Markov Chain Monte Carlo and Exact Logistic Regression

描述（由申请人提供）：今天，用于将逻辑回归模型拟合到二进制数据的软件属于每个专业生物统计学家，流行病学家和社会科学家的工具包。这一发展的自然后续是主流生物统计学家和数据分析师在任何基于大样本最大似然理论的统计分析的准确性受到怀疑的情况下采用精确逻辑回归。生物计量学和许多其他领域的前沿研究人员已经认识到，有必要对基于大样本方法的推断进行补充，对小样本、稀疏和不平衡数据进行精确推断。Cytel软件公司开发的LogXact软件包满足了这一需求。自1993年成立以来，它一直用于对临床试验、流行病学、疾病监测、保险、犯罪学、金融、会计、社会学和生态学等广泛领域产生的数据进行精确推断。在所有这些应用中都采用了精确逻辑回归，因为研究者事先清楚地认识到相应渐近过程的局限性，并且精确推理在计算上是可行的。但大多数情况下，渐近方法和精确方法是否适用并不明显。理想情况下，如果对渐近推理的适当性有任何疑问，人们更愿意运行两种类型的分析。然而，由于精确算法的计算限制，研究人员目前无法尝试精确分析。计算需要多长时间，甚至在计算机内存耗尽之前是否会产生任何结果，都是不确定的。目前的项目通过引入新一代利用基于网络的蒙特卡罗拒绝抽样的数值算法来消除这种不确定性。第一阶段的进度报告已经证明，这些新算法可以将计算速度提高50到1000倍，相对于目前在LogXact中可用的算法。更重要的是，它们可以预测工作需要多长时间，这样用户就可以决定是立即进行还是在更好的时间进行。第二阶段的工作旨在将新一代的计算算法整合到LogXact的未来版本中。

DESCRIPTION (provided by applicant): Today, software for fitting logistic regression models to binary data belongs in the toolkit of every professional biostatistician, epidemiologist, and social scientist. A natural follow-up to this development is the adoption of exact logistic regression by mainstream biostatisticians and data analysts for any setting in which the accuracy of a statistical analysis based on large-sample maximum likelihood theory is in doubt. Cutting-edge researchers in biometry and numerous other fields have already recognized that it is necessary to supplement inference based on large-sample methods with exact inference for small, sparse and unbalanced data. The LogXact software package developed by Cytel Software Corporation fills this need. It has been used since its inception in 1993 to produce exact inferences for data generated from a wide range fields including clinical trials, epidemiology, disease surveillance, insurance, criminology, finance, accounting, sociology and ecology. In all these applications exact logistic regression was adopted because the limitations of the corresponding asymptotic procedures were clearly recognized in advance by the investigators and the exact inference was computationally feasible. But most of the time it will not be obvious whether asymptotic or exact methods are applicable. Ideally one would prefer to run both types of analyses if there is any doubt about the appropriateness of the asymptotic inference. However, because of the computational limits of the exact algorithms, investigators are currently inhibited from attempting the exact analysis. There is uncertainty about the how long the computations will take and even whether they will produce any results at all before the computer runs out of memory. The current project eliminates this uncertainty by introducing a new generation of numerical algorithms that utilize network based Monte Carlo rejection sampling. The Phase 1 progress report has demonstrated that these new algorithms can speed up the computations by factors of 50 to 1000 relative to what is currently available in LogXact. More importantly they can predict how long a job will take so that the user may decide whether to proceed at once or at a better time. The Phase 2 effort aims to incorporate this new generation of computing algorithms into future versions of LogXact.