HDR 15.8.12
Vital Statistics
Example:
EventCOUGH / No event
NO COUGH / Total
Intervention
VITAMIN C / 14 / 30 / 44
Control
PLACEBO / 15 / 35 / 50
RISK: is the chance, or probability, of having a specific event.
For example, of 44 women taking Vitamin C for the treatment of Flu, 14 had the event 'still coughing' after 3 weeks. The risk of continuing with a cough was 14/44 = 0.32.
ODDS: is the ratio of events to non-events ie it's the risk of having an event divided by the risk of not having it.
If we look at the 44 women taking the Vitamin C for Flu, 14/44 (risk of cough) divided by 30/44 (risk of no cough) = 0.47.
Sometimes risk and odds can be very similar (not exactly the same) especially when the groups are small– but beware this is not always the case!
RISK RATIO (same as relative risk): the risk of the event in one group divided by the risk of the event in the other group.
RR = Number with event in treatment group ÷ Number with event in control group
Number in treatment groupNumber in control group
14/44 ÷15/50= 1.06
ODDS RATIO: odds ratio is an alternative way of comparing how 'likely' events are between two groups. It is the odds of the event occurring in one group divided by the odds of the event occurring in the other group.
OR = Number with event in treatment group ÷ Number with event in control group
Number without event in treatment group Number without event in control group
14/30 ÷15/35= 1.09
If an intervention has an identical effect to the control, the RR and OR will be 1.
If it reduces the chance of having the event, the RR and OR will be < 1.
If it increases the chance of having the event, the RR and OR will > 1.
Odds ratios and risk ratios will be similar when the event is rare, but will differ when the event is common. In situations of common events, the odds and odds ratio can be misleading, because people tend to interpret an odds ratio as if it were a risk ratio.
RISK DIFFERENCE: The risk in one group minus the risk in the other
RD = Risk in Vitamin C group – Risk in placebo group
0.32 - 0.47 = -0.15
The risk difference describes the absolute change in risk that is attributable to the intervention.
If an intervention has an identical effect to the control, the risk difference will be 0.
If it reduces risk, the risk difference will be < 0.
If it increases risk, the risk difference will be 0.
The risk difference cannot be above 1 or below -1. Switching between good and bad outcomes for the risk difference causes a change of sign, from + to - or - to +.
Sometimes it may be useful to present figures for 100 times the RD, or 1000 times the RD, which describe how many people have avoided (or incurred) the event for every 100 or 1000 treated, respectively. Another way of looking at the risk difference is the number needed to treat (NNT).
NUMBER NEEDED TO TREAT: the number of patients you would need to treat with the experimental treatment rather than the control in order to prevent a single event.
NNT = 1 / risk difference (forget about the minus sign)
NNT = 1 / 0.15 = 6.7
In other words, if we treat 100 people, 15 more will benefit when we use the intervention, who would not have benefited if given control. So how many would we need to treat to help one person? 100/15 or 6.7. We always round up NNT to the next whole number. Also, it is important with NNT to link it to a time frame, so in this case we would need to treat 7 people for 3 weeks to prevent a single extra person from not experiencing the cough.
Where the risk difference is greater than 0 (i.e. the risk of the event we are trying to prevent actually increases) the same calculation produces a number known as the NNH – NUMBER NEEDED TO HARM.
SENSITIVITY : the proportion of people with disease who have a positive test result.
= true positive
(true positive + false negative)
SPECIFICITY: the proportion of people without disease who have a negative test result
= true negative
(true negative + false positive)
PPV: proportion of positive test results that are true positives
= number of true positives
No. of true positives + no. of false positives
NPV: proportion of negative test results that are true negatives
= number of true negatives
No. of true negatives + no. of false negatives
Good Resources
CASP for critical appraisal check lists
has very useful section on stats including risk, odds and NNT
has very useful summary of stats terms, concentrating on meta analysys and systematic reviews
again a summary of ‘stats made easy’