Statistical Modelling 11 (2011), 471–488
Bayesian first order auto-regressive latent variable models for multiple binary sequences
Federica Giardina
Swiss Tropical and Public Health Institute
Basel
Switzerland
Alessandra Guglielmi
Politecnico di Milano,
Dipartimento di Matematica,
Piazza Leonardo da Vinci, 32
I–20133 Milano
Italy
and
CNR-IMATI
Milano
Italy
eMail: alessandra.guglielmi@polimi.it
Fernando A Quintana
Pontificia Universidad Católica de Chile
Santiago
Chile
Fabrizio Ruggeri
CNR-IMATI
Milano
Italy
Abstract:
Longitudinal clinical trials often collect long sequences of binary data monitoring a disease process over time. Our application is a medical study conducted in the US by the Veterans Administration Cooperative Urological Research Group to assess the effectiveness of a chemotherapy treatment (thiotepa) in preventing recurrence on subjects affected by bladder cancer. We propose a generalized linear model with latent auto-regressive structure for longitudinal binary data following a Bayesian approach. We discuss inference as well as sensitivity to prior choices for the bladder cancer data. We find that there is a significant treatment effect in the sense that treated patients have much smaller predicted recurrence probabilities than placebo patients.
Keywords:
binary longitudinal data; first order auto-regressive model; hierarchical Bayesian modelling; latent variables
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