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Major efforts to sequence cancer genomes are now occurring throughout the world. Though the emerging data from these studies are illuminating, their reconciliation with epidemiologic and clinical observations poses a major challenge. In the…
Early detection of clinical outcomes such as cancer may be predicted based on longitudinal biomarker measurements. Tracking longitudinal biomarkers as a way to identify early disease onset may help to reduce mortality from diseases like…
We consider the inverse problem of reconstructing the posterior measure over the trajec- tories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive…
We present recent results on Piecewise Deterministic Markov Processes (PDMPs), involved in biological modeling. PDMPs, first introduced in the probabilistic literature by Davis (1984), are a very general class of Markov processes and are…
Piecewise Deterministic Markov Processes (PDMPs) are studied in a general framework. First, different constructions are proven to be equivalent. Second, we introduce a coupling between two PDMPs following the same differential flow which…
Cancer subtyping plays a crucial role in informing prognosis and guiding personalized treatment strategies. However, conventional subtyping approaches often rely on static, biopsy-derived scores that hardly capture the biological…
Experiments, in particular on biological systems, typically probe lower-dimensional observables which are projections of high-dimensional dynamics. In order to infer consistent models capturing the relevant dynamics of the system, it is…
In this paper, we present a probabilistic analysis of a dynamical particle model for the self-adaptive immune response to cancer, as proposed by the first author in a previous work. The model is motivated by the interplay between immune…
We propose a method for inference on moderately high-dimensional, nonlinear, non-Gaussian, partially observed Markov process models for which the transition density is not analytically tractable. Markov processes with intractable transition…
The availability of cancer measurements over time enables the personalised assessment of tumour growth and therapeutic response dynamics. However, many tumours are treated after diagnosis without collecting longitudinal data, and cancer…
We propose an algorithm for the efficient and robust sampling of the posterior probability distribution in Bayesian inference problems. The algorithm combines the local search capabilities of the Manifold Metropolis Adjusted Langevin…
The objectives of this "perspective" paper are to review some recent advances in sparse feature selection for regression and classification, as well as compressed sensing, and to discuss how these might be used to develop tools to advance…
As cancer advances, cells often spread from the primary tumor to other parts of the body and form metastases. This is the main cause of cancer related mortality. Here we investigate a conceptually simple model of metastasis formation where…
Point and interval estimation of future disability inception and recovery rates are predominantly carried out by combining generalized linear models (GLM) with time series forecasting techniques into a two-step method involving parameter…
Analyzing disease progression patterns can provide useful insights into the disease processes of many chronic conditions. These analyses may help inform recruitment for prevention trials or the development and personalization of treatments…
In the era of precision medicine, more and more clinical trials are now driven or guided by biomarkers, which are patient characteristics objectively measured and evaluated as indicators of normal biological processes, pathogenic processes,…
The paper studies an improved estimate for the rate of convergence for nonlinear homogeneous discrete-time Markov chains. These processes are nonlinear in terms of the distribution law. Hence, the transition kernels are dependent on the…
In cancer biomarker development, a key objective is to evaluate whether a new biomarker, when combined with an established one, improves early cancer detection compared to using the established biomarker alone. Incremental value is often…
Often in Phase 3 clinical trials measuring a long-term time-to-event endpoint, such as overall survival or progression-free survival, investigators also collect repeated measures on biomarkers which may be predictive of the primary…
Biomarker-guided designs are increasingly used to evaluate personalized treatments based on patients' biomarker status in Phase II and III clinical trials. With adaptive enrichment, these designs can improve the efficiency of evaluating the…