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E^{3} is a new feature of the Indiana Epidemiology Newsletter dedicated to exploring the fundamentals of epidemiology. Each month, a different epidemiology concept will be explored to enhance understanding of basic epidemiology.
Tracy Powell, MPH
ISDH Field Epidemiologist, District 4
As epidemiologists, we use the odds ratio (or risk ratio) to assess the statistical relationship between two or more variables, e.g., assessing the risk of a particular outcome if a certain exposure is present. But, how do we know if the odds ratio is significant to our investigation?
We calculate a confidence interval!
The confidence interval is a range of values on either side of the odds ratio or point estimate. It allows us to look beyond the dichotomy of “significant” and “not significant” and instead focus on a range of likely values. Ideally, the point estimate will be somewhere in the middle of the confidence interval.
The confidence interval consists of three components: the upper bound number, the lower bound number, and the confidence level. In public health, most confidence intervals have a confidence level of 95 percent, but other levels are commonly used, e.g., 90 percent, 99 percent. With a 95 percent confidence interval, if we repeated the investigation and used the same procedure each time (data gathering instruments, etc.), we would expect to see a point estimate in our interval range 95 percent of the time. This means we have a 5 percent chance of error or a 5 percent chance that the true value is not contained within the confidence interval. Most public health professionals are comfortable with this level of error.
The width of the confidence interval, i.e., the difference between the upper and lower bound numbers, signifies data precision. A narrow confidence interval suggests greater precision and usually results from having more data points (which usually means a larger sample size). Another factor that affects the interval width is the level of confidence. Looking at the same set of data, a 95 percent confidence interval is wider than a 90 percent confidence interval, and a 99 percent confidence interval is wider than a 95 percent confidence interval. Thus, the higher the confidence level, the wider the interval. The example below shows the different intervals with varying confidence levels.
Confidence Interval Example
Odds Ratio |
Confidence Level |
Confidence Interval |
Confidence Width |
23.3 |
90% |
6.29–84.72 |
±78.43 |
95% |
4.92–108.98 |
±104.06 | |
99% |
3.01–2,972 |
±2,968.99 |
As you can see from the example, the widths of the confidence intervals are large even with the 90 percent confidence level. The wider confidence interval suggests lower precision and is probably due to a small sample size.
To bring the idea of the confidence interval all together, we will look at foodborne illness in Indiana residents who shopped at Store A compared to those who did not shop at Store A. The odds ratio or point estimate was 47.5, and the 95 percent confidence interval for the estimate was 10.08-224.36. We can say that the risk of illness in people who shopped at Store A (exposed) was 47.5 times the risk than in those who did not shop at Store A (unexposed). The confidence interval gives us an idea of how precise the odds ratio is and can also indicate statistical significance. A confidence interval that includes one is not statistically significant.
If you recall from a previous newsletter article on odds ratios, an odds ratio greater than one indicates a greater risk among those exposed, and an odds ratio of one means no difference between those exposed and unexposed. The lower bound number of the confidence interval was 10.08, which is greater than one. Thus, we can conclude that people who shopped at Store A were more likely to become ill with foodborne illness than those who did not shop at Store A.
Odds Ratio |
95% Confidence Interval |
p-value |
47.5 |
10.8–224.36 |
<0.005 |
When results of an investigation are reported, including the confidence interval along with the p-value and odds ratio is necessary in order for the reader to appropriately comprehend the data and draw relevant conclusions.
Understanding statistical methods is an overwhelming task that can take years and many daunting statistics courses. However, over the past several months we have presented the odds ratio, risk ratio, p-value, and confidence interval, which are a few statistical methods that can be easily applied to most public health investigations. Understanding these basic concepts will assist you in reporting and understanding investigation findings.
References
1.Kuzma, Jan. Basic Statistics for the Health Sciences. 3^{rd} Edition. 1998.
2.Leonard Braitman. Confidence Intervals Assess Both Clinical and Statistical Significance, Annals of Internal Medicine, 1991; Vol. 114, pp 515-517.