To interpret the observed versus expected data from these tables, divide the observed number of cases by the expected number. If the observed number is greater than the expected value, the incidence ratio will be greater than 1.0. This result suggests an excess of cancer. The incidence ratios for a gender group could be calculated and then ranked to determine priority cancer concerns. If such a ranking were prepared, about as many incidence ratios greater than 1.0 would be found as those less than 1.0. Such "balancing" of patterns is common in nature. This "balancing" argues against making any interpretation based on the one incidence ratio. The entire gender-specific pattern for cancer in a county should be considered, since these data represent only one year and year-to-year variation can be large.
In evaluating incidence ratios, a paramount question is "how large" must a value be to consider it meaningful. There is a statistical means of answering this question. Generally, a ratio is meaningfully large if there is at least a 95 percent chance that the ratio is truly greater than 1.0. The determination that a ratio is truly greater than 1.0 uses a test criterion called the 95 percent "Lower Confidence Limit (LCL)" and is computed by:

where **obs** = observed cases and **exp** = expected cases. [Source: Franklin, H. and Krankowitz, W. (1987). Cancer Cluster in the Workplace. *Journal of Occupational Medicine* 29(12):942-53.]

If the 95 percent LCL is greater than 1.0, then the calculated incidence ratio may be meaningfully large and the ratio represents a "statistically significant" excess.

This same formula may be used to evaluate an incidence ratio below 1.0 simply by changing the minus to a plus and calculating the 95 percent "Upper Confidence Limit (UCL)." If the UCL is below 1.0, then the SIR represents a statistically significant low risk of cancer.

The 1.64 value in this formula arises from the decision to evaluate a 95 percent confidence limit. For further guidance with manipulating this formula, consult a statistician. Common values for other confidence limits using this process are 1.96 for a 97.5 percent confidence limit; 2.33 for a 99 percent confidence limit, etc. Further assistance with interpreting these data or calculating these measures is available upon request.

The pivotal role of the expected value is obvious in the formula above. Another precaution: be cautious when the expected value is small. An expected value that is a fraction (e.g. 0.5) is meaningless. Cancer cases are whole people. Consider an extreme instance where one cancer case occurs with 0.1 cases expected. Without regard for this consideration of small numbers, this observation could be misrepresented as a 10-fold excess. As a rule of thumb, five expected cases is a good cutoff; below that the numbers are considered too small to be reliable. Ten cases is the number that is preferred for analysis by the State Center for Health Statistics.