Statistical Methods for Multi-Chemical Toxicity Studies

多种化学品毒性研究的统计方法

基本信息

批准号：
8336654
负责人：
Gregg Dinse
金额：
$ 19.52万
依托单位：
NATIONAL INSTITUTE OF ENVIRONMENTAL HEALTH SCIENCES
依托单位国家：
美国
项目类别：
财政年份：
资助国家：
美国
起止时间：
至
项目状态：
未结题

项目摘要

Over the past year, the majority of my research on this project was performed in four areas: (1) fitting a Hill model to dose-response data, (2) identifying situations in which Hill model parameters cannot be uniquely estimated, (3) generalizing the concept of relative potency, and (4) developing statistical methods for making inferences about generalized relative potency functions. These four areas of research are described in more detail below. Area 1: The Hill model is a popular nonlinear model often used to characterize dose-response data from toxicity studies. When the response data are binary, the Hill model corresponds to a 4-parameter logistic model. Compared to the usual 2-parameter logistic model, the Hill model allows the dose-response curve to have a lower limit that is greater than zero and an upper limit that is less than one. Thus, we can envision a scenario with three categories of subjects: those who will always respond regardless of dose (which leads to a lower limit above zero), those who will never respond regardless of dose (which leads to an upper limit below one), and those whose risk of response is a function of dose. We can postulate a missing data problem, where subjects were observed to respond or not, but we do not know which responders were "destined" to respond, nor do we know which non-responders were "unsusceptible" to response. We developed an EM algorithm to solve this missing data problem, which provides maximum likelihood estimates of the parameters in a Hill model for binary response. The EM algorithm is easy to program, covariates are simple to incorporate, and certain natural constraints are satisfied automatically. In ongoing research, we are investigating a similar approach for continuous dose-response data. We are again implementing an EM algorithm, but the analogy with responders who were "destined" to respond and non-responders who were "unsusceptible" to response no longer applies. In the continuous response situation, we envision two latent variables that are normally distributed and the sum of which equals the observed response. The mean of the first latent variable is a constant that corresponds to the lower limit of mean response. The mean of the second latent variable is the product of a dose-dependent probability and a constant that corresponds to the difference between the upper and lower limits of mean response. An EM algorithm can be used to estimate the parameters in this latent-variable model, which correspond to the parameters in a Hill model for continuous dose-response data. An article about the EM algorithm for binary dose-response data was published in the Journal of Agricultural, Biological, and Environmental Statistics. I also gave a talk about this research at the Joint Statistical Meetings of the American Statistical Association and the International Biometrics Society in Miami on March 22, 2011. Area 2: In related research, we are studying ways to determine the number of uniquely estimable parameters when a Hill model is fitted to binary data. It is well known that there are identifiability problems if all or none of the subjects respond. Similar problems arise if all subjects receiving a dose below a certain level do not respond and all subjects receiving a higher dose do respond. On the other hand, if there are several observed response rates and they tend to be ordered with respect to dose, then typically the Hill model parameters are uniquely estimable. For intermediate cases, however, the number of uniquely estimable parameters appears to be related to the number of distinct nonparametric estimates obtained under a monotonicity constraint on the dose-response curve (i.e., the number of level sets in a