Asymptotics of Bayesian Uncertainty Estimation in Random Features Regression

In this paper we compare and contrast the behavior of the posterior predictive distribution to the risk of the maximum a posteriori estimator for the random features regression model in the overparameterized regime. We will focus on the variance of the posterior predictive distribution (Bayesian model average) and compare its asymptotics to that of the risk of the MAP estimator. In the regime where the model dimensions grow faster than any constant multiple of the number of samples, asymptotic agreement between these two quantities is governed by the phase transition in the signal-to-noise ratio. They also asymptotically agree with each other when the number of samples grow faster than any constant multiple of model dimensions. Numerical simulations illustrate finer distributional properties of the two quantities for finite dimensions. We conjecture they have Gaussian fluctuations and exhibit similar properties as found by previous authors in a Gaussian sequence model, which is of independent theoretical interest.Comment: 11 pages, 3 figure

The clinical landscape of cell-free DNA alterations in 1671 patients with advanced biliary tract cancer

BACKGROUND: Targeted therapies have transformed clinical management of advanced biliary tract cancer (BTC). Cell-free DNA (cfDNA) analysis is an attractive approach for cancer genomic profiling that overcomes many limitations of traditional tissue-based analysis. We examined cfDNA as a tool to inform clinical management of patients with advanced BTC and generate novel insights into BTC tumor biology. PATIENTS AND METHODS: We analyzed next-generation sequencing data of 2068 cfDNA samples from 1671 patients with advanced BTC generated with Guardant360. We carried out clinical annotation on a multi-institutional subset (n = 225) to assess intra-patient cfDNA-tumor concordance and the association of cfDNA variant allele fraction (VAF) with clinical outcomes. RESULTS: Genetic alterations were detected in cfDNA in 84% of patients, with targetable alterations detected in 44% of patients. Fibroblast growth factor receptor 2 (FGFR2) fusions, isocitrate dehydrogenase 1 (IDH1) mutations, and BRAF V600E were clonal in the majority of cases, affirming these targetable alterations as early driver events in BTC. Concordance between cfDNA and tissue for mutation detection was high for IDH1 mutations (87%) and BRAF V600E (100%), and low for FGFR2 fusions (18%). cfDNA analysis uncovered novel putative mechanisms of resistance to targeted therapies, including mutation of the cysteine residue (FGFR2 C492F) to which covalent FGFR inhibitors bind. High pre-treatment cfDNA VAF was associated with poor prognosis and shorter response to chemotherapy and targeted therapy. Finally, we report the frequency of promising targets in advanced BTC currently under investigation in other advanced solid tumors, including KRAS G12C (1.0%), KRAS G12D (5.1%), PIK3CA mutations (6.8%), and ERBB2 amplifications (4.9%). CONCLUSIONS: These findings from the largest and most comprehensive study to date of cfDNA from patients with advanced BTC highlight the utility of cfDNA analysis in current management of this disease. Characterization of oncogenic drivers and mechanisms of therapeutic resistance in this study will inform drug development efforts to reduce mortality for patients with BTC

Statistical methods for modeling the spatial structure on the visual field in glaucoma progression research

Diagnosing glaucoma progression is critical for limiting irreversible vision loss. A common method for assessing glaucoma progression uses a longitudinal series of visual fields (VF) acquired at regular intervals. VF data are characterized by a complex spatiotemporal structure due to the data generating process and ocular anatomy. Thus, advanced statistical methods are needed to make clinical determinations regarding progression status. In this dissertation, we introduce new modeling techniques that produce flexible spatial dependency structures within the framework of hierarchical Bayesian spatial models. The developed methodology is applied to VF data from the Vein Pulsation Study Trial in Glaucoma and the Lions Eye Institute trial registry. In chapter 2, we work within the framework of boundary detection and introduce a spatiotemporal boundary detection model that allows the underlying anatomy of the optic disc to dictate localized spatial structure on the VF. We show that our new method provides insight into vision loss that improves diagnosis of glaucoma progression in actual glaucoma patients. Simulations are presented, showing the proposed methodology is preferred over existing spatial methods for VF data. An R package womblR is provided that implements the method. Chapter 3 aims to introduce the modeling framework from chapter 2 to the ophthalmology community. An optimal form of the metric is established and compared with standard methods for assessing glaucoma progression using a statistical diagnostic framework. In particular, we demonstrate the added value of using the novel metric in addition to established prediction models based on standard operating characteristics. Finally, we detail the procedure for implementing our novel technique in the clinical setting. In chapter 4, we present a framework that brings together vital aspects of glaucoma management, i) prediction of future VF sensitivities, ii) predicting the timing and location of future vision loss, iii) making clinical decisions regarding progression, and, iv) incorporation of anatomical information to create plausible data-generating models. We show that our method improves prediction and estimation of progression, and simulations are presented, showing the proposed methodology is preferred over existing models for VF data. An R package called spCP is provided that implements the method.Doctor of Philosoph

High throughput detection of M6P/IGF2R intronic hypermethylation and LOH in ovarian cancer

Cell surface mannose 6-phosphate/insulin-like growth factor II receptors (M6P/IGF2R) bind and target exogenous insulin-like growth factor II (IGF2) to the prelysosomes where it is degraded. Loss of heterozygosity (LOH) for M6P/IGF2R is found in cancers, with mutational inactivation of the remaining allele. We exploited the normal allele-specific differential methylation of the M6P/IGF2R intron 2 CpG island to rapidly evaluate potential LOH in ovarian cancers, since every normal individual is informative. To this end, we developed a method for bisulfite modification of genomic DNA in 96-well format that allows for rapid methylation profiling. We identified ovarian cancers with M6P/IGF2R LOH, but unexpectedly also found frequent abnormal acquisition of methylation on the paternally inherited allele at intron 2. These results demonstrate the utility of our high-throughput method of bisulfite modification for analysis of large sample numbers. They further show that the methylation status of the intron 2 CpG island may be a useful indicator of LOH and biomarker of disease