Are exposures associated with disease? Chapter 6
Are exposures associated with disease? Epidemiology matters: a new introduction to methodological foundations Chapter 6 Seven steps 1. Define the population of interest 2. Conceptualize and create measures of exposures and health indicators 3. Take a sample of the population 4. Estimate measures of association between exposures and health indicators of interest 5. Rigorously evaluate whether the association observed suggests a causal association 6. Assess the evidence for causes working together 7. Assess the extent to which the result matters, is externally valid, to other populations Epidemiology Matters – Chapter 1 2 1. Associations 2. Ratio measures 3. Difference measures 4. Population attributable risk proportion 5. Summary Epidemiology Matters – Chapter 6 3 1. Associations 2. Ratio measures 3. Difference measures 4. Population attributable risk proportion 5. Summary Epidemiology Matters – Chapter 6 4 Associations First we start with measures of disease occurrence and frequency Association now involves the comparison of two measures Epidemiology Matters – Chapter 6 5 Example: Farrlandia associations Farrlandia population 10,000 people without heart disease Follow population for 5 years 3,000 people smoke 410 of smokers develop heart disease No loss to follow-up or change in smoking status over time Epidemiology Matters – Chapter 6 6 Example: Farrlandia associations Risk of heart disease among 3,000 smokers and 7,000 nonsmokers, over 5 years Epidemiology Matters – Chapter 6 7 Example: Farrlandia risk Incidence (risk) Risk of disease among exposed (smokers) diseased smokers population at baseline Epidemiology Matters – Chapter 6 8 Example: Farrlandia risk Incidence (risk) Risk of disease among unexposed (non-smokers) diseased non-smokers population at baseline Epidemiology Matters – Chapter 6 9 Example: Farrlandia risk Incidence of heart disease among smokers = 13.7% Incidence of heart disease among non-smokers = 5% How much larger is 13.7% than 5%? Is the difference between 13.7% and 5% meaningful? Epidemiology Matters – Chapter 6 10 1. Associations 2. Ratio measures 3. Difference measures 4. Population attributable risk proportion 5. Summary Epidemiology Matters – Chapter 6 11 Ratios A way to quantify the magnitude of difference between two measures of disease Epidemiology Matters – Chapter 6 12 Ratios Risk ratios 95% confidence interval for a risk ratio Example of 95% confidence intervals for a risk ratio Central Limit Theory assumptions and confidence intervals Rate ratios Odds ratios 95% confidence interval for the odds ratio Epidemiology Matters – Chapter 6 13 Risk ratio Numerator Conditional risk of disease among exposed Denominator Conditional risk of disease among unexposed Epidemiology Matters – Chapter 6 14 a b a+b c d c+d a+c b+d Epidemiology Matters – Chapter 6 a+b+c+d 15 Risk ratio Numerator Risk of disease in exposed Denominator Risk of disease in unexposed Epidemiology Matters – Chapter 6 = a a+b c c+d 16 Disease incidence over time Non-diseased Diseased Exposed Epidemiology Matters – Chapter 6 Unexposed 17 Disease incidence over time Epidemiology Matters – Chapter 6 18 Disease incidence over time Epidemiology Matters – Chapter 6 19 Disease incidence over time Epidemiology Matters – Chapter 6 20 2 x 2 table Epidemiology Matters – Chapter 6 21 Risk ratio Numerator Risk of disease in exposed Denominator Risk of disease in unexposed Epidemiology Matters – Chapter 6 = a a+b c c+d 22 2 x 2 table Risk ratio = Epidemiology Matters – Chapter 6 8 --10 -------- = 1.6 5 --10 23 2 x 2 table Risk ratio = 8 --10 -------5 --10 Risk ratio = a --a+b -------c --c+d Epidemiology Matters – Chapter 6 24 Risk ratio interpretation Ratios > 1.0 indicate rate is higher among exposed than unexposed Ratios = 1.0 indicate no association Ratios < 1.0 indicate rate is lower among exposed than unexposed Epidemiology Matters – Chapter 6 25 Risk ratio 95% confidence interval Sample, by chance, will often not represent exact disease and exposure experience of population Confidence