Before describing how to calculate rate ratios and differences, we first need to decide on a reference group, or group we compare another group (or individual) to. The reference groups help us to establish a benchmark, with which we compare, to determine whether a disparity exists. The reference can also be a larger population rather than another group, for example the overall COVID-19 rate/100,000 in the U.S.

Generally, we employ the most “well-off” or privileged group as the reference group, as this group usually has a more favorable group rate (the rate reflecting better health status or less risk). Examples of common reference groups include non-Hispanic whites, men, the able bodied population, U.S. born population, commercially insured people, non-segregated neighborhoods, non-impoverished neighborhoods, etc. However, decisions about the appropriate reference group should be based on theory and reflect the historical and cultural context of the hypothesis tested. For the following explanation, we’ll use non-Hispanic whites as our reference group, and measure racial disparities in COVID-19 incidence rates in Philadelphia.

Rate differences, also known as risk or absolute differences, provide a measure of the health impact of the disparity. A rate difference is measured as the arithmetic difference between the rate of interest and the reference group rate, expressed in the same units as the rates.

Rate Difference = rate of interest–reference group rate = R_i – R_r

As an example, if the rate among non-Hispanic Blacks is 2,550 per 100,000 and the rate among non-Hispanic whites is 1,369, then the rate difference equals the rate among Blacks minus the rate among whites, which equals 1,181 per 100,000, or a disparity of 1,181 per 100,000 deaths among non-Hispanic Blacks compared to non-Hispanic whites.

Rate ratio=rate of interest/reference group rate= R_i / R_r

By multiplying the rate ratio by 100, we can then convert the rate to a percentage difference. A ratio of 1 indicates no disparity, ratio of >1 indicates a disparity between the group of interest and reference group, and ratio <1 indicates higher rates in the reference group than the group of interest.

Taking the same numbers as we used for the rate difference, the rate ratio equals the rate among non-Hispanic Blacks (2,550/100,000) divided by the rate among non-Hispanic whites (1,369/100,000), or 1.86. The case rate among non-Hispanic rates is 1.86 times the rate among whites, or 86% higher among Blacks than whites.

Large relative disparities can mask small absolute differences, particularly when overall rates are low: for example, if the Black death rate is 15/100,000 and non-Hispanic white rate is 5/100,000, the relative disparity will show a Black rate 3 times that of the white rate, but only an absolute difference of 10 deaths per 100,000 persons. Analogously small relative differences can mask large absolute differences if the rate is high. To draw conclusions about disparities and changes in disparities, it is therefore best to measure both absolute and rate differences concurrently.

To measure inequities in spatial access to COVID-19 testing, we are using testing site location data provided by Castlight Health. We have calculated two types of COVID-19 testing metrics: potential demand and spatial accessibility. Inequities in accessibility to COVID-19 are measured by comparing these metrics between neighborhoods in the top and bottom quartiles of the neighborhood characteristic.

To measure inequities in COVID-19 vaccination, we have compiled a series of metrics that measure both the rates of vaccination and barriers to vaccination. Specifically, we have calculated:

• Fully vaccinated: % of the total population that has been fully vaccinated (taking into consideration the nunber of doses required for each vaccine).
• Partially vaccinated: % of the total population that has been only partially vaccinated (e.g., one dose of an mRNA-based vaccine).
• At least partially vaccinated: % of the total population that has been either partially or fully vaccinated.
• Doses per capita: total number of administered vaccine doses per 1000 individuals.
• Hesitancy: % of the adults in the city who describe themselves as “probably not” or “definitely not” going to get a COVID-19 vaccine once available to them.
• Strong Hesitancy: % of the adults in the city who describe themselves as “definitely not” going to get a COVID-19 vaccine once available to them.