CONDITIONAL LOGISTIC, POLYTOMOUS AND POISSON REGRESSION

二元Logistic回归及其在无序多裂中的推广 反应、有序多分支反应和泊松反应属于 流行病学家武器库中最强大的工具或应用 分析离散生物医学数据的生物统计学家。通常的方法是 对这类模型的推断是无条件最大似然的。对于大型 平衡良好的数据集，或者对于只有几个参数的数据， 方法是令人满意的。然而，无条件的最大似然 估计可能会产生不一致的点估计、不准确的p值 对于小的或不平衡的数据集，不准确的置信度区间，以及 对于具有大量参数的数据集 观察。有时，这种方法完全失败，因为没有任何估计。 找到了使无条件似然函数最大化的方法。一个 方法论上合理的替代方法，不具备上述任何一项 缺点是有条件的方法。在这里，人们只估计 感兴趣的参数，从可能性中消除其他参数 通过他们充分的统计数据来发挥作用。方法是 服从精确的和渐近的推理。因此，它产生了 无论数据多小或多不平衡，都能做出可靠的推论。虽然 条件推理的理论基础从 R.A.Fisher的时间，进行条件推理的数值算法 在计算上是可行的，只是在过去五年里才开发出来的。 它们发表在应用程序通常不会阅读的技术期刊上 生物统计学家和流行病学家。基于这些新功能的软件 条件方法稀缺、昂贵且难以开发。那里 是对好的教育材料和伴随的公共领域的需求 推广条件Logistic回归方法的软件和 它的延伸。如果没有这些材料，这些方法将继续存在 只有学术上的重要性，因为它们将不会被 大多数统计学家和流行病学家。在这项建议下， 二进制和分类数据的条件推理的现代方法 将提供给一般的统计和流行病学研究人员 以三种方式建立社区：编写一本详细的工作手册 适合自学或课堂教学；通过发展 工作手册附带的公共领域软件；通过写作 关于这一主题的说明性论文，并以应用的形式出版 而不是理论期刊。

Binary logistic regression and its extensions to unordered polytomous response, ordered polytomous response, and Poisson response are among the most powerful tools in the arsenal of the epidemiologist or applied biostatistician analyzing discrete biomedical data. The usual method of inference for such models is unconditional maximum likelihood. For large well balanced data sets or for data with only a few parameters this approach is satisfactory. However unconditional maximum likelihood estimation can produce inconsistent point estimates, inaccurate p-values and inaccurate confidence intervals for small or imbalanced data sets, and for data sets with a large number of parameters relative to the number of observations. Sometimes the method fails entirely as no estimates can be found which maximize the unconditional likelihood function. A methodologically sound alternative approach which has none of the above drawbacks is the conditional approach. Here one only estimates the parameters of interest, eliminating the others from the likelihood function by conditioning on their sufficient statistics. The method is amenable to both exact and asymptotic inference. Hence it produces reliable inferences no matter how small or imbalanced the data. Although the theoretical basis for conditional inference has been established since the time of R.A.Fisher, numerical algorithms making conditional inference computationally feasible have been developed only in the past five years. They are published in technical journals not normally read by applied biostatisticians and epidemiologists. Software based on these new conditional methods is scarce, expensive, and difficult to develop. There is a need for good educational materials and accompanying public domain software to popularize the conditional approach to logistic regression and its extensions. Without these materials the methods will remain of academic importance only, since they will not be accessible to the majority of statisticians and epidemiologists. Under this proposal, the modern methods of conditional inference for binary and categorical data would be made accessible to the general statistical and epidemiological communities in three ways: through the preparation of a detailed work-book suitable for self-study or classroom instruction; through the development of public domain software to accompany the work-book; through the writing of expository papers on the subject, and publishing them in applied rather than theoretical journals.