User:Psarka/PR2 computed example
This is a proposal to replace the ARR RRR template by two separate templates, one for risk reduction, and one for risk increase.
Motivation[edit]
The current ARR RRR template is as follows:
| Example 1: risk reduction | Example 2: risk increase | |||||
|---|---|---|---|---|---|---|
| Experimental group (E) | Control group (C) | Total | (E) | (C) | Total | |
| Events (E) | EE = 15 | CE = 100 | 115 | EE = 75 | CE = 100 | 175 |
| Non-events (N) | EN = 135 | CN = 150 | 285 | EN = 75 | CN = 150 | 225 |
| Total subjects (S) | ES = EE + EN = 150 | CS = CE + CN = 250 | 400 | ES = 150 | CS = 250 | 400 |
| Event rate (ER) | EER = EE / ES = 0.1, or 10% | CER = CE / CS = 0.4, or 40% | EER = 0.5 (50%) | CER = 0.4 (40%) | ||
| Equation | Variable | Abbr. | Example 1 | Example 2 |
|---|---|---|---|---|
| EER − CER | < 0: absolute risk reduction | ARR | (−)0.3, or (−)30% | N/A |
| > 0: absolute risk increase | ARI | N/A | 0.1, or 10% | |
| (EER − CER) / CER | < 0: relative risk reduction | RRR | (−)0.75, or (−)75% | N/A |
| > 0: relative risk increase | RRI | N/A | 0.25, or 25% | |
| 1 / (EER − CER) | < 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 |
In my opinion it is cognitively overloaded, as the differences between risk reduction and risk increase are quite significant, so it is cumbersome to merge them to one. In particular:
- many fields contain missing values, indicating the difference
- if/else logic (expressed as <0 or >0) is necessary to separate the terms
- shared formulas for ARR & ARI, RRR & RRI, NNT & NNH are actually not shared in the main literature, so the actual separation is even larger.
Changes[edit]
This is a proposed example for the risk reduction:
| Example 1: risk reduction | |||
|---|---|---|---|
| Experimental group (E) | Control group (C) | Total | |
| Events (E) | EE = 15 | CE = 100 | 115 |
| Non-events (N) | EN = 135 | CN = 150 | 285 |
| Total subjects (S) | ES = EE + EN = 150 | CS = CE + CN = 250 | 400 |
| Event rate (ER) | EER = EE / ES = 0.1, or 10% | CER = CE / CS = 0.4, or 40% | |
| Equation | Variable | Abbr. | Value |
|---|---|---|---|
| CER - EER | absolute risk reduction | ARR | 0.3, or 30% |
| (CER - EER) / CER | relative risk reduction | RRR | 0.75, or 75% |
| 1 / (CER − EER) | number needed to treat | NNT | 3.33 |
| EER / CER | relative risk | RR | 0.25 |
| (EE / EN) / (CE / CN) | odds ratio | OR | 0.167 |
| 1 − RR | preventive fraction | PF | 0.75 |
This is a proposed example for the risk increase:
| Example 2: risk increase | |||
|---|---|---|---|
| Experimental group (E) | Control group (C) | Total | |
| Events (E) | EE = 75 | CE = 100 | 115 |
| Non-events (N) | EN = 75 | CN = 150 | 285 |
| Total subjects (S) | ES = EE + EN = 150 | CS = CE + CN = 250 | 400 |
| Event rate (ER) | EER = EE / ES = 0.5, or 50% | CER = CE / CS = 0.4, or 40% | |
| Equation | Variable | Abbr. | Value |
|---|---|---|---|
| EER − CER | absolute risk increase | ARI | 0.1, or 10% |
| (EER − CER) / CER | relative risk increase | RRI | 0.25, or 25% |
| 1 / (EER − CER) | number needed to harm | NNH | 10 |
| EER / CER | relative risk | RR | 1.25 |
| (EE / EN) / (CE / CN) | odds ratio | OR | 1.5 |
| (RR − 1) / RR | attributable risk percent | ARP | 20% |
While they duplicate some of the content, separate examples are, in my opinion, easier to comprehend at a glance.