Bayesian Analysis of Zero-Truncated Poisson Model: Application to the Self-Controlled Case-series Design

Henry Athiany,George Orwa,Samuel Mwalili,Anthony Wanjoya

doi:10.11648/j.ijdsa.20200606.12

Abstract

A Bayesian Self-Controlled Case-Series (BSCCS) method is proposed and used to estimate the relative risk of an adverse drug event (ADE) given transient exposure to a drug or vaccine. Markov Chain Monte Carlo (MCMC) methods through WinBUGS are used to estimate parameters of the model given different settings and sample sizes. The method explores full posterior distribution for the model to obtain the relative risk estimates which at times is a challenge in likelihood analysis of complex models. Data was simulated for 10, 20 or 50 children aged between 365 and 730 days, and received their first dose of the measles, mumps, and rubella (MMR) vaccine within this follow-up period. Each child had the outcome event – viral-meningitis, in the follow-up period. Results of the data analysis indicated an increased risk of viral meningitis within 14-35 days post vaccination. Results of Bayesian approach are quite similar to the MLE risk estimates, assuming a non-informative prior. However, with more informative priors, BSCCS method produced better results with narrow credible intervals. For the real data, children aged 365 and 730 days, exposed to MMR vaccine, with viral meningitis (single exposure) were considered. While the frequentist approach estimated the incidence rate ratio (IRR) as IRR 12.037 (95% CI (3.002 - 48.259)), the Bayesian estimate was IRR 8.971 (95% CI 2.869 - 27.994). This is similar to the MLE results but with narrow credible intervals. In all cases, there is significantly higher risk of viral meningitis within 14-35 days post MMR vaccination. Results from the simulation study and real data revealed that the BSCCS model fitted better than the SCCS model.

Highlights

Truncated data arise when we restrict the range of possible outcomes of the data in some way [1]
The same model was later fitted to the real data sets of MMR vaccine, with the adverse drug event (ADE) being viral meningitis [5]
Brook-Gelman-Rubin statistic obtained was 1.05 which is very close to the recommended value of 1.1. This confirms that convergence of the Markov Chain Monte Carlo (MCMC) has been attained, and that a large portion of the samples being drawn are from distributions that are similar to the target distribution

Summary

Introduction

Truncated data arise when we restrict the range of possible outcomes of the data in some way [1]. Given the underlying assumptions of the supported count distributions; Hardin and Hilbe [3] pointed out that modeling such count data using regression methods that are based on non-truncated distributions is more likely to give biased results. This, becomes more likely when the mean response is closer to zero [3] To deal with this problem of influence on inference from biased results, several methods of regression have been proposed by researchers to model such data for different situations [3]. These include among others, the Zero-Truncated Negative Binomial (ZTNB) and the Zero-Truncated Poisson (ZTP) regression. One of the modelling designs that employs the ZTP approach is the self-controlled case-series (SCCS) design [4]

Methods

Results

Discussion

Conclusion