Generalisation of the Fractional Polynomial procedure for semi-continuous variables in epidemiology and clinical research

在流行病学和临床研究中，一个共同的目标是通过使用适当的回归模型定量地估计协变量对结果的影响。这些协变量通常具有零暴露个体的比例，而暴露人群的分布是连续的（所谓的峰值为零的变量），例如吸烟、母乳喂养持续时间或饮酒。然后可以用申请者开发的一种方法对剂量-反应函数进行建模，这种方法是分数多项式方法的扩展。该项目的目的是开发新的改进方法来分析具有半连续变量的研究，将这些方法应用于研究分析，并提供软件工具来传播这些方法。到目前为止的结果：我们已经开发并发布了最近发布的过程的改进版本，用于处理峰值为零的变量。通过研究特定的分布类，我们已经为这个过程提供了理论依据。在一个脉冲变量的模拟研究中，我们可以证明与前一种方法相比，这种新方法的性能有所改善。对于两个尖峰变量，我们提出了几种方法来扩展该过程。实例表明，处理两个峰值变量的方法强烈依赖于变量的二元分布和相关结构。这些方法将在项目的模拟研究过程中得到进一步评价。对于三个或更多的峰值变量，我们提出了一个策略。在实际应用方面，我们从几项流行病学和临床研究中获得了数据，并准备用我们的方法进行分析。该方法在第一个资助期已经开始应用于这些数据，并将持续到项目结束。工作计划：首先，在模拟研究中，我们将调查是否从逻辑模型的结果转移到Cox模型的审查生存数据。然后，我们将在一个大型模拟研究中评估两个峰值变量的不同方法。必须确定适当的标准来评估财产和比较不同的建议。在一个具有三个峰值变量的示例中，我们将研究所提出的策略是否合适，或者是否需要进一步扩展。最近研究治疗和连续变量之间相互作用的方法将扩展到零变量的峰值。我们将以激素受体的作用和对乳腺癌患者的激素治疗为例。对于吸烟，最近提出了几种剂量指标（如综合吸烟指数）。使用我们的方法，我们将得出新的剂量指标，并将其与文献中的建议进行比较。

In epidemiology and in clinical research, a common goal is to estimate the effect of covariables on an outcome quantitatively by using appropriate regression models. These covariates often have a proportion of individuals with zero exposure, while the distribution of the population exposed is continuous (variables with so-called spike at zero), e.g. smoking, duration of breastfeeding, or alcohol consumption. Modelling of the dose-response function is then possible with a method developed by the applicants which is an extension of the fractional polynomial approach. The aim of the project is to develop new improved methods for analysis of studies with semi-continuous variables, to apply them for the analysis of studies and to provide software tools to disseminate the methods.Results until now: We have developed and published an improved version of the recently published procedure to handle variables with a spike at zero. We have developed theoretical justifications for the procedure by investigating specific distribution classes. In a simulation study for one spike variable we could show improved properties of this new procedure in comparison to the former. For two spike variables we have proposed several approaches for an extension of the procedure. Examples have shown that methods of handling two spike variables are strongly dependent upon the bivariate distribution and the correlation structure of the variables. The approaches will be further evaluated in the course of the project in simulation studies. For three or more spike variables we have proposed a strategy. For practical applications, we have obtained data from several epidemiological and clinical studies and made these ready for analyses with our methods. Application of the method to these data has already started in the first funding period and will last until the end of the project. Work plan: First, in a simulation study we will investigate whether results from the logistic model transfer to the Cox model for censored survival data. Then we are going to evaluate the different approaches for two spike variables in a large simulation study. Suitable criteria to assess properties and to compare the different proposals have to be defined. In an example with three spike variables we will investigate whether the proposed strategy is suitable or whether further extensions are required. A recent approach to investigate for interactions between treatment and a continuous variable will be extended for spike at zero variables. We will use the role of hormonal receptors and treatment of breast cancer patients with hormonal therapy as an example. For smoking several dose metrics (e.g. comprehensive smoking index) have been proposed recently. Using our approaches we will derive new dose metrics and compare these with proposals from the literature.