HEC Montréal, Canada, May 2 - 4, 2011

2011 Optimization Days

HEC Montréal, Canada, 2 — 4 May 2011

Schedule Authors My Schedule

MA10 Données de survie et processus de Poisson / Survival Data and Poisson Processes

May 2, 2011 10:30 AM – 12:10 PM

Location: Van Houtte

Chaired by Marc Fredette

4 Presentations

  • 10:30 AM - 10:55 AM

    The Poisson-Maximum Entropy Model for homogeneous Poisson Processes

    • Lotfi Khribi, presenter, HEC Montréal
    • Brenda MacGibbon, GERAD - Université du Québec à Montréal
    • Marc Fredette, GERAD - HEC Montréal

    This article proposes the use of the maximum entropy principle for the prediction of recurrent events. The maximum entropy (MaxEnt) distribution is the one that maximizes the entropy subject to specific constraints.
    We suggest a Bayesian model with the maximum entropy prior distribution to predict the number of future events for subjects already under observation. In our case, the intensity function we will use to model these events will be the one corresponding to a homogeneous Poisson process where the unknown rates are unobservable i.i.d. random effects. The prior distribution for these random rates was based on the principle of maximum entropy and obtained by maximizing Shannon's entropy subject to the conditions that the first two theoretical moments equal the empirical ones. In this article, we propose an approach which uses a Poisson-Maximum Entropy (P-MaxEnt) model based on the maximum entropy prior distribution as a competitor to the negative binomial model (NB). There are several reasons for comparing the (P-MaxEnt) model to a NB for the recurrent events. First, the (NB) is most commonly used model for over-dispersed recurrent events data and many data analysts are not familiar with the (P-MaxEnt). Secondly; there could be several models that provide a reasonable fit for a particular data set, but maximizing entropy is based on sound philosophical principles and merits study in this case. Therefore, we will investigate the advantages and the disadvantages of each.
    For the first two theoretical moments, the (MaxEnt) prior distribution corresponds to the truncated normal prior and for this reason the (P-truncated normal) model was compared with the (NB) one via two methods of estimation matching moments and maximum likelihood. The performance of the proposed approach is studied through Monte Carlo simulations.

  • 10:55 AM - 11:20 AM

    On Estimation and Testing for Jumps in the Hazard Density from Right Censored Prevalent Cohort Survival Data

    • Yassir Rabhi, presenter, McGill University

    We propose a methodology for estimating both the location and the size of a possible jump (change) in the hazard function based on right-censored data collected on prevalent cases. Both large and small sample behavior of the estimators are studied, analytically and by the means of simulations. The methodology is then applied to analyze a set of survival data collected as part of the Canadian Study of Health and Aging (CSHA) on patients with dementia.

  • 11:20 AM - 11:45 AM

    Sample Size/Power Calculation for Poisson and ZIP Regression Models

    • Nabil Channouf, presenter, GERAD
    • Marc Fredette, GERAD - HEC Montréal
    • Brenda MacGibbon, GERAD - Université du Québec à Montréal

    We investigate an approach for sample size calculations proposed by Shieh (2001) and we propose an extension to the ZIP regression model.
    We also study the effect of additional covariates on the Poisson regression
    model with various types of correlation matrices when the covariates have a multivariate normal distribution.

  • 11:45 AM - 12:10 PM

    Modélisation multidimensionnelle de données de comptage présentant de la surdispersion

    • Blache Paul Akpoué, presenter, Université de Montréal
    • Jean-François Angers, Université de Montréal

    Très souvent observé dans la réalité, le phénomène de surdispersion a largement été étudié dans le cas unidimensionnel. Cependant, le traitement des données multidimensionnelles souffrant de cette particularité s'avère nettement plus complexe. Nous présentons un modèle de Poisson multidimensionnel avec effets aléatoires afin de traduire la surdispersion. Une nouvelle méthode d’estimation basée sur l'intégration par Monte Carlo y est présentée, de même que les résultats d’une simulation. Enfin, une application en écologie mettant en relief l'impact des changements climatiques sur la répartition des espèces animales et végétales au Québec selon différents scénarii servira d’illustration.