nonparametric isotonic regression analysis). Area 3: Relative potency plays an important role in toxicology. Estimates of relative potency are used to rank chemicals by their effects, to calculate equivalent doses of test chemicals compared to a standard, and to weight contributions of constituent chemicals when evaluating mixtures. Within a class of chemicals having "similar" dose-response curves, the relative potency of one chemical compared to another is the ratio of doses producing the same toxicity response, and this ratio is constant across all levels of response. If the dose-response curves are non-similar, however, relative potency need not be constant and typically varies according to where along the dose-response curves the dose ratio is calculated. In practice, relative potency is usually characterized by a constant dilution factor, even when non-similar dose-response curves indicate that constancy is inappropriate. Improperly regarding relative potency as constant may distort conclusions and potentially mislead investigators or policymakers. We developed a more general approach that allows relative potency to vary as a function of the dose of either chemical, the level of a specific response, or the percentage of the range of possible response levels. Distinct functions can be defined, each generalizing different but equivalent descriptions of constant relative potency. These relative potency functions are constructed from dose-response curves for test and reference chemicals, and they all provide fundamentally equivalent information if the chemicals have the same lower and upper limits of response. In fact, if two chemicals differ only with respect to their ED50s (i.e., their dose-response curves are similar), then all of the relative potency functions are constant and equal to the ratio of the ED50s. Otherwise, if the response limits differ, relative potency as a function of the response-range percentage is distinct from the other functions and embodies a modified definition of relative potency. Non-constant relative potency functions may cross the baseline value of 1.0, indicating that one chemical is more potent than another for some doses, responses, or response-range percentages and vice versa for others. If chemicals have non-similar dose-response curves, then inferences based on ratios of ED50s or based on models that force the other parameters to be identical can be misleading. Thus, we propose the use of relative potency functions, where the preferred function depends on the application (e.g., chemical ranking or dose conversion) and whether one views differences in response limits as intrinsic to the chemicals or as extrinsic, arising from idiosyncrasies of data sources. Relative potency functions offer a unified and principled description of relative potency for non-similar dose-response curves. We published an article about our generalized concept of relative potency in Regulatory Toxicology and Pharmacology. Also, I am scheduled to give an invited talk about this research at the Conference on Risk Assessment and Evaluation of Predictions to be held in the Washington DC area on October 12-14, 2011. Area 4: In ongoing research, we are working on formal statistical methods for analyzing relative potency functions. First, we will describe techniques for estimating parameters in the underlying dose-response models (e.g., Hill models), assessing model adequacy, quantifying variability of parameter estimates, constructing confidence intervals for model parameters, and testing hypotheses about model parameters. Then, based on specific models for the dose-response curves, we will develop procedures for making inferences about the resulting relative potency functions and any summaries obtained from these functions. These procedures will deal with function estimation, variance estimation, construction of pointwise confidence intervals and simultaneous confidence bands, and testing of hypotheses.

