PROJECT SUMMARY/ABSTRACT If detected early, many cancers can be successfully treated, leading to a high rate of survival. Unfortunately, cancer is often detected only at late stages since current screening technologies have insufficient sensitiv- ity and specificity at low tumor fractions. Further, screening itself is often invasive or even harmful, leading health policy experts to recommend delaying or avoiding screening since the disadvantages may outweigh the benefit. Cell-free DNA (cfDNA) sequencing presents an exciting recent possibility for highly accurate, non- invasive cancer screening. When cells die, they often release small fragments of their DNA into the body, and these cell-free DNA fragments temporarily circulate in the bloodstream. Thus, when cancer is present, plasma obtained from routine blood draws contains DNA fragments from cancer cells. By performing genome sequencing on this plasma cfDNA, it is possible to non-invasively detect and analyze cancers. However, ad- vanced statistical methods are needed to extract the signal from the noise. The fraction of tumor-derived cfDNA fragments is very small, on the order of 1/1000 or less for early stage cancers. The main objective of the proposed project is to develop and test a flexible suite of statistical methods for cancer detection and analysis using cfDNA sequencing data at low tumor fractions. Our central hypothesis is that structured prob- abilistic models of genomic signals of cancer in cfDNA data, along with careful handling of errors and biases, will enable cancer detection and classification with high sensitivity and specificity. (Aim 1) Develop robust non- parametric Poisson regression framework, applied to mutational signatures. The mutational processes that lead to cancer exhibit characteristic genome-wide signatures that are naturally modeled using nonnegative matrix factorization (NMF). We generalize the Poisson NMF model to a nonparametric hierarchical Bayesian regression model with priors informed by latent cancer type/subtype, covariates, known biological structure, and large databases of cancer genomes. (Aim 2) Develop grammar-based methods for complex models of sequential data, applied to SCNAs. Accurate genome-wide SCNA modeling requires continuous and dis- crete latent states, asynchronous emissions, inhomogeneous transition kernels, and informed priors based on previously observed cancer/normal genomes. We develop a grammar and algorithms for complex sequence models with these features. (Aim3) Develop integrated Bayesian framework for robust cancer detection from cfDNA sequencing. We will combine the methods from Aims 1 and 2 in a hierarchical model with cancer type/subtype as a latent variable. (Aim 4) Develop software, provide documentation, and disseminate results to facilitate reproducibility. We will provide user-friendly open-source software, preprocessed public data, and thorough documentation to enable reproducibility and maximize ease-of-use.