# Primary Outcome Measure

Time of analysis: From the 1st of January 2011 to 31st December 2012. Analyses were conducted in patient-days, which was defined as “number of days of patients’ hospitalisation during a specified period” (Slimings et al, 2014)

The estimated incidence rate for all states (excluding ACT) is 0.00036, or 3.60 per 10,000 patient-days. On average, 36 in every 100,000 patients will have a HI-CDI infection every

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The proportion is a point based estimate and does not take into account time at risk whereas the incidence rate considers time at risk and includes it in the denominator. Therefore, as the denominator for the incidence rate includes this time component and the proportion does not, you would expect the proportion to differ. Furthermore, proportions are unit-less, whereas the incidence rate does have units.

β_0 represents the rate for those in the short treatment group and treatment program A.

The estimated incidence rate of relapse for those in the short treatment group and program A was 1.50 per person-year: Approximately 1.5 (15 people per 10 years) people per year will have a relapse if they are in the short treatment and program A. We are 95% confident that the true population incidence rate for people in the short treatment and program A could be as much as 1.72 people per year or as little as 1.31 people per

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The estimated incidence rate for those on the short treatment assignment within program A is 1.55. Approximately 1.55 people per year (155 people every 100 years) will relapse if in the short treatment of program A. The P-value for this estimate is <0.0001. This provides strong evidence against the null hypothesis, that there is no difference between the two models. Therefore, it is likely that model 3 is better than model 2. Since these statistics indicate that the more complex model of model 3 is going to provide better results than the simpler model, I would suggest the more complex model would be most appropriate at drawing conclusions. Despite including additional terms in our regression and therefore reducing the power, we would still expect to get more statistically significant results from model 3 when compared to model 1 or 2. This is because, even with weak evidence for interaction in model 3, model 3 will be better as it also controls for the confounding effect of