Tesi di LAUREA SPECIALISTICA |
Titolo | Bayesian nonparametric AR(1)-Models for multiple binary sequences |
Data | 2011-12-30 |
Autore/i | Cadonna, Annalisa |
Relatore | Guglielmi, A. |
Relatore | Quintana, F.A. | Full text | non disponibile |
Abstract | In this work we provide a class of Bayesian nonparametric models for longitudinal binary data and an application of these models to a clinical study. After a brief introduction to the nonparametric Bayesian approach and the Dirichlet process, we outline the main properties of the dependent Dirichlet process (DDP). This process is a component part of the models we propose. The dataset we consider originate from a bladder cancer study conducted in the USA in the 1971 by the Veterans Administration Cooperative Urological Research Group (VACURG) on the effectiveness of the chemiotherapic treatment (thiotepa) in preventing recurrence of bladder cancer tumors. The patients in the study are assigned to a treatment or a placebo group. The dataset consists of binary observations recording every three month indicators of recidive. Specically, we propose three new Bayesian rst order autoregressive
nonparametric models. These models take into account the correlation within each subject via the introduction of latent variables with a Markovian structure. All the inferences for the proposed models were computed via the JAGS software. Moreover, we derived the analytical expressions of the fullconditional distributions of the parameters needed to build a MCMC Gibbs sampler algorithm and we coded the algorithm in C language for one of the proposed models. We computed posterior Bayesian estimates of the parameters of interest and of the probability of having a recidive for some subjects already in the study or for a new subject assigned either to treatment or to
placebo group. |
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