New Methods to reduce Bias and Mean Square Error of Maximum Likelihood Estimators

描述（由申请人提供）：分类结果在生物医学研究中无处不在，广义线性模型（GLMs）代表了最广泛应用的方法，用于测试分类变量和固定调查因素之间的关联。特别是逻辑回归是最常用的二进制数据模型，在健康、行为和物理科学中具有广泛的适用性。King和Ryan（2002）指出，在1999年发表的研究论文中，有2770篇论文的标题或关键词中出现了“逻辑回归”。King和Zeng（2001）将最大似然法在逻辑回归中的使用称为“几乎通用的方法”。逻辑回归的最大似然估计（MLE）基于大样本近似，对于大样本问题和响应比例不太小或太大的问题是可靠的。然而，多年来人们已经知道，对于小的、稀疏的或不平衡的数据集，MLE是不可靠的，后者指的是响应变量的0和1的数量之间的相当大的差异。最近的研究提出了一种灵活的方法来纠正最大似然偏差并提高性能，使用基于惩罚似然的方法，但基本理论尚未完全应用于实际使用。在本项目中，我们将扩展第一阶段开始的工作，采用逻辑回归(1)对各种其他GLM（包括泊松、多项、负二项和审查生存数据）实施偏差校正方法；(2)提供新的诊断程序，以识别具有近可分离性和MLE偏差的潜在问题；(3)实现并评估一种用于逻辑回归偏倚校正的精确目标估计方法；(4)改进目标1-3所需的计算算法；考虑到分类回归在公共卫生和生物医学研究中的普遍存在，这一努力的最终结果将在分析标准大样本方法不可靠和小样本精确方法不可行的数据时提供关键的中间替代方案。

DESCRIPTION (provided by applicant): Categorical outcomes are ubiquitous in biomedical research, and generalized linear models (GLMs) represent the most widely applied methodology for testing associations between categorical variables and fixed investigative factors. Logistic regression in particular is the most frequently used model for binary data and has widespread applicability in the health, behavioral, and physical sciences. King and Ryan (2002) stated that there were 2,770 research papers published in 1999 in which "logistic regression" was in the title of the paper or among the keywords. King and Zeng (2001) referred to the use of the maximum likelihood method in logistic regression as "the nearly universal method". Maximum likelihood estimates (MLE) for logistic regression are based on large sample approximations that are reliable for problems with large samples and when the proportion of responses is not too small or too large. However, it has been known for several years that MLE are not reliable for small, sparse or unbalanced datasets, with the latter referring to a considerable difference between the number of zeros and ones of the response variable. Recent research has suggested a flexible means of correcting MLE bias and improving performance using a penalized likelihood-based approach, but the underlying theory has not been fully applied and implemented for practical use. In this project, we will extend the work begun during Phase 1 with logistic regression by (1) implementing the bias correction approach for a variety of other GLM's that include Poisson, multinomial, negative binomial, and censored survival data; (2) provide new diagnostic procedures that identify potential problems with near separability and MLE bias; (3) implement and evaluate an exact target estimation approach for bias correction in logistic regression; (4) improve the computational algorithms required for Aims 1-3; and (5) additionally implement the procedures in a SAS PROC. Given the ubiquity of categorical regression in public health and biomedical research, the final product of this effort will provide a critical intermediate alternative when analyzing data for which standard large-sample methods are unreliable and small-sample exact methods are infeasible.