本文初步讨论了贝叶斯框架下的逻辑回归模型及其应用。贝叶斯方法结合样本信息和先验信息，通过后验分布估计参数，通常取后验分布的期望作为参数的贝叶斯估计。MCMC算法可以从任意分布上采样，用采样出来的数据均值作为对该分布期望的估计。因此可以使用MCMC算法计算参数的贝叶斯估计。对乳腺癌数据进行实证研究，建立乳腺癌生存率预测模型，使用MCMC算法拟合模型并监测收敛性，结果表明生成的马尔科夫链是收敛的。模型结果表明手术时患者年龄、检测到的阳性腋下淋巴结数与患者5年内存活概率呈负相关，手术年份与患者5年内存活概率呈正相关；阳性腋下淋巴结数的多少对患者5年内是否存活的影响最大，其次为患者年龄，影响最小的是手术年份。模型参数也具有解释性。本研究为基于MCMC算法的逻辑回归模型在医学方面的应用提供了参考和借鉴价值。

This paper preliminarily discusses logistic regression models under Bayesian frameworks and their applications. Bayesian method combines sample information and prior information, estimates parameters by posterior distribution, and usually takes the expectation of posterior distribution as Bayesian estimation of parameters. The MCMC algorithm can sample from any distribution and use the mean of the sampled data as an estimate of the expected distribution. Bayesian estimates of parameters can therefore be calculated using the MCMC algorithm. Empirical research on breast cancer data, a breast cancer survival prediction model was established, and the MCMC algorithm was used to fit the model and monitor convergence, and the results showed that the generated Markov chain converged. The model results showed that the age of the patient at the time of surgery and the number of positive axillary lymph nodes detected were inversely correlated with the probability of survival within 5 years, and the year of surgery was positively correlated with the probability of survival within 5 years. The number of positive axillary lymph nodes had the greatest impact on whether the patient survived within 5 years, followed by the patient's age, and the year of surgery had the least impact. Model parameters are also interpretive. This study provides reference and reference value for the application of logistic regression model based on MCMC algorithm in medicine.