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Applied Epidemiologic Analysis

This lecture provides an overview of measures of effect and association in epidemiologic analysis, including absolute and relative measures, effect measure modification, and noncollapsibility. Examples and scenarios are discussed to illustrate the concepts.

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Applied Epidemiologic Analysis

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  1. Applied Epidemiologic Analysis Patricia Cohen, Ph.D. Henian Chen, M.D., Ph. D. Teaching Assistants Julie Kranick Sylvia Taylor Chelsea Morroni Judith Weissman

  2. Outline Lecture 2 1) Measures of effect/measures of association 2) Review of Study Design 3) Introduction to Data Handling

  3. Learning Objectives • To understand the relationship between and among absolute and relative measures. • To understand the relationship between measures of effect and measures of association • To understand some of the features of measures of effect including effect measure modification and noncollapsibility

  4. Measures of effect • Effect • endpoint of a causal mechanism • amount of change in a population disease frequency caused by a specific factor • Absolute effects • differences in incidence rates, proportions, prevalences or incidence times • Relative effect • ratios of these measures

  5. Absolute measures Causal rate difference Causal risk difference

  6. Relative measures Causal Rate Ratio Causal Risk Ratio

  7. Relationship between Ratio Measures Risk Ratio because R = A/N and I=A/T Risk Ratio = Rate Ratio * Ratio of Persontime

  8. Odds Ratio = = =

  9. Scenarios when relative measures approximate relative risk Time period sufficiently small that average T for exposed population is only slightly smaller than T for unexposed • means T1 and T0 are approximately equal and rate ratio approximates risk ratio • Sufficiently small proportion of onsets • means R1 and R0 are small, S1 and S0 are close to 1 (odds ratio • approximates risk ratio)

  10. Odds Ratio will overestimate the risk ratio Scenario 1 where factor increases risk R1 > R0

  11. Odds Ratio will underestimate the risk ratio Scenario 2 where factor decreases risk R1 < R0

  12. Rate Ratio with respect to Risk Ratio Scenario 1 where factor increases risk If R1 > R0 then The risk ratio will be closer to null than the rate ratio.

  13. Rate Ratio with respect to Risk Ratio Scenario 2 where factor decreases risk If R1 < R0 then The risk ratio will be closer to null than the rate ratio.

  14. Magnitude of effect ratios • If exposure increases disease: 1.0 < Risk ratio < Rate ratio < Odds ratio • If exposure prevents disease: • 1.0 > Risk ratio > Rate ratio > Odds ratio Because, given equal N, disease occurance shortens cumulative time of exposed subjects.

  15. Example 1: Rare disease Cohort data Cases Noncases TotalExposed 200 99,800 100,000 Unexposed 100 99,900 100,000 Risk ratio = (200/100,000)/(100/100,000) = 2.0 Case-control Cases Noncases TotalExposed 200 99.8 299.8 Unexposed 100 99.9 199.9 Odds ratio = (200*99.9)/(100*99.8) = 2.0 Rate = ln (1.0-risk)/time assume time = 1 year Rate (unexposed) = .001 Rate (exposed) = .002 Rate ratio = 2.0

  16. Example 2: Non-rare disease Cohort data Cases Noncases TotalExposed 40,000 60,000 100,000 Unexposed 20,000 80,000 100,000 Risk ratio = (40,000/100,000)/(20,000/100,000) = 2.0 Case-control Cases Noncases TotalExposed 40,000 60 40,060 Unexposed 20,000 80 20,080 Risk ratio = (40,000*80)/(20,000*60) = 2.67 Rate = ln (1.0-risk)/time assume time = 1 year Rate (unexposed) = .22 Rate (exposed) = .51 Rate ratio = 2.29

  17. Effect measure modification If exposure has any effect on an occurrence measure, at most one of the ratio or difference measures of effect can be uniform across strata

  18. Two Examples: Effect Measure Modification Example 1 Here you see that the risk ratio is constant but the risk difference varies by strata.

  19. Two Examples: Effect Measure Modification Example 2 Here you see that the risk ratio varies by strata but the risk difference remains constant.

  20. Relation of Stratum-specific measures to overall • Risk differences and ratio • entire cohort measure must fall in the midst of stratum specific measures • Causal odds ratio and rate ratio • entire cohort measure can be closer to null than any of the causal odds ratios for the strata • noncollapsibility of the causal odds ratio • odds ratio not a weighted average

  21. Example of Non-collapsability Combined Risk (exp) = .5*.5 + .5*.08 = .29 Risk (unexp) = .5*.2 +.5*02 = .11 Odds ratio = (.29/71)/(.11/89) = 3.3 Risk ratio = .29/.11 = 2.6

  22. Combining Strata for Rate Ratios • Non-collapsibility can also occur for rate ratio • Only a problem if the outcome is common in a particular strata

  23. C’ C E Causation and Causal Attributable Fraction Assume 2 sufficient causes Without exposure, can get disease only through C’. If exposed, can get disease through either sufficient cause (whichever acts first). Rate difference (I1- I0) does not necessarily equal the proportion of onsets attributable to exposure.

