Assaults on staff are fairly uncommon in our facilities with between 70-140 in a year at a given facility. Time, similar to 'person years' in epidemiology, is tracked as 'number of bed days' (i.e., number of days a bed is occupied). Bed days per facility range from 75,000 to 135,000.
For the comparisons, I'm thinking to calculate Confidence Intervals modeled with Poisson distribution with a Bonferonni correction on the confidence level for multiple comparisons (comparing x facility with both y and z facilities; hence confidence level set to 0.975[see below]).
- facility x assaults=71; days stay=93,516
- facility y assaults=61; days stay=74,272
- facility z assaults=142; days stay=133,699
R procedures and output (EpiTools package):
1. > pois.exact(71, 93516, conf.level = 0.975) x pt rate lower upper conf.level 1 71 93516 0.0007592284 0.0005717496 0.0009874694 0.975 2. > pois.exact(61, 74272, conf.level = 0.975) x pt rate lower upper conf.level 1 61 74272 0.0008213055 0.0006038488 0.001090219 0.975 3. > pois.exact(142, 133699, conf.level = 0.975) x pt rate lower upper conf.level 1 142 133699 0.001062087 0.0008724176 0.001279991 0.975
As there is overlap of CIs between facility x and both y and z, there is no significant difference in assault rates.
Does this analysis look alright?