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International audience; We introduce binacox, a prognostic method to deal with the problem of detecting multiple cut-points per feature in a multivariate setting where a large number of continuous features are available. The method is based on the Cox model and combines one-hot encoding with the binarsity penalty, which uses total-variation regularization together with an extra linear constraint, and enables feature selection. Original nonasymptotic oracle inequalities for prediction (in terms of Kullback-Leibler divergence) and estimation with a fast rate of convergence are established. The statistical performance of the method is examined in an extensive Monte Carlo simulation study, and then illustrated on three publicly available genetic cancer data sets. On these high-dimensional data sets, our proposed method outperforms state-of-the-art survival models regarding risk prediction in terms of the C-index, with a computing time orders of magnitude faster. In addition, it provides powerful interpretability from a clinical perspective by automatically pinpointing significant cut-points in relevant variables.

Multi-state models can capture the different patterns of disease evolution. In particular, the illness-death model is used to follow disease progression from a healthy state to an intermediate state of the disease and to a death-related final state. We aim to use those models in order to adapt treatment decisions according to the evolution of the disease. In state-of-the art methods, the risks of transition between the states are modeled via (semi-) Markov processes and transition-specific Cox proportional hazard (P.H.) models. The Cox P.H. model assumes that each variable makes a linear contribution to the model, but the relationship between covariates and risks can be more complex in clinical situations. To address this challenge, we propose a neural network architecture called illness-death network (IDNetwork) that relaxes the linear Cox P.H. assumption within an illness-death process. IDNetwork employs a multi-task architecture and uses a set of fully connected subnetworks in order to learn the probabilities of transition. Through simulations, we explore different configurations of the architecture and demonstrate the added value of our model. IDNetwork significantly improves the predictive performance compared to state-of-the-art methods on a simulated data set, on two clinical trials for patients with colon cancer and on a real-world data set in breast cancer.

We introduce a supervised learning mixture model for censored durations (C-mix) to simultaneously detect subgroups of patients with different prognosis and order them based on their risk. Our method is applicable in a high-dimensional setting, i.e. with a large number of biomedical covariates. Indeed, we penalize the negative log-likelihood by the Elastic-Net, which leads to a sparse parameterization of the model and automatically pinpoints the relevant covariates for the survival prediction. Inference is achieved using an efficient Quasi-Newton Expectation Maximization algorithm, for which we provide convergence properties. The statistical performance of the method is examined on an extensive Monte Carlo simulation study and finally illustrated on three publicly available genetic cancer datasets with high-dimensional covariates. We show that our approach outperforms the state-of-the-art survival models in this context, namely both the CURE and Cox proportional hazards models penalized by the Elastic-Net, in terms of C-index, AUC( t) and survival prediction. Thus, we propose a powerful tool for personalized medicine in cancerology.

Background & Aims Recent studies have shown that cancers arise as a result of the positive selection of driver somatic events in tumor DNA, with negative selection playing only a minor role, if any. However, these investigations were concerned with alterations at nonrepetitive sequences and did not take into account mutations in repetitive sequences that have very high pathophysiological relevance in the tumors showing microsatellite instability (MSI) resulting from mismatch repair deficiency investigated in the present study. Methods We performed whole-exome sequencing of 47 MSI colorectal cancers (CRCs) and confirmed results in an independent cohort of 53 MSI CRCs. We used a probabilistic model of mutational events within microsatellites, while adapting pre-existing models to analyze nonrepetitive DNA sequences. Negatively selected coding alterations in MSI CRCs were investigated for their functional and clinical impact in CRC cell lines and in a third cohort of 164 MSI CRC patients. Results Both positive and negative selection of somatic mutations in DNA repeats was observed, leading us to identify the expected true driver genes associated with the MSI-driven tumorigenic process. Several coding negatively selected MSI-related mutational events (n = 5) were shown to have deleterious effects on tumor cells. In the tumors in which deleterious MSI mutations were observed despite the negative selection, they were associated with worse survival in MSI CRC patients (hazard ratio, 3; 95% CI, 1.1–7.9; P = .03), suggesting their anticancer impact should be offset by other as yet unknown oncogenic processes that contribute to a poor prognosis. Conclusions The present results identify the positive and negative driver somatic mutations acting in MSI-driven tumorigenesis, suggesting that genomic instability in MSI CRC plays a dual role in achieving tumor cell transformation. Exome sequencing data have been deposited in the European genome–phenome archive (accession: EGAS00001002477)., Graphical abstract

