Definitions and calculations Flashcards
Definition of ‘risk’
The probability that an event will occur in a group, whether it be a good or bad event
Definition of ‘probability’
An estimate of the chance of an event occurring divided by the total number of chances available
- e.g. if a player owns 1 of 4 tickets, probability of winning is 1 in 4
What is a p-value?
The probability that the observed difference was observed by chance
What is relative risk?
The change in probability of an event occurring due to a certain factor
How is relative risk/risk ratio calculated and when is it used?
Divide the probability of an event occurring for one group by the probability of an event occurring for a second group
- used as a comparison of a treatment/intervention group and placebo group in a clinical trial
What are odds?
Ratio of a player’s chances of losing to the player’s chances of winning
- average frequency of a loss to average frequency of a loss
What is absolute risk?
The individual risk of developing a disease over a time period, calculated by the number of events in a group divided by the number of people in that group
What is the difference between relative risk and absolute risk?
Relative risk compares the absolute risk of both groups being compared.
Absolute risk is the independent risk for each individual group.
What statistical measures are used to assess probability of an event and odds of an event?
Probability = relative risk, so use relative risk in the hypotheses
Odds = odds ratio, so use odds ratio in the hypotheses
Formula for odds ratio?
Using 2x2 tables
OR = (AxD)/(BxC)
Formula for relative risk?
Using 2x2 tables
RR = (A/(A+B))/(C/(C+B))
What are the different values of relative risk and what do they mean?
RR = 1 - this means that the exposure is not associated with the outcome
RR < 1 - this means that the risk of the outcome is decreased by the exposure
RR > 1 - this means that the risk of the outcome is increased by the exposure
How can the Odds Ratio be interpreted?
The same as relative risk
OR = 1 means exposure is not associated with outcome
OR > 1 means higher odds of outcome occurring with exposure/increased risk
OR < 1 means lower odds of outcome occurring with exposure/decreased risk
How are confidence intervals associated with OR/RR?
95% confidence interval is used to estimate the precision of the RR/OR
- this is a range of values that you can be 95% certain contains the true mean of the population
How can confidence intervals for RR/OR be interpreted?
If the confidence intervals overlap the null value e.g. RR = 0.85 (CI = 0.6 to 1.2) and null value is RR = 1 then it is not statistically significant
If they don’t overlap the null value, the events can be described as SIGNIFICANTLY more/less likely to occur with exposure
When can odds (odds ratio) be used to estimate probability (relative risk)?
When the outcome is rare (<10%) - here, the odds and probability will be similar hence the OR will provide a reasonable estimate of the RR
When the outcome is not rare (>10%), the odds and probability begin to differ by enough that the OR can no longer provide a reasonable estimate of the RR
What is the difference between odds and difference in terms of their calculation?
Probability is calculated as occurrences divided by total number of occurrences and non-occurrences
Odds is calculated as occurrences divided by number of non-occurrences
e.g. 10 smokers, 3 have heart attacks, 7 don’t
Probability = 3/10 (7+3) = 0.30
Odds = 3/7 = 0.43
Calculation of Absolute Risk (AR)
Outcomes divided by number of people in the group
e.g. 10/100 = 0.1/10%
Calculation of Absolute Risk Reduction (ARR)
AR unexposed - AR exposed = ARR
e.g. 0.1 - 0.3 = -0.2
AR reduced by 20%
Calculation of Relative Risk involving absolute risk
AR exposed divided by AR unexposed
e.g. 0.3/0.1 = RR = 3
Calculation of Relative Risk Reduction (RRR)
(AR unexposed - AR exposed)/AR unexposed
e.g. (0.1-0.3)/0.1 = -2 = -200% (2x reduced risk)
Other method is 1 - RR (if you have it)
e.g. 1 - 3 = -2 = 200% reduction
Which is more specific, ARR or RRR?
ARR
- RRR will tend to overestimate the individual risk reduction for a patient (ARR)
- ARR and RRR will differ depending on sample size
Why is sole use of relative risk and hence RRR problematic?
Sometimes problematic when used to present the results of a randomised controlled trial.
- since it almost always overestimates the significance of a risk factor for the population’s health, AR and ARR would be better measurements for significance for public health as RRR can overestimate the significance.
What is recommended regarding use of absolute and relative risk and risk reduction?
BOTH should be presented together
