Variances | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Model | IRR | (SE) | (95% CI) | p≤ | ESS | Level | Variance (SE) | (95% CI) | ESS | ||

Unmatched | 1 | 4.756 | (1.027) | (4.600 to 4.918) | 0.0001 | ||||||

Matched | 2 | 4.744 | (1.028) | (4.582 to 4.912) | 0.0001 | 2 | 1.012 | (0.041) | (0.931 to 1.092) | ||

Over dispersed | 3 | 4.878 | (1.141) | (4.145 to 5.740) | 0.0001 | 2 | 8.535 | (0.156) | (8.229 to 8.842) | ||

3 | 0.025 | (0.065) | (−0.103 to 0.152) | ||||||||

MCMC over dispersed | 4 | 5.789 | (1.075) | (5.343 to 6.273) | 0.0001 | 6551 | 2 | 1.267 | (0.046) | (1.180 to 1.360) | 7081 |

DIC=22 370 | 3 | 0.109 | (0.023) | (0.066 to 0.157) | 1647 |

Model 1 is a single level Poisson model comparing the rates of hospital admission between individuals with type I diabetes compared to normal population controls estimated using quasi-likelihood approach. Model 2 is multilevel Poisson model which accounts for the matched design using a 2 level variance component model, estimated using quasi-likelihood approach. Model 3 is a multilevel Poisson model which accounts for the matched design and overdispersion using a 3 level variance component model, estimated using quasi likelihood. Results from models 1 to 3 are reported using maximum quasi-likelihood IRR, asymptotic SE, 95% CIs and two-sided p values. Model 4 is the same as model 3, except estimated using MCMC. Results are reported using the mean of the posterior distribution to indicate IRR, the SD of the posterior chain is used to indicate the parameter SE, 95% posterior probability intervals (95% CI) represent the 2.5th and 97.5th centiles of the posterior distribution, and directional posterior probabilities (p≤). ESS indicates the effectiveness of MCMC chain mixing. Bayesian DIC is used to indicate model fit.

DIC, Deviance Information Criterion; ESS, effective sample size; MCMC, Markov Chain Monte; Carlo IRR, incidence rate ratio.