Analysis of Quantitative High Throughput Screening Data

数千种广泛商业使用的化学品尚未测试对人类的不利影响，但存在于环境中。因此，需要改进用于体内毒性测试的化学品优先级，并且最终需要找到用于评估大量潜在有害物质的基于细胞的替代品。定量高通量筛选（qHTS）试验是多浓度实验，在国家毒理学计划的努力中发挥着重要作用，以应对这些测试挑战，并将毒理学从主要的观察性科学推进到主要的预测性科学。qHTS可以在一个广阔的化学空间内同时分析数千种化学物质，降低每种物质的成本。 先前用于从qHTS数据进行活动调用的方法是基于寻求最小化假阳性的制药应用，并且通常依赖于化学分析而不是统计测试来进行活动调用。因此，我们开发了一种三阶段算法，将来自qHTS数据的物质分类为与毒理学评价相关的统计学支持的活性类别，寻求提高灵敏度，同时最大限度地降低I类错误率（Shockley，2012）。我们的方法的第一阶段拟合四参数Hill方程，以找到在测试浓度范围内具有稳健浓度响应曲线的活性物质。稳健性标准规定，使用未加权和加权非线性最小二乘（NLS和WNLS）回归，响应曲线具有统计学显著性。NLS对所有数据点的权重相等，因此可能无法区分具有沿着两条渐近线的数据的轮廓和由单个点支持的轮廓。WNLS基于1/s2对每个响应点进行加权，其中s是根据包含感兴趣响应点的定义浓度范围内的所有响应数据估计的样本标准差，因此对具有相似响应水平的相邻数据点的影响大于具有非常不同响应的相邻数据点。第二阶段寻找在最低测试浓度下具有实质性活性的相对强效物质，即第一阶段未捕获的物质。第三阶段也是最后一阶段，将具有统计学意义的特征与缺乏统计学上令人信服的支持或不活跃的响应分开。该框架可容纳大量的qHTS数据，容忍丢失的数据，并且不需要重复测量。 我们通过广泛的模拟评估了这种三阶段分类算法（Shockley，2012）。使用受试者工作特征曲线下面积（AUC）评估性能。使用AUC统计，我们的算法优于整体F检验，比较了Hill方程与水平线（无响应）的拟合，当半最大响应浓度（AC 50）小于0.1微摩尔时。当AC 50大于0.001微摩尔时，它在检测已知活性物质方面也优于t检验方法。当响应在模拟测定的可检测区域（>阳性对照的25%）时，三阶段决策策略对于14点浓度-响应曲线产生良好（AUC>= 0.75）至高（AUC >= 0.9）性能。我们的方法能够检测相对有效的物质（例如，AC 50 = 0.001微摩尔），当检测响应至少为阳性对照响应的50%时，数据点少至4个。 上述三阶段算法基于希尔方程模型。然而，浓度-响应数据可能很复杂，并且在数据中找到不基于S形曲线拟合的替代模式可能更具信息性。我们目前正在开发的方法来找到复杂的模式，在qHTS数据的基础上，顺序限制推理的原则。多重假设检验用于比较所有搜索模式的显著性，并确定描述响应曲线的最适当模式。 由于非线性回归模型拟合qHTS实验中生成的数据得出的参数估计值存在很大的不确定性，因此通常不清楚如何为后续研究确定化学品的优先顺序。因此，我们还使用加权熵分数（WES）作为平均活性水平的度量，以便在qHTS实验中对化学品进行排名。WES评分可用于在没有预先指定的模型结构的情况下对测试库中的所有化学品进行排名，或者WES可用于通过对返回的“命中”进行排名来补充现有方法。WES的性能进行了评估，使用希尔模型模拟的数据。在qHTS研究的典型条件下，WES优于基于AC 50（半数最大反应的估计浓度）的排名。

Thousands of chemicals in wide commercial use have not been tested for adverse effects on humans, but are present in the environment. Accordingly, there is a need to improve chemical prioritization for in vivo toxicity testing and, ultimately, to find cell-based alternatives for evaluating the large inventory of potentially harmful substances. Quantitative high throughput screening (qHTS) assays are multiple-concentration experiments with an important role in the efforts of the National Toxicology Program to meet these testing challenges and advance toxicology from a predominantly observational science to a predominantly predictive science. qHTS can simultaneously assay thousands of chemicals over a wide chemical space with reduced cost per substance. Previous approaches for making activity calls from qHTS data were based on pharmaceutical applications seeking to minimize false positives and usually relied on heuristics rather than statistical tests to make activity calls. For that reason, we developed a three-stage algorithm to classify substances from qHTS data into statistically supported activity categories relevant to toxicological evaluation, seeking to improve sensitivity while minimizing Type I error rate (Shockley, 2012). The first stage of our approach fits a four-parameter Hill equation to find active substances with a robust concentration-response profile within the tested concentration range. The robust criterion specifies that response profiles are statistically significant using both unweighted and weighted non-linear least squares (NLS and WNLS) regression. NLS weights all data points equally and, consequently, may not discriminate between a profile with data along both asymptotes and a profile supported by a single point. WNLS weights each response point based on 1/s2, where s is the sample standard deviation estimated from all response data within a defined concentration range containing the response point of interest, so that more influence is given to neighboring data points with similar response levels than neighboring data points with very different responses. The second stage finds relatively potent substances with substantial activity at the lowest tested concentration, substances not captured in the first stage. The third and final stage separates statistically significant profiles from responses that lack statistically compelling support, or inactives. This framework accommodates large volumes of qHTS data, tolerates missing data, and does not require replicate measurements. We evaluated this three-stage classification algorithm via extensive simulations (Shockley, 2012). The area under receiver operating characteristic curves (AUC) was used to assess performance. Using AUC statistics, our algorithm outperformed overall F-tests comparing the fit of the Hill equation to a horizontal line (no response) when the concentration for half maximal response (AC50) was less than 0.1 micro molar. It also outperformed t-test approaches in detecting known actives when the AC50 was greater than 0.001 micro molar. The three-stage decision strategy yielded good (AUC >= 0.75) to high (AUC >= 0.9) performance for 14 point concentration-response curves when the response was in the detectable region of the simulated assay (>25% of the positive control). Our approach was able to detect relatively potent substances (e.g., AC50 = 0.001 micro molar) with as few as 4 data points when the tested response was at least 50% of the positive control response. The three-stage algorithm described above is based on the Hill equation model. However, concentration-response data can be complex and it may be more informative to find alternative patterns in the data not based on fits to sigmoidal curves. We are currently developing approaches to find complex patterns in qHTS data based on principles of order restricted inference. Multiple hypothesis testing is used in order to compare the significance of all searched patterns and identify the most appropriate pattern describing a response profile. It is often unclear how to prioritize chemicals for follow-up studies due to the large uncertainties that accompany parameter estimates derived from nonlinear regression model fits to data generated in qHTS experiments. Therefore, we have also used a weighted entropy score (WES) as a measure of average activity level in order to rank chemical in qHTS experiments. WES scores can be used to rank all chemicals in a tested library without a pre-specified model structure, or WES can be used to complement existing approaches by ranking returned "hits". The performance of WES has been evaluated using data simulated from a Hill model. WES outperforms rankings based on AC50 (estimated concentration of half-maximal response) across the full range of conditions that are typical of qHTS studies.