| Simulation Model |
κ |
Method |
Bias |
MCSE |
Mean of SEs |
MSE |
CP (%) |
| Weibull |
0 |
NB |
-0.389 |
0.131 |
0.108 |
0.169 |
88.7 |
| |
|
PWNB |
-0.234 |
0.093 |
0.091 |
0.063 |
94.5 |
| Mixed Poisson |
1 |
NBM |
0.002 |
0.134 |
0.116 |
0.018 |
92.0 |
| |
|
PWNB |
0.010 |
0.131 |
0.130 |
0.017 |
94.6 |
| Mixed Poisson |
2 |
NB |
-0.002 |
0.184 |
0.157 |
0.034 |
91.4 |
| |
|
PWNB |
0.015 |
0.175 |
0.173 |
0.031 |
94.3 |
| Increase+Stable |
½ |
NBM |
0.040 |
0.083 |
0.082 |
0.008 |
92.0 |
| |
|
PWNB |
0.010 |
0.092 |
0.09 |
0.008 |
95.3 |
| Increase+Stable |
1 |
NB |
0.064 |
0.113 |
0.107 |
0.017 |
89.3 |
| |
|
PWNB |
0.015 |
0.135 |
0.134 |
0.018 |
94.8 |
| Increase+Decrease |
½ |
NB |
-0.114 |
0.119 |
0.111 |
0.027 |
89.5 |
| |
|
PWNB |
-0.059 |
0.111 |
0.111 |
0.016 |
94.4 |
| Increase+Decrease |
1 |
NB |
-0.112 |
0.162 |
0.145 |
0.038 |
89.2 |
| |
|
PWNB |
-0.048 |
0.153 |
0.154 |
0.026 |
93.9 |
|
| 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 2: 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 = 0.6 for treatment versus control groups). |
