Unformatted text preview: Comparing Rates and Proportions
Part I Crude, specific and adjusted rates Introduction to concept of confounding Adjusted rates: what they are and how to calculate ageadjusted rates BREAK Part II Measures of Association: Difference measures Ratio measures Interpreting measures of association Inclass exercise EPID 301: Principles of Epidemiology Concept Map Version 3 Harriet Richardson and Patti Groome What health problem?
W ha t
Sub stan tive E is kn ow n?
t Wha consis t of? pide miol ogy
ra Lite Epidemiologic S tud ies What does tha ys a l an An Pl t step is Dise a se Risk Freque n Fac tors cy
igns Des sis ly Ana e do w d nee ture i ew Re v to kn Study Design What is epidemiology? ow? Stu d P yV Sig reci alidi n s ific ion ty an ce ing ign dy n tu atio S ul p Po Cr it Is the qu es ic a lA pp rai s Disease Model s De tio n al d? a ns we re Outer Ring: Line of Enquiry Middle Ring: Course Objectives Inner Ring: Epidemiologist's Toolkit Wh at is th e ne xt step ? Measures of Association Measures of disease frequency (proportions or rates) are compared between those with and those without the exposure of interest Comparison can be summarized using ratios or differences:
Rateexposed / Rateunexposed Rateexposed Rateunexposed Difference Measures of Association
For Cumulative Incidence: Risk Difference = IRc(exposed)  IRc(unexposed) For PersonTime Incidence: Rate Difference = IRPT(exposed)  IRPT(unexposed) Expressed in terms of cumulative or persontime incidence rates Magnitude does not express strength of association because it's influenced by rate in unexposed (baseline rate) Useful in public health when causality is established because it indicates how much of the disease in the exposed is due to the exposure Measuring the Absolute (Difference) Effect versus the Relative (Ratio) Effect Consider two investments: an investment of $100 that yields $120 and an investment of $1000 that yields $1150 Absolute yields: $20 and $150 Relative yields: 20% and 15% Which was the stronger result? Ratio Measures of Association: Risk Ratios
Cumulative Incidence (IRc) = Risk or Probability
Number of new events occurring during a specified time period Population at risk Ratio of cumulative incidence rates: RR = IRc(exposed) / IRc(unexposed) Risk Ratios
Example from the Honolulu Heart Program
Design: Prospective Cohort Study Population: males age 4565 Inclusions: free of diabetes at baseline, consent Followup: 6 years Exposure: Body Mass Index (high vs. low/normal) Outcome: Diabetes Risk Ratios
Example from the Honolulu Heart Program 6,000 eligible subjects 6,000 tested for diabetes at 6 years followup 300 diagnosed Diabetes
BMI High Low/ Normal Total Yes 140
a No 1860
b Total 2000 4000 6000 160
c 3840
d 300 5700 Risk Ratios
Example from the Honolulu Heart Program
Total incidence?
300 / 6000 = 5 per 100 Diabetes BMI High Yes 140 160 300 No 1860 3840 5700 2000 4000 IRc(exposed)?
140 / 2000 = 7 per 100 IRc(unexposed)?
160 / 4000 = 4 per 100 Is BMI related to risk of diabetes? Low/ Norm Total Risk Ratio = 7/4 or 1.75 Ratio Measures of Association Rate Ratios
PersonTime Incidence Rate (IRpt)
Number of new events in a specified time period Total person time at risk Ratio of persontime incidence rates: RR = IRPT(exposed) / IRPT(unexposed) Rate Ratios
Example from the Honolulu Heart Program Diabetes 6,300 eligible subjects Exams every 6 months for 6 years 1,000 lost to followup 300 diagnosed BMI High Yes 140 PersonTime 9000 18000 27000 Low/ 160 Norm Total 300 Calculation of persontime units
01/ 07/ 01/ 07/ 01/ 07/ 01/ 07/ 01/ 07/ 01/ 07/ 01 97 97 98 98 99 99 00 00 01 01 02/ 02/ 03
Death from other cause Total time at risk (yrs) Subject 1 Subject 2 Subject 3 . . O    O         to   Lost followup O       Diabetes 2.5 6.0 3.5
. . Subject 500 . . Subject 6,000 Total years at risk O     Diabetes 3.0
. . 2.5 O     27,000 personyears Rate Ratios
Example from the Honolulu Heart Program Incidence rate overall?
300/27000 = 11.1 per 1000 pys Diabetes BMI High orm Yes 140 PersonTime 9000 IRPT(exposed)?
