Program:

09:00 – 09:05 : Opening

Abstracts for YRD September 20, 2024:

09:05 - 09:25 : Anas Mourahib
Title: Statistics of Extremes

Abstract:
On September 7, 2024, a flood tragically claimed the lives of at least 18 people in southern Morocco. To prevent such disasters in the future, we aim to construct a dike that is 1 meter higher than the ``once per 10000 year'' sea level. The challenge is that we have less than 100 years of data, which is similar to estimating the likelihood of an event that has not yet occurred. This is where Extreme Value Theory (EVT), a branch of statistics developed since the 1970s, comes into play. In this presentation, we will introduce two well-established main methods in EVT: the Block Maxima approach and the Threshold Exceedances approach. A brief application will follow to demonstrate how these methods can help in designing the dike.

09:25 - 09:50 : Stephane Lhaut
Title: Testing parametric models for the angular measure for bivariate extremes

Abstract:
The angular measure on the unit sphere characterizes the first-order dependence structure of the components of a random vector in extreme regions and is defined in terms of standardized margins. Its statistical recovery is an important step in learning problems involving observations far away from the center. In this paper, we consider the goodness-of- fit problem which consists of testing the adequacy of the extremal dependence structure of a bivariate random sample to a given parametric model. The proposed test statistic consists of a weighted L1-Wasserstein distance between a purely non-parametric, rank-based, estimator of the true angular measure obtained by maximizing a Euclidean likelihood, and an estimated version of the angular measure under the postulated parametric model. The asymptotic distribution of the test statistic is derived and used to obtain critical values for the proposed testing procedure via a parametric bootstrap. Consistency of the bootstrap algorithm is proved. A simulation study illustrates the finite-sample performance of the test for two popular models: the logistic and the Hüsler-Reiss models.

09:50 - 10:15 : Benjamin Deketelaere
Title: Quantile Regression with a Censored Covariate

Abstract:
In the last few years, there has been growing interest in regression with censored covariates. This is of interest e.g. when studying the symptom trajectory of a neurodegenerative disease. We are interested in studying quantile regression models with covariates that are either left, right or interval censored.  Quantile regression offers many advantages over more classical mean regression, like e.g. its ability to study the whole distribution as opposed to the center of the distribution. For instance, in a study on the factors that influence high blood pressure, quantile regression allows to focus on the factors that are important for individuals in the upper tail of the blood pressure distribution. We propose a linear quantile regression model, and propose a two-stage estimation procedure of the regression coefficients, in which both steps are based on maximum likelihood estimation. The first step consists in modeling the distribution of the censored covariate given the other covariates, whereas in the second step the quantile regression coefficients are estimated. To do this, we propose to use families of enriched exponential and enriched Laplace distributions, respectively, both of which use Laguerre polynomial expansions to make the families sufficiently rich and flexible. We investigate the finite sample performance of the proposed method by means of extensive simulations.  The developed methodology is also used to study the National Health and Nutrition Examination Survey data on the factors influencing high blood pressure.

10:15 - 10:40 : Coffee break 

10:40 - 11:15 : Patricia Ortega-Jiménez
Title: Comparisons of VaR and CoVaR in terms of the value of the conditional variable.

