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| 合理进行均值比较——泊松分布回归模型 |
| Reasonably carry out mean value comparison： Poisson distribution regression models |
| 投稿时间：2023-03-03 修订日期：2023-03-03 |
| DOI：10.11886/scjsws20230201003 |
| 中文关键词: 泊松分布回归模型 偏移量 标准化死亡比 偏差信息准则 最高后验密度区间 |
| 英文关键词:Poisson distribution regression model Offset Standardized mortality ratio Deviation information criterion Highest posterior density interval |
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| 中文摘要: |
| 本文目的是介绍与泊松分布回归模型有关的6个基本概念、计算方法、一个临床调查实例及其SAS实现。基本概念包括泊松分布、泊松分布回归模型、偏移量、标准化死亡比（SMR）、偏差信息准则和最高后验密度区间。计算方法涉及泊松分布回归参数的经典估算方法和贝叶斯估算方法。临床调查实例涉及1975年-1980年苏格兰56个县的唇癌观察和预期病例的数据。本文给出了采用SAS处理实例中计数资料的全过程，包括基于bglimm过程构建5个泊松分布回归模型和展示预测的SMR与观测的SMR之间的吻合程度。对输出结果作出了解释，并基于模型拟合效果评价统计量，对所构建的多个泊松分布回归模型进行比较，得出了适合本文资料的最优泊松分布回归模型。 |
| 英文摘要: |
| The purpose of this paper was to introduce 6 basic concepts， calculation methods， a clinical investigation example and its SAS implementation related to the Poisson distribution regression model. The basic concepts included the Poisson distribution， Poisson distribution regression models， offsets， standardized mortality ratio （SMR）， deviation information criteria and the highest posterior density intervals. The calculation method involved the classical estimation method and the Bayesian estimation method of the Poisson distribution regression parameters. The clinical investigation example involved the data on observed and expected cases of lip cancer in 56 Scottish counties from 1975 to 1980. This article presented the whole process of using SAS software to deal with the count data in the example， including constructing five Poisson distribution regression models based on the bglimm procedure and showing the degree of agreement between the predicted SMR and the observed SMR. The output results were explained， and based on the evaluation statistics of the model fitting effect， the multiple constructed Poisson distribution regression models were compared， and finally the optimal Poisson distribution regression model suitable for the data in the paper was obtained. |
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