GAMLSS for biostatistical regression modeling. Refinements and Further Developments

鉴于个性化治疗和诊断工具的快速发展，高维数据分析在生物医学研究中变得相当重要。因此，生物统计方法开发的一个挑战是从各种(可能是高维的)数据源中提取相关信息，并将这些信息组合在一起以给出准确的统计预测规则。为此，DFG项目的第一阶段致力于开发AUC优化的二进制和删失临床结果变量的预测规则。由于生物医学研究中临床和记忆信息的收集越来越详细，以及分子数据生成技术的快速发展，生物统计学家越来越重要的任务是开发将先前的生物学或临床知识融入统计预测规则的新方法。因此，有必要将在第一个项目阶段开发的数据驱动方法与能够适应现有知识和信息的回归模型的优化相结合。GAMLSS方法是解决这些问题的一个非常有前途的工具，它允许对各种连续和分类的结果变量进行灵活的建模。因此，GAMLSS方法是拟议的第二个项目期工作方案的主要主题。特别是，它们允许根据先验知识指定灵活的均值和方差结构。此外，通过在第一个项目期间开发的技术，GAMLSS中的变量选择是可能的。尽管GAMLSS具有许多优点，但目前仍存在一些限制，这些限制往往会阻碍GAMLSS在生物医学研究中的广泛使用。这些限制涉及在高维环境下构建有效的假设检验，但也没有考虑通过GAMLSS估计预测区间的不确定性。此外，没有对多维结果变量进行扩展。因此，拟议项目的主要目标是分析GAMLSS的上述局限性，并开发解决由此产生的问题的方法。对新开发的方法的评估尤其将包括对临床和流行病学研究数据的分析。这一分析将基于申请者目前的研究和合作项目。此外，将实施新开发的方法，并通过开放源码软件向用户提供。

In view of the rapid development of personalized therapies and diagnostic tools, high-dimensional data analysis has gained considerable importance in biomedical research. A challenge for biostatistical method development is therefore to extract relevant information from various (possibly high-dimensional) data sources and to combine this information to give accurate statistical prediction rules. To this purpose, the first period of DFG Project was concerned with the development of AUC-optimized prediction rules for binary and censored clinical outcome variables.Because of the more and more detailed collection of clinical and anamnestic information in biomedical studies, and also because of the rapid development of technologies for generating molecular data, an increasingly important task for biostatisticians is to develop new methods that incorporate prior biological or clinical knowledge into statistical prediction rules. Consequently, there is a need for combining the data-driven methods developed in the first project period with the optimization of regression models that can be adapted to existing knowledge and information.A highly promising tool to address these issues is the GAMLSS methodology, which allows for the flexible modeling of a large variety of continuous and categorical outcome variables. For this reason GAMLSS methods are the main subject of the work program of the proposed second project period. In particular, they allow for the specification of flexible mean and variance structures according to prior knowledge. In addition, variable selection in GAMLSS is possible via the techniques developed in the first project period.Despite the many advantages of GAMLSS, there are several limitations that currently tend to prevent the broad use of GAMLSS in biomedical research. These limitations concern the construction of valid hypothesis tests in high-dimensional settings but also the non-consideration of uncertainty in the estimation of prognosis intervals via GAMLSS. Moreover, there are no extensions to multi-dimensional outcome variables. The main goal of the proposed project is therefore to analyze the aforementioned limitations of GAMLSS and to develop methods to solve the resulting problems.The evaluation of the newly developed methods will, in particular, comprise the analysis of clinical and epidemiological study data. This analysis will be based on current research and collaboration projects of the applicants. In addition, newly developed methods will be implemented and made available to users via open source software.