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# Control event rate

In epidemiology and biostatistics, the control event rate (CER) is a measure of how often a particular statistical event (such as response to a drug, adverse event or death) occurs within the scientific control group of an experiment .

This value is very useful in determining the therapeutic benefit or risk to patients in experimental groups, in comparison to patients in placebo or traditionally treated control groups.

Three statistical terms rely on CER for their calculation: Absolute risk reduction, Relative risk reduction and Number needed to treat.

## Worked example

In a trial of hypothetical drug "X" where we are measuring event "Z", we have two groups. Our control group (25 people) is given a placebo, and the experimental group (25 people) is given drug "X".

Event "Z" in control group : 4 in 25 people Control Event Rate : 4/25

Event "Z" in experimental group : 12 in 25 people Experimental Event Rate : 12/25

Another worked example is as follows:

Example 1: risk reduction Example 2: risk increase
Experimental group (E) Control group (C) Total (E) (C)
Events (E) EE = 15 CE = 100 115 EE = 75 CE = 100
Non-events (N) EN = 135 CN = 150 285 EN = 75 CN = 150
Total subjects (S) ES = EE + EN = 150 CS = CE + CN = 250 400 ES = 150 CS = 250
Event rate (ER) EER = EE / ES = 0.1, or 10% CER = CE / CS = 0.4, or 40% N/A EER = 0.5 (50%) CER = 0.4 (40%)
Equation Variable Abbr. Example 1 Example 2
CER − EER < 0: absolute risk reduction ARR (−)0.3, or (−)30% N/A
> 0: absolute risk increase ARI N/A 0.1, or 10%
(CER − EER) / CER < 0: relative risk reduction RRR (−)0.75, or (−)75% N/A
> 0: relative risk increase RRI N/A 0.25, or 25%
1 / (CER − EER) < 0: number needed to treat NNT (−)3.33 N/A
> 0: number needed to harm NNH N/A 10
EER / CER relative risk RR 0.25 1.25
(EE / EN) / (CE / CN) odds ratio OR 0.167 1.5
EER − CER attributable risk AR (−)0.30, or (−)30% 0.1, or 10%
(RR − 1) / RR attributable risk percent ARP N/A 20%
1 − RR (or 1 − OR) preventive fraction PF 0.75, or 75% N/A