AI 中文总结
针对医学研究中多分类结局相关性被忽略的问题，提出带ANOVA分解的多变量多项Logit模型，结合MM算法与桥惩罚项实现高效估计和变量选择，经模拟及AURORA数据验证有效。
AI 中文摘要
在医学研究中，患者常存在多个相互关联的结局，如创伤幸存者的创伤后应激障碍（PTSD）、抑郁症和疼痛。多数现有研究采用多项回归分别分析这些关联结局，忽略了并发病症间的相关性，这种遗漏可能导致信息丢失和预测精度降低。考虑多个分类结局间的相关性需要高维参数空间，使模型估计颇具挑战。本文提出一种多变量多项Logit模型，可捕捉结局间的相关性，并利用参数空间的ANOVA分解减少参数数量。ANOVA分解支持显式条件模型公式，使模型估计的复合似然计算大幅简化。我们开发了一种高效的Minorization-Maximization（MM）算法来最大化复合似然，该算法还通过桥惩罚项实现变量选择。通过模拟研究评估了所提方法，结果表明其在参数估计和变量选择方面具有准确性，我们进一步使用AURORA研究的数据对该方法进行了实例验证。
英文摘要
In medical research, patients often have multiple interdependent outcomes, such as posttraumatic stress disorder (PTSD), depression, and pain among trauma survivors. Most existing research uses multinomial regression to analyze these interdependent outcomes separately, which ignores correlations between concurrent conditions. This omission may lead to loss of information and reduced predictive accuracy. Accounting for correlations between multiple categorical outcomes requires a high-dimensional parameter space, making model estimation challenging. In this paper, we propose a multivariate multinomial logit model that captures outcome correlations and uses the ANOVA decomposition of the parameter space to reduce the number of parameters. The ANOVA decomposition enables explicit conditional model formulations, which allow for a computationally much simpler composite likelihood for model estimation. We develop an efficient Minorization-Maximization (MM) algorithm to maximize the composite likelihood, which also incorporates variable selection via a bridge penalty. Simulation studies are conducted to evaluate our method, demonstrating its accuracy in parameter estimation and variable selection. We further illustrate our method using data from the AURORA study.
