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 ζ_{3}, 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 (NonConstant Relative Rate). 