We consider the problem of estimating the intensity of a counting process in high-dimensional time-varying Aalen and Cox models. We introduce a covariate-specific weighted total-variation penalization, using data-driven weights that correctly scale the penalization along the observation interval. We provide theoretical guaranties for the convergence of our estimators and present a proximal algorithm to solve the convex studied problems. The practical use and effectiveness of the proposed method are demonstrated by simulation studies and real data example.

IF 5.65; International audience; Background Every colorectal cancer (CRC) patient should be tested for microsatellite instability (MSI, a marker for defective DNA mismatch repair) as a first screen for Lynch syndrome (LS). In this study, we investigated whether it may be possible to improve the detection of MSI in CRC. We examined whether the HT17 DNA repeat (critical for correct splicing of the chaperone HSP110) might constitute a superior marker for diagnosis of the MSI phenotype in patients with CRC compared with the standard panel of markers (pentaplex).Methods The HT17 polymorphism was analysed in germline DNA from 1037 multi-ethnic individuals. We assessed its sensitivity and specificity for detecting MSI in a multicentre, population-based cohort of 685 patients with CRC and an additional series of 70 patients with CRC considered to be at-risk of LS. All cases were screened earlier for MSI using pentaplex markers. Cases showing discordant HT17/pentaplex results were further examined for the expression of mismatch repair proteins.Results HT17 status was analysed independently and blinded to previous results from pentaplex genotyping. HT17 showed no germline allelic variation outside a very narrow range. Compared with the pentaplex panel, HT17 showed better sensitivity (0.984 (95% CI 0.968 to 0.995) vs 0.951 (95% CI 0.925 to 0.972)) and similar specificity (0.997 (95% CI 0.989 to 1.000) for both) for the detection of MSI. Furthermore, HT17 alone correctly classified samples judged to be uncertain with the pentaplex panel and showed excellent ability to detect MSI in patients with LS.Conclusions HT17 simplifies and improves the current standard molecular methods for detecting MSI in CRC.

International audience; The purpose of this article is to provide an adaptive estimator of the baseline function in the Cox model with high-dimensional covariates. We consider a two-step procedure : first, we estimate the regression parameter of the Cox model via a Lasso procedure based on the partial log-likelihood, secondly, we plug this Lasso estimator into a least-squares type criterion and then perform a model selection procedure to obtain an adaptive penalized contrast estimator of the baseline function. Using non-asymptotic estimation results stated for the Lasso estimator of the regression parameter , we establish a non-asymptotic oracle inequality for this penalized contrast estimator of the baseline function, which highlights the discrepancy of the rate of convergence when the dimension of the covariates increases.

This paper deals with a model of possibly dependent competing risks in the presence of additional independent censoring. Under the assumption that the cumulative incidence functions are proportional or equivalently that the cause-specific cumulative hazard functions are proportional, we derive a maximum likelihood estimator for the cumulative incidence functions. Asymptotic results are derived for our estimator namely strong consistency, convergence rate, weak convergence and strong approximation. Pointwise confidence bands are then constructed. Simulation results are carried out to assess the accuracy of the pointwise confidence bands and to investigate the effect of model misspecification. We also briefly consider the case of independent competing risks with proportional net cumulative hazard functions in the presence of independent censoring.

