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Evidence Based Medicine

Statistics

Question 62 of 180

Regarding the interpretation of risk of an outcome event when comparing a treatment and control group, how is the relative risk reduction calculated:

Answer:

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 = 1 – RR Where ARC = absolute risk of outcome event in control group and ART = absolute risk of outcome event in treatment group.

Absolute and Relative Risk

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

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