intervals help to understand variability in study estimates due to chance in sampling process Epidemiology Matters – Chapter 6 26 Steps: risk ratio 95% confidence interval 1. Take natural log of risk ratio ln (Risk ratio) 2. Estimate standard error (SE) Epidemiology Matters – Chapter 6 27 Steps: risk ratio 95% confidence interval 3. Estimate upper and lower bounds on log scale 95% confidence interval upper bound ln(Risk ratio) + 1.96(SE[ln(Risk ratio)]) 95% confidence interval lower bound ln(Risk ratio) - 1.96(SE[ln(Risk ratio)]) Epidemiology Matters – Chapter 6 28 Steps: risk ratio 95% confidence interval 4. Exponentiate upper and lower bounds 5. Report and interpret estimate and confidence interval Sample: In these data, the exposed individuals had [risk ratio estimate] times the risk of the outcome compared with the unexposed, with a 95% confidence interval for the observed risk ratio ranging from [lower bound] to [upper bound]. Epidemiology Matters – Chapter 6 29 Example: risk ratio 95% confidence interval Measure association between family history of Alzheimer’s disease (AD) and incidence of AD among those aged >70 Random sample of 1,000 individuals aged >70, no symptoms of AD Followed for 20 years Measure symptoms of AD every year No losses to follow-up Epidemiology Matters – Chapter 6 30 Example: risk ratio 95% confidence interval Risk ratio = Epidemiology Matters – Chapter 6 a --a+b -------c --c+d 31 Example: risk ratio 95% confidence interval 1. Take natural log of risk ratio ln (Risk ratio) = ln(1.548) = 0.437 2. Estimate standard error (SE) Epidemiology Matters – Chapter 6 32 Example: risk ratio 95% confidence interval 3. Estimate upper and lower bounds on log scale 95% confidence interval upper bound ln(Risk ratio) + 1.96(SE[ln(Risk ratio)]) 0.437 + 1.96(0.1796) 95% confidence interval lower bound ln(Risk ratio) - 1.96(SE[ln(Risk ratio)]) 0.437 - 1.96(0.1796) Epidemiology Matters – Chapter 6 33 Steps: risk ratio 95% confidence interval 4. Exponentiate upper and lower bounds 5. Report and interpret estimate and confidence interval Individuals >70 in Farrlandia with a family history of AD had 1.55 times the risk of developing AD over 20 years, with a 95% confidence interval for the risk ratio of 1.09 to 2.20. Epidemiology Matters – Chapter 6 34 Central Limit Theory Validity of confidence interval relies on Central Limit Theory (CLT) Remember, assumptions of CLT Large sample size Each cell in 2 x 2 ≥ 5 Epidemiology Matters – Chapter 6 35 Rate ratio Risk ratios ideal with little or no loss to follow-up Most studies have substantial loss to follow-up Rate ratio more accurate representation of incidence when loss to follow-up an issue Epidemiology Matters – Chapter 6 36 Rate ratio Epidemiology Matters – Chapter 6 37 Rate ratio Numerator Rate of disease in exposed Denominator Rate of disease in unexposed = Epidemiology Matters – Chapter 6 38 Rate ratio interpretation Similar to risk ratio Ratios > 1.0 indicate rate is higher among exposed than unexposed Ratios = 1.0 indicate no association Ratios < 1.0 indicate rate is lower among exposed than unexposed Epidemiology Matters – Chapter 6 39 Steps: rate ratio 95% confidence interval 1. Take natural log of rate ratio ln (Rate ratio) 2. Estimate standard error (SE) Epidemiology Matters – Chapter 6 40 Steps: rate ratio 95% confidence interval 3. Estimate upper and lower bounds on log scale 95% confidence interval upper bound ln(Rate ratio) + 1.96(SE[ln(Rate ratio)]) 95% confidence interval lower bound ln(Rate ratio) - 1.96(SE[ln(Rate ratio)]) Epidemiology Matters – Chapter 6 41 Steps: rate ratio 95% confidence interval 4. Exponentiate upper and lower bounds 5. Report and interpret estimate and confidence interval Sample: In these data, the exposed individuals had [rate ratio estimate] times the rate of the outcome compared with the unexposed, with a 95% confidence interval for the observed rate ratio ranging from [lower bound] to [upper bound]. Epidemiology Matters – Chapter 6 42 Odds ratio Appropriate measure of association for prospective study is risk or rate ratio