In addition to the right-censoring of the lifetimes, sampling bias pos- sibly occurs in many situations while collecting the data. In practical situations, the form of the bias function is always assumed to be known, but if no information is available on the selection bias this can turn out to be unbearable. We provide a model selection strategy for estimating the hazard and the density functions in presence of both censoring and unknown sampling bias. We use a new sampling scheme description based on the Lexis diagram including time-window or cohort studies. Adaptive projection estimators on trigonometric bases are developed by contrast penalization and optimal nonparametric rates of convergence are given. Both estimators are practically studied through simulation experiments in the case of the time-window study. observable r.v. has p.d.f. given by w(x)f(x)/ R w(u)f(u)du, for all x > 0. In this case, the r.v. is said to suffer from a "selection bias" and one may heuristically say that selection bias arises when the event {X = x} is observed with a probability proportional to w(x). Bias may occur in the following kind of model. Consider, in a population of individuals I, the r.v.'s of their birth dates (�i)i2I, and the non-negative r.v.'s of

The aim of this paper is to carry out statistical inference in a competing risks setup when only selection-biased observation of the data of interest is available. We introduce estimators of the cumulative incidence functions and study their joint large sample behavior.

In a population of individuals, where the random variable (r.v.) σ denotes the birth time and X the lifetime, we consider the case, where an individual can be observed only if its life-line $$\mathcal{L}$$ (σ, X) = {(σ + y, y), 0 ≤ y ≤ X} intersects a given Borel set S in ℝ × ℝ+. Denoting by σ S and X S the birth time and lifetime for the observed individuals, we point out that the distribution function (d.f.) F S of the r.v. X S suffers from a selection bias in the sense that F S = ∝ w d F/μ S, where w and μ S depend only on the distribution of σ and on F, the d.f. of X. Assuming in addition that the r.v. X S is randomly right-censored as soon as the individual is selected, we construct a productlimit estimator $$\hat F_\mathcal{S} $$ for the d.f. F S and a nonparametric estimator ŵ for the weight function w. We prove a consistency result for ŵ and a weak convergence result for $$\hat F_\mathcal{S} $$ . We establish in addition an exponential bound for $$\hat F_\mathcal{S} $$ .

We 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 independent identically distributed 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 data set.

Resume Nous considerons le probleme de l'estimation de la fonction de repartition G d'une variable aleatoire (v.a.) positive X a partir de l'observation d'une v.a. biaisee Y de fonction de repartition F w = ∫ w ( x ) d G ( x ) / μ w , ou w est une fonction de poids inconnue. En supposant de plus que l'echantillon issu de la fonction de repartition F w est censure a droite, nous construisons un estimateur G ˆ de la fonction de repartition G pour lequel on enonce un theoreme de consistance forte et de convergence faible. Pour citer cet article : A. Guilloux, C. R. Acad. Sci. Paris, Ser. I 342 (2006).

In many practical situations, such as cross-sectional sampling, the observed random sample suffers from selection bias in the sense that it does not represent the target population. This paper considers the problem of estimating the target survivor function when the data for two independent competing risks having proportional hazards is observed under such a selection bias. The large sample behavior of the proposed estimator is studied through martingale representation and stochastic integrals.

Resume Nous considerons une population dans laquelle la duree de vie X est censuree a droite de facon informative par une v.a. positive Y, on obtient alors une v.a. Z = X ∧ Y . Cette v.a. Z est a son tour censuree a droite de facon non informative par une v.a. positive C. Dans le modele de Koziol–Green generalise, c'est-a-dire en supposant que X et Y ont des fonctions de risques proportionnelles, nous introduisons un estimateur Λ ˆ X de la fonction de risque cumule Λ X de X et etudions ses proprietes asymptotiques. Pour citer cet article : S. Geffray, A. Guilloux, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

Resume Considerons une population d'individus sujets a deux causes de mort. Nous observons les individus vivants au temps t 0 et nous les suivons jusqu'a la mort. A partir de cet echantillon biaise en longueur, nous proposons un estimateur de la fonction de survie pour les durees de vie initiales (i.e. pour toute la population) sous l'hypothese des risques proportionnels pour les deux causes de mort. Le comportement asymptotique de notre estimateur est egalement etudie. Pour citer cet article : J.-Y. Dauxois et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).

