Search for: All records

ABSTRACT We give a decomposition of the predictive variance based on the law of total variance by making the response variable dependent on a finite dimensional discrete random variable representing our modeling assumptions. Then, we test which terms in this decomposition are small enough to ignore. This allows us to identify which of the discrete random variables, that is, aspects of modeling, are most important to prediction variance. The terms in the decomposition admit interpretations based on conditional means and variances and are analogous to the terms in a Cochran's theorem decomposition of squared error often used in analysis of variance. Thus, the modeling features are treated as factors in completely randomized design. 

Abstract Quantitative structure–activity relationship (QSAR) modeling has become a critical tool in drug design. Recently proposed Topological Regression (TR), a computationally efficient and highly interpretable QSAR model that maps distances in the chemical domain to distances in the activity domain, has shown predictive performance comparable to state-of-the-art deep learning-based models. However, TR’s dependence on simple random sampling-based anchor selection and utilization of radial basis function for response reconstruction constrain its interpretability and predictive capacity. To address these limitations, we propose Adaptive Topological Regression (AdapToR) with adaptive anchor selection and optimization-based reconstruction. We evaluated AdapToR on the NCI60 GI50 dataset, which consists of over 50,000 drug responses across 60 human cancer cell lines, and compared its performance to Transformer CNN, Graph Transformer, TR, and other baseline models. The results demonstrate that AdapToR outperforms competing QSAR models for drug response prediction with significantly lower computational cost and greater interpretability as compared to deep learning-based models. 

Abstract Quantitative structure-activity relationship (QSAR) modeling is a powerful tool for drug discovery, yet the lack of interpretability of commonly used QSAR models hinders their application in molecular design. We propose a similarity-based regression framework, topological regression (TR), that offers a statistically grounded, computationally fast, and interpretable technique to predict drug responses. We compare the predictive performance of TR on 530 ChEMBL human target activity datasets against the predictive performance of deep-learning-based QSAR models. Our results suggest that our sparse TR model can achieve equal, if not better, performance than the deep learning-based QSAR models and provide better intuitive interpretation by extracting an approximate isometry between the chemical space of the drugs and their activity space. 

When dealing with very high-dimensional and functional data, rank deficiency of sample covariance matrix often complicates the tests for population mean. To alleviate this rank deficiency problem, Munk et al. (J Multivar Anal 99:815–833, 2008) proposed neighborhood hypothesis testing procedure that tests whether the population mean is within a small, pre-specified neighborhood of a known quantity, M. How could we objectively specify a reasonable neighborhood, particularly when the sample space is unbounded? What should be the size of the neighborhood? In this article, we develop the modified neighborhood hypothesis testing framework to answer these two questions.We define the neighborhood as a proportion of the total amount of variation present in the population of functions under study and proceed to derive the asymptotic null distribution of the appropriate test statistic. Power analyses suggest that our approach is appropriate when sample space is unbounded and is robust against error structures with nonzero mean. We then apply this framework to assess whether the near-default sigmoidal specification of dose-response curves is adequate for widely used CCLE database. Results suggest that our methodology could be used as a pre-processing step before using conventional efficacy metrics, obtained from sigmoid models (for example: IC50 or AUC), as downstream predictive targets.