Hypothesis testing and Bayesian estimation using a sigmoid Emax model applied to sparse dose-response designs

Application of a sigmoid Emax model is described for the assessment of dose-response with designs containing a small number of doses (typically, three to six). The expanded model is a common Emax model with a power (Hill) parameter applied to dose and the ED50 parameter. The model will be evaluated following a strategy proposed by Bretz et al. (2005). The sigmoid Emax model is used to create several contrasts that have high power to detect an increasing trend from placebo. Alpha level for the hypothesis of no dose-response is controlled using multiple comparison methods applied to the p-values obtained from the contrasts. Subsequent to establishing drug activity, Bayesian methods are used to estimate the dose-response curve from the sparse dosing design. Bayesian estimation applied to the sigmoid model represents uncertainty in model selection that is missed when a single simpler model is selected from a collection of non-nested models. The goal is to base model selection on substantive knowledge and broad experience with dose-response relationships rather than criteria selected to ensure convergence of estimators. Bayesian estimation also addresses deficiencies in confidence intervals and tests derived from asymptotic-based maximum likelihood estimation when some parameters are poorly determined, which is typical for data from common dose-response designs.     

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.     

假设检验的接拒不定域

介绍假设检验接拒不定域的概念,明确给出出现条件及计算方法,通过实例较好解释了统计假设检验实践中的常见疑惑。     

Sigmoid model versus median-effect analysis for obtaining dose-response curves for in vitro chemosensitivity testing

AIM: The aim of this study was to determine how the in vitro dose-response effects of chemotherapeutic agents should be analyzed and reported. METHODS: We arbitrarily evaluated the effects of mitomycin-C and 4-OH-cyclophosphamide on the human ovarian cancer cell line CAOV-3. Dose-response curves (DRCs) were calculated by non-linear (sigmoid model: SigmaPlot) and linear curve fitting (median-effect analysis: CalcuSyn). RESULTS: In theory and practice, the sigmoid model provided better curve fits and graphical presentation than the median-effect analysis. CONCLUSION: Thus, this model should preferably be used as a basis for selection of anti-cancer drugs for clinical use.     

A dose-response model for refractory ceramic fibers

Refractory ceramic fibers (RCFs) are man-made vitreous fibers commonly used in insulation applications above 1000 degrees C. Although they have been subjected to considerable toxicologic evaluation, only the pooled results from two rat inhalation studies provide data that may be suitable for performing a numerical risk assessment. Even in these inhalation studies, good evidence exists that the maximum tolerated dose (MTD) was exceeded and that pulmonary overload occurred, a condition that will cause tumors whatever the dust responsible. Indeed, a significant yield of tumors was only obtained at the highest dose tested. If these results are omitted, there is no statistically significant evidence of carcinogenicity within the RCF results. Although there is little evidence that overload-related tumors are relevant to human risk, we adopted a conservative approach to obtain the estimates of risk regardless of overload, using a biologically based model, the two-stage clonal expansion model, as well as various statistical models, including the benchmark dose model. We argue that the data favor the use of a biologically based model, which gives the best fit when the highest dose RCF exposures are omitted. Continuing with this model, we show that available data from the RCF experiment, less outliers, coupled with results from other experiments with man-made mineral fibers (MMVFs), demonstrate that all MMVFs are potentially carcinogenic, with any risk mediated by the fibers' biopersistence. Application of this "all MMVF data set" model yields a maximum likely estimate for RCF excess unit risk of 4.6 x 10(-5) (95% upper confidence limit = 9.2 x 10(-5) per fiber/ml). This implies that the risk from occupational exposure to RCFs at 1 fiber/ml for a typical working lifetime would not exceed 10(-4).     

