Measures of Association

Question 10:

A randomized controlled trial compared a new asthma medication (“Weezenuf”) to placebo in two groups of 100 patients over 1 year. The medication or placebo was administered once daily to the assigned groups. The primary outcome was an asthma “event” based on self-reported symptoms (cough, wheezing, and chest tightness). Patients reporting 2 or more asthma symptoms per week were considered to have an “event,” while less frequent asthma symptoms were classified as “no event.”

Event No Event
“Weezenuf” Medication Treatment 1 person 99 people
Placebo 10 people 90 people

The control group event rate (CER) was 10% and the experimental group event rate (EER) was 1%.


Which one of the following can be concluded by the results of this study?

  1. The new asthma medication has an absolute risk reduction of 11%
  2. The number needed to treat is the inverse of the relative risk reduction.
  3. Twelve patients will need to use the medication to prevent one “asthma event.”
  4. The relative risk reduction is 9%.

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Event No Event
Exposure Treatment A B A+B
Controll C D C+D

Experimental Event Rate (EER)

Event rate in the treatment group.
EER = A/(A+B)

Control Event Rate (CER)

Event rate in the control group.
CER = C/(C+D)

Relative Risk (RR)

Relative risk is used to compare the probability of an event in two distinct groups. This number represents the event rate in an exposed group divided by the event rate in the unexposed group (STATS, George Mason University). Also known as risk ratio, RR is often reported in randomized clinical trials and cohort studies, because knowledge of the incidence is required to calculate the relative risk. In a randomized clinical trial comparisons might be made between groups with different screening or treatment assignments, while in cohort studies, comparison groups will usually have different exposures (e.g., smokers and non-smokers). Research has shown that smokers have a higher risk of developing certain diseases compared to (relative to) non-smokers.
RR = EER / CER = A/(A+B) / C/(C+D)

Relative risk reduction (RRR)

“The proportional reduction in rates of bad outcomes between experimental and control participants in a trial” (Centre for Evidence Based Medicine Web Site 2008). This number is often used because the numerical value appears to be huge, but often overestimates clinical relevance.
RRR = |EER – CER|/CER = |A/(A+B) – C/(C+D)| / C/(C+D)

Absolute Risk (AR)

Absolute risk is the individual risk of developing a disease over a time-period. We all have absolute risks of developing various diseases such as heart disease, cancer, stroke, etc. The same absolute risk can be expressed in different ways. For example, say you have a 1 in 10 risk of developing a certain disease in your life. This can also be stated that you have a 10% risk, or a 0.1 risk.

Absolute risk reduction (ARR)

ARR represents the risk difference between the control group event rate and the experimental group event rate.
ARR = CER – EER = C/(C+D) – A/(A+B)

Odds Ratio

Odds are a comparison of the probability of an event to the probability that an event does not take place. The odds ratio divides the odds of finding or not finding a particular outcome in the exposed group by the odds of finding or not finding an outcome in the unexposed group (STATS, George Mason University). In case-control or other studies where the incidence is unknown, only associations can be measured, and expressed using the odds ratio for comparison. Because of the ambiguity in the odds ratio, drawing conclusions can sometimes be difficult. In cohort and other prospective studies, where the incidence is known (and causality might be inferred), relative risk is a more appropriate comparison. Use of the odds ratio in these situations should raise suspicion.
Odds Ratio = (A/B) / (C/D) = (AxD)/(BxC)

Number Needed to Treat (NNT)

The number needed to treat (NNT) represents the number of patients who need to be treated in order to prevent one additional bad outcome. It is the inverse of the absolute risk reduction (ARR).
NNT = 100% / ARR

Two important caveats to remember about NNT:

  1. When the likelihood of an outcome is low, the NNT will be high.
  2. The NNT will decrease as either the likelihood of the outcome increases or as the benefit of treatment increases.
Numbers Needed To Treat (NNT) in the Treatment of Hypertension
Therapy Event Prevented Duration of Follow-up NNT
Treatment of Mild Hypertension One heart attack, stroke, or death 1 year 700
Treatment of Severe Hypertension One heart attack, stroke, or death 1 year 15

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