Adaptive kernel estimation of the baseline function in the Cox model, with high-dimensional covariates

The aim of this article is to propose a novel kernel estimator of the baseline function in a general high-dimensional Cox model, for which we derive non-asymptotic rates of convergence. To construct our estimator, we first estimate the regression parameter in the Cox model via a Lasso procedure. We then plug this estimator into the classical kernel estimator of the baseline function, obtained by smoothing the so-called Breslow estimator of the cumulative baseline function. We propose and study an adaptive procedure for selecting the bandwidth, in the spirit of Gold-enshluger and Lepski (2011). We state non-asymptotic oracle inequalities for the final estimator, which reveal the reduction of the rates of convergence when the dimension of the covariates grows

On the Generalization Capacities of Neural Controlled Differential Equations

We consider a supervised learning setup in which the goal is to predicts an outcome from a sample of irregularly sampled time series using Neural Controlled Differential Equations (Kidger, Morrill, et al. 2020). In our framework, the time series is a discretization of an unobserved continuous path, and the outcome depends on this path through a controlled differential equation with unknown vector field. Learning with discrete data thus induces a discretization bias, which we precisely quantify. Using theoretical results on the continuity of the flow of controlled differential equations, we show that the approximation bias is directly related to the approximation error of a Lipschitz function defining the generative model by a shallow neural network. By combining these result with recent work linking the Lipschitz constant of neural networks to their generalization capacities, we upper bound the generalization gap between the expected loss attained by the empirical risk minimizer and the expected loss of the true predictor.Comment: Edited typo

A penalized algorithm for event-specific rate models for recurrent events

We introduce a covariate-specific total variation penalty in two semiparametric models for the rate function of recurrent event process. The two models are a stratified Cox model, introduced in Prentice et al. (1981), and a stratified Aalen's additive model. We show the consistency and asymptotic normality of our penalized estimators. We demonstrate, through a simulation study, that our estimators outperform classical estimators for small to moderate sample sizes. Finally an application to the bladder tumour data of Byar (1980) is presented

Learning the intensity of time events with change-points

International audienceWe consider the problem of learning the inhomogeneous intensity of a counting process, under a sparse segmentation assumption. We introduce a weighted total-variation penalization, using data-driven weights that correctly scale the penalization along the observation interval. We prove that this leads to a sharp tuning of the convex relaxation of the segmentation prior, by stating oracle inequalities with fast rates of convergence, and consistency for change-points detection. This provides first theoretical guarantees for segmentation with a convex proxy beyond the standard i.i.d signal + white noise setting. We introduce a fast algorithm to solve this convex problem. Numerical experiments illustrate our approach on simulated and on a high-frequency genomics dataset

Estimation in a Competing Risks Proportional Hazards Model Under Length-biased Sampling With Censoring

International audienceWhat population does the sample represent? The answer to this question is of crucial importance when estimating a survivor function in duration studies. As is well-known, in a stationary population, survival data obtained from a cross-sectional sample taken from the population at time $t_0$ represents not the target density $f(t)$ but its length-biased version proportional to $tf(t)$, for $t>0$. The problem of estimating survivor function from such length-biased samples becomes more complex, and interesting, in presence of competing risks and censoring. This paper lays out a sampling scheme related to a mixed Poisson process and develops nonparametric estimators of the survivor function of the target population assuming that the two independent competing risks have proportional hazards. Two cases are considered: with and without independent consoring before length biased sampling. In each case, the weak convergence of the process generated by the proposed estimator is proved. A well-known study of the duration in power for political leaders is used to illustrate our results. Finally, a simulation study is carried out in order to assess the finite sample behaviour of our estimators

Nonsense-Mediated mRNA Decay Impacts MSI-Driven Carcinogenesis and Anti-Tumor Immunity in Colorectal Cancers

Nonsense-mediated mRNA Decay (NMD) degrades mutant mRNAs containing premature termination codon (PTC-mRNAs). Here we evaluate the consequence of NMD activity in colorectal cancers (CRCs) showing microsatellite instability (MSI) whose progression is associated with the accumulation of PTC-mRNAs encoding immunogenic proteins due to frameshift mutations in coding repeat sequences. Inhibition of UPF1, one of the major NMD factors, was achieved by siRNA in the HCT116 MSI CRC cell line and the resulting changes in gene expression were studied using expression microarrays. The impact of NMD activity was also investigated in primary MSI CRCs by quantifying the expression of several mRNAs relative to their mutational status and to endogenous UPF1 and UPF2 expression. Host immunity developed against MSI cancer cells was appreciated by quantifying the number of CD3ε-positive tumor-infiltrating lymphocytes (TILs). UPF1 silencing led to the up-regulation of 1251 genes in HCT116, among which a proportion of them (i.e. 38%) significantly higher than expected by chance contained a coding microsatellite (P<2×10−16). In MSI primary CRCs, UPF1 was significantly over-expressed compared to normal adjacent mucosa (P<0.002). Our data provided evidence for differential decay of PTC-mRNAs compared to wild-type that was positively correlated to UPF1 endogenous expression level (P = 0.02). A negative effect of UPF1 and UPF2 expression on the host's anti-tumor response was observed (P<0.01). Overall, our results show that NMD deeply influences MSI-driven tumorigenesis at the molecular level and indicate a functional negative impact of this system on anti-tumor immunity whose intensity has been recurrently shown to be an independent factor of favorable outcome in CRCs