KAAKAI Sarah

This paper deals with the stochastic modeling of a class of heterogeneous population dynamics in a random environment. These Birth-Death-Swap populations generalize Markov multi-type Birth-Death processes, by considering swap events (moves between subgroups) in addition to demographic events, and allowing event intensities to be random functional of the population. The complexity of the problem is significantly reduced by modeling the jumps measure of the population, described by a multivariate counting process. In the spirit of Massouli\'e (1998), this process is defined as the solution of a stochastic differential system with random coefficients, driven by a multivariate Poisson random measure. The solution is obtained under weaker assumptions than usual, by thinning of a dominating point process driven by the same Poisson measure.This key construction rely on a general comparison result of independent interest. The second part is dedicated to averaging results when swap events are more frequent than demographic events. An important ingredient is the stable convergence which extends naturally the convergence in distribution in the presence of a random environment. The pathwise construction by domination yields straightforward tightness results, in particular for the population process which is considered as a simple variable on $\Omega \times \mathbb R^+$. At the limit, the demographic intensity functionals are averaged against random kernels depending on swap events. Finally, we show under a natural assumption the convergence of the aggregated population to a ``true'' Birth-Death process in random environment with density-dependence.

Background: This project was prompted by the ambition to investigate, from the outset, the potential consequences of a future translation to a human context of research on natural death prediction today actively conducted in the biology of ageing field. It is centered on ethical issues, challenges faced in medical decision processes and finally their implications in economic and insurance matters. Recent advances in biology have made predicting the onset of natural death a technically feasible prospect. Methods: This project resulted in a study ahead of application based on an interdisciplinary approach, a combination of philosophy, clinical psychology, medicine, demography, biology and actuarial science. The question was put into perspective with regard to contemporary theories of ageing as well as our understanding of what death is. Philosophy (literature review and conceptual analysis) and psychology (theory and clinical experience) have allowed us to break down into distinct themes the individual relationship to death, its anticipation and its prediction in order to better understand the challenges that the prediction of natural incoming death might raise. Our approach to the problem in the medical field has been focused on intensive care because of the high frequency of death secondary to acute illnesses. It is therefore natural that we have examined how the development of tools to predict the risk of death could become a medical decision-making tool and enable the teams involved to better cope with it. Demographic and actuarial approaches have allowed us to put prediction of death in the context of the long-standing analysis of mortality tables. Novel methods of death prediction pose new challenges to long-established assumptions of demographic models used in the implementation of pension and public health policies and insurance decisions. Outcomes: This interdisciplinary work has led to the co-construction of a framework for scientific and ethical reflection that can be relevant to define public health policy. Unlike a downstream approach that only provides data after the fact or at least after society has adopted a scientific and/or technological innovation, this work strives to accompany the implementation of the innovation and to anticipate its effects. Interpretation: In this study, we propose a first sketch of what the implications of death prediction as such could be - inasmuch as it affects both the awareness of death and its anticipation - from an individual, medical and social point of view . The potential benefits of such tools for society may yet be outweighed by ethically problematic applications. Here, we seek to provide a framework for reflection ahead of such applications. Funding: This project was partially funded by the IHSS (Institut Humanités, Sciences et Sociétés, Université Paris Diderot), the CNRS (Centre National de la Recherche Scientifique) and ATIP/Avenir young group leader program.

Abstract Background The discovery of biomarkers of ageing has led to the development of predictors of impending natural death and has paved the way for personalised estimation of the risk of death in the general population. This study intends to identify the ethical resources available to approach the idea of a long-lasting dying process and consider the perspective of death prediction. The reflection on human mortality is necessary but not sufficient to face this issue. Knowledge about death anticipation in clinical contexts allows for a better understanding of it. Still, the very notion of prediction and its implications must be clarified. This study outlines in a prospective way issues that call for further investigation in the various fields concerned: ethical, psychological, medical and social. Methods The study is based on an interdisciplinary approach, a combination of philosophy, clinical psychology, medicine, demography, biology and actuarial science. Results The present study proposes an understanding of death prediction based on its distinction with the relationship to human mortality and death anticipation, and on the analogy with the implications of genetic testing performed in pre-symptomatic stages of a disease. It leads to the identification of a multi-layered issue, including the individual and personal relationship to death prediction, the potential medical uses of biomarkers of ageing, the social and economic implications of the latter, especially in regard to the way longevity risk is perceived. Conclusions The present study work strives to propose a first sketch of what the implications of death prediction as such could be - from an individual, medical and social point of view. Both with anti-ageing medicine and the transhumanist quest for immortality, research on biomarkers of ageing brings back to the forefront crucial ethical matters: should we, as human beings, keep ignoring certain things, primarily the moment of our death, be it an estimation of it? If such knowledge was available, who should be informed about it and how such information should be given? Is it a knowledge that could be socially shared?.

