| Simulation Model |
κ |
Method |
Bias |
MCSE |
Mean of SEs |
MSE |
CP (%) |
| Weibull |
0 |
NB |
0.0004 |
0.128 |
0.105 |
0.016 |
89.1 |
| |
|
PWNB |
0.0002 |
0.087 |
0.080 |
0.008 |
94.9 |
| Mixed Poisson |
1 |
NBM |
0.001 |
0.135 |
0.116 |
0.018 |
90.8 |
| |
|
PWNB |
0.001 |
0.143 |
0.143 |
0.020 |
95.4 |
| Mixed Poisson |
2 |
NB |
0.002 |
0.185 |
0.157 |
0.034 |
90.4 |
| |
|
PWNB |
0.001 |
0.198 |
0.198 |
0.039 |
95.2 |
| Increase+Stable |
1/2 |
NBM |
0.001 |
0.081 |
0.078 |
0.007 |
94.6 |
| |
|
PWNB |
0.001 |
0.094 |
0.095 |
0.008 |
95.5 |
| Increase+Stable |
1 |
NB |
-0.003 |
0.109 |
0.102 |
0.012 |
94.2 |
| |
|
PWNB |
-0.005 |
0.137 |
0.138 |
0.019 |
95.0 |
| Increase+Decrease |
1/2 |
NB |
0.004 |
0.117 |
0.109 |
0.014 |
93.2 |
| |
|
PWNB |
0.003 |
0.107 |
0.108 |
0.011 |
95.1 |
| Increase+Decrease |
1 |
NB |
-0.003 |
0.157 |
0.140 |
0.025 |
92.4 |
| |
|
PWNB |
-0.002 |
0.153 |
0.152 |
0.023 |
94.8 |
|
| 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 1: Comparison of NB and PWNB regressions through bias, MCSE, mean of SEs, and MSE of log(risk rate) and 95% CI coverage probability (CP) based on 5,000 Monte Carlo simulations (true relative rate ζ=1.0 for treatment versus control groups). |