If sample individuals with and without disease and retrospectively assess exposure status, appropriate measure of association is odds ratio Epidemiology Matters – Chapter 6 43 Example A Research question: Is smoking cigarettes during pregnancy a potential cause of offspring attention-deficit hyperactivity disorder (ADHD)? Sample: Recruit 5,000 women during pregnancy who are smokers, and 5,000 women during pregnancy who are not smokers in Farrlandia Prospective study Assume no loss to follow-up Measures: Follow offspring at age 10 and determine which children developed ADHD and which did not Epidemiology Matters – Chapter 6 44 Example A: risk ratio Risk ratio = Epidemiology Matters – Chapter 6 a --a+b -------c --c+d 45 Example A: risk ratio interpretation From the prospective study, offspring of women who smoked in pregnancy have 1.5 times the risk of developing ADHD over 10 years compared to offspring of women who did not smoke in pregnancy. Epidemiology Matters – Chapter 6 46 Odds ratio Numerator Odds of disease in exposed Denominator Odds of disease in unexposed Epidemiology Matters – Chapter 6 47 Example A: odds ratio Epidemiology Matters – Chapter 6 48 Example A: odds ratio Odds of ADHD among exposed Odds of ADHD among unexposed Odds ratio Epidemiology Matters – Chapter 6 49 Example A: odds ratio interpretation The odds of developing ADHD in the first 10 years of life among those exposed are 1.53 times the odds of disease in the unexposed. Epidemiology Matters – Chapter 6 50 Example A: odds and risk ratio Odds ratio = 1.53 Risk ratio = 1.5 Ratios similar when outcome is relatively rare in the population Epidemiology Matters – Chapter 6 51 Example B: odds ratio Research question: Is smoking cigarettes during pregnancy a potential cause of offspring attention-deficit hyperactivity disorder (ADHD)? Sample: 500 10-year-old children in Farrlandia who are seeking care hyperactivity For each child we find with ADHD, we select two children of the same age from the same physician offices who present for routine well visits (do not have ADHD) – a purposive sample Case control study Measures: Mothers respond to questions, including whether they smoked cigarettes while they were pregnant Epidemiology Matters – Chapter 6 52 Example B: odds ratio Epidemiology Matters – Chapter 6 53 Example B: odds ratio Odds of exposure among those with ADHD: Odds of exposure among those without ADHD: Odds ratio in the case control study: Epidemiology Matters – Chapter 6 54 Example B: odds ratio interpretation The odds of exposure (mother smoking in pregnancy) among those with ADHD are 1.53 times higher among cases than among controls. Epidemiology Matters – Chapter 6 55 Example A and B: odds ratios Odds ratio in prospective cohort study = 1.53 Odds ratio in case control study = 1.48 Epidemiology Matters – Chapter 6 56 Odds ratio: why we use it (1) Exposure odds ratio and disease odds ratio are mathematically equal! In the prospective study, we estimated the odds of disease among exposed and odds of disease among unexposed In the case control study, we estimated the odds of exposure among the diseased and the odds of exposure among the nondiseased. When we select our cases and controls correctly, we get an unbiased estimate of the exposure odds even though we estimate the disease odds. This odds ratio is approximately equivalent to the risk ratio when the disease is rare. Epidemiology Matters – Chapter 6 57 Odds ratio: why we use it (2) “When we select our cases and controls correctly”… – In our example, cases and controls were selected from the same underlying population base as the sample from the prospective study. – When cases and controls are selected from the same population base, we can get the same estimate of the association between exposure and disease from the case control study that we would have gotten from a prospective study from the same population base. Epidemiology Matters – Chapter 6 58 Steps: odds ratio 95% confidence interval 1. Take natural log of odds ratio ln (Odds ratio) 2. Estimate standard error (SE) Epidemiology