Functional limit laws for the intensity measure of point processes and applications

Motivated by applications to the study of depth functions for tree-indexed random variables generated by point processes, we describe functional limit theorems for the intensity measure of point processes. Specifically, we establish uniform laws of large numbers and uniform central limit theorems over a class of bounded measurable functions for estimates of the intensity measure. Using these results, we derive the uniform asymptotic properties of half-space depth and, as corollaries, obtain the asymptotic behavior of medians and other quantiles of the standardized intensity measure. Additionally, we obtain uniform concentration upper bound for the estimator of half-space depth. As a consequence of our results, we also derive uniform consistency and uniform asymptotic normality of Lotka-Nagaev and Harris-type estimators for the Laplace transform of the point processes in a branching random walk.Comment: 38 page

Analytical and statistical properties of local depth functions motivated by clustering applications

General local depth functions ($LGD$) are used for describing the local geometric features and mode(s) in multivariate distributions. In this paper, we undertake a rigorous systematic study of $LGD$ and establish several analytical and statistical properties. First, we show that, when the underlying probability distribution is absolutely continuous with density $f(\cdot)$, the scaled version of $LGD$ (referred to as $\tau$-approximation) converges, uniformly and in $L^d(\mathbb{R}^p)$ to $f(\cdot)$ when $\tau$ converges to zero. Second, we establish that, as the sample size diverges to infinity the centered and scaled sample $LGD$ converge in distribution to a centered Gaussian process uniformly in the space of bounded functions on $\mathcal{H}_G$, a class of functions yielding $LGD$. Third, using the sample version of the $\tau$-approximation ($S \tau \hspace{-0.06cm} A$) and the gradient system analysis, we develop a new clustering algorithm. The validity of this algorithm requires several results concerning the uniform finite difference approximation of the gradient system associated with $S \tau \hspace{-0.06cm} A$. For this reason, we establish \emph{Bernstein}-type inequality for deviations between the centered and scaled sample $LGD$, which is also of independent interest. Finally, invoking the above results, we establish consistency of the clustering algorithm. Applications of the proposed methods to mode estimation and upper level set estimation are also provided. Finite sample performance of the methodology are evaluated using numerical experiments and data analysis.Comment: 39+235 pages, 1+126 figures, 1+15 table

Impact of safety-related dose reductions or discontinuations on sustained virologic response in HCV-infected patients: Results from the GUARD-C Cohort

BACKGROUND: Despite the introduction of direct-acting antiviral agents for chronic hepatitis C virus (HCV) infection, peginterferon alfa/ribavirin remains relevant in many resource-constrained settings. The non-randomized GUARD-C cohort investigated baseline predictors of safety-related dose reductions or discontinuations (sr-RD) and their impact on sustained virologic response (SVR) in patients receiving peginterferon alfa/ribavirin in routine practice. METHODS: A total of 3181 HCV-mono-infected treatment-naive patients were assigned to 24 or 48 weeks of peginterferon alfa/ribavirin by their physician. Patients were categorized by time-to-first sr-RD (Week 4/12). Detailed analyses of the impact of sr-RD on SVR24 (HCV RNA <50 IU/mL) were conducted in 951 Caucasian, noncirrhotic genotype (G)1 patients assigned to peginterferon alfa-2a/ribavirin for 48 weeks. The probability of SVR24 was identified by a baseline scoring system (range: 0-9 points) on which scores of 5 to 9 and <5 represent high and low probability of SVR24, respectively. RESULTS: SVR24 rates were 46.1% (754/1634), 77.1% (279/362), 68.0% (514/756), and 51.3% (203/396), respectively, in G1, 2, 3, and 4 patients. Overall, 16.9% and 21.8% patients experienced 651 sr-RD for peginterferon alfa and ribavirin, respectively. Among Caucasian noncirrhotic G1 patients: female sex, lower body mass index, pre-existing cardiovascular/pulmonary disease, and low hematological indices were prognostic factors of sr-RD; SVR24 was lower in patients with 651 vs. no sr-RD by Week 4 (37.9% vs. 54.4%; P = 0.0046) and Week 12 (41.7% vs. 55.3%; P = 0.0016); sr-RD by Week 4/12 significantly reduced SVR24 in patients with scores <5 but not 655. CONCLUSIONS: In conclusion, sr-RD to peginterferon alfa-2a/ribavirin significantly impacts on SVR24 rates in treatment-naive G1 noncirrhotic Caucasian patients. Baseline characteristics can help select patients with a high probability of SVR24 and a low probability of sr-RD with peginterferon alfa-2a/ribavirin