Background: This project was prompted by the ambition to investigate, from the outset, the potential consequences of a future translation to a human context of research on natural death prediction today actively conducted in the biology of ageing field. It is centered on ethical issues, challenges faced in medical decision processes and finally their implications in economic and insurance matters. Recent advances in biology have made predicting the onset of natural death a technically feasible prospect. Methods: This project resulted in a study ahead of application based on an interdisciplinary approach, a combination of philosophy, clinical psychology, medicine, demography, biology and actuarial science. The question was put into perspective with regard to contemporary theories of ageing as well as our understanding of what death is. Philosophy (literature review and conceptual analysis) and psychology (theory and clinical experience) have allowed us to break down into distinct themes the individual relationship to death, its anticipation and its prediction in order to better understand the challenges that the prediction of natural incoming death might raise. Our approach to the problem in the medical field has been focused on intensive care because of the high frequency of death secondary to acute illnesses. It is therefore natural that we have examined how the development of tools to predict the risk of death could become a medical decision-making tool and enable the teams involved to better cope with it. Demographic and actuarial approaches have allowed us to put prediction of death in the context of the long-standing analysis of mortality tables. Novel methods of death prediction pose new challenges to long-established assumptions of demographic models used in the implementation of pension and public health policies and insurance decisions. Outcomes: This interdisciplinary work has led to the co-construction of a framework for scientific and ethical reflection that can be relevant to define public health policy. Unlike a downstream approach that only provides data after the fact or at least after society has adopted a scientific and/or technological innovation, this work strives to accompany the implementation of the innovation and to anticipate its effects. Interpretation: In this study, we propose a first sketch of what the implications of death prediction as such could be - inasmuch as it affects both the awareness of death and its anticipation - from an individual, medical and social point of view . The potential benefits of such tools for society may yet be outweighed by ethically problematic applications. Here, we seek to provide a framework for reflection ahead of such applications. Funding: This project was partially funded by the IHSS (Institut Humanités, Sciences et Sociétés, Université Paris Diderot), the CNRS (Centre National de la Recherche Scientifique) and ATIP/Avenir young group leader program.

A growing number of studies indicate a widening of socioeconomic inequalities in mortality over the past decades. It has therefore become crucially important to understand the impact of heterogeneity and its evolution on the future mortality of heterogeneous populations. In particular, recent developments in multi-population mortality have raised a number of questions, among which is the issue of evaluating cause-of-death reduction targets set by national and international institutions in the presence of heterogeneity. The aim of this paper is to show how the study of the population data and the population dynamics framework contribute to addressing these issues, by providing a new viewpoint on the evolution of aggregate mortality indicators in the presence of heterogeneity. Our findings rely on two datasets on the English population and cause-specific number of deaths by socioeconomic circumstances, over the period 1981-2015. The analysis of the data first highlights the complexity of recent demographic developments, characterized by significant composition changes in the population, with considerable variations according to the age class or cohort, along with a widening of socioeconomic inequalities. We then introduce a dynamic framework for studying the impact of composition changes on the mortality of the global population. In particular, we are interested in quantifying the impacts of cause-of-death mortality reduction in comparison with changes of composition in a heterogeneous population. We show how a cause of death reduction could be compensated for in the presence of heterogeneity, which could lead to misinterpretations when assessing public policies impacts and/or for the forecasting of future trends.