  24. Causation and Causal Attributable Fraction Excess fraction: Preventable fraction:

  25. Generalizing Exposure in Definition of Effect A sample of three people smoke one pack of cigarettes daily at the start of a 5 year period. What is the effect of different patterns of mailing anti- smoking literature to them?

  26. Generalizing Exposure in Definition of Effect Causal rate difference 3/8 yr-1 - 2/10 yr-1= .175 Causal rate ratio (3/8)/(2/10) = 1.875 Causal risk difference 1-2/3 = 1/3 = .33 Causal risk ratio 1/(2/3) = 1.5

  27. Example cont. Key points: Even though same overall portion of the sample are exposed to the three types of mailing in the two patterns, • effects on I are not same as effect on R • not all individuals respond alike to exposures or treatments • Therefore • effects are defined for populations, not individuals. • Individual characteristics affecting exposure response are used to stratify analyses

  28. Measures of Association Given separate exposed and unexposed populations: Confounding is defined by observed rate differences not equal to the causal rate difference. • true for ratio measures, average risks, incidence times, or prevalences • odds are risk-based measures, odds ratios are confounded under same circumstances as risk ratio

  29. A Counterfactual Approach to Causal Reasoning • Considers the experience of an exposed cohort if, contrary to fact, was unexposed • and/or the experience of an unexposed cohort if, contrary to fact, was exposed.

  30. Disease under Proportion in Exposure No exposure Description Cohort 1 (exposed) Cohort 0 (unexposed) D D Doomed (other causes sufficient) p1 q1 D 0 Exposure is causal p2 q2 0 D Exposure is preventive p3 q3 0 0 Immune p4 q4 Sum 1.0 1.0

  31. If Cohort 1 represented the population: Note: null value  no effect, unless no preventive effect is possible, rather null means balance between causal and preventive effects

  32. In an actual study: Associational measure = causal counterparts if and only if q1 + q3 = p1 + p3 Confounder explains a discrepancy between the desired (but unobservable) counterfactual risk or rate and the unexposed risk or rate that was its substitute

  33. A Counterfactual Approach to Causal Reasoning, cont. Consider the effect of child abuse on young adult depression: Counterfactual: a) abused children had not been abused b) not abused children had been abused What are barriers to assuming observed association Is causal?

  34. Types of Epi Studies • Experimental • Non-experimental • The ideal design, where only one factor varies, is unrealistic (because of biologic variation). • Settle for amount of variation in key factors that might affect outcome small in comparison to the variation of the key factor under study

  35. Experimental Studies • Classifications • Clinical treatment or prevention trials • patients as subjects • Field trial • non-patient subjects • Community intervention trials • interventions assigned to the whole community • Characteristics • Investigator assigns exposure based only on study protocol, not needs of patient • ethical only when adherence to protocol does not conflict with subject’s best interest • all treatment alternatives should be equally acceptable under present knowledge

  36. Non-experimental studies • Cohort • classified (& possibly selected on) exposure • direct analog of the experiment but investigator does not assign exposure • Case-control • can be more efficient (sample on outcome) • introduces avenues for bias not present in cohort studies • the critical issue is defining a source population

  37. Non-experimental studies (cont) • Control group • main purpose is to determine relative (not absolute) size of exposed and unexposed denominators within the source population • to do so, controls must be sampled independently of exposure status: do not select on exposure or potential confounders

  38. Non-experimental studies (cont) • Use of prospective & retrospective • use these terms for timing of the disease occurrence with respect to exposure measurement • in cohort studies, usually involves follow-up for disease occurance • in case-control studies, prospective exposures are usually measured via pre-existing records

  39. Non-experimental studies (cont) • Cross-sectional • can classify under case-control • main problem is with assessing sequencing and timing • consequently, emphasis is often on prevalence • but, current exposure may be too recent to be etiologically relevant

  40. Non-experimental studies (cont) • Proportional Mortality Rate • best to think of as a type of case-control study • main problem is that cannot distinguish whether exposure causes the index causes of death or prevents the reference causes of death • cannot distinguish between the extent to which exposure causes disease or worsens prognosis

  41. Introduction to Data Handling 1) Collection 2) Coding 3) Entry 4) Repeat entry 5) Checking & Editing (logic checks, outliers, fix where possible) 6) Reduction (creation of global variables) 7) Analysis

  42. Types of variables • Quantitative • e.g., height, weight, body mass index, age • Qualitative • e.g., gender, race, ICD codes, case/control status, smoker/non-smoker status • Ordinal • age in discrete years, low/medium/high consumption

  43. Data coding 1) Make enough categories to avoid non-responses 2) Code all responses (even for don’t know or refusal or not applicable responses) 3) Avoid open-ended questions 4) Record exact values rather than categories 5) Record exact date (of birth, death, diagnosis) rather than ages

  44. Data editing 1) Check for illegal or unusual values for each variable 2) Check codes for unknown or missing values 3) Check distribution of variables - expected proportion of subjects in each category - check ranges of values 4) Check consistency of variable distribution (e.g., whether nonsmokers have recorded values for the number of cigarettes per day of duration of smoking etc.)

  45. Learning Objectives • To understand the relationship between and among absolute and relative measures. • To understand the relationship between measures of effect and measures of association • To understand some of the features of measures of effect including effect measure modification and noncollapsibility

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