Improving adaptive seamless designs through Bayesian optimization

We propose to use Bayesian optimization (BO) to improve the efficiency of the design selection process in clinical trials. BO is a method to optimize expensive black-box functions, by using a regression as a surrogate to guide the search. In clinical trials, planning test procedures and sample sizes is a crucial task. A common goal is to maximize the test power, given a set of treatments, corresponding effect sizes, and a total number of samples. From a wide range of possible designs, we aim to select the best one in a short time to allow quick decisions. The standard approach to simulate the power for each single design can become too time consuming. When the number of possible designs becomes very large, either large computational resources are required or an exhaustive exploration of all possible designs takes too long. Here, we propose to use BO to quickly find a clinical trial design with high power from a large number of candidate designs. We demonstrate the effectiveness of our approach by optimizing the power of adaptive seamless designs for different sets of treatment effect sizes. Comparing BO with an exhaustive evaluation of all candidate designs shows that BO finds competitive designs in a fraction of the time

Combining heterogeneous subgroups with graph-structured variable selection priors for Cox regression

Important objectives in cancer research are the prediction of a patient's risk based on molecular measurements such as gene expression data and the identification of new prognostic biomarkers (e.g. genes). In clinical practice, this is often challenging because patient cohorts are typically small and can be heterogeneous. In classical subgroup analysis, a separate prediction model is fitted using only the data of one specific cohort. However, this can lead to a loss of power when the sample size is small. Simple pooling of all cohorts, on the other hand, can lead to biased results, especially when the cohorts are heterogeneous. For this situation, we propose a new Bayesian approach suitable for continuous molecular measurements and survival outcome that identifies the important predictors and provides a separate risk prediction model for each cohort. It allows sharing information between cohorts to increase power by assuming a graph linking predictors within and across different cohorts. The graph helps to identify pathways of functionally related genes and genes that are simultaneously prognostic in different cohorts. Results demonstrate that our proposed approach is superior to the standard approaches in terms of prediction performance and increased power in variable selection when the sample size is small.Comment: under review, 19 pages, 10 figure

Extending model-based optimization with resource-aware parallelization and for dynamic optimization problems

This thesis contains two works on the topic of sequential model-based optimization (MBO). In the first part an extension of MBO towards resource-aware parallelization is presented and in the second part MBO is adapted to optimize dynamic optimization problems. Before the newly developed methods are introduced the reader is given a detailed introduction into various aspects of MBO and related work. This covers thoughts on the choice of the initial design, the surrogate model, the acquisition functions, and the final optimization result. As most methods in this thesis rely on the Gaussian process regression it is covered in detail as well. The chapter on “Parallel MBO” dives into the topic of making use of multiple workers that can evaluate the black-box and especially focuses on the problem of heterogeneous runtimes. Strategies that tackle this problem can be divided into synchronous and asynchronous methods. Instead of proposing one configuration in an iterative fashion, as done by ordinary MBO, synchronous methods usually propose as many configurations as there are workers available. Previously proposed synchronous methods neglect the problem of heterogeneous runtimes which causes idling, when evaluations end at different times. This work presents current methods for parallel MBO that cover synchronous and asynchronous methods and presents the newly proposed Resource-Aware Model-based Optimization (RAMBO) Framework. This work shows that synchronous and asynchronous methods each have their advantages and disadvantages and that RAMBO can outperform common synchronous MBO methods if the runtime is predictable but still obtains comparable results in the worst case. The chapter on “MBO with Concept Drift” (MBO-CD) explains the adaptions that have been developed to allow optimization of black-box functions that change systematically over time. Two approaches are explained on how MBO can be taught to handle black-box functions where the relation between input and output changes over time, i.e. where a concept drift occurs. The window approach trains the surrogate only on the most recent observations. The time-as-covariate approach includes the time as an additional input variable in the surrogate, giving it the ability to learn the effect of the time. For the latter, a special acquisition function, the temporal expected improvement, is proposed

Weighted Cox regression for the prediction of heterogeneous patient subgroups

An important task in clinical medicine is the construction of risk prediction models for specific subgroups of patients based on high-dimensional molecular measurements such as gene expression data. Major objectives in modeling high-dimensional data are good prediction performance and feature selection to find a subset of predictors that are truly associated with a clinical outcome such as a time-to-event endpoint. In clinical practice, this task is challenging since patient cohorts are typically small and can be heterogeneous with regard to their relationship between predictors and outcome. When data of several subgroups of patients with the same or similar disease are available, it is tempting to combine them to increase sample size, such as in multicenter studies. However, heterogeneity between subgroups can lead to biased results and subgroup-specific effects may remain undetected. For this situation, we propose a penalized Cox regression model with a weighted version of the Cox partial likelihood that includes patients of all subgroups but assigns them individual weights based on their subgroup affiliation. Patients who are likely to belong to the subgroup of interest obtain higher weights in the subgroup-specific model. Our proposed approach is evaluated through simulations and application to real lung cancer cohorts. Simulation results demonstrate that our model can achieve improved prediction and variable selection accuracy over standard approaches.Comment: under review, 15 pages, 6 figure

Model-Based Optimization of Subgroup Weights for Survival Analysis

To obtain a reliable prediction model for a specific cancer subgroup or cohort is often difficult due to the limited number of samples and, in survival analysis, even more due to potentially high censoring rates. Sometimes similar datasets are available for other patient subgroups with the same or a similar disease and treatment, e.g., from other clinical centers. Simple pooling of all subgroups can decrease the variance of the predicted parameters of the prediction models, but also increase the bias due to potential high heterogeneity between the cohorts. A promising compromise is to identify which subgroups are similar enough to the specific subgroup of interest and then include only these for model building. Similarity here refers to the relationship between input and output in the prediction model, and not necessarily to the distributions of the input and output variables themselves. Here, we propose a subgroup-based weighted likelihood approach and evaluate it on a set of lung cancer cohorts. When interested in a prediction model for a specific subgroup, then for every other subgroup, an individual weight determines the strength with which its observations enter into the likelihood-based optimization of the model parameters. A weight close to 0 indicates that a subgroup should be discarded, and a weight close to 1 indicates that the subgroup fully enters into the model building process. MBO (model based optimization) can be used to quickly find a good prediction model in the presence of a large number of hyperparameters to be tuned. Here, we use MBO to identify the best model for survival prediction in lung cancer subgroups, where besides the parameters of a Cox model additionally the individual values of the subgroup weights are optimized. Interestingly, often the resulting models with highest prediction quality are obtained for a mixed weight structure, i.e. both weights close to 0, weights close to 1, and medium weights are optimal, reflecting the similarity of the corresponding cancer subgroups