The polymorphism L412F in TLR3 inhibits autophagy and is a marker of severe COVID-19 in males

The polymorphism L412F in TLR3 has been associated with several infectious diseases. However, the mechanism underlying this association is still unexplored. Here, we show that the L412F polymorphism in TLR3 is a marker of severity in COVID-19. This association increases in the sub-cohort of males. Impaired macroautophagy/autophagy and reduced TNF/TNFα production was demonstrated in HEK293 cells transfected with TLR3L412F-encoding plasmid and stimulated with specific agonist poly(I:C). A statistically significant reduced survival at 28 days was shown in L412F COVID-19 patients treated with the autophagy-inhibitor hydroxychloroquine (p = 0.038). An increased frequency of autoimmune disorders such as co-morbidity was found in L412F COVID-19 males with specific class II HLA haplotypes prone to autoantigen presentation. Our analyses indicate that L412F polymorphism makes males at risk of severe COVID-19 and provides a rationale for reinterpreting clinical trials considering autophagy pathways. Abbreviations: AP: autophagosome; AUC: area under the curve; BafA1: bafilomycin A1; COVID-19: coronavirus disease-2019; HCQ: hydroxychloroquine; RAP: rapamycin; ROC: receiver operating characteristic; SARS-CoV-2: severe acute respiratory syndrome coronavirus 2; TLR: toll like receptor; TNF/TNF-α: tumor necrosis factor

Impact of Safety-Related Dose Reductions or Discontinuations on Sustained Virologic Response in HCV-Infected Patients: Results from the GUARD-C Cohort.

BACKGROUND: Despite the introduction of direct-acting antiviral agents for chronic hepatitis C virus (HCV) infection, peginterferon alfa/ribavirin remains relevant in many resource-constrained settings. The non-randomized GUARD-C cohort investigated baseline predictors of safety-related dose reductions or discontinuations (sr-RD) and their impact on sustained virologic response (SVR) in patients receiving peginterferon alfa/ribavirin in routine practice. METHODS: A total of 3181 HCV-mono-infected treatment-naive patients were assigned to 24 or 48 weeks of peginterferon alfa/ribavirin by their physician. Patients were categorized by time-to-first sr-RD (Week 4/12). Detailed analyses of the impact of sr-RD on SVR24 (HCV RNA <50 IU/mL) were conducted in 951 Caucasian, noncirrhotic genotype (G)1 patients assigned to peginterferon alfa-2a/ribavirin for 48 weeks. The probability of SVR24 was identified by a baseline scoring system (range: 0-9 points) on which scores of 5 to 9 and <5 represent high and low probability of SVR24, respectively. RESULTS: SVR24 rates were 46.1% (754/1634), 77.1% (279/362), 68.0% (514/756), and 51.3% (203/396), respectively, in G1, 2, 3, and 4 patients. Overall, 16.9% and 21.8% patients experienced ≥1 sr-RD for peginterferon alfa and ribavirin, respectively. Among Caucasian noncirrhotic G1 patients: female sex, lower body mass index, pre-existing cardiovascular/pulmonary disease, and low hematological indices were prognostic factors of sr-RD; SVR24 was lower in patients with ≥1 vs. no sr-RD by Week 4 (37.9% vs. 54.4%; P = 0.0046) and Week 12 (41.7% vs. 55.3%; P = 0.0016); sr-RD by Week 4/12 significantly reduced SVR24 in patients with scores <5 but not ≥5. CONCLUSIONS: In conclusion, sr-RD to peginterferon alfa-2a/ribavirin significantly impacts on SVR24 rates in treatment-naive G1 noncirrhotic Caucasian patients. Baseline characteristics can help select patients with a high probability of SVR24 and a low probability of sr-RD with peginterferon alfa-2a/ribavirin.This study was sponsored by F. Hoffmann-La Roche Ltd, Basel, Switzerland. Support for third-party writing assistance for this manuscript, furnished by Blair Jarvis MSc, ELS, of Health Interactions, was provided by F. Hoffmann-La Roche Ltd, Basel, Switzerland

