Simulation Model κ Estimate Bias MCSE Mean of SEs MSE CP (%) Increase+Stable 1 -0.122 0.018 0.018 0.015 94.4   -0.010 0.022 0.021 0.001 94.5   -0.014 0.021 0.021 0.001 94.8 Increase+Decrease 1 -0.071 0.009 0.009 0.005 94.9   -0.088 0.007 0.007 0.008 94.6   -0.068 0.009 0.009 0.005 95.4 Decrease+Stable 1 0.049 0.079 0.079 0.009 94.8   -0.026 0.064 0.063 0.005 94.4   -0.009 0.065 0.064 0.004 94.5

Bias and MSE are calculated based on the overall relative rates defined by ζ3, and 95% Coverage probabilities are calculated as the rejection rate for testing the null hypothesis with regard to their perspective definitions of overall relative rates. Abbreviations: NB=Negative binomial; PWNB=Piecewise negative binomial; MCSE=Monte Carlo standard error; SE=Stand error; MSE=Means square error; CP =95% CI coverage probability; κ=Overdispersion parameter

Table 4: Comparison of different estimates of the overall relative rate through bias, MCSE, mean of SEs, and MSE of relative rate and 95% CI coverage probability (CP) based on 5,000 Monte Carlo simulations (Non-Constant Relative Rate).