Biomarker selection and cutoff estimation in drug development

In this cumulative thesis we discuss topics in the area of biomarker selection and cutoff estimation, where both subjects are related to the usability and applicability of biomarkers in drug development. The growing role of targeted medicine has led to an increased focus on the development of actionable biomarkers. Current penalized selection methods that are used to identify biomarker panels for classification in high-dimensional data, however, often result in highly complex panels that need careful pruning for practical use. In the framework of regularization methods, a penalty that is a weighted sum of the L1 and L0 norm has been proposed to account for the complexity of the resulting model. In practice, the limitation of this penalty is that the objective function is non-convex, non-smooth, the optimization is computationally intensive and the application to high-dimensional settings is challenging. In the first part of the thesis, we propose a stepwise forward variable selection method which combines the L0 with L1 or L2 norms. The penalized likelihood criterion that is used in the stepwise selection procedure results in more parsimonious models, keeping only the most relevant features. Moreover in this thesis, we introduce a new approach to derive the distribution of the cutoff and predictive values of a biomarker assay. To enable targeted therapies and enhance medical decision-making, biomarkers are increasingly used as screening and diagnostic tests. When using quantitative biomarkers for classification purposes, this often implies that an appropriate cutoff for the biomarker has to be determined and its clinical utility must be assessed. In the context of drug development, it is of interest how the probability of response changes with increasing values of the biomarker. Unlike sensitivity and specificity, predictive values are functions of the accuracy of the test, depend on the prevalence of the disease and therefore are a useful tool in this setting. We propose a Bayesian method to not only estimate the cutoff value using the negative and positive predictive values, but also estimate the uncertainty around this estimate. We use a step function, which serves as an approximate model facilitating classification into two groups that have different response rates. The advantage of using the step function is that both the cutoff and the predictive values are parameters of the model. Using Bayesian inference allows us to incorporate prior information and obtain posterior estimates and credible intervals for the cut-off and associated predictive values. Lastly, we further discuss the simultaneous variable selection and cutoff estimation (of the selected variables) by controlling the clinical utility, which is expressed in terms of negative and positive predictive values. A Bayesian variable selection method is introduced, which incorporates information about the predictive values into the biomarker selection process and simultaneously estimates the cutoff value on the risk score of the selected markers. The selection of the predictors in the final model is done under the constraint that the predictive values can take values in prespecified interval. The choice of different prior distributions is discussed. We conclude with discussions at each chapter of the dissertation