The mortality and incidence from stomach cancer were compared in Japan (a country with a high incidence where there was full application of mass screening during this period) and 2 countries with no screening policy: the USA (with a very low incidence) and Slovenia (with an intermediate rate). The registered cases of stomach cancer were from the Osaka Cancer Registry, the Slovenian National Cancer Registry and the Surveillance, Epidemiology, and End Results (SEER) registries in the USA. In the period 1975-95, the age-adjusted incidence rate (/100,000) of stomach cancer declined in the 3 countries, as follows: Japan, from 76.0 to 53.0 in men and 38.4 to 21.3 in women; Slovenia, from 40.2 to 24.1 in men and 16.6 to 10.8 in women; and the USA, from 9.5 to 6.9 in men and 4.3 to 2.9 in women. During the same period, the age-adjusted mortality rate declined, as follows: Japan, from 60.2 to 34.2 in men and 30.5 to 14.1 in women; Slovenia, from 37.7 to 21.2 in men and 13.8 to 9.0 in women; the USA, from 5.6 to 4.7 in men and 2.5 to 2.3 in women. In the period studied, specific trends on incidence and mortality with a cohort effect occurred only in Japan: analysis by the age period-cohort model confirmed that the decline has occurred since the generations born in 1910. The trend therefore corresponds to unplanned prevention through changes in environmental factors occurring since the early 20th century. The study of stage-specific incidence rates confirmed the declining trend for regional cancer, whereas there was an increase in the incidence of localized cancer, associated with a period effect in 1975-95. This is attributed to the policy of early detection of stomach cancer, with the inclusion of intramucosal lesions of favorable prognosis and explains why mortality decreased faster than incidence during the period.

International audience; This paper considers statistical inference for the rate function of a recurrent event process. We study two semi-parametric models of event-specific types. These kind of models are stratified with respect to each event which allows more flexibility to fit the data. The first model studied in this paper was introduced by Prentice et al. and has a multiplicative form. The second one is based on the Aalen model introduced in the context of survival data and has an additive form. For reasonable sizes of sample in event-specific models the number of estimated parameters can be very large compared to the number of covariates. In order to remedy to this over-parametrization, a total-variation penalty is used which constrain some of the parameters to be constant. The asymptotic behavior of the penalized estimator is derived. Through a simulation study and analysis of real data, the performance of our estimator is compared with the unconstrained estimator and the Andersen and Gill constant estimator.

International audience; What 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.

International audience; We consider the problem of estimation from right-censored data, when the censoring indicator is possibly missing. We compare different estimatio/imputation strategies for recovering nuisance functional parameters. More precisely, we propose either a parametric strategy following a logistic model standard or a pure nonparametric regression strategy. We provide theoretical properties and numerical comparisons for these procedures.

International audience; In this paper, we consider the problem of hazard rate estimation in presence of covariates, forsurvival data with censoring indicators missing at random. We propose in the context usually denoted by MAR (missing at random, in opposition to MCAR, missing completely at random, which requires an additional independence assumption), nonparametric adaptive strategies based on model selection methods for estimators admitting finite dimensional developments in functional orthonormal bases. Theoretical risks bounds are provided, they prove that the estimators behave well in term of Mean Square Integrated Error (MISE). Simulation experiments illustrate the statistical procedure.

