# 1.3.2.1 Calculating confidence intervals for incidence rates

The confidence interval for an IR can be calculated for a population with the same time at risk using the method described in section 1.3.3.2.1 below, where Z_{∝}_{ }is based on the Poisson distribution and n is an individual-time constant. In reality the IR is often not homogenous within a population. For instance, a random sample of honey bee colonies would express hygienic behaviour differently. As highly hygienic colonies are more likely to resist brood diseases, these colonies would be less likely to be diagnosed with the condition. Conversely, it is conceivable that the diagnosis of a certain brood disease in a given colony is a marker for increased susceptibility for the disease. Therefore, in comparison to disease-free colonies, a second diagnosis is more likely to occur in colonies that were previously diseased. This phenomenon is referred to as extra-Poisson variation and if left uncorrected will result in a confidence interval that is too narrow. To address this, a multivariate logistic regression model with terms for previous disease should be employed.

Just as the IR is not the same for all individuals in a population, it is also not likely to be constant over time. The prevalence of many bee diseases changes over time, thus affecting 95% CI calculation. This problem can be overcome by restricting analysis to sub-periods or “time bands” so that differences in IR over time are not a factor. Alternatively, time itself can be used as a predictor of disease when performing a multivariate analysis (Koepsell and Weiss, 2003).