Sinha Samiran, Mukherjee Bhramar, Ghosh Malay
Department of Statistics, University of Florida, Gainesville, Florida 32611, USA.
Biometrics. 2004 Mar;60(1):41-9. doi: 10.1111/j.0006-341X.2004.00169.x.
We present a Bayesian approach to analyze matched "case-control" data with multiple disease states. The probability of disease development is described by a multinomial logistic regression model. The exposure distribution depends on the disease state and could vary across strata. In such a model, the number of stratum effect parameters grows in direct proportion to the sample size leading to inconsistent MLEs for the parameters of interest even when one uses a retrospective conditional likelihood. We adopt a semiparametric Bayesian framework instead, assuming a Dirichlet process prior with a mixing normal distribution on the distribution of the stratum effects. We also account for possible missingness in the exposure variable in our model. The actual estimation is carried out through a Markov chain Monte Carlo numerical integration scheme. The proposed methodology is illustrated through simulation and an example of a matched study on low birth weight of newborns (Hosmer, D. A. and Lemeshow, S., 2000, Applied Logistic Regression) with two possible disease groups matched with a control group.
我们提出一种贝叶斯方法，用于分析具有多种疾病状态的匹配“病例对照”数据。疾病发展的概率由多项逻辑回归模型描述。暴露分布取决于疾病状态，并且可能在不同分层中有所变化。在这样的模型中，分层效应参数的数量与样本量成正比增长，即使使用回顾性条件似然，也会导致感兴趣参数的极大似然估计不一致。相反，我们采用半参数贝叶斯框架，假设在分层效应分布上具有混合正态分布的狄利克雷过程先验。我们还在模型中考虑了暴露变量可能存在的缺失情况。实际估计通过马尔可夫链蒙特卡罗数值积分方案进行。通过模拟以及对新生儿低出生体重进行匹配研究的一个示例（Hosmer, D. A. 和 Lemeshow, S., 2000,《应用逻辑回归》）来说明所提出的方法，该示例中有两个可能的疾病组与一个对照组进行匹配。
