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).