What is the magnitude and precision of the association between the exposure and the outcome?
Let's begin by drawing a 2x2 table using the data from the RCT that we found.
| Adverse Event | Totals | ||
|---|---|---|---|
| Present (Case) | Absent (Control) | ||
| Experimental group (d-solatol) | 78 a |
1471 b |
1549 a + b |
| Control group (placebo) | 48 c |
1524 d |
1572 c + d |
Totals | a + c 126 |
b + d 2995 |
6242 |
For RCTs and cohort studies, we look at the risk of the event in the treatment group relative to the risk of the event in the untreated patient. This 'relative risk' is calculated as:
RR = [ a/(a+b) ] / [ c/(c+d) ]
Using the values in the table, the relative risk for death in patients receiving d-sotalol is:
RR = [ 78/1549 ] / [ 48/1572 ]
RR = 1.65
Case control studies sample outcomes, not exposure and therefore we can't calculate the relative risk. Instead, the strength of association is estimated indirectly using the odds ratio = ad/bc.
How big should the relative risk (RR) or odds ratio (OR) be for us to be impressed by it? OR and RR > 1 indicate that there is an increased risk of the adverse outcome with the exposure. Because cohort studies and case control studies are susceptible to many biases, we need to ensure that the OR/RR is greater than that which could occur from bias alone. We also need to look at the confidence interval around the OR and RR to see how precise the estimate is.
A more clinically useful measure than the OR and RR is the number of patients that we'd need to treat with the putative agent in order to cause 1 additional harmful event (number needed to harm or NNH). Using the OR, the NNH can be calculated as:
NNH = [ PEER (OR-1) + 1 ] / [ PEER (OR-1) x (1-PEER) ]
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Where PEER = the patient's expected event rate
Alternatively, we can refer to the tables below for this information. We can see from these tables that for different PEER, the same OR can generate very different NNHs.
When OR < 1:
| For Odds Ratios LESS than 1 | ||||||||
|---|---|---|---|---|---|---|---|---|
| 0.9 | 0.8 | 0.7 | 0.6 | 0.5 | 0.4 | 0.3 | ||
| Patient Expected Event Rate (PEER) | 0.05 | 209 | 104 | 69 | 52 | 41 | 34 | 29 |
| 0.10 | 110 | 54 | 36 | 27 | 21 | 18 | 15 | |
| 0.20 | 61 | 30 | 20 | 14 | 11 | 10 | 8 | |
| 0.30 | 46 | 22 | 14 | 10 | 8 | 7 | 5 | |
| 0.40 | 40 | 19 | 12 | 9 | 7 | 6 | 4 | |
| 0.50 | 38 | 18 | 11 | 8 | 6 | 5 | 4 | |
| 0.70 | 44 | 20 | 13 | 9 | 6 | 5 | 4 | |
| 0.90 | 101 | 46 | 27 | 18 | 12 | 9 | 4 | |
When OR > 1:
| For Odds Ratios GREATER than 1 | ||||||||
|---|---|---|---|---|---|---|---|---|
| 1.1 | 1.25 | 1.5 | 1.75 | 2 | 2.25 | 2.5 | ||
| Patient Expected Event Rate (PEER) | 0.05 | 212 | 86 | 44 | 30 | 23 | 18 | 16 |
| 0.10 | 113 | 46 | 24 | 16 | 13 | 10 | 9 | |
| 0.20 | 64 | 27 | 14 | 10 | 8 | 7 | 6 | |
| 0.30 | 50 | 21 | 11 | 8 | 7 | 6 | 5 | |
| 0.40 | 44 | 19 | 10 | 8 | 6 | 5 | 5 | |
| 0.50 | 42 | 18 | 10 | 8 | 6 | 5 | 4 | |
| 0.70 | 51 | 23 | 13 | 10 | 9 | 8 | 7 | |
| 0.90 | 121 | 55 | 33 | 25 | 22 | 19 | 18 | |
We can also convert the RR to an NNT/NNH using the following equations:
- For RR < 1
- NNT = 1/(1-RR) x PEER
- For RR > 1
- NNT (or NNH) = 1/(RR-1) x PEER
Using the PEER (3.1%) from the study we found and the RR (1.65) that we calculated, the NNH for death from d-sotalol in the study is:
NNH = 1/(1.65-1) x 0.031
NNH = 50
Therefore we would need to treat 50 people with d-sotalol to cause 1 additional death. We can also calculate the confidence interval around this estimate using the inverse of the confidence interval for the absolute risk increase.