Calculation of Phase 2 dose-finding study sample size for reliable Phase 3 dose selection

Sample sizes of Phase 2 dose-finding studies, usually determined based on a power requirement to detect a significant dose–response relationship, will generally not provide adequate precision for Phase 3 target dose selection. We propose to calculate the sample size of a dose-finding study based on the probability of successfully identifying the target dose within an acceptable range (e.g., 80%–120% of the target) using the multiple comparison and modeling procedure (MCP-Mod). With the proposed approach, different design options for the Phase 2 dose-finding study can also be compared. Due to inherent uncertainty around an assumed true dose–response relationship, sensitivity analyses to assess the robustness of the sample size calculations to deviations from modeling assumptions are recommended. Planning for a hypothetical Phase 2 dose-finding study is used to illustrate the main points. Codes for the proposed approach is available at https://github.com/happysundae/posMCPMod .     

Adaptive modelling of dose–response relationships using smoothing splines

We consider the use of smoothing splines for the adaptive modelling of dose–response relationships. A smoothing spline is a nonparametric estimator of a function that is a compromise between the fit to the data and the degree of smoothness and thus provides a flexible way of modelling dose–response data. In conjunction with decision rules for which doses to continue with after an interim analysis, it can be used to give an adaptive way of modelling the relationship between dose and response. We fit smoothing splines using the generalized cross‐validation criterion for deciding on the degree of smoothness and we use estimated bootstrap percentiles of the predicted values for each dose to decide upon which doses to continue with after an interim analysis. We compare this approach with a corresponding adaptive analysis of variance approach based upon new simulations of the scenarios previously used by the PhRMA Working Group on Adaptive Dose‐Ranging Studies. The results obtained for the adaptive modelling of dose–response data using smoothing splines are mostly comparable with those previously obtained by the PhRMA Working Group for the Bayesian Normal Dynamic Linear model (GADA) procedure. These methods may be useful for carrying out adaptations, detecting dose–response relationships and identifying clinically relevant doses. Copyright © 2009 John Wiley & Sons, Ltd.     

Exploratory assessment of dose proportionality: review of current approaches and proposal for a practical criterion

This article reviews currently used approaches for establishing dose proportionality in Phase I dose escalation studies. A review of relevant literature between 2002 and 2006 found that the power model was the preferred choice for assessing dose proportionality in about one-third of the articles. This article promotes the use of the power model and a conceptually appealing extension, i.e. a criterion based on comparing the 90% confidence interval for the ratio of predicted mean values from the extremes of the dose range (R(dnm)) to pre-defined equivalence criterion (theta(L),theta(U)). The choice of bioequivalence default values of theta(L)=0.8 and theta(U)=1.25 seems reasonable for dose levels only a doubling apart but are impractically strict when applied over the complete dose range. Power calculations are used to show that this prescribed criterion lacks power to conclude dose proportionality in typical Phase I dose-escalation studies. A more lenient criterion with values theta(L)=0.5 and theta(U)=2 is proposed for exploratory dose proportionality assessments across the complete dose range.     

Derivation of Noncancer Reference Values for Acrylonitrile

Dose‐response assessments were conducted for the noncancer effects of acrylonitrile (AN) for the purposes of deriving subchronic and chronic oral reference dose (RfD) and inhalation reference concentration (RfC) values. Based upon an evaluation of available toxicity data, the irritation and neurological effects of AN were determined to be appropriate bases for deriving reference values. A PBPK model, which describes the toxicokinetics of AN and its metabolite 2‐cyanoethylene oxide (CEO) in both rats and humans, was used to assess the dose‐response data in terms of an internal dose measure for the oral RfD values, but could not be used in deriving the inhalation RfC values. Benchmark dose (BMD) methods were used to derive all reference values. Where sufficient information was available, data‐derived uncertainty factors were applied to the points of departure determined by BMD methods. From this assessment, subchronic and chronic oral RfD values of 0.5 and 0.05 mg/kg/day, respectively, were derived. Similarly, subchronic and chronic inhalation RfC values of 0.1 and 0.06 mg/m³, respectively, were derived. Confidence in the reference values derived for AN was considered to be medium to high, based upon a consideration of the confidence in the key studies, the toxicity database, dosimetry, and dose‐response modeling.     

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.     

Dose intra-subject escalation to an event (DIETE): A new method for phase 1 dose-finding utilizing systematic intra-subject dose escalation with application to T-cell engagers

T-cell engagers are a class of oncology drugs which engage T-cells to initiate immune response against malignant cells. T-cell engagers have features that are unlike prior classes of oncology drugs (e.g., chemotherapies or targeted therapies), because (1) starting dose level often must be conservative due to immune-related side effects such as cytokine release syndrome (CRS); (2) dose level can usually be safely titrated higher as a result of subject's immune system adaptation after first exposure to lower dose; and (3) due to preventive management of CRS, these safety events rarely worsen to become dose limiting toxicities (DLTs). It is generally believed that for T-cell engagers the dose intensity of the starting dose and the peak dose intensity both correlate with improved efficacy. Existing dose finding methodologies are not designed to efficiently identify both the initial starting dose and peak dose intensity in a single trial. In this study, we propose a new trial design, dose intra-subject escalation to an event (DIETE) design, that can (1) estimate the maximum tolerated initial dose level (MTD1); and (2) incorporate systematic intra-subject dose-escalation to estimate the maximum tolerated dose level subsequent to adaptation induced by the initial dose level (MTD2) with a survival analysis approach. We compare our framework to similar methodologies and evaluate their key operating characteristics.     