Impact of safety-related dose reductions or discontinuations on sustained virologic response in HCV-infected patients: Results from the GUARD-C Cohort

Background: Despite the introduction of direct-acting antiviral agents for chronic hepatitis C virus (HCV) infection, peginterferon alfa/ribavirin remains relevant in many resource-constrained settings. The non-randomized GUARD-C cohort investigated baseline predictors of safety-related dose reductions or discontinuations (sr-RD) and their impact on sustained virologic response (SVR) in patients receiving peginterferon alfa/ribavirin in routine practice. Methods: A total of 3181 HCV-mono-infected treatment-naive patients were assigned to 24 or 48 weeks of peginterferon alfa/ribavirin by their physician. Patients were categorized by time-to-first sr-RD (Week 4/12). Detailed analyses of the impact of sr-RD on SVR24 (HCV RNA <50 IU/mL) were conducted in 951 Caucasian, noncirrhotic genotype (G)1 patients assigned to peginterferon alfa-2a/ribavirin for 48 weeks. The probability of SVR24 was identified by a baseline scoring system (range: 0-9 points) on which scores of 5 to 9 and <5 represent high and low probability of SVR24, respectively. Results: SVR24 rates were 46.1 % (754/1634), 77.1% (279/362), 68.0% (514/756), and 51.3% (203/396), respectively, in G1,2, 3, and 4 patients. Overall, 16.9% and 21.8% patients experienced 651 sr-RD for peginterferon alfa and ribavirin, respectively. Among Caucasian noncirrhotic G1 patients: female sex, lower body mass index, pre-existing cardiovascular/pulmonary disease, and low hematological indices were prognostic factors of sr-RD; SVR24 was lower in patients with 651 vs. no sr-RD by Week 4 (37.9% vs. 54.4%; P = 0.0046) and Week 12 (41.7% vs. 55.3%; P = 0.0016); sr-RD by Week 4/12 significantly reduced SVR24 in patients with scores <5 but not 655. Conclusions: In conclusion, sr-RD to peginterferon alfa-2a/ribavirin significantly impacts on SVR24 rates in treatment-naive G1 noncirrhotic Caucasian patients. Baseline characteristics can help select patients with a high probability of SVR24 and a low probability of sr-RD with peginter-feron alfa-2a/ribavirin

Genetic mechanisms of critical illness in COVID-19.