Matters – Chapter 6 59 Steps: odds ratio 95% confidence interval 3. Estimate upper and lower bounds on log scale 95% confidence interval upper bound ln(Odds ratio) + 1.96(SE[ln(Odds ratio)]) 95% confidence interval lower bound ln(Odds ratio) - 1.96(SE[ln(Odds ratio)]) Epidemiology Matters – Chapter 6 60 Steps: odds ratio 95% confidence interval 4. Exponentiate upper and lower bounds 5. Report and interpret estimate and confidence interval Sample: In these data, the exposed individuals had [odds ratio estimate] times the odds of the outcome compared with the exposed, with a 95% confidence interval for the observed odds ratio ranging from [lower bound] to [upper bound]. Epidemiology Matters – Chapter 6 61 Summary: odds ratio Cannot estimate the risk of disease directly when we sample people based on whether they have the disease or not (case control study) Can estimate proportion exposed among diseased and non-diseased Estimate odds ratio for exposure Odds ratio for exposure = odds ratio for disease If disease is rare in population, the odds ratio approximates the risk ratio from a prospective study Epidemiology Matters – Chapter 6 62 1. Associations 2. Ratio measures 3. Difference measures 4. Population attributable risk proportion 5. Summary Epidemiology Matters – Chapter 6 63 Risk difference Difference between two risks = Interpretation: Excess risk due to the exposure Example: If the risk of disease is 10 per 100,000 in the unexposed and 15 per 100,000 in the exposed, then 5 per 100,000 cases is associated with the exposure of interest. Epidemiology Matters – Chapter 6 64 Example: Nutrition and obesity Research question: Are nutrition classes in middle school associated with the development of obesity in adolescence? Sample: Middle school A, 400 students, receives health education (intervention) Middle school B, 300 students, in neighboring district, does not receive health nutrition class Purposive Measures: Schools collect students’ height and weight yearly for 5 years Epidemiology Matters – Chapter 6 65 Example: risk difference Epidemiology Matters – Chapter 6 66 Example: risk difference Incidence proportion (or risk) of obesity among those who had nutrition class = 0.175 or 17.5% Incidence proportion (or risk) of obesity among those who did not have nutrition class = 0.33 or 33% Risk difference Incidence proportion of exposed – incidence proportion of unexposed 0.175 – 0.33= - 0.155 Interpretation: There are approximately 15.5 fewer cases of obesity during adolescence for every 100 adolescents associated with nutrition class in middle school Epidemiology Matters – Chapter 6 67 Steps: risk difference 95% confidence interval 1. Estimate standard error (SE) Epidemiology Matters – Chapter 6 68 Steps: risk difference 95% confidence interval 2. Estimate upper and lower bounds 95% confidence interval upper bound Risk difference + 1.96(SE[Risk difference]) 95% confidence interval lower bound Risk difference - 1.96(SE[Risk difference]) Epidemiology Matters – Chapter 6 69 Steps: risk difference 95% confidence interval 3. Report and interpret estimate and confidence interval Sample Positive: In these data, exposure was associated with an excess of [risk difference estimate] cases compared with the unexposed, with a 95% confidence interval for the observed excess cases ranging from [lower bound] to [upper bound]. Sample Negative: In these data, exposure was associated with an [risk difference estimate] fewer cases compared with the unexposed, with a 95% confidence interval for the observed decrease in cases ranging from [lower bound] to [upper bound]. Epidemiology Matters – Chapter 6 70 Example: risk difference 95% confidence interval 1. Estimate standard error (SE) Epidemiology Matters – Chapter 6 71 Example: risk difference 95% confidence interval 2. Estimate upper and lower bounds 95% confidence interval upper bound Risk difference + 1.96(SE[Risk difference]) - 0.155 + 1.96(0.02) = -0.1158 95% confidence interval lower bound Risk difference - 1.96(SE[Risk difference]) - 0.155 - 1.96(0.02) = -0.1942 Epidemiology Matters – Chapter 6 72 Example: risk difference 95% confidence interval 3. Report and interpret estimate and confidence interval Negative: Middle high nutrition education is associated with 15.5 fewer cases of obesity per 100 adolescents over five years, with a 95% confidence interval for the observed decrease in cases from 11.6 to 19.4 fewer cases. Epidemiology Matters – Chapter 6 73 Rate difference Difference between two rates Interpretation: Similar to risk difference; excess rate due to the exposure Example: If the rate of disease is 8 per 100,000 person years in the exposed and 4 per 100,000 person years in the unexposed, then 4 per 100,000 person-years of exposure is associated with the exposure of interest Epidemiology Matters – Chapter 6 74 Steps: rate difference 95% confidence interval 1. Estimate standard error (SE) PY1 = total person time contributed among exposed PY2 = total person time contributed among the unexposed Epidemiology Matters – Chapter 6 75 Steps: rate difference 95% confidence interval 2. Estimate upper and lower bounds 95% confidence interval upper bound Rate difference + 1.96(SE[Rate difference]) 95% confidence interval lower bound Rate difference - 1.96(SE[Rate difference]) Epidemiology Matters – Chapter 6 76 Steps: rate difference 95% confidence interval 3. Report and interpret estimate and confidence interval Sample Positive: In these data, exposure was associated with an increases of [rate difference estimate] in the rate compared with the unexposed, with a 95% confidence interval for the observed excess rate ranging from [lower bound] to [upper bound]. Sample Negative: In these data, exposure was associated with an decrease of [rate difference estimate] in the rate compared with the unexposed, with a 95% confidence interval for the observed decrease in the rate ranging from [lower bound] to [upper bound]. Epidemiology Matters – Chapter 6 77 Risk/rate differences Risk/rate ratios When is a ratio measure appropriate versus a difference measure? Why would we use one over the other? Epidemiology Matters – Chapter 6 78 Risk/rate differences Risk/rate ratios Difference measures (risk / rate difference) provide a measure of the potential direct public health benefit of intervention. Ratio measures (risk / rate / odds ratio) provide an intuitive summary of the magnitude of differences in two exposures. Epidemiology Matters – Chapter 6 79 1. Associations 2. Ratio measures 3. Difference measures 4. Population attributable risk proportion 5. Summary Epidemiology Matters – Chapter 6 80 Population attributable risk proportion (PARP) Population attributable fraction Measure of the proportion of the total disease burden associated with exposure Epidemiology Matters – Chapter 6 81 Example: PARP Proportion of people who develop heart disease among smokers and nonsmokers Risk of heart disease in smokers = 13.7% Risk of heart disease in nonsmokers = 5% PARP would be calculated as: Epidemiology Matters – Chapter 6 82 Example PARP Interpretation A: 64% of the heart disease in the population of Farrlandia is potentially attributable to smoking. Interpretation B: If we were to convince all of the smokers to quit, we would reduce the incidence of heart disease by 64%. PARP is particularly useful measure in public health practice Epidemiology Matters – Chapter 6 83 1. Associations 2. Ratio measures 3. Difference measures 4. Population attributable risk proportion 5. Summary Epidemiology Matters – Chapter 6 84 Seven steps 1. Define the population of interest 2. Conceptualize and create measures of exposures and health indicators 3. Take a sample of the population 4. Estimate measures of association between exposures and health indicators of interest 5. Rigorously evaluate whether the association observed suggests a causal association 6. Assess the evidence for causes working together 7. Assess the extent to which the result matters, is externally valid, to other populations Epidemiology Matters – Chapter 1 85 epidemiologymatters.org Epidemiology Matters – Chapter 1 86
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