140/9000 = 15.6 per 1000 pys IRPT(unexposed)?
160/18000 = 8.9 per 1000 pys Is BMI related to Low/N of diabetes? risk 160 18000 Total 300 27000 Rate Ratio = 15.6 / 8.9 or 1.75 Relative Risk Technically, refers to risk ratios but often used as a generic term for: Risk ratios based on cumulative incidence Rate ratios based on persontime incidence Odds ratios when the disease is rare (next part of our lecture) Interpretation of Relative Risks Range: 0 to infinity, no units RR=1 ? RR <1 ? RR >1 ? Strength of association (rule of thumb*):
Inverse 0.710.99 0.410.70 0.000.40 Positive 1.011.50 1.513.00 >= 3.01 Relative Strength Weak association Moderate association Strong association *Oleckno Fig 61 taken from Occupational Epidemiology Interpretation of Relative Risks A high RR is not necessarily associated with a high risk of the disease Risk ratio varies with the time of observation Risk ratios and rate ratios are similar only when risk of outcome is low (rare disease) Public health perspective requires consideration of: Prevalence of disease and exposure Severity of disease Ratio Measures of Association Can be applied where levels of exposure are not dichotomous: BMI and diabetes example: Low BMI (baseline) RR=1.0 Normal BMI RR=1.15 High BMI RR=1.89 Risk Ratios
Example from the Honolulu Heart Program
Diabetes Low BMI (baseline) RR=1.0 Normal BMI RR= (90/2110) / (70/1890)= 1.15 High BMI RR= (140/2000) / (70/1890)=1.89 BMI Low Norm High Yes 70 90 140 No 1820 2020 1860 OR REF 1.15 1.89 Usefulness of Ratio Measures of Association Measures the strength of an association between an exposure and outcome Useful in uncovering causal factors Common reference point of 1, which represents no difference in the rates compared Adjustment of Measures of Association We've just reviewed crude measures of association As with rates, adjustment is often needed to address confounding factors Stratified methods of adjustment are similar to the standardization approach Also use regression and other multivariate methods A review: Odds Ratio of the probability (P) or number of ways that something is so to the probability or number of ways that it is not so (1P) Odds = P / 1P Example if the probability a horse will win a race is 60%, the odds of winning to losing is: 60/40 = 60:40 = 1.5:1 = 1.5 Odds Ratio The ratio of two odds: Odds of disease(exposed) Odds of disease(unexposed) Example  the odds of getting lung cancer if you are a smoker over the odds of getting lung cancer if you aren't a smoker: 80:2000 / 40:6000 = 0.04/0.0067 = 5.97 Odds Ratios
Example from the Honolulu Heart Program
Design: Prospective Cohort Study Population: males age 4565 Inclusions: free of diabetes at baseline, consent Followup: 6 years Exposure: Body Mass Index (high vs. low/normal) Outcome: Diabetes Odds Ratios
Example from the Honolulu Heart Program
Diabetes 6,000 eligible subjects 6,000 tested for diabetes at 6 years followup 300 diagnosed BMI High Yes 140 No 1860 3840 5700 2000 4000 Low/ 160 Norm Total 300 Odds Ratios
Example from the Honolulu Heart Program
Overall odds?
300/5700 BMI High Diabetes Yes 140 No 1860 3840 5700 2000 4000 Odds(exposed)?
140/1860 Odds(unexposed)?
