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Etude de consistance et applications du modèle Poisson-Gamma : modélisation d'une dynamique de recrutement multicentrique.

Abstract : A clinical trial is a biomedical research which aims to consolidate and improve the biological and medical knowledges. The number of patients required il the minimal number of patients to include in the trial in order to insure a given statistical power of a predefined test. The calculation of this number is mandatory for the study to be published. The constitution of this patients' database is one of the fundamental issues of a clinical trial. To do so several investigation centres are opened. The duration between the first opening of a centre and the last recruitment of the needed number of patients is called the recruitemtn duration that we aim to model. The fisrt model goes back 50 years ago with the work of Lee, Williford et al. and Morgan with the idea to model the recruitment dynamic using Poisson processes. One problem emerge, that is the lack of caracterisation of the variabliity of recruitment between centers that is mixed with the mean of the recruitment rates. The most effective model is called the Poisson-gamma model which is baed on Poisson processes with random rates (Cox process) with gamma distribution. This model is at the very heart of this project. Different objectives have motivated the realisation of this thesis. First of all the validity of the Poisson-gamma model is established asymptotically. A simulation study that we made permits to give precise informations on the model validity in specific cases. Then some breaks in the recruitment process are possible. A question that arise is : How and must we take into account this phenomenon for the prediction of the recruitment duration. The study made tends to show that it is not necessary to take them into account. It also veered around to measure the impact of these breaks on the estimations of the model, that do not impact its validity under some stability hypothesis. An other issue inherent to a patient recruitment dynamic is the phenomenon of screening failure. An empirical Bayesian technique analogue to the one of the recruitment process is used to model the screening failure issue. This hierarchical Bayesian model permit to estimate the duartion of recruitment with screening failure consideration as weel as the probability to drop out from the study using the data at some interim time of analysis, giving predictions on the randomisation dynamic. The recruitment dynamic has an influence on the intrinsic caracteristics of the recruitment (number of empty centres, probabilities od recrutment for each centre, number of patients still on the ongoing study). These fundamental aspects give relevant indicators for the study follow-up. Multiples pplications in this sense are computed. The problematic of the recruitment dynamic can also be coupled with the dynamic of the study itself when it is longitudinal. The independance between these two processes allows easy estimations of the different parameters. The result is a global model of the patient pathway in the trail. Two key examples of such situations are survival data - the model permit to estimate the duration of the trail when the stopping criterion is the number of events observed, and the Markov model – the model permit to estimate the number of patients in a certain state for a given duartion of analysis. Finally a cost model is introduced and studied.
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Nathan Minois. Etude de consistance et applications du modèle Poisson-Gamma : modélisation d'une dynamique de recrutement multicentrique.. Statistiques [math.ST]. Université Toulouse III Paul Sabatier (UT3 Paul Sabatier), 2016. Français. ⟨tel-01815592⟩

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