在过去的一年中，我对该项目的大部分研究是在四个领域进行的：（1）将山坡模型拟合到剂量反应数据中，（2）识别无法唯一估计的山丘模型参数的情况，（3）概括相对效能的概念，以及（4）开发有关涉及广义相对效力的统计方法的统计方法。这四个研究领域将在下面更详细地描述。区域1：山丘模型是一种流行的非线性模型，通常用于表征毒性研究中的剂量反应数据。当响应数据为二进制时，山坡模型对应于4参数逻辑模型。与通常的2参数逻辑模型相比，山坡模型允许剂量响应曲线的下限大于零，并且上限小于一个。因此，我们可以设想一个具有三类主题的场景：那些总是会反应的人，无论剂量如何（导致下限高于零的下限），无论剂量什么都不会反应的人（这会导致上限的上限），而那些反应风险的人则是剂量的函数。我们可以假设一个缺失的数据问题，其中观察到受试者是否有响应，但我们不知道哪些响应者是“注定”以响应的，也不知道哪些非反应者对响应“不舒服”。我们开发了一种EM算法来解决此缺失的数据问题，该算法为二进制响应的山丘模型中的参数提供了最大的似然估计。 EM算法易于编程，协变量易于合并，并且某些自然约束会自动满足。在正在进行的研究中，我们正在研究连续剂量反应数据的类似方法。我们再次实施了EM算法，但是与“注定”响应的响应者和不再适用响应“不舒服”的无反应者的反应者的类比。在连续的响应情况下，我们设想两个正态分布的潜在变量，其总和等于观察到的响应。第一个潜在变量的平均值是一个常数，对应于平均响应的下限。第二个潜在变量的平均值是剂量依赖性概率的乘积，而常数对应于平均响应的上和下限之间的差异。 EM算法可用于估计该潜伏模型中的参数，该参数与连续剂量反应数据的山山模型中的参数相对应。关于二进制剂量响应数据的EM算法的文章发表在《农业，生物学和环境统计》杂志上。我还在2011年3月22日在美国统计协会和迈阿密国际生物识别学会的联合统计会议上发表了一项研究。区域2：在相关研究中，我们正在研究确定丘陵模型拟合到二元数据时确定可估计参数数量的方法。众所周知，如果所有受试者都反应，存在可识别性问题。如果所有接受剂量以下剂量以下的受试者没有反应，并且所有接受较高剂量的受试者都会做出反应，则会出现类似的问题。另一方面，如果有几个观察到的响应率，并且倾向于对剂量进行排序，则通常可以唯一估计山丘模型参数。但是，对于中间情况，可唯一估计的参数的数量似乎与在剂量反应曲线上单调性约束下获得的不同非参数估计的数量有关（即，非参数同位素回归分析中的水平集数量）。区域3：相对效力在毒理学中起重要作用。相对效力的估计值用于通过其作用对化学品进行对，以计算与标准品相比的等效剂量的测试化学物质，以及评估混合物时组成化学物质的权重贡献。在具有“相似”剂量反应曲线的化学物质中，与另一种化学物相比，一种化学物质的相对效力是产生相同毒性反应的剂量的比率，并且在所有水平的响应中，该比率均保持恒定。但是，如果剂量反应曲线是非相似的，则相对效力不必恒定，并且通常根据沿剂量反应曲线的位置而变化，则计算剂量比。实际上，即使非相似剂量反应曲线表明恒定性不合适，相对效力通常以恒定稀释因子为特征。关于恒定的相对效力不当可能会扭曲结论，并可能误导研究人员或决策者。我们开发了一种更通用的方法，该方法允许相对效力随着化学剂量的函数而变化，特定响应水平或可能响应水平的范围的百分比。可以定义不同的功能，每个功能都概括了恒定相对效力的不同但等效的描述。这些相对效力函数是由用于测试和参考化学物质的剂量响应曲线构建的，如果化学物质具有相同的下层和上限响应，它们都提供了等效的信息。实际上，如果两种化学物质仅在其ED50上有所不同（即它们的剂量反应曲线相似），则所有相对效力函数均恒定并且等于ED50的比率。否则，如果响应限制差异，则相对效力与响应范围百分比的函数不同于其他功能，并体现了对相对效力的修改定义。非恒定相对效力函数可能会超过1.0的基线值，这表明一种化学物质比另一种化学物质对某些剂量，响应或响应范围的百分比更有效，反之亦然。如果化学物质具有非相似剂量反应曲线，则基于ED50的比率或基于迫使其他参数相同的模型的推论可能会误导。因此，我们提出了相对效力函数的使用，其中首选函数取决于应用（例如化学排名或剂量转换），以及一个人认为响应限制的差异是化学物质固有的还是外在的，是由数据源的特质引起的。相对效能功能提供了对非相似剂量响应曲线相对效力的统一和原则描述。我们发表了一篇有关我们在监管毒理学和药理学方面相对效力的广义概念的文章。另外，我计划在2011年10月12日至14日在华盛顿特区地区举行的风险评估和预测评估会议上发表有关这项研究的邀请。区域4：在正在进行的研究中，我们正在研究用于分析相对效力功能的形式统计方法。首先，我们将描述用于估算基础剂量响应模型（例如山丘模型）中参数的技术，评估模型是否足够，量化参数估计值的可变性，为模型参数构建置信区间以及对模型参数的测试假设。然后，基于剂量响应曲线的特定模型，我们将开发有关推断产生的相对效力函数以及从这些功能获得的任何摘要的过程。这些过程将处理功能估计，方差估计，置换置信区间的构建和同时置信频段以及假设的测试。