160/3840 Low/ 160 Norm Total 300 Odds Ratio = (a/b) / (c/d) (140/1860)/(160/3840) = 1.81 Odds Ratios Notation for Case Control Studies
First select: Then measure past exposure: Were exposed Were not exposed Cases (with disease) a c Controls (without disease) b d Exposure Odds Ratio: a/c / b/d =Odds of exposure (cases) / Odds of exposure (controls) which is equal to a computationally easier: Odds Ratio: ad / bc Odds Ratios and CaseControl Studies
Example: dietary nitrate intake and stomach cancer
Subjects: aged 5075 Outcome: new cases of stomach cancer diagnosed during a 2year period Cases: patients diagnosed with stomach cancer Controls: nonpatients from the same source population (2 controls per case) Exposure: high versus low/normal nitrate consumption Odds Ratios and CaseControl Studies
Example: dietary nitrate intake and stomach cancer
Exposure odds overall? 292/848 = 0.34 Exposure odds (cases)? 140/240 = 0.58 Exposure odds (controls)? 152/608 = 0.25
Cases Exposed 140 Controls 152 608 Unexposed 240 Odds Ratio = 0.58/0.25 or 2.32 Interpretation of Odds Ratios As with RR, the more the OR departs from 1, the stronger the association If disease is rare: OR RR
Cases Controls a b c d Exposed Unexposed RR=(a/a+b)/(c/c+d) If disease is rare: a+b b c+d d RR a/b/c/d = OR Interpretation of Odds Ratios
recall from the Honolulu Heart Program
Diabetes BMI High Low/ Norm Yes 140 (a) 160 (c) No 1860 (b) 3840 (d) IR(ex) = 140 / (140 + 1860) = 0.07 IR(unexp) =160 / (160 +3840) = 0.04 RR = 0.07 / 0.04 = 1.75 If disease is rare: (a+b) ~b: (140 + 1860) ~ 1860 (c+d) ~d: (160 + 3840) ~ 3840 In which case; RR~(a/b) / (c/d) = ad / bc = OR
OR = ad / bc = 140 x 3840 / 160 x 1860 = 1.81 Risk Ratio = 1.75 versus Odds Ratio = 1.81 Attributable Risks and Attributable Rates
Attributable Risk = IRc(exposed)  IRc(unexposed) Attributable Rate = IRPT(exposed)  IRPT(unexposed) Risk differences have a specific meaning when the risk factor is causal Number of cases in the exposed that can be attributed to the exposure itself In the absence of the exposure, people who would have been exposed still experience the background risk of disease represented by the unexposed rate For expediency, we will focus on attributable risk same thinking for attributable rates... Attributable Risk
Smoking and lung cancer example in Oleckno pg.112 Attributable Risk = IRc(exp)  IRc(unexp) Lung cancer and smoking Attributable risk: 180 per 100,000  20 per 100,000 AR=160 per 100,000 Interpretation: "The risk of lung cancer in smokers due only to smoking is 160 per 100,000" Attributable Risk Percent
AR% = IRc(exposed)  IRc(unexposed)  X 100 IRc(exposed) Percent of disease in the RR1 exposed that is  X 100 due to the RR exposure OR AR% = Attributable Risk Percent
Smoking and lung cancer example in Oleckno pg.112 AR% = IRc(exposed)  IRc(unexposed) IRc(exposed) X 100 Example: Lung cancer AR% = 160 per 100,000 / 180 per 100,000 = 88.9% Interpretation: "~89% of the incidence of lung cancer among smokers is due to smoking" Population Attributable Risk
The incidence (mortality) of a disease in the whole population that is due to a given exposure Population Attributable Risk = IRc(population)  IRc(unexposed) Population Attributable Risk
Smoking and lung cancer example in Oleckno pg.112 Population Attributable Risk = IRc(population)  IRc(unexposed) Population AR = 60 per 100,000 20 per 100,000 = 40 per 100,000 Interpretation: "If smoking were eliminated from this population the overall cumulative incidence rate of lung cancer would drop by 40 per 100,000." Population Attributable Risk Percent
PAR% = IRc(population)  IRc(unexposed)  X 100 IRc(population) OR PAR% = Prevalence(exposed)(RR1)  X 100 Prevalence(exposed)(RR1) + 1 Population Attributable Risk Percent
Smoking and lung cancer example in Oleckno pg.112 PAR% = Prevalence(exposed)(RR1)  X 100 Prevalence(exposed)(RR1) + 1 If RR=9 & P(e) of smokers was 25%; Pop AR% = {0.25(91)} / {0.25 (91)+1} x 100 Pop AR% = 66.7% "If smoking were eliminated from this population we would expect a 66.7% decrease in the cumulative incidence of lung cancer" Causes of Death and PAR
Population attributable risk has tangible public health significance.
Nine factors account for about 50% of deaths in the United States (McGinnis and Foege see Oleckno page 133)  tobacco, diet and activity, alcohol, microbial agents, toxic agents, firearms, sexual behaviour, motor vehicles, and illicit use of drugs All are modifiable through primary prevention Summary Crude disease rate comparisons are often distorted by age distribution differences and need adjustment Ratio measures of association assess the strength of the association between an exposure and a outcome Difference measures of association assess the impact of an exposure on a population when the exposure is causal Summary Odds ratios are measures of association that can be calculated from the results of cohort studies and are the only measure of association possible in casecontrol studies Attributable risk and its correlates address the public health impact of an exposure on the burden of disease ...
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 Spring '09
 Richardson&Aronson
 Epidemiology, Honolulu Heart Program

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