Abstract:
Let us consider a random vector (X, Y ). Given a risk level v ∈ [0, 1], the most extended risk measure is the Value at Risk, V aRv(Y ) = F−1(v), which represents the maximum expected loss. However, the V aRv (Y ) measures the risk of the single institution without accounting for interactions with other risks. A dependence-adjusted version of the Value at Risk is the Co- Value at risk, CoV aRv,u(Y |X), which stands for V aRv(Y |X = V aRu(X)) for the risk levels v ∈ [0,1] and u ∈ [0,1]. Our goal is to find the values of the institution X that lead to the CoV aR being greater than the V aR of Y , as relying solely on the V aR may not be sufficient to face financial losses. We compare these two measures in terms of the risk-level of the conditional variable, u. For v ∈ (0, 1), under regularity conditions and a positive dependence structure, there exists a unique cut point uv such that CoV aRv,uv (Y |X) ≥ V aRv(Y ) if and only if u ≥ uv. We will see that this value uv only depends on the dependence structure of the vector. In addition we will discuss sufficient conditions and implications of the existence of an upper bound u∗ ∈ (0, 1) such that.  uv ≤u∗ forall v∈(0,1).
Several examples of copulas with bounded and unbounded cut points are analyzed and a non-parametric estimator is provided. The presented results are mainly based on the recent paper: Ortega-Jiménez, P., Pellerey, F., Sordo, M. A., and Suárez-Llorens, A. (2024). Probability equivalent level for CoVaR and VaR. Insurance: Mathematics and Economics, 115, 22-35.

11:15 - 11:40 : Oussama Belhouari
Title: The Three-step method in a dynamic setting

Abstract:
A crucial issue in a dynamic framework, is how risk valuations at different times are interrelated. In this regard, the notion of time consistency was widely introduced and discussed in the literature. A time-consistent dynamic valuation is a pricing method according to which a product that will be, in almost all states of nature, cheaper than another one at a future date should already be cheaper today. Common actuarial premium principles are not time consistent. To this end, we link the latter with an iterated property. This paper aims at constructing a time-consistent, dynamic version of the Three-step method introduced in [Deelstra and Hieber, 2020], employing a backward iteration scheme. The backward scheme is exemplified in a dual-iteration approach using a classical application, specifically a Pure Endowment. Furthermore, we explore the continuous-time limit of the backward scheme, incorporating profit-sharing into the Pure Endowment to investigate a hybrid life payoff. Our analysis reveals that, due to time consistency, the price of the actuarial component in the Three-step method undergoes a substantial increase. To address this, and in accordance with [Devolder and Lebègue, 2016], we present a reduced time-consistent variant by decreasing the safety loads in each iterative step of the backward scheme.

11:40 - 12:15 : Luc Boone
Title: Application of inverse probability of censoring weighting (IPCW) in open-label cancer clinical trials with centrally reviewed endpoints: Illustrating and extending the methodology

Abstract:
Blinding of investigators (and patients) in randomized controlled trials is not always feasible. For subjective endpoints or outcome measures, this is especially problematic considering that assessment bias cannot be ruled out. In oncology, the endpoint progression-free survival (PFS) is commonly used and is defined as the time from randomization until tumor progression or death, whichever occurs first.  
Tumor progression assessment is mostly done through radiographic images, which is prone to assessment bias in open-label (non-blinded) clinical trials.
Blinded independent central review (BICR) of endpoints such as progression-free survival is carried out in open-label cancer trials to mitigate assessment bias of unblinded local investigators. In many cases, BICR takes places retrospectively. Patients for whom progressive disease was not confirmed by BICR are commonly censored at the last time of (local investigator) assessment, in the absence of follow-up radiographic assessment. The censoring for such unconfirmed progressions is generally assumed to be independent when estimating survival curves and hazard ratios, which is questionable. Rather, the censoring in this case might be dependent and violate the assumption of independent censoring, and bias the commonly used estimators.
The goals of the research project are to: First, illustrate and study the application of inverse probability of censoring weighting (IPCW) to adjust for dependent censoring (Robins, 1993) in the context of open-label cancer clinical trials with centrally reviewed subjective endpoints; Second, propose and study the extension of the methodology of IPCW in the described setting through the use of joint models for longitudinal and time-to-event data; And lastly, offer recommendations to applied clinical trial statisticians on when and how to implement the illustrated and proposed methods.
-    Robins JM. Information recovery and bias adjustment in proportional hazards regression analysis of randomized trials using surrogate markers. Proceedings of the Biopharmaceutical Section, American Statistical Association 1993; 24–33.