A Dirichlet process mixture regression model for the analysis of competing risk events

We develop a regression model for the analysis of competing risk events. The joint distribution of the time to these events is flexibly characterized by a random effect which follows a discrete probability distribution drawn from a Dirichlet Process, explaining their variability. This entails an additional layer of flexibility of this joint model, whose inference is robust with respect to the misspecification of the distribution of the random effects. The model is analysed in a fully Bayesian setting, yielding a flexible Dirichlet Process Mixture model for the joint distribution of the time to events. An efficient MCMC sampler is developed for inference. The modelling approach is applied to the empirical analysis of the surrending risk in a US life insurance portfolio previously analysed by Milhaud and Dutang (2018). The approach yields an improved predictive performance of the surrending rates.</p

Survival analysis of actuarial data with missing observations

Combining information from pension scheme datasets is of fundamental importance in order to obtain more consistent and efficient estimates of mortality rates, which are used when assessing and managing longevity risk. A major problem faced in these type of analysis is given by the case, not uncommon, that pension scheme datasets provide different sets of informations. In this work we develop techniques, based on missing data statistics, which aim at carrying out mortality analysis by making the best use of available information, with particular emphasis on individual socio-economic characteristics. In particular, the stratification of the combined mortality experience is avoided and the information not available for all units therein is not discarded. The techniques of this work are analysed from a three-fold perspective: i) the analysis of the mathematical conditions needed to uniquely identify the probability distribution of interest; ii) the analysis, adaptation and the development of fitting algorithms for tackling the inferential task; and iii) the analysis of the impact of using these techniques for the estimation of demographic and financial quantities of interest for an actuary

A hierarchical model for the joint mortality analysis of pension scheme data with missing covariates

A hierarchical model is developed for the joint mortality analysis of pension scheme datasets. The proposed model allows for a rigorous statistical treatment of missing data. While our approach works for any missing data pattern, we are particularly interested in a scenario where some covariates are observed for members of one pension scheme but not the other. Therefore, our approach allows for the joint modelling of datasets which contain different information about individual lives. The proposed model generalizes the specification of parametric models when accounting for covariates. We consider parameter uncertainty using Bayesian techniques. Model parametrization is analysed in order to obtain an efficient MCMC sampler, and address model selection. The inferential framework described here accommodates any missing-data pattern, and turns out to be useful to analyse statistical relationships among covariates. Finally, we assess the financial impact of using the covariates, and of the optimal use of the whole available sample when combining data from different mortality experiences

Inference on latent factor models for informative censoring

This work discusses the problem of informative censoring in survival studies. A joint model for the time to event and the time to censoring is presented. Their hazard functions include a latent factor in order to identify this joint model without sacrificing the flexibility of the parametric specification. Furthermore, a fully Bayesian formulation with a semi-parametric proportional hazard function is provided. Similar latent variable models have been described in literature, but here the emphasis is on the performance of the inferential task of the resulting mixture model with unknown number of components. The posterior distribution of the parameters is estimated using Hamiltonian Monte Carlo methods implemented in Stan. Simulation studies are provided to study its performance and the methodology is implemented for the analysis of the ACTG175 clinical trial dataset yielding a better fit. The results are also compared to the non-informative censoring case to show that ignoring informative censoring may lead to serious biases

A hierarchical model for the joint mortality analysis of pension scheme data with missing covariates

A hierarchical model is developed for the joint mortality analysis of pension scheme datasets. The proposed model allows for a rigorous statistical treatment of missing data. While our approach works for any missing data pattern, we are particularly interested in a scenario where some covariates are observed for members of one pension scheme but not the other. Therefore, our approach allows for the joint modelling of datasets which contain different information about individual lives. The proposed model generalizes the specification of parametric models when accounting for covariates. We consider parameter uncertainty using Bayesian techniques. Model parametrization is analysed in order to obtain an efficient MCMC sampler, and address model selection. The inferential framework described here accommodates any missing-data pattern, and turns out to be useful to analyse statistical relationships among covariates. Finally, we assess the financial impact of using the covariates, and of the optimal use of the whole available sample when combining data from different mortality experiences

Survival analysis of pension scheme mortality when data are missing

Missing data is a problem that may be faced by actuaries when analysing mortality data. In this paper we deal with pension scheme data, where the future lifetime of each member is modelled by means of parametric survival models incorporating covariates, which may be missing for some individuals. Parameters are estimated by likelihood-based techniques. We analyse statistical issues, such as parameter identifiability, and propose an algorithm to handle the estimation task. Finally, we analyse the financial impact of including covariates maximally, compared with excluding parts of the mortality experience where data are missing; in particular we consider annuity factors and mis-estimation risk capital requirements

Affine Mortality Models with Jumps: Parameter Estimation and Forecasting

In this paper, we investigate the dynamics of age-cohort survival curves under the assumption that the instantaneous mortality intensity is driven by an affine jump-diffusion (AJD) process. Advantages of an AJD specification of mortality dynamics include the avail- ability of closed-form expressions for survival probabilities afforded by an affine mortality specification and the ease with which we can incorporate sudden positive and negative shocks in mortality dynamics, reflecting events such as wars, pandemics, and medical advancements. As we are interested in modelling the evolution of mortality rates, we propose a state-space approach to calibrate the parameters of the affine mortality process. This ensures consistent survival curves in the sense that forecasts of survival probabilities have the same parametric form as the fitted survival curves. As the resulting state-space model is non-Gaussian due to the presence of jumps, we apply and assess a particle filter-based Markov chain Monte Carlo approach to estimate the model parameters. We illustrate our methodology by fitting one- factor Cox-Ingersoll-Ross and Blackburn-Sherris mortality models with asymmetric double exponential jumps to historical age-cohort mortality data from USA. We find that these one-factor models with jumps have good in-sample fit, but their forecasting performance suggests the need for additional latent factors to improve the accuracy of forecasts

Survival analysis of pension scheme mortality when data are missing

Missing data is a problem that may be faced by actuaries when analysing mortality data. In this paper we deal with pension scheme data, where the future lifetime of each member is modelled by means of parametric survival models incorporating covariates, which may be missing for some individuals. Parameters are estimated by likelihood-based techniques. We analyse statistical issues, such as parameter identifiability, and propose an algorithm to handle the estimation task. Finally, we analyse the financial impact of including covariates maximally, compared with excluding parts of the mortality experience where data are missing; in particular we consider annuity factors and mis-estimation risk capital requirements

LLM-based Solutions for Healthcare Chatbots: a Comparative Analysis

This paper discusses the challenges of using Large Language Models (LLMs) in medical chatbots for chronic disease self-management. Accordingly, we define an architecture specifically devised to deal with issues related to reliability, clinical trials, and privacy. Two solutions are compared to prevent data disclosure: a filtering mechanism for sensitive data with an external LLM, and a locally deployed LLM using open-source models. Experimental results underscore the challenges in effectively instructing the local LLM so as to provide performances comparable to GPT-3.5