Definitions and calculations

Question 1

Definition of ‘risk’

Answer 1

The probability that an event will occur in a group, whether it be a good or bad event

Question 2

Definition of ‘probability’

Answer 2

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

Question 3

What is a p-value?

Answer 3

The probability that the observed difference was observed by chance

Question 4

What is relative risk?

Answer 4

The change in probability of an event occurring due to a certain factor

Question 5

How is relative risk/risk ratio calculated and when is it used?

Answer 5

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

Question 6

What are odds?

Answer 6

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

Question 7

What is absolute risk?

Answer 7

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

Question 8

What is the difference between relative risk and absolute risk?

Answer 8

Relative risk compares the absolute risk of both groups being compared.
Absolute risk is the independent risk for each individual group.

Question 9

What statistical measures are used to assess probability of an event and odds of an event?

Answer 9

Probability = relative risk, so use relative risk in the hypotheses

Odds = odds ratio, so use odds ratio in the hypotheses

Question 10

Formula for odds ratio?

Answer 10

Using 2x2 tables

OR = (AxD)/(BxC)

Question 11

Formula for relative risk?

Answer 11

Using 2x2 tables

RR = (A/(A+B))/(C/(C+B))

Question 12

What are the different values of relative risk and what do they mean?

Answer 12

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

Question 13

How can the Odds Ratio be interpreted?

Answer 13

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

Question 14

How are confidence intervals associated with OR/RR?

Answer 14

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

Question 15

How can confidence intervals for RR/OR be interpreted?

Answer 15

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

Question 16

When can odds (odds ratio) be used to estimate probability (relative risk)?

Answer 16

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

Question 17

What is the difference between odds and difference in terms of their calculation?

Answer 17

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

Question 18

Calculation of Absolute Risk (AR)

Answer 18

Outcomes divided by number of people in the group

e.g. 10/100 = 0.1/10%

Question 19

Calculation of Absolute Risk Reduction (ARR)

Answer 19

AR unexposed - AR exposed = ARR
e.g. 0.1 - 0.3 = -0.2
AR reduced by 20%

Question 20

Calculation of Relative Risk involving absolute risk

Answer 20

AR exposed divided by AR unexposed

e.g. 0.3/0.1 = RR = 3

Question 21

Calculation of Relative Risk Reduction (RRR)

Answer 21

(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

Question 22

Which is more specific, ARR or RRR?

Answer 22

ARR

• RRR will tend to overestimate the individual risk reduction for a patient (ARR)
• ARR and RRR will differ depending on sample size

Question 23

Why is sole use of relative risk and hence RRR problematic?

Answer 23

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.

Question 24

What is recommended regarding use of absolute and relative risk and risk reduction?

Answer 24

BOTH should be presented together