L20 Measures of Association

Question 1

What are measures of association?

Answer 1

Statistical quantity that gives an indication of the magnitude (strength) of association between exposure & outcome.

1) Relative risk (RR): Risk ratio
2) Relative risk (RR): Rate ratio
3) Odds ratio (OR)

Determine after constructing 2x2 contingency table of:
Rows: Exposure (Yes | No)
Columns: Outcome (Yes | No)

Question 2

State the purpose of using measures of association in observational studies.

Answer 2

To test the H0 that there is no association of the independent variable X (typically an exposure or risk factor or predictor variable) on the dependent variable Y (typically an outcome).

H0: RR or OR = 1
H1: RR or OR =/= 1

Range of values = 0 to infinity

• RR or OR = 1: NO association between exposure & outcome (i.e. null hypothesis H0)
• RR or OR > 1: Positive association i.e. exposure is associated with an increased risk of outcome
• RR or OR < 1: Negative association i.e. exposure is associated with a decreased risk of outcome

Question 3

E.g. of expressing relative risk or odds ratio in words:

Answer 3

RR or OR = 1.2:
Those who are exposed have 1.2 times the risk/odds (i.e. 20% more likely) of developing the outcome compared with those who are unexposed.

RR or OR = 0.8:
Those who are exposed have a 20% reduction in the risk odds (i.e. are 20% less likely) of developing the outcome compared with those who are unexposed.

Question 4

When is the risk ratio used in the statistical analysis of observational studies?

Answer 4

Used in cohort study when all subjects are followed for the same duration of time.

Risk ratio
= cumulative incidence in exposed group / cumulative incidence in unexposed group
= [a / (a + b)] / [c / (c + d)]

Question 5

When is the rate ratio used in the statistical analysis of observational studies?

Answer 5

Used in cohort study when all subjects are followed for the different lengths of follow-up.
- Units of time when each subject is observed = person-time (e.g. person-years)

Rate ratio
= incidence rate in exposed group / incidence rate in unexposed group
= (a / PTe) / (c / PT0)

Question 6

When is the odds ratio used in the statistical analysis of observational studies?

Answer 6

Used in case-control study

• Since relative risk cannot be calculated directly, where subjects are identified based on outcome status
• Thus, cannot calculate incidence in the exposed or unexposed group

However, can also be calculated in cross-sectional study & cohort studies (though less common).

Question 7

How is odds ratio calculated?

Answer 7

Odds ratio
= odds that a case was exposed / odds that a control was exposed
= ad / bc (via cross-product ratio of 2R x 2C contingency table)

Rows: Exposure (Yes | No)
Columns: Outcome (Yes | No)

Odds of an event = no. of events / no. of non-events

Question 8

When is an odds ratio a good estimate of the risk ratio?

Answer 8

When outcome is rare i.e. < 10%

• i.e. a is very small as compared to b
• i.e. c is very small as compared to d

given odds ratio
= odds that a case was exposed / odds that a control was exposed
= ad / bc (via cross-product ratio of 2R x 2C contingency table)
AND
Risk ratio
= cumulative incidence in exposed group / cumulative incidence in unexposed group
= [a / (a + b)] / [c / (c + d)]

Question 9

For observational analytical studies with multiple exposure groups, how are the measures of association calculated?

Answer 9

Reference group of least exposed group is selected, comparison with other exposure groups (e.g. never smoked or low exposure group)

Question 10

E.g. of how to write conclusion of involving multiple exposure groups when using multivariable logistic regression analysis.

Answer 10

Compared with those exposed to low level of radiation exposure, those exposed to medium level of radiation exposure had 1.16 (95% CI: 1.05 - 4.57) times the risk of developing cancer, and those exposed to high level of radiation exposure had 1.53 (95% CI: 1.04 - 4.55) times the risk of developing cancer, after controlling/adjusting for gender.

Question 11

A wide CI of RR or OR suggests an (1) result & indicates that the results should be interpreted (2) regardless of (3) significance.

Answer 11

1) imprecise
- Width of CI affected by confidence level, sample size & standard deviation
2) (clinically) with caution
3) statistical

Question 12

RR and OR should be reported with (1) as they are (2) than p-values, where they provide information on (3) & (4).

Answer 12

1) their 95% confidence intervals
2) more informative
3) statistical significance on association
4) precision on point estimate of RR or OR