What is a rate ratio?

Why person time is the denominator

In a registry or long cohort, people are not all watched for the same length of time. Some join late, some move away, some die of other causes. Counting cases per person at the start would treat someone followed for one year the same as someone followed for five. Person time fixes that by adding up the time each person was actually at risk. The CDC's Principles of Epidemiology course describes a rate ratio as the ratio of two rates and explains that it is used in cohort studies to compare the rate of disease in an exposed group with the rate in an unexposed group. A rate ratio above one points to higher occurrence in the first group.

A worked example

The epidemiology example on this site reports a fictional five year registry study of Ross River virus. Coastal districts recorded 5,420 confirmed cases over about 8.63 million person years, an incidence of 62.8 per 100,000 person years. Inland districts recorded 2,816 cases over about 10.79 million person years, or 26.1 per 100,000. Dividing 62.8 by 26.1 gives 2.4, reported with its 95 percent confidence interval of 2.3 to 2.5. Every part of that arithmetic can be checked from the board, because the case counts, the person years and the rates are all printed, which is the standard a rate ratio should meet.

Rate ratio against risk and odds ratios

The three measures answer slightly different questions. A risk ratio compares the proportion of people who develop the outcome over a set period and suits trials where everyone is followed for the same time. An odds ratio compares odds and is the natural output of case control studies and logistic regression. When the outcome is rare, all three give similar numbers, but they diverge as outcomes become common. The Cochrane Handbook's chapter on effect measures sets out when each applies and cautions against interpreting odds ratios as if they were risk ratios.

Reporting a rate ratio well

The STROBE statement for observational studies asks authors to report the numbers of outcome events or summary measures over time, and to give unadjusted estimates and, if applicable, confounder adjusted estimates with their precision. On a poster that means printing, for each group, the cases, the person time and the rate, then the rate ratio with its interval, and saying whether it is crude or adjusted for age, sex or other factors. If rates were age standardised, name the standard population. Report the absolute rate difference alongside, so readers see the burden as well as the ratio.

Common mistakes

Calling a rate ratio a relative risk blurs the denominator and can mislead when follow up varies. Printing only the ratio, without the two rates, hides whether the outcome is common or rare. Comparing crude rates between populations with different age structures exaggerates or hides differences for age related diseases. Reporting a ratio without its interval gives no sense of precision. And a mismatch between the case counts in the records flow and the cases used in the rates undermines the whole board.

Where it shows up in the poster builder

A rate ratio usually sits in a key number block, available on 27 of the 40 layouts, with the ratio as the value and the interval in the detail line, while a bar chart figure compares the rates by group. Chart figures take category labels and values, so the rates per 100,000 plot directly; they carry no error bars, so intervals belong in the caption or the results. Ten layouts carry a participant flow block of six nodes and an aside, which the epidemiology example uses as a records flow from notification to analysed cases. Because the generator fills every key number and flow count from the brief, give it the case counts and person years for each group, not only the final ratio, so the arithmetic on the finished board can be checked.

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