Background & Aims Patients with colorectal tumors with microsatellite instability (MSI) have better prognoses than patients with tumors without MSI, but have a poor response to 5-fluorouracil–based chemotherapy. A dominant-negative form of heat shock protein (HSP)110 (HSP110DE9) expressed by cancer cells with MSI, via exon skipping caused by somatic deletions in the T 17 intron repeat, sensitizes the cells to 5-fluorouracil and oxaliplatin. We investigated whether HSP110 T 17 could be used to identify patients with colorectal cancer who would benefit from adjuvant chemotherapy with 5-fluorouracil and oxaliplatin. Methods We characterized the interaction between HSP110 and HSP110DE9 using surface plasmon resonance. By using polymerase chain reaction and fragment analysis, we examined how the size of somatic allelic deletions in HSP110 T 17 affected the HSP110 protein expressed by tumor cells. We screened 329 consecutive patients with stage II–III colorectal tumors with MSI who underwent surgical resection at tertiary medical centers for HSP110 T 17 . Results HSP110 and HSP110DE9 interacted in a 1:1 ratio. Tumor cells with large deletions in T 17 had increased ratios of HSP110DE9:HSP110, owing to the loss of expression of full-length HSP110. Deletions in HSP110 T 17 were mostly biallelic in primary tumor samples with MSI. Patients with stage II–III cancer who received chemotherapy and had large HSP110 T 17 deletions (≥5 bp; 18 of 77 patients, 23.4%) had longer times of relapse-free survival than patients with small or no deletions (≤4 bp; 59 of 77 patients, 76.6%) in multivariate analysis (hazard ratio, 0.16; 95% confidence interval, 0.012–0.8; P = .03). We found a significant interaction between chemotherapy and T 17 deletion ( P = .009). Conclusions About 25% of patients with stages II–III colorectal tumors with MSI have an excellent response to chemotherapy, due to large, biallelic deletions in the T 17 intron repeat of HSP110 in tumor DNA.

The historical model of hematopoiesis, mainly derived from murine studies, is based on the existence of a single hematopoietic stem cell (HSC) capable of generating all blood cell lineages. However this model has been challenged by the proposal of four types of murine HSC, which differ by their relative contribution to the myeloid and lymphoid lineages. Here we have used data from a gene therapy trial to treat Wiskott-Aldrich syndrome (WAS) to explore hematopoiesis in humans. In the trial, the therapeutic vector (lentivirus) integrates into the genome at unique positions in each hematopoietic stem and progenitor cell (HSPC) and is consequently transmitted to all its progeny. Thus hematopoietic ontogeny in humans can be inferred by tracking the appearance of unique integration sites in fractionated blood cell populations. This provides a unique opportunity to model the developmental complexity of the human haematological system. Considerable effort over the last 15 years has been devoted to optimizing retroviral integration sites (RIS) analysis using ligation mediated PCR (LM-PCR), combined with acoustic shearing and high-throughput Illumina sequencing. Acoustic shearing enables more precise quantification of RIS abundance through the enumeration of the various sizes of shear fragments (SonicAbundance) containing a given RIS, which correspond to individual ancestor HSPC and its blood progeny. In four WAS patients treated by gene therapy, we have sorted peripheral blood samples for 5 cell types: myeloid (granulocytes and monocytes) and lymphoid subpopulations (T, B and NK cells), and analysed their RIS profile. Each RIS corresponds to a particular stem/progenitor cell clone, with a particular pattern defined by its presence or absence in each of the 5 lineages. These data are then use to reconstruct aspects of the hematopoietic hierarchy. In order to face the challenging issue of cell sorting contamination we have been using a stringent sort precision mode and we treat residual contamination explicitly in downstream statistical models. Using these approaches, we have characterized up to tens of thousands RIS per patients with a follow up of 4 years. In order to minimize biases due to sparse sampling, we concentrate on the more abundant RIS clones that can be more easily caught and are therefore analysed more reliably. We showed that a significant fraction of RIS clones are detected in a single lineage, while other RIS clones are characterized by different levels of contribution to the myeloid and lymphoid lineages, highlighting the heterogeneity of human HSC. Clones contributing to all 5 lineages are readily recovered but this study also unravels a diversity of inferred hematopoietic programs with various potentials contributing to human blood homeostasis. Longitudinal analysis of clonal dynamics is ongoing, with preliminary results highlighting the maintenance of this heterogeneity of HSPC over time. These new findings provide unique data on human hematopoiesis based on gene corrected WAS patients. Disclosures No relevant conflicts of interest to declare.