Alzheimer's disease drugs: an application of the hormetic dose-response model

This article provides an evaluation of the dose-response features of drugs that are intended to improve memory, some of which have been used in the treatment of Alzheimer's disease (AD). A common feature of these drugs is that they act via an inverted U-shaped dose response, consistent with the hormetic dose response model. This article assesses historical foundations that lead to the development of AD drugs, their dose-response features and how the quantitative features of such dose responses affected drug discovery and development, and the successes and possible failures of such agents in preclinical and clinical settings. This story begins about 150 years ago with the discovery of an active agent in the Calabar bean plant called physostigmine, its unfolding medical applications, and its implications for dose-response relationships, memory enhancement, and improved drug discovery activities. The article also demonstrates the occurrence of U-shaped dose responses for memory with numerous endogenous agonists including neurosteroids, various peptides (e.g., vasopressin, CCK-8, neuropeptide Y), and other agents (e.g., epinephrine, antagonists for platelet activity factor and nicotinic receptors), supporting the generalizability of the hormetic biphasic dose response. Finally, the significance of the U-shaped dose response is critical for successful clinical application, since it defines the therapeutic window.     

The hormetic dose-response model is more common than the threshold model in toxicology.

The threshold dose-response model is widely viewed as the most dominant model in toxicology. The present study was designed to test the validity of the threshold model by assessing the responses of doses below the toxicological NOAEL (no observed adverse effect level) in relationship to the control response (i.e., unexposed group). Nearly 1,800 doses below the NOAEL, from 664 dose-response relationships derived from a previously published database that satisfied a priori entry criteria, were evaluated. While the threshold model predicts a 1:1 ratio of responses "greater than" to "less than" the control response (i.e., a random distribution), a 2.5:1 ratio (i.e., 1171:464) was observed, reflecting 31% more responses above the control value than expected (p < 0.0001). The mean response (calculated as % control response) of doses below the NOAEL was 115.0% +/- 1.5 standard error of the mean (SEM). These findings challenge the long-standing belief in the primacy of the threshold model in toxicology (and other areas of biology involving dose-response relationships) and provide strong support for the hormetic-like biphasic dose-response model characterized by a low-dose stimulation and a high-dose inhibition. These findings may affect numerous aspects of toxicological and biological/biomedical research related to dose-response relationships, including study design, risk assessment, as well as chemotherapeutic strategies.     

On use of the multistage dose-response model for assessing laboratory animal carcinogenicity

We explore how well a statistical multistage model describes dose-response patterns in laboratory animal carcinogenicity experiments from a large database of quantal response data. The data are collected from the US EPA's publicly available IRIS data warehouse and examined statistically to determine how often higher-order values in the multistage predictor yield significant improvements in explanatory power over lower-order values. Our results suggest that the addition of a second-order parameter to the model only improves the fit about 20% of the time, while adding even higher-order terms apparently does not contribute to the fit at all, at least with the study designs we captured in the IRIS database. Also included is an examination of statistical tests for assessing significance of higher-order terms in a multistage dose-response model. It is noted that bootstrap testing methodology appears to offer greater stability for performing the hypothesis tests than a more-common, but possibly unstable, "Wald" test.     

Probabilistic dose-response modeling: case study using dichloromethane PBPK model results

A revised assessment of dichloromethane (DCM) has recently been reported that examines the influence of human genetic polymorphisms on cancer risks using deterministic PBPK and dose-response modeling in the mouse combined with probabilistic PBPK modeling in humans. This assessment utilized Bayesian techniques to optimize kinetic variables in mice and humans with mean values from posterior distributions used in the deterministic modeling in the mouse. To supplement this research, a case study was undertaken to examine the potential impact of probabilistic rather than deterministic PBPK and dose-response modeling in mice on subsequent unit risk factor (URF) determinations. Four separate PBPK cases were examined based on the exposure regimen of the NTP DCM bioassay. These were (a) Same Mouse (single draw of all PBPK inputs for both treatment groups); (b) Correlated BW-Same Inputs (single draw of all PBPK inputs for both treatment groups except for bodyweights (BWs), which were entered as correlated variables); (c) Correlated BW-Different Inputs (separate draws of all PBPK inputs for both treatment groups except that BWs were entered as correlated variables); and (d) Different Mouse (separate draws of all PBPK inputs for both treatment groups). Monte Carlo PBPK inputs reflect posterior distributions from Bayesian calibration in the mouse that had been previously reported. A minimum of 12,500 PBPK iterations were undertaken, in which dose metrics, i.e., mg DCM metabolized by the GST pathway/L tissue/day for lung and liver were determined. For dose-response modeling, these metrics were combined with NTP tumor incidence data that were randomly selected from binomial distributions. Resultant potency factors (0.1/ED(10)) were coupled with probabilistic PBPK modeling in humans that incorporated genetic polymorphisms to derive URFs. Results show that there was relatively little difference, i.e., <10% in central tendency and upper percentile URFs, regardless of the case evaluated. Independent draws of PBPK inputs resulted in the slightly higher URFs. Results were also comparable to corresponding values from the previously reported deterministic mouse PBPK and dose-response modeling approach that used LED(10)s to derive potency factors. This finding indicated that the adjustment from ED(10) to LED(10) in the deterministic approach for DCM compensated for variability resulting from probabilistic PBPK and dose-response modeling in the mouse. Finally, results show a similar degree of variability in DCM risk estimates from a number of different sources including the current effort even though these estimates were developed using very different techniques. Given the variety of different approaches involved, 95th percentile-to-mean risk estimate ratios of 2.1-4.1 represent reasonable bounds on variability estimates regarding probabilistic assessments of DCM.     

