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Odds Ratio and Relative Risk can easily be calculated in Excel using the function “ODDSRATIO”. This function takes the number of events in the two different categories as the arguments and returns the odds ratio and relative risk in the form of a decimal value. For example, ODDSRATIO(5,10) returns 0.5, which is the odds ratio and relative risk for the two categories.
We often use the odds ratio and relative risk when performing an analysis on a 2-by-2 table, which takes on the following format:
The odds ratio tells us the ratio of the odds of an event occurring in a treatment group to the odds of an event occurring in a control group. It is calculated as:
Odds ratio = (A*D) / (B*C)
The relative risk tells us the ratio of the probability of an event occurring in a treatment group to the probability of an event occurring in a control group. It is calculated as:
Relative risk = [A/(A+B)] / [C/(C+D)]
This tutorial explains how to calculate odds ratios and relative risk in Excel.
How to Calculate the Odds Ratio and Relative Risk
Suppose 50 basketball players use a new training program and 50 players use an old training program. At the end of the program we test each player to see if they pass a certain skills test.
The following table shows the number of players who passed and failed, based on the program they used:
The odds ratio is calculated as (34*11) / (16*39) = 0.599
We would interpret this to mean that the odds that a player passes the test by using the new program are just 0.599 times the odds that a player passes the test by using the old program.
In other words, the odds that a player passes the test are actually lowered by 40.1% by using the new program.
The relative risk is calculated as [34/(34+16)] / [39/(39+11)] = 0.872
Because this value is less than 1, it indicates that the probability of passing is actually lower under the new program compared to the old program.
We could also see this by directly computing the probability that a player passes under each program:
Probability of passing under new program = 34 / 50 = 68%
Probability of passing under old program = 39 / 50 = 78%
How to Calculate Confidence Intervals
Once we calculate the odds ratio and relative risk, we may also be interested in computing confidence intervals for these two metrics.
A 95% confidence interval for the odds ratio can be calculated using the following formula:
95% C.I. for odds ratio = [ e^(ln(OR) – 1.96*SE(ln(OR))), e^(ln(OR) – 1.96*SE(ln(OR))) ]
where SE(ln(OR)) =√1/A + 1/B + 1/C + 1/D
The 95% C.I. for the odds ratio turns out to be (.245, 1.467). The image below shows the formula we used to calculate this confidence interval:
A 95% confidence interval for the relative risk can be calculated using the following formula:
95% C.I. for relative risk = exp(ln(RR) – 1.96*SE(ln(RR))) to exp(ln(RR) – 1.96*SE(ln(RR)))
where SE(ln(RR)) =√1/A + 1/C – 1/(A+B) – 1/(C+D)
The 95% C.I. for the relative risk turns out to be (.685, 1.109). The image below shows the formula we used to calculate this confidence interval:
The following tutorials offer additional information on how to interpret odds ratios and relative risk: