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In this thesis, three different topics regarding the calculation of alert concentrations are considered. In toxicology, an alert concentration is the concentration where the response variable of interest attains or exceeds a pre-specified threshold. The first topic, handling deviating control values, considers cytotoxicity data. Often, response values for the lowest tested concentrations and the negative control do not coincide. This leads to the inability to properly interpret or even calculate the concentration where the curve attains a pre-specified percentage. Four different methods are proposed and compared in a controlled simulation study. All of these methods are based on the family of log-logistic functions. Based on the results from this simulation study, a concrete algorithm is stated, which method to use in which case. The second topic is called identification of alert concentrations and considers gene expression data. Four methods to calculate specific alert concentrations are compared in a controlled simulation study, two based on the discrete observations only and two based on a parametric model fit, with one method taking the significance into account, respectively, and one method considering absolute exceedance of the threshold only. Results show that generally, the methods based on modelling of curves less drastically overestimate the true underlying alert concentrations while at the same time, the number alerts at too low concentrations, does not exceed the significance level. The third topic aims at improving the estimation of the parameter in a 4pLL model corresponding to the half-maximal effect by conducting some information sharing across. Two approaches are presented: The first approach is to conduct a meta-analysis for estimates of this parameters for all genes that are `similar' to each other. The second method makes use of an empirical Bayes procedure to effectively calculate a weighted mean between individual observed value and the mean of all observed parameter values for a large dataset. The meta-analysis approach performs worse than directly estimating the parameter of interest, but results for the Bayes method improved in contrast to the direct estimate in terms of the MSE. |
