2.4.1 relative measures

1. Relative measures
• Measures to be
discussed
– Risk/rate ratio
– Prevalence ratio
– Odds ratio

2. Relative measures
•
• Risk/rate ratio (RR) – aka relative risk
• – “Risk” in relative risk used generically to include risk or rate
• Provides information about relative association between an exposure
and a disease
• The risk/rate of disease in the exposed is compared to the same
measure among the unexposed as a ratio
•RR = Rexposed / Runexposed = Re / Ru
• Where R indicates either risk or rate – (i.e., CI (cumulative
incidence) or ID (incidence density))

3. Relative measures
• RR can be used to refer generically to these relative
measures
• CIR is the specific term when cumulative incidence is
used
• IDR is the specific term when incidence density is used
• Used to see term RR used generically for any relative
measure (including OR, PR) but current trend is toward
specific terms

4. Relative measures
• Interpretations of RR:
• Relative difference in the risk/rate of disease between
the exposed and unexposed
• Interpretation of RR=5: Risk/rate of disease in the
exposed is 5 times the risk/rate in the unexposed
• Interpretation of RR=0.5: Risk/rate of disease in the
exposed is 0.5 times the risk/rate in the unexposed

5. Relative measures
• Example: study of oral contraceptive (OC) use and
bacteriuria among women 16-49 yrs
over 1 year
• RR = ?
• What measures of disease incidence can we estimate
from this data?
• How do we compare them to estimate RR?

6. Relative measures
• Can estimate CIs
• Take ratio to estimate RR
• RR = CIR = CIe/CIu=
• RR = (27/482)/(77/1908) = 1.39
• Women who use OCs have 1.39 times the risk of
bacteriuria (over 1 year) compared with women who do
not use OCs
• Note that as with CI, CIR is only interpretable with
information on the time period over which it was
calculated

7. Relative measures
• Prevalence ratio (PR)
• Provides information about relative association between an expo
and a disease, using prevalence as the measure of disease
• – Analogous to RR
• PR = Prevexposed / Prevunexposed = Preve / Prevu

8. Relative measures
• Interpretations of PR:
• Relative difference in the prevalence of disease
between the exposed and unexposed
• Interpretation of PR=5: Prevalence of disease among
the exposed is 5 times the prevalence in the unexposed
• Interpretation of PR=0.5: Prevalence of disease in the
exposed is 0.5 times the prevalence of disease in the
unexposed

9. Relative measures
• A brief aside on odds
• Odds – two equivalent definitions
– Odds = number of people with event / number of people without
an event
– Odds = probability of event occurring / probability of event not
occurring = P / (1-P)
• Example:
– 10 people in a classroom of 50 have a cold
– Probability of having a cold = 10/50 = 0.2
– Probability of not having a cold = 40/50 = 0.8
– Odds of having a cold = 10/40 = 0.2/0.8 = 0.25
• Odds range from 0 to positive infinity

10. Relative measures
• Utility of odds will become apparent when we discuss
study design and analysis of epidemiologic data
– When a disease is rare, odds can be modeled in place of risks
with similar results
– In some study designs (case-control varieties) odds estimate
pseudo-risks/rates (more in study design)

12. Relative measures
• Odds ratio (OR)
• Provides information about relative association between an expo
and a disease, using odds as the measure of disease
• – Analogous to RR
• •OR = (Pe/(1-Pe))/(Pu/(1-Pu))
• OR = Odds(disease)e / Odds(disease)u
JC: discuss (Disease Odds) vs. (Exposure Odds)

13. Relative measures
• Interpretations of OR:
• Relative difference in the odds of disease between the
exposed and unexposed
• Interpretation of OR=5: Odds of disease is in the
exposed is 5 times the odds in the unexposed
• Interpretation of OR=0.5: The odds of disease in the
exposed is 0.5 times the odds of disease in the
unexposed
• Note: it is incorrect to interpret the odds ratio as the
risk/rate ratio
– Exception for particular case-control study designs (more in
study design module)

14. Relative measures
• OR always more extreme than RR (further from null)
– When the disease is rare the values will be close
– Note that this is not relevant for designs in which OR captures a
risk/rate ratio directly (more in study design)

15. Relative measures
• OR versus RR
• Example:
– Recall the example of students having a cold
• P=0.2
• Odds=0.25
– Say we wanted to compare this classroom to an office
– In the office, 10 out of 100 people have a cold.
• P = 10/100 = 0.1
• Odds = 10/90 = 0.111
– Exposed are students, unexposed are office workers, outcome
is cold
– RR comparing students to workers: RR = 0.2 / 0.1 = 2
– OR comparing students to workers: OR = 0.25 / 0.111 = 2.25

16. Relative measures
• OR = ?
• OR = Odds(dis)exposed/Odds(dis)unexposed
• OR = (a/b)/(c/d) = ad/bc
• OR = (27x1831)/(77x455) = 1.41
• Women who use OCs have 1.41 times the odds of
bacteriuria compared to women who do not use OCs
JC: mention disease odds vs. exposure odds

17. Relative measures
• Formula review
– RR = Re / Ru
– PR = Preve / Prevu
– OR = (Pe/(1-Pe))/(Pu/(1-Pu))
– OR = Odds(dis)e/Odds(dis)u

18. Relative measures
• Exercise for home (discuss in lab)
• Hypothetical RCT for injection drug users
– Primary outcomes are cessation of drug use
– HIV as a secondary outcome of interest

19. Relative measures
• Exercise at home / in lab
• 60 people randomized to a 12-month residential
detoxification program
– 49 tested HIV negative at the start of the trial
– At the end of the trial, 5 participants tested positive
for HIV who had been negative at the start of the trial
• 60 people randomized to 12-months of
outpatient treatment
– 50 tested HIV negative at the start of the trial
– At the end of the trial, 3 participants tested positive
for HIV who had been negative at the start of the trial

20. Relative measures
• Exercise at home / in lab
• Calculate and interpret relative measures of
association of potential interest from these trial
results