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.
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 |