We consider a general high-dimensional additive hazards model in a non-asymptotic setting, including regression for censored-data. In this context, we consider a Lasso estimator with a fully data-driven ℓ1 penalization, which is tuned for the estimation problem at hand. We prove sharp oracle inequalities for this estimator. Our analysis involves a new “data-driven” Bernstein’s inequality, that is of independent interest, where the predictable variation is replaced by the optional variation.

We propose in this work an original estimator of the conditional intensity of a marker-dependent counting process, that is, a counting process with covariates. We use model selection methods and provide a non asymptotic bound for the risk of our estimator on a compact set. We show that our estimator reaches automatically a convergence rate over a functional class with a given (unknown) anisotropic regularity. Then, we prove a lower bound which establishes that this rate is optimal. Lastly, we provide a short illustration of the way the estimator works in the context of conditional hazard estimation., 31 pages, 3 figures

Background: The aim was to determine the values of p53 tumour expression and microsatellite instability (MSI) phenotype to predict benefit from adjuvant chemotherapy of colon cancer by 5-fluorouracil and leucovorin (FL) alone or with oxaliplatin (FOLFOX). Patients and methods: This retrospective study included 233 unselected patients with stage III colon cancer treated by FL (n = 124) or FOLFOX (n = 109). The impact of p53 expression and MSI on disease-free survival (DFS) was defined using univariate and multivariate analyses. A Cox proportional hazards model was specifically designed to evaluate the interaction between chemotherapy and these genetic alterations. Results: In univariate analyses, addition of oxaliplatin significantly improved DFS provided that tumour overexpressed p53 [hazard ratio (HR) 0.39; 95% confidence interval (CI) 0.19–0.82; P = 0.01] or displayed MSI phenotype (HR 0.17; 95% CI 0.04–0.68; P = 0.01). In multivariate analyses, p53 was confirmed as an independent factor predictive of benefit from FOLFOX (P = 0.03), while the interaction of MSI with chemotherapy could not be determined in the absence of relapse in the MSI group treated with FOLFOX. Conclusion: Our observations indicate that MSI status and p53 expression may influence the impact of oxaliplatin on adjuvant treatment of stage III colon cancer patients.

We consider projection estimator methods for the nonparametric estimation of the density of i.i.d. biased observations with a general known bias function w and under right censoring. Adaptive procedures to catch the optimal estimator among a collection by contrast penalization are investigated and proved to give efficient estimators with optimal nonparametric rates of convergence. Monte-Carlo experiments complete the study and illustrate the method.

In a population of individuals, where the random variable (r.v.) σ denotes the birth time and X the lifetime, we consider that an individual can be observed only if its life-line L(σ, X) = {(σ + y, y),0 ≤ y ≤ X} intersects a general Borel set S in ℝ × ℝ+. Denoting by σ s and X s the birth time and lifetime for the observed individuals, we point out that the distribution function (d.f.) F s of the r.v. X s suffers from a selection bias in the sense that F s = ƒ wdF/μ s , where w and μ s depend only on the distribution of σ and F is the d.f. of X. Considering in addition that the r.v. X s is randomly right-censored, as soon as the individual is selected, we construct a product-limit estimator F s for the d.f. F s and a nonparametric estimator ŵ for the weighting function w. We investigate the behavior of these estimators through a simulation study.

Consider a population of individuals who experience K dierent causes of death.We observe the ones alive at time t0 and follow them until death or possiblecensoring time. Given this length biased sample, we introduce estimators ofthe cumulative incidence functions of "initial survival times" (i.e. for the entirepopulation) in a competing risks setup. The large sample behavior of our estimatorsis studied and tests for equality of cumulative incidence functions aredeveloped.