A Probabilistic Approach to Assess External Doses to the Public Considering Spatial Variability of Radioactive Contamination and Interpopulation Differences in Behavior Pattern

Dose assessment is an important issue from the viewpoints of protecting people from radiation exposure and managing postaccident situations adequately. However, the radiation doses received by people cannot be determined with complete accuracy because of the uncertainties and the variability associated with any process of defining individual characteristics and in the dose assessment process itself. In this study, a dose assessment model was developed based on measurements and surveys of individual doses and relevant contributors (i.e., ambient dose rates and behavior patterns) in Fukushima City for four population groups: Fukushima City Office staff, Senior Citizens’ Club, Contractors’ Association, and Agricultural Cooperative. In addition, probabilistic assessments were performed for these population groups by considering the spatial variability of contamination and interpopulation differences resulting from behavior patterns. As a result of comparison with the actual measurements, the assessment results for participants from the Fukushima City Office agreed with the measured values, thereby validating the model and the approach. Although the assessment results obtained for the Senior Citizens’ Club and the Agricultural Cooperative differ partly from the measured values, by addressing further considerations in terms of dose reduction effects due to decontamination and the impact of additional exposure sources in agricultural fields, these results can be improved. By contrast, the measurements obtained for the participants from the Contractors’ Association were not reproduced well in the present study. To assess the doses to this group, further investigations of association members’ work activities and the related dose reduction effects are needed.     

Estimation of a Benchmark Dose in the Presence or Absence of Hormesis Using Posterior Averaging

U.S. Environment Protection Agency benchmark doses for dichotomous cancer responses are often estimated using a multistage model based on a monotonic dose‐response assumption. To account for model uncertainty in the estimation process, several model averaging methods have been proposed for risk assessment. In this article, we extend the usual parameter space in the multistage model for monotonicity to allow for the possibility of a hormetic dose‐response relationship. Bayesian model averaging is used to estimate the benchmark dose and to provide posterior probabilities for monotonicity versus hormesis. Simulation studies show that the newly proposed method provides robust point and interval estimation of a benchmark dose in the presence or absence of hormesis. We also apply the method to two data sets on carcinogenic response of rats to 2,3,7,8‐tetrachlorodibenzo‐p‐dioxin.     

Mesothelioma: Risk Apportionment Among Asbestos Exposure Sources

The mesothelioma epidemic in the United States, which peaked during the 2000–2004 period, can be traced to high‐level asbestos exposures experienced by males in occupational settings prior to the full recognition of the disease‐causing potential of asbestos and the establishment of enforceable asbestos exposure limits by the Occupational Safety and Health Administration (OSHA) in 1971. Many individuals diagnosed with mesothelioma where asbestos has been identified as a contributing cause of the disease have filed claims seeking compensation from asbestos settlement trusts or through the court system. An individual with mesothelioma typically has been exposed to asbestos in more than one setting and from more than one asbestos product. Apportioning risk for mesothelioma among contributing factors is an ongoing problem faced by occupational disease compensation boards, juries, parties responsible for paying damages, and currently by the U.S. Senate in its efforts to formulate a bill establishing an asbestos settlement trust. In this article we address the following question: If an individual with mesothelioma where asbestos has been identified as a contributing cause were to be compensated for his or her disease, how should that compensation be apportioned among those responsible for the asbestos exposures? For the purposes of apportionment, we assume that asbestos is the only cause of mesothelioma and that every asbestos exposure contributes, albeit differentially, to the risk. We use an extension of the mesothelioma risk model initially proposed in the early 1980s to quantify the contribution to risk of each exposure as a percentage of the total risk. The percentage for each specific discrete asbestos exposure depends on the start and end dates, the intensity, and the asbestos fiber type for the exposure. We provide justification for the use of the mesothelioma risk model for apportioning risk and discuss how to assess uncertainty associated with its application.     

Testing for Additivity at Select Mixture Groups of Interest Based on Statistical Equivalence Testing Methods

Several assumptions, defined and undefined, are used in the toxicity assessment of chemical mixtures. In scientific practice mixture components in the low-dose region, particularly subthreshold doses, are often assumed to behave additively (i.e., zero interaction) based on heuristic arguments. This assumption has important implications in the practice of risk assessment, but has not been experimentally tested. We have developed methodology to test for additivity in the sense of Berenbaum (Advances in Cancer Research, 1981), based on the statistical equivalence testing literature where the null hypothesis of interaction is rejected for the alternative hypothesis of additivity when data support the claim. The implication of this approach is that conclusions of additivity are made with a false positive rate controlled by the experimenter. The claim of additivity is based on prespecified additivity margins, which are chosen using expert biological judgment such that small deviations from additivity, which are not considered to be biologically important, are not statistically significant. This approach is in contrast to the usual hypothesis-testing framework that assumes additivity in the null hypothesis and rejects when there is significant evidence of interaction. In this scenario, failure to reject may be due to lack of statistical power making the claim of additivity problematic. The proposed method is illustrated in a mixture of five organophosphorus pesticides that were experimentally evaluated alone and at relevant mixing ratios. Motor activity was assessed in adult male rats following acute exposure. Four low-dose mixture groups were evaluated. Evidence of additivity is found in three of the four low-dose mixture groups. The proposed method tests for additivity of the whole mixture and does not take into account subset interactions (e.g., synergistic, antagonistic) that may have occurred and cancelled each other out.