A growing number of studies indicate a widening of socioeconomic inequalities in mortality over the past decades. It has therefore become crucially important to understand the impact of heterogeneity and its evolution on the future mortality of heterogeneous populations. In particular, recent developments in multi-population mortality have raised a number of questions, among which is the issue of evaluating cause-of-death reduction targets set by national and international institutions in the presence of heterogeneity. The aim of this paper is to show how the study of the population data and the population dynamics framework contribute to addressing these issues, by providing a new viewpoint on the evolution of aggregate mortality indicators in the presence of heterogeneity. Our findings rely on two datasets on the English population and cause-specific number of deaths by socioeconomic circumstances, over the period 1981-2015. The analysis of the data first highlights the complexity of recent demographic developments, characterized by significant composition changes in the population, with considerable variations according to the age class or cohort, along with a widening of socioeconomic inequalities. We then introduce a dynamic framework for studying the impact of composition changes on the mortality of the global population. In particular, we are interested in quantifying the impacts of cause-of-death mortality reduction in comparison with changes of composition in a heterogeneous population. We show how a cause of death reduction could be compensated for in the presence of heterogeneity, which could lead to misinterpretations when assessing public policies impacts and/or for the forecasting of future trends.

This paper deals with the stochastic modeling of a general class of heterogeneous population dynamics structured by discrete subgroups. Such processes generalize classical multitype Birth- Death processes by allowing swap events, i.e. transfers from one subgroup to another. The variability of the environment is also included and the population evolution is not Markovian. We propose a new representation of the population based on its jump measure, characterized as a multivariate counting process with specific support conditions, and which together with the population defines a Birth-Death-Swap (BDS) system. We first prove a general result, on the construction by strong domination of multivariate counting processes solutions of stochastic differential equations driven by extended Poisson measures. Under weaker assumptions than usual, the existence of BDS systems strongly dominated by a Cox-Birth process is obtained. This pathwise comparison is the main tool to obtain tightness results in the second part of the paper. The BDS system in the presence of two timescales is then studied, when swap events occur at a faster timescale than demographic events. A general averaging result for the demographic counting process is proven. Classical averaging results obtained in the Markov case cannot be applied here, and in order to overcome this difficulty, we rely on the stable convergence of processes involved. This mode of convergence is particularly well-suited to our general framework. At the limit, the aggregated population become a Birth-Death process with averaged intensities, resulting from a non-trivial aggregation of the subgroups birth and death intensities.

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This thesis deals with the probabilistic modeling of heterogeneity in human populations and of its impact on longevity. Over the past few years, numerous studies have shown a significant increase in geographical and socioeconomic inequalities in mortality. New issues have emerged from this paradigm shift that traditional demographic models are not able solve, and whose formalization requires a careful analysis of the data, in a multidisciplinary environment. Using the framework of population dynamics, this thesis aims at illustrating this complexity according to different points of view: We explore the link between heterogeneity and non-linearity in the presence of composition changes in the population, from a mathematical modeling viewpoint. The population dynamics, called Birth Death Swap, is built as the solution of a stochastic equation driven by a Poisson measure, using a more general pathwise comparison result. When swaps occur at a faster rate than demographic events, an averaging result is obtained by stable convergence and comparison. In particular, the aggregated population converges towards a nonlinear dynamic. In the second part, the impact of heterogeneity on aggregate mortality is studied from an empirical viewpoint, using English population data structured by age and socioeconomic circumstances. Based on numerical simulations, we show how a cause of death reduction could be compensated in presence of heterogeneity. The last point of view is an interdisciplinary survey on the determinants of longevity, accompanied by an analysis on the evolution of tools to analyze it and on new modeling issues in the face of this paradigm shift.

This thesis deals with the probabilistic modeling of the heterogeneity of human populations and its impact on longevity. In recent years, numerous studies have shown an alarming increase in geographic and socioeconomic mortality inequalities. This paradigm shift poses problems that traditional demographic models cannot solve, and whose formalization requires a fine observation of data in a multidisciplinary context. With population dynamics models as a guideline, this thesis proposes to illustrate this complexity from different points of view: The first one proposes to show the link between heterogeneity and nonlinearity in the presence of changes in population composition. The process called Birth Death Swap is defined by an equation directed by a Poisson measure using a trajectory comparison result. When swaps are faster than demographic events, an averaging result is established by stable convergence and comparison. In particular, the aggregate population tends towards non-linear dynamics. We then study empirically the impact of heterogeneity on aggregate mortality, using data from the English population structured by age and socioeconomic circumstances. We show through numerical simulations how heterogeneity can compensate for the reduction of a cause of mortality. The last point of view is an interdisciplinary review on the determinants of longevity, accompanied by a reflection on the evolution of the tools to analyze it and the new modeling challenges in the face of this paradigm shift.