Robust Classification Methods for Categorical Regression

描述(由申请人提供)：改进统计方法，为分类回归提供更好的分类性能和新的分析能力，对医学和卫生保健研究界将是无价的。分类回归模型(例如，二元逻辑、多项逻辑)被广泛用于识别酒精相关症状的模式、筛查障碍和评估政策。此外，此类模型还广泛应用于其他研究领域，如精神疾病、癌症、创伤和艾滋病相关病理学。然而，许多这样的模型在开发时没有足够的支持来充分分析和利用其结果的内在概率性质。这一点至关重要，因为卫生研究人员、临床医生和管理人员经常面临使用分类回归模型的分类决策，以确定不可接受的风险、适当的结果和可接受的筛查、诊断、治疗和护理质量指南。在存在模型错误指定、缺失协变量和不可忽略的缺失数据生成过程的情况下，商业上可用的统计软件不提供用于稳健估计后验概率的复杂方法。这种稳健的缺失数据处理方法提供了处理验证偏差和对具有复杂抽样设计的相关、纵向或调查数据进行建模的自然机制。此外，商业上可用的统计软件不提供使用估计的后验概率来针对不同的最优标准做出最优分类决策的自动化方法。具体而言，诸如折衷特异度与敏感度的多个决策标准(分配规则)、决策阈值可信区间、用于评估后验概率的正确规格的统计测试、用于比较竞争分类器阈值的统计测试以及用于多结果分类和推断的方法等自动化特征并不容易获得。第二阶段研究将扩展二元Logistic回归的第一阶段研究结果，以开发和实现用于多项Logistic回归建模的自动稳健分类方法，该方法也适用于输出后验概率的更大类别的非线性分类回归模型。第二阶段的软件原型将提供：1)新的用户可选择的稳健判决阈值估计器，2)判决阈值估计器的稳健可信区间，3)新的分类器阈值比较测试，4)新的结果概率规范测试，5)在存在不可忽略的无响应数据的情况下的有效缺失数据处理方法，以及6)用于改进小样本和罕见事件结果概率估计的二阶解析和基于模拟的贝叶斯方法。这些新方法将被整合到一个用户友好的原型软件包中，通过广泛的模拟研究进行评估，然后通过与相关领域的专家合作，将这些方法应用于在以下领域遇到的现实世界分类问题：酒精、精神疾病(抑郁症、躁郁症、精神分裂症)、癌症(前列腺癌)、创伤(急诊室)和传染病(艾滋病)。总之，第二阶段的研究将为第三阶段的商业化奠定必要的技术基础，目标是提供一套新的分类分析方法，作为改进流行病学、临床和公共卫生研究的先进统计工具。

DESCRIPTION (provided by applicant): Improving statistical methods to provide better classification performance and new analytical capabilities for categorical regression would be invaluable to the medical and health care research communities. Categorical regression models (e.g., binary logistic, multinomial logistic) are used extensively to identify patterns of alcohol-related symptoms, screen for disorders, and assess policies. In addition, such models are used extensively in other areas of research such as mental illness, cancer, traumatic injuries, and AIDS-related pathologies. However, many such models are developed with inadequate support to fully analyze and exploit the intrinsically probabilistic nature of their results. This is of critical importance as health researchers, clinicians, and administrators are often faced with classification decisions using categorical regression models to identify unacceptable risks, adequate outcomes, and acceptable guidelines for screening, diagnoses, treatment, and quality of care. Commercially available statistical software does not offer sophisticated methods for robust estimation of posterior probabilities in the presence of model misspecification, missing covariates, and nonignorable missing data generating processes. Such robust missing data handling methods provide natural mechanisms for dealing with verification bias and modeling correlated, longitudinal, or survey data with complex sampling designs. Moreover, commercially available statistical software does not provide automated methods for using estimated posterior probabilities to make optimal classification decisions with respect to different optimality criteria. In particular, automated features such as optimizing multiple decision criteria (allocation rules) that trade off specificity against sensitivity, decision threshold confidence intervals, statistical tests for evaluating correct specification of posterior probabilities, statistical tests for comparing competing classifier thresholds, and methods for multi-outcome classification and inference are not readily available. Phase II research will extend Phase I findings for binary logistic regression to develop and implement automated robust classification methods for multinomial logistic regression modeling, which also applies to the larger class of nonlinear categorical regression models that output posterior probabilities. The Phase II software prototype will provide: 1) new user-selectable robust decision threshold estimators, 2) robust confidence intervals on decision threshold estimators, 3) new classifier threshold comparison tests, 4) new outcome probability specification tests, 5) efficient missing data handling methods in the presence of nonignorable nonresponse data, and 6) second-order analytic and simulation-based Bayesian methods for improved small sample and rare event outcome probability estimation. These new methodologies will be integrated into a prototype user-friendly software package, evaluated with extensive simulation studies, and then applied to real world classification problems encountered in: alcohol, mental illness (depression, bipolar, schizophrenia), cancer (prostate), trauma (emergency room), and infectious disease (AIDS) through collaborations with domain experts in those respective fields. In summary, Phase II research will establish the essential technical foundation for Phase III commercialization with the objective of providing a suite of new classification analysis methods as an advanced statistical tool that improves epidemiologic, clinical, and public health research.