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- Measures of AssociationSPH 231February 7, 2013
- Measures of Association• Comparing the frequency of diseasebetween exposed and unexposed• Measures of association (effect)• There are two types of measures ofassociation– Absolute measures– Relative measures
- Measures of Association• Show the strength of the relationshipbetween an exposure and outcome• Indicate how more or less likely a group isto develop disease as compared toanother group
- Absolute Measures of Association• Based on DIFFERENCE between twomeasures of disease frequency• May range from -1 to 1– If value of difference measure=0 then nodifference between exposed and unexposed• Difference measures are useful forassessing the public health impact of anexposure
- Absolute Measures of Association• Incidence– Risk difference = Cumulative Incidence inExposure – Cumulative Incidence inUnexposed– Rate Difference = Incidence Rate in Exposed– Incidence Rate in Unexposed• Prevalence– Prevalence Difference = Prevalence inExposed – Prevalence in Unexposed
- Absolute Measures of Association• Incidence Differences– Both differences measure the excess numberof NEW cases among the exposed comparedto the unexposed• Prevalence Differences– Measures excess number of EXISTING casesamong exposed compared to unexposed at aparticular point in time
- Relative Measures of Association• The RATIO of two disease frequencies– Risk Ratio (aka Cumulative Incidence Ratio,aka Relative Risk)– Rate Ratio– Prevalence Ratio• Relative measures may be interpreted asthe excess Risk, Rate, or Prevalence inexposed relative to the unexposed
- Relative Measures of Association• Relative measures may range from 0 toinfinity• Relative measures assess the strength ofassociation between exposure anddisease and are useful in identifying riskfactors
- Data Layouts• Typically, epidemiologists organize studydata as a 2x2 table– Column = Disease or Outcome status (Yes orNo)– Row = Exposure Status (Yes or No)• Study participants assigned to one of thefour cells according to their individualexposure and disease state• Results used to calculate and comparefrequency of disease according toexposure
- 2 x 2 TablesUsed to summarize counts of disease andexposure to calculate measures of associationOutcomeExposure Yes No TotalYes a b a + bNo c d c + dTotal a + c b + d a + b + c + d
- 2 x 2 Tablesa = number exposed with outcomeb = number exposed without outcomec = number not exposed with outcomed = number not exposed without outcome******************************a + b = total number exposedc + d = total number not exposeda + c = total number with outcomeb + d = total number without outcomea + b + c + d = total study population (N)a bc dOutcomeYes NoExposureYesNo
- Example100 900100 1900ExposedUnexposed1,0002,000200 2,800 3,000Diseased Non-diseased* Assume incidence data over 1 year
- Cumulative incidence• Cumulative incidence in the exposed =• Cumulative incidence in the unexposed =aa bcc d
- Example100 900100 1900ExposedUnexposed1,0002,000200 2,800 3,000Diseased Non-diseased* Assume incidence data over 1 year
- Example• Cumulative incidence in the exposed =• Cumulative incidence in the unexposed =
- Interpretation• Cumulative incidence in the exposed:-10% of the exposed group developed thedisease in the study period• Cumulative incidence in the unexposed:-5% of the unexposed group developedthe disease in the study period
- Risk difference and ratio• Risk Difference =• Risk Ratio (Relative Risk, RR) =a ca b c daa bcc d
- Example100 900100 1900ExposedUnexposed1,0002,000200 2,800 3,000Diseased Non-diseased* Assume incidence data over 1 year
- Example• Risk Difference =• Risk Ratio =
- Interpretation• Risk Difference:In a population of 100 exposed people, therewould be 5 additional cases of disease thanwhat you would observe if exposure wasabsent in the study period• Risk Ratio:The risk of developing the disease in theexposed group is two times the risk ofdeveloping the disease in the unexposed groupin the study period
- Relative Risk ExampleEscherichia coli?Pinkhamburger Yes NoTotalYes 23 10 33No 7 60 67Total 30 70 100a / (a + b) 23 / 33RR = = = 6.67c / (c + d) 7 / 67
- Odds Ratio• Used with case-control studies• Population at risk is not known (selectedparticipants by disease status)• Calculate odds instead of risksa x dOR =b x c
- 2x2 tablesa bc dDiseased Non-diseasedExposedUnexposeda+bc+da+c a+d a+b+c+d = N* Assume incidence data over 1 year
- Odds• Odds of disease in the exposed =• Odds of disease in the unexposed =abcd
- Odds Ratio• Odds Ratio == a/b x d/c= a x d / b x ca/bc/d
- Example• Odds of disease in the exposed =• Odds of disease in the unexposed =1000.119001000.051900
- Example• Odds Ratio =100100 *1900900 2.11100 100 * 9001900
- Interpretation• Odds Ratio:(OR as an estimate of RR)The risk of developing the disease in theexposed group is 2.11 times the risk ofdeveloping the disease in the unexposedgroup during the study period
- Odds Ratio ExampleIncreased BloodPressureCaffeineintake “high”? Yes NoTotalYes 130 115 245No 120 135 255Total 250 250 500a x d 130 x 135OR = = = 1.27b x c 115 x 120
- Interpreting Risk and OddsRatiosRR or OR< 1• Exposureassociatedwithdecreasedrisk ofoutcomeRR or OR= 1• NoassociationbetweenexposureandoutcomeRR or OR> 1• Exposureassociatedwithincreasedrisk ofoutcome
- Interpretation• RR = 5– People who were exposed are 5 times more likely tohave the outcome when compared with persons whowere not exposed• RR = 0.5– People who were exposed are half as likely to havethe outcome when compared with persons who werenot exposed• RR = 1– People who were exposed are no more or less likelyto have the outcome when compared to persons whowere not exposed
- Measures of Association (Effect)• Prevalence difference• Prevalence ratio• Risk difference• Risk ratio• Incidence rate difference• Incidence rate ratio• Odds ratioAPPROPRIATE MEASURE DEPENDS ON THESTUDY YOU HAVE CONDUCTED

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