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2.4.1 relative measures

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The document discusses several relative measures used to compare the risk or odds of a disease between exposed and unexposed groups: 1) The rate ratio (RR) compares the risk or rate of disease between exposed and unexposed groups. An RR of 2 means the risk is twice as high in the exposed group. 2) The prevalence ratio (PR) is analogous to the RR but uses prevalence as the measure of disease. 3) The odds ratio (OR) uses odds rather than risk/rate. It is generally further from 1 than the RR. The OR compares the odds of disease between exposed and unexposed groups.

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Relative measures • Measures to be discussed – Risk/rate ratio – Prevalence ratio – Odds ratio
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))
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
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
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?
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
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
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
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
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)
2.4.1 relative measures
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)
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)
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)
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
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
Relative measures • Formula review – RR = Re / Ru – PR = Preve / Prevu – OR = (Pe/(1-Pe))/(Pu/(1-Pu)) – OR = Odds(dis)e/Odds(dis)u
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
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
Relative measures • Exercise at home / in lab • Calculate and interpret relative measures of association of potential interest from these trial results

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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