Artificial regression testing in the GARCH-in-mean model

Summary The issue of finite-sample inference in Generalised Autoregressive Conditional Heteroskedasticity (GARCH)-like models has seldom been explored in the theoretical literature, although its potential relevance for practitioners is obvious. In some cases, asymptotic theory may provide a very poor approximation to the actual distribution of the estimators in finite samples. The aim of this paper is to propose the application of the so-called double length regressions (DLR) to GARCH-in-mean models for inferential purposes. As an example, we focus on the issue of Lagrange Multiplier tests on the risk premium parameter. Simulation evidence suggests that DLR-based Lagrange Multiplier (LM) test statistics provide a much better testing framework than the more commonly used LM tests based on the outer product of gradients (OPG) in terms of actual test size, especially when the GARCH process exhibits high persistence in volatility. This result is consistent with previous studies on the subject.     

Exercise, induced bronchospasm in asthmatic children as a dose-response model for theophylline

Efficacy and dose-response activity of oral theophylline were evaluated in 21 asthmatic children, using inhibition of exercise-induced bronchospasm (EIB) as a therapeutic marker. An aqueous theophylline suspension free of alcohol, sugar, and dye was found to be effective for prevention of EIB when given in usual maintenance doses of 4 to 6 mg/kg every 6 hours for 3 weeks, following single loading doses of 8 mg/kg. Pulmonary function measurements (FEV1, FEF25%-75%, PEFR) following standardized treadmill exercise stress were signifcantly improved during both acute and chronic theophylline administration compared to pre-drug control evaluations. There were no signs of developing tolerance to theophylline. The drug produced at least 50% inhibition of EIB in 16 to 21 patients treated. Individualized adjustment of maintenance dosage resulted in optimal theophylline serum concentrations of 10 to 18 microgram/ml in 17 patients. Signs of drug toxicity were observed only when serum levels exceeded 20 microgram/ml following loading doses in 6 patients. Although some children required higher maintenance dosage because of variability in theophylline pharmacokinetics, no child experienced adverse effects after dosage adjustment. Serum half-life ranged between 86 and 351 minutes (mean, 259 minutes); mean peak serum concentration of theophylline after 3 weeks of treatment was 14.9 microgram/ml.     

A model of cytotoxic dose-response nonlinearities arising from adaptive cell inventory management in tissues

