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The Supporting Information also reports a negative binomial model for the number of symptoms persisting 25 weeks post treatment initiation.

The random effect is subsequently modeled with an inverted beta distribution, resulting in an inverted beta binomial model for the observed count data.

Therefore, we employed the negative binomial model for the LOS variable because the unconditional variances of this variable were larger than the unconditional means.

In our experiments we computed b using a simple binomial model for the null distribution of fold change estimates and a fixed significance level α = 0.05.

We had significant results for the Vuong test, which supported the zero-inflated negative binomial model over the negative binomial model for the LOS outcome (p <0.0001).

For example, we chose the zero-inflated negative binomial model for the outcome variable of LOS in order to account for both overdispersion and excess zeroes.

For the tortoise data, optimization of the negative-binomial model confirms that is infinite in the negative binomial model for these data; after 500 iterations, the estimates had reached As noted in Couturier et al. (2013), the fit is much improved compared to the Poisson case, with -maximum log-likelihood 540.34 versus 576.27, but at the expense of becoming infinite.

The results of the negative binomial model for this population are shown in Table 3.

As an alternative to the GEE model approach based on a logistic link, log binomial models for the relative risk were also fit.

We will use linear regression for continuous variables, logistic regression for dichotomous variables, and negative binomial models for the outcome variable of number of bed days because of its non-parametric data distribution.

The models described above require prior distributions for the baseline treatment effect, for the effect due to MTX, for the between trial standard deviation and in the binomial models for the log odds of response in the control group and the meta-regression parameter.