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

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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.