Why do low-level exposures to environmental toxins often elicit over-compensating responses that reduce risk to an organism? Conversely, if these responses improve health, why wait for an environmental challenge to trigger them? This paper presents a mathematical modeling framework that addresses both questions using the principle that evolution favors tissues that hedge their bets against uncertain environmental challenges. We consider a tissue composed of differentiated cells performing essential functions (e.g., lung tissue, bone marrow, etc.). The tissue seeks to maintain adequate supplies of these cells, but many of them may occasionally be killed relatively quickly by cytotoxic challenges. The tissue can “order replacements” (e.g., via cytokine network signaling) from a deeper compartment of proliferative stem cells, but there is a delivery lag because these cells must undergo maturation, amplification via successive divisions, and terminal differentiation before they can replace the killed functional cells. Therefore, a “rational” tissue maintains an inventory of relatively mature cells (e.g., the bone marrow reserve for blood cells) for quick release when needed. This reservoir is replenished by stimulating proliferation in the stem cell compartment. Normally, stem cells have a very low risk of unrepaired carcinogenic (or other) damage, due to extensive checking and repair. But when production is rushed to meet extreme demands, error rates increase. We use a mathematical model of cell inventory management to show that decision rules that effectively manage the inventory of mature cells to maintain tissue function across a wide range of unpredictable cytotoxic challenges imply that increases in average levels of cytotoxic challenges can increase average inventory levels and reduce the average error rate in stem cell production. Thus, hormesis and related nonlinearities can emerge as a natural result of cell-inventory risk management by tissues.     

Effects of repeated testing in two inbred strains on flesinoxan dose-response curves in three mouse models for anxiety

Over the last decade, many genetically modified mice have been developed as models for psychiatric diseases such as anxiety. Limited availability of such mutant mice highlights the importance of studying the possibility of repeatedly testing the same individuals. We tested mice four times with 1-week intervals with the same dose of the 5-HT(1A) receptor agonist flesinoxan (0-0.3-1.0-3.0 mg/kg s.c.) in three anxiety-related paradigms: light-dark exploration, open-field activity and stress-induced hyperthermia. The two inbred strains studied were the highly anxious 129S6/SvEvTac (S6) and low-anxiety C57BL/6J (B6) mice. The results indicate that the effects of repeated testing were relatively mild. B6 mice showed some mild habituation in the open-field test when treated with vehicle, whereas S6 mice developed reduced initial activity in the light-dark box after drug treatment. In contrast, responses to flesinoxan treatment were strong and highly consistent for most parameters. In the open-field and light-dark tests, B6 mice showed reduced activity and anxiogenic-like behavioral responses, whereas S6 mice were minimally affected. Anxiolytic-like responses were found in both strains in the stress-induced hyperthermia paradigm. We conclude that B6 and S6 mice can be tested repeatedly with agents such as 5-HT(1A) receptor agonists with 1-week intervals in the three paradigms tested.     

2,4-二硝基酚所致小鼠发热模型的建立及阳性解热药物的选择

目的：建立一种简便的小鼠发热模型，使之应用于解热药物药效初筛。方法：①2，4－二硝基酚14mg/kg、28mg/kg和35mg/kg皮下给药后，分别于0．5、1．0和1．5小时三个时间点测定小鼠体温。②在造模前0．5小时，口服乙酰水杨酸0．8g/kg和腹腔给予安痛定（按所含氨基比林20mg/kg给药），并于造模后0．5、1．0和1．5小时测定小鼠体温。结果：2，4－二硝基酚可引起小鼠发热，升温1℃左右。乙酰水杨酸作为阳性对照药应用于此模型引起大量动物死亡。安痛定的解热作用肯定。结论：小鼠应用2，4－二硝基酚可建立化学性发热模型，但升温持续时间短暂，对作用快速且强大的解热药物经效初筛具有应用价值，乙酰水杨酸不能作为阳性对照药应用于此模型。     

Efficacy of choice testing to predict chronic ingestion of drinking solutions adulterated with chemicals

The feasibility of using a measure of palatability in a 2-bottle choice paradigm to determine detriments in fluid intake when unpalatable solutions containing drugs or chemicals were provided as a sole source of fluid was examined. Palatability measures obtained from testing various concentrations of quinine with water in a two-bottle choice paradigm were compared with intake of these same solutions when they were the sole fluid source for 20 consecutive days. Mice were observed to significantly avoid quinine solutions at concentrations as low as 0.0001 mg/ml in a choice situation while fluid intake was reduced in a forced drinking situation only at a concentration of 0.1 mg/ml. Palatability altered forced fluid intake only when quinine solutions comprised 20% or less of total intake in a choice situation. This approach was successfully employed to predict whether various concentrations of halogenated hydrocarbons could be administered in a repetitive forced drinking situation without reducing total fluid intake of mice.