding correlation in TD₅₀ values for these two species. The implications of these results for cancer risk assessment are examined in light of the large variation in potency among chemicals known to induce tumors in rodents.     

Stochastic approximation methods and their use in bioassay and phase i clinical trials

Stochastic approximation procedures are sequential estimation methods which provide estimates for the point at which a general regression function attains a given value. The application of such methods to the problem of estimating the median effective does in bioassay and to the problem of estimating the maximally tolerated does in phase I clinical trials is discussed. it is argued that these methods could be very useful in practice.