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 ^[1].

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

See also

• Experimental event rate
• Absolute risk reduction
• Relative risk reduction
• Number needed to treat

References

1. ^ http://www.medicine.ox.ac.uk/bandolier/booth/glossary/CER.html

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