Host-mediated lung inflammation is present1, and drives mortality2, in the critical illness caused by coronavirus disease 2019 (COVID-19). Host genetic variants associated with critical illness may identify mechanistic targets for therapeutic development3. Here we report the results of the GenOMICC (Genetics Of Mortality In Critical Care) genome-wide association study in 2,244 critically ill patients with COVID-19 from 208 UK intensive care units. We have identified and replicated the following new genome-wide significant associations: on chromosome 12q24.13 (rs10735079, P = 1.65 × 10-8) in a gene cluster that encodes antiviral restriction enzyme activators (OAS1, OAS2 and OAS3); on chromosome 19p13.2 (rs74956615, P = 2.3 × 10-8) near the gene that encodes tyrosine kinase 2 (TYK2); on chromosome 19p13.3 (rs2109069, P = 3.98 ×  10-12) within the gene that encodes dipeptidyl peptidase 9 (DPP9); and on chromosome 21q22.1 (rs2236757, P = 4.99 × 10-8) in the interferon receptor gene IFNAR2. We identified potential targets for repurposing of licensed medications: using Mendelian randomization, we found evidence that low expression of IFNAR2, or high expression of TYK2, are associated with life-threatening disease; and transcriptome-wide association in lung tissue revealed that high expression of the monocyte-macrophage chemotactic receptor CCR2 is associated with severe COVID-19. Our results identify robust genetic signals relating to key host antiviral defence mechanisms and mediators of inflammatory organ damage in COVID-19. Both mechanisms may be amenable to targeted treatment with existing drugs. However, large-scale randomized clinical trials will be essential before any change to clinical practice

Funciones de profundidad local y aplicaciones a clasificación no supervisada

RESUMEN En la primera parte de esta tesis revisamos las funciones de profundidad y de los cuantiles multidimensionales. Complementamos los resultados existentes en la literatura con nuevos conocimientos matemáticos sobre la teoría general de las funciones estadísticas de profundidad. Mientras que las funciones de profundidad se utilizan para describir las características globales de distribuciones multidimensionales, las funciones de profundidad local (FPL) también detectan características locales como las modas y las zonas de baja probabilidad. Presentamos una clase general de funciones de profundidad local y estudiamos sus propiedades. En particular, mostramos que, a medida que el parámetro de localización diverge hacia el infinito, las FPL convergen a las funciones de profundidad, mientras que, cuando el parámetro de localización converge a cero, bajo la escala adecuada, las FPL convergen a la función de densidad correspondiente. Bajo ciertas hipótesis de diferenciabilidad, también obtenemos convergencia de sus derivadas. Esto abre la puerta a una serie de aplicaciones que incluyen la clasificación no supervisada, estimación de modas y de conjuntos de nivel. En particular, proponemos un nuevo algoritmo de clasificación no supervisada haciendo uso de FPL escalados. Finalmente, ilustramos el comportamiento muestral, finito, de las metodologías propuestas mediante experimentos numéricos y análisis de datos.ABSTRACT In the first part of this thesis we review depth functions and multidimensional quantiles. We complement results from the literature with new mathematical insights into the general theory of statistical depth functions. While depth functions are used to describe the global features of multidimensional distributions, local depth functions (LDFs) can also detect local features such as modes and regions with low probability mass. We introduce a general class of local depth functions and study its properties. Specifically, we show that, as the localizing parameter diverges to infinity, LDFs converge to depth functions, whereas, as the localizing parameter converges to zero and under appropriate scaling, LDFs converge to the underlying density. Under appropriate differentiability assumptions, we also obtain convergence of its derivatives. This opens the door to a series of applications including clustering, mode estimation, and upper level set estimation. In particular, we propose a new clustering algorithm via scaled LDFs. Finally, we illustrate the finite sample behavior of the proposed methods via numerical experiments and data analyses

Functional Symmetry and Statistical Depth for the Analysis of Movement Patterns in Alzheimer’s Patients

Black-box techniques have been applied with outstanding results to classify, in a supervised manner, the movement patterns of Alzheimer’s patients according to their stage of the disease. However, these techniques do not provide information on the difference of the patterns among the stages. We make use of functional data analysis to provide insight on the nature of these differences. In particular, we calculate the center of symmetry of the underlying distribution at each stage and use it to compute the functional depth of the movements of each patient. This results in an ordering of the data to which we apply nonparametric permutation tests to check on the differences in the distribution, median and deviance from the median. We consistently obtain that the movement pattern at each stage is significantly different to that of the prior and posterior stage in terms of the deviance from the median applied to the depth. The approach is validated by simulation