Limit distributions of scale-invariant probabilistic models of correlated random variables with the q-Gaussian as an explicit example

Extremization of the Boltzmann-Gibbs (BG) entropy under appropriate norm and width constraints yields the Gaussian distribution. Also, the basic solutions of the standard Fokker-Planck (FP) equation (related to the Langevin equation with additive noise), as well as the Central Limit Theorem attractors, are Gaussians. The simplest stochastic model with such features is N to infinity independent binary random variables, as first proved by de Moivre and Laplace. What happens for strongly correlated random variables? Such correlations are often present in physical situations as e.g. systems with long range interactions or memory. Frequently q-Gaussians become observed. This is typically so if the Langevin equation includes multiplicative noise, or the FP equation to be nonlinear. Scale-invariance, i.e. exchangeable binary stochastic processes, allow a systematical analysis of the relation between correlations and non-Gaussian distributions. In particular, a generalized stochastic model yielding q-Gaussians for all q (including q>1) was missing. This is achieved here by using the Laplace-de Finetti representation theorem, which embodies strict scale-invariance of interchangeable random variables. We demonstrate that strict scale invariance together with q-Gaussianity mandates the associated extensive entropy to be BG.Comment: 6 pages, 1 fig, to appear in EPJ

The path to a better biomarker: Application of a risk management framework for the implementation of PD-L1 and TILs as immuno-oncology biomarkers in breast cancer clinical trials and daily practice

Immune checkpoint inhibitor therapies targeting PD-1/PD-L1 are now the standard of care in oncology across several hematologic and solid tumor types, including triple negative breast cancer (TNBC). Patients with metastatic or locally advanced TNBC with PD-L1 expression on immune cells occupying 651% of tumor area demonstrated survival benefit with the addition of atezolizumab to nab-paclitaxel. However, concerns regarding variability between immunohistochemical PD-L1 assay performance and inter-reader reproducibility have been raised. High tumor-infiltrating lymphocytes (TILs) have also been associated with response to PD-1/PD-L1 inhibitors in patients with breast cancer (BC). TILs can be easily assessed on hematoxylin and eosin\u2013stained slides and have shown reliable inter-reader reproducibility. As an established prognostic factor in early stage TNBC, TILs are soon anticipated to be reported in daily practice in many pathology laboratories worldwide. Because TILs and PD-L1 are parts of an immunological spectrum in BC, we propose the systematic implementation of combined PD-L1 and TIL analyses as a more comprehensive immuno-oncological biomarker for patient selection for PD-1/PD-L1 inhibition-based therapy in patients with BC. Although practical and regulatory considerations differ by jurisdiction, the pathology community has the responsibility to patients to implement assays that lead to optimal patient selection. We propose herewith a risk-management framework that may help mitigate the risks of suboptimal patient selection for immuno-therapeutic approaches in clinical trials and daily practice based on combined TILs/PD-L1 assessment in BC. \ua9 2020 Pathological Society of Great Britain and Ireland. Published by John Wiley & Sons, Ltd

Application of a risk-management framework for integration of stromal tumor-infiltrating lymphocytes in clinical trials

Stromal tumor-infiltrating lymphocytes (sTILs) are a potential predictive biomarker for immunotherapy response in metastatic triple-negative breast cancer (TNBC). To incorporate sTILs into clinical trials and diagnostics, reliable assessment is essential. In this review, we propose a new concept, namely the implementation of a risk-management framework that enables the use of sTILs as a stratification factor in clinical trials. We present the design of a biomarker risk-mitigation workflow that can be applied to any biomarker incorporation in clinical trials. We demonstrate the implementation of this concept using sTILs as an integral biomarker in a single-center phase II immunotherapy trial for metastatic TNBC (TONIC trial, NCT02499367), using this workflow to mitigate risks of suboptimal inclusion of sTILs in this specific trial. In this review, we demonstrate that a web-based scoring platform can mitigate potential risk factors when including sTILs in clinical trials, and we argue that this framework can be applied for any future biomarker-driven clinical trial setting