# Table 1

Estimated probability (and 99% CI) of rejecting the null hypothesis when there is no true difference between groups for a variety of statistical models and underlying distributions (results that do not include the alpha level of 0.05 are bolded)

Analysis model fit

True Distribution:

Poisson

ODP

NB

ZIP

Poisson (Var = 5)

.053 (.041,.064)

.054 (.042,.066)

.047 (.036,.058)

.055* (.043,.067)

NB (Var = 13)

.225 (.204,.247)

.049 (.038,.060)

.049 (.038,.060)

.050 (.039,.061)

NB (Var = 40)

.467 (.441,.493)

.047 (.036,.058)

.044 (.033,.055)

.046 (.036,.057)

NB (Var = 70)

.584 (.558,.609)

.052 (.041,.063)

.048 (.037,.059)

.062 (.049,.074)

ZIP (Var = 8)

.179 (.159,.199)

.058 (.046,.070)

.031 (.022,.040)

.051 (.040,.063)

all distributions except ZIP have E[Yi] = λ = 5, for ZIP E[Yi] = 0.8 * 5 = 4.

ODP (over-dispersed Poisson); NB (negative binomial); ZIP (zero-inflated Poisson)

* For the true distribution under the Poisson, the ZIP model failed to converge for n = 672 of the simulations.

Horton et al. BMC Medical Research Methodology 2007 7:9   doi:10.1186/1471-2288-7-9