Some biomedical studies lead to mixture data. When a discrete covariate defining subgroup membership is missing for some of the subjects in a study, the distribution of the outcome follows a mixture distribution of the subgroup-specific distributions. Taking into account the uncertain distribution of the group membership and the covariates, we model the relation between the disease onset time and the covariates through transformation models in each sub-population, and develop a nonparametric maximum likelihood based estimation implemented through EM algorithm along with its inference procedure. We further propose methods to identify the covariates that have different effects or common effects in distinct populations, which enables parsimonious modeling and better understanding of the difference across populations. The methods are illustrated through extensive simulation studies and a real data example.

中文翻译：

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在缺少亚组标识符的情况下通过转换模型预测疾病风险

一些生物医学研究导致混合数据。当研究中的某些受试者缺少定义亚组成员资格的离散协变量时，结果的分布遵循亚组特定分布的混合分布。考虑到组成员和协变量的不确定分布，我们通过每个亚群中的转换模型对疾病发作时间和协变量之间的关系进行建模，并开发了通过 EM 算法实现的基于非参数最大似然的估计及其推理过程。我们进一步提出了识别在不同人群中具有不同影响或共同影响的协变量的方法，这使得简约建模和更好地理解不同人群的差异成为可能。