Abstract:
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Poisson regression models are commonly used in Environmental Epidemiology for count data in health outcomes, but sometimes data are censored because of confidential concerns. Previous work usually defined the censored data as missingness, and removed them from statistical analysis, while the statistical power reduces apparently. The censored Poisson model was developed to deal with censored data, but the estimating algorithm is hard to reach convergence in practical research. This study adopted the Markov chain Monte Carlo (MCMC) and integrated nested Laplace approximation (INLA) for estimating unknown parameters in the censored Poisson model. Compared to MCMC, simulations in the study result in estimated coefficients closer to true values from INLA when the censored proportion got larger. The relative error is 0.4 for MCMC and 0.005 for INLA. In addition, INLA ran faster than MCMC about 390-fold (2 minutes vs. 13 hours) when fitting a censored Poisson model. In conclusion, the INLA provides an efficient algorithm to conduct accurate estimates in the censored Poisson model regardless the proportion of censorship.
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