Evidence Based Medicine
Statistics
A randomised controlled trial (RCT) is performed where 1000 men are treated with a lipid-lowering drug, Superstatin, and 1000 given a placebo. Two years later the number of patients who have had a myocardial infarction (MI) is recorded and shown below. What is the absolute risk reduction of treatment in preventing an MI:
| Myocardial infarction Yes | Myocardial infarction No | Total | |
|---|---|---|---|
| Superstatin | 20 | 980 | 1000 |
| Placebo | 40 | 960 | 1000 |
| Total | 60 | 1940 | 2000 |
Answer:
- The AR of having an MI in the treatment group (ART) = 20/1000 = 0.02 (2%)
- therefore the risk of having an MI while taking Superstatin is 2%.
- The AR of having an MI in the control group (ARC) = 40/1000 = 0.04 (4%)
- therefore the risk of having an MI while not taking Superstatin is 4%.
- The ARR = ARC – ART = (40/1000) – (20/1000) = 0.04 – 0.02 = 0.02 (2%)
- therefore Superstatin reduces the absolute risk of having an MI by 2%.
Absolute and Relative Risk
Evidence Based Medicine / Statistics
Last Updated: 21st April 2019
| Outcome event | No outcome event | Total | |
|---|---|---|---|
| Treatment | a | b | a+b |
| Control | c | d | c+d |
| Total | a+c | b+d | n=a+b+c+d |
N.B. The 'outcome event' always refers to the worst outcome
Absolute Risk and Absolute Risk Reduction
The absolute risk (AR) is the risk of an outcome event occurring over a set time period (the incidence rate of the outcome event). It is calculated by dividing the number of outcome events that occur by the total number of people at risk of that event occurring.
The absolute risk reduction (ARR) is the difference between the absolute risk of outcome event in the control group (ARC) and the absolute risk of outcome event in the treatment group (ART).
ARC = c/(c + d)
ART = a/(a+b)
ARR = ARC – ART
Relative Risk and Relative Risk Reduction
The relative risk (RR) is the ratio of the risk of outcome event in the treatment group compared to the risk of outcome event in the control group.
RR = ART/ARC
- A risk ratio of 1 indicates no difference in risk between groups.
- If the risk ratio of an outcome event is > 1, the rate of that event is increased in the treatment group compared to the control group.
- If the risk ratio is < 1, the rate of that outcome event is reduced in the treatment group compared to the control group.
The relative risk reduction (RRR) is the proportional reduction in rates of outcome event between the control group and the treatment group.
RRR = (ARC - ART)/ARC or 1 – RR
Number Needed To Treat
The number needed to treat (NNT) is the number of patients who need to be treated with the intervention, compared with the control, in order for one extra patient to experience a beneficial effect.
It is the reciprocal of the absolute risk reduction and therefore gives us information about absolute benefit.
NNT = 1/ARR
NNT is always a number between 1 and infinity. The ideal NNT is 1, where everyone that receives the treatment receives benefit. In theory, the higher the NNT, the less effective the treatment, because more people need to receive the treatment to see a benefit in one but NNT should be interpreted in clinical context. Comparisons between NNTs can only be made if the baseline risks are the same.
A negative number would indicate that the treatment has a harmful effect and would therefore represent the number needed to harm (NNH), defined as the number of patients who need to be treated for one extra patient to experience a harmful effect. The lower the NNH, the higher the rate of harmful effects. The NNH:NNT ratio is indicative of the risk/benefit ratio.
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- Biochemistry
- Blood Gases
- Haematology
| Biochemistry | Normal Value |
|---|---|
| Sodium | 135 – 145 mmol/l |
| Potassium | 3.0 – 4.5 mmol/l |
| Urea | 2.5 – 7.5 mmol/l |
| Glucose | 3.5 – 5.0 mmol/l |
| Creatinine | 35 – 135 μmol/l |
| Alanine Aminotransferase (ALT) | 5 – 35 U/l |
| Gamma-glutamyl Transferase (GGT) | < 65 U/l |
| Alkaline Phosphatase (ALP) | 30 – 135 U/l |
| Aspartate Aminotransferase (AST) | < 40 U/l |
| Total Protein | 60 – 80 g/l |
| Albumin | 35 – 50 g/l |
| Globulin | 2.4 – 3.5 g/dl |
| Amylase | < 70 U/l |
| Total Bilirubin | 3 – 17 μmol/l |
| Calcium | 2.1 – 2.5 mmol/l |
| Chloride | 95 – 105 mmol/l |
| Phosphate | 0.8 – 1.4 mmol/l |
| Haematology | Normal Value |
|---|---|
| Haemoglobin | 11.5 – 16.6 g/dl |
| White Blood Cells | 4.0 – 11.0 x 109/l |
| Platelets | 150 – 450 x 109/l |
| MCV | 80 – 96 fl |
| MCHC | 32 – 36 g/dl |
| Neutrophils | 2.0 – 7.5 x 109/l |
| Lymphocytes | 1.5 – 4.0 x 109/l |
| Monocytes | 0.3 – 1.0 x 109/l |
| Eosinophils | 0.1 – 0.5 x 109/l |
| Basophils | < 0.2 x 109/l |
| Reticulocytes | < 2% |
| Haematocrit | 0.35 – 0.49 |
| Red Cell Distribution Width | 11 – 15% |
| Blood Gases | Normal Value |
|---|---|
| pH | 7.35 – 7.45 |
| pO2 | 11 – 14 kPa |
| pCO2 | 4.5 – 6.0 kPa |
| Base Excess | -2 – +2 mmol/l |
| Bicarbonate | 24 – 30 mmol/l |
| Lactate | < 2 mmol/l |
