Lecture 5: Measures of Association Flashcards
How are measures of association categorised?
- Continuous objective 2. Continuous subjective measures 3. Categorical
What category is: a) HbA1C (blood glucose level) b) positive/negative - disease/no disease c) pain levels
a) continuous objective b) categorical c) continuous subjective
Define dichotomy
A division or contrast between two things that are or are represented as being opposed or entirely different. e.g. “a rigid dichotomy between science and mysticism”
How can effects of new treatments with dichotomous outcomes be expressed? Why are these measures used?
- Relative risk - Risk difference - Odds ratio These measures show the direction and magnitude of association between two variables e.g. treatment and outcome
What is probability?
Probability is a measure of the chance of getting an outcome of interest from an event
What is ‘probability of an outcome’?
The number of times the outcome of interest occurs divided by the total number of possible outcomes
What do probabilities always lie between?
Probabilities always lie between 0 and 1
What does a probability of 1 mean?
A probability of 1 means that the outcome is certain
What does a probability of 0 mean?
A probability of 0 means that the outcome cannot happen
How do percentage chances differ from probabilities?
This is simply the probability multiplied by 100: Thus they range from 0% to 100%. A probability of 0.5, or 50%, means there is an equal chance of the event occurring or not.
What is ‘risk’ used to express in healthcare?
Risk is a way of expressing treatment effects
What is ‘risk’?
The probability of an outcome or event occurring
What is the ‘absolute risk’ of a disease?
Absolute risk of a disease is your risk of developing the disease over a time period
How is absolute risk calculated?
By dividing the number of events by the number of people at risk.
If one in every 100 patients suffers a side effect from a treatment, what is the absolute risk?
1/100 = 0.01
- What is the absolute risk in aspirin users?
- What is the absolute risk in non-aspirin users?
- 22/73 = 0.30
- 21/27 = 0.78
What is ‘relative risk’?
Relative risk indicates the ratio of the risk of an outcome in one group
(e. g. exposed) compared to the risk of the outcome in another group
(e. g. unexposed group).
E.g. in RCTs the groups of interest could be treatment group vs control group
In relative risk, what is the numerator? What is the denominator?
The numerator contains the group of interest (e.g. treatment or exposed group) and the denominator the control or unexposed group.
General formula for calculating relative risk
- The relative risk can be calculated from a simple 2x2 table
- In the above 2x2 table, rows represent the study groups, columns the outcomes
Risk in exposed = a/a+b, risk in the unexposed = c/c+d
RR=(a/(a+b))/(c/(c+d))
If RR = 1, what does this mean?
The risk in exposed group is the same as the risk in unexposed group.
If RR <1, what does this mean?
The risk in exposed group is less than the risk in unexposed group.
If RR >1, what does this mean?
The risk in exposed group is higher than the risk in unexposed group RR.
What do RR values range from?
0 to infinity
For relative risks <1, how can the the percent reduction be calculated?
Subtracting the RR from 1 to obtain the percent reduction: (1-RR)x100
If the risk in aspirin users to be 0.30 and the risk in non-aspirin users to be 0.78, what is the RR? What is the % reduction?
- RR = 0.30/0.78 = 0.3
- This means that the probability of developing MI for aspirin users is lower that that for non-aspirin users.
- RR <1: (1-0.38)x100= 62% reduction
- There is a 62% reduction in developing MI if you are an aspirin user compared to non-aspirin users
What do large RR values indicate?
A strong association –> but always interpret in association with confidence interval
Table below shows the effects of a history of antidepressant use on Ischaemic Heart Disease (IHD).
1) Calculate the risk of having IHD in patients who use anti depressants
2) Calculate the risk of having IHD in patients who do not use anti depressants
3) Calculate the risk ratio and interpret it
1) 217/1088 = 0.1994
2) 716/5361 = 0.1336
3) 0.1994/0.1336 = 1.46
The risk of developing IHD in AD users is 1.49 times that of non AD users.
Instead of risk, we can use ‘odds’. What are ‘odds’?
Odds are the probability of an event occurring divided by the probability of the event not occurring. Odds are calculated by dividing the number of times an event happens by the number of times it does not happen.
E.g. If 1 in 100 patients suffers from a side effect then the odds are
1/99 = 0.0101
The individual odds are not as easily interpretable as the risk. What must be done before interpreting results?
Calculate an odds ratio
What is an odds ratio? How is it calculated?
Odds ratio is the odds of the event in one group.
E.g. exposed to a drug divided by the odds in another group not exposed.
By convention, the numerator contains the group of interest (e.g. exposed group) and the denominator the unexposed group.
- What is the odds in exposed?
- What is the odds in unexposed?
- What is the OR?
- Odds in exposed; a/b
- Odds in unexposed; c/d
- OR = (a/b) / (c/d)
When OR = 1, what does this mean?
The odds in exposed group is the same as the odds in unexposed group
When OR<1, what does this mean?
The odds in exposed group is less than the odds in unexposed group
When OR>1, what does this mean?
The odds in exposed group is higher than the odds in unexposed group
What do odds ratio values range from/to?
From zero to infinity
Table below shows the effects of a history of antidepressant use on Ischaemic Heart Disease (IHD).
- What are the odds of having IHD in AD users?
- What are the odds of having IHD in non-AD users?
- What is the OR? What does this mean?
- Odds of having IHD in AD users; 217/871 = 0.25
- Odds of having IHD in non-AD users; 716/4645 = 0.15
- OR = 0.25/0.15 = 1.67
- For AD users, the odds of having IHD are 1.67 times that of non AD users
What does a large OR mean?
Large values indicate a strong association
N.B. association does not mean causation.
How should you always interpret odds ratios?
Using confidence interval
What is the confidence interval (CI)?
The confidence interval (CI) is a range of values that’s likely to include a population value with a certain degree of confidence.
What does a 95% CI mean? What is it used to estimate?
- The 95% confidence interval is a range of values that you can be 95% certain contains the true mean of the population.
- The 95% CI is used to estimate the precision of the OR, RR
What does a large CI mean?
Low precision of OR, RR
What does a small CI mean?
Higher precision of the OR, RR
What does it mean if the confidence interval crosses 1? e.g. 95% CI 0.9- 2.5
This implies no statistical significant difference between exposed and unexposed groups.
When are relative risks (RR) the most appropriate measure of association?
Mostly used in randomised controlled trials (RCT’s) or cohort studies, prospective studies (i.e. where the subjects are initially chosen by their exposure and followed up over time to see their outcome)
When should RR not be used? Why?
Relative risks should not be used in case-control or other retrospective studies as they are not meaningful (as the proportion of cases / controls is chosen by the researcher)
When are odds ratios the most appropriate measure of association?
- In case-control or other retrospective studies.
- Odds ratios are commonly reported in logistic regression analysis
N.B. If the disease / outcome is rare, then the RR with be similar to the OR
What is risk difference (RD)?
The difference in risk of outcome between e.g. the exposed and unexposed groups or treatment group and control
E.g. the difference between the risk of MI in non-aspirin users and the risk of MI in aspirin users.
If the risk of MI in aspirin users = 0.30; for non-aspirin users = 0.78. What is the risk difference? How can you intepret this?
0.78-0.30 = 0.48
There is a 48% increase in risk of developing MI if you are a non-aspirin users compared to aspirin users
What is ‘number needed to treat’ (NNT)?
NNT is the number of people who need to receive the treatment in order to achieve the required outcome in one of them.
NNT = 1/risk difference
