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Intermediate methods in observational epidemiology 2008

Intermediate methods in observational epidemiology 2008. Confounding - II. Age. Pop. . No. dths. Mort. (%). Pop. . No. dths. Mort. (%). <65. 100. 10. 10. 425. 77. 18. 65+. 400. 100. 25. 75. 30. 40. Total. 500. 110. 22. 500. 107. 21. Age as a confounding variable.

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Intermediate methods in observational epidemiology 2008

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  1. Intermediate methods in observational epidemiology 2008 Confounding - II

  2. Age Pop. No. dths Mort. (%) Pop. No. dths Mort. (%) <65 100 10 10 425 77 18 65+ 400 100 25 75 30 40 Total 500 110 22 500 107 21 Age as a confounding variable Unexposed Exposed

  3. Age Pop. No. dths Mort. (%) Pop. No. dths Mort. (%) <65 100 10 10 425 77 18 65+ 400 100 25 75 30 40 Total 500 110 22 500 107 21 Different distributions between the groups Age Age as a confounding variable Unexposed Exposed

  4. Age Pop. No. dths Mort. (%) Pop. No. dths Mort. (%) <65 100 10 10 425 77 18 65+ 400 100 25 75 30 40 Total 500 110 22 500 107 21 Different distributions between the groups Age Associated with mort. (older ages have >mort.) Age as a confounding variable Unexposed Exposed AND

  5. Age N No. dths Mort. (%) N No. dths Mort. (%) <65 100 10 10 425 77 18 65+ 400 100 25 75 30 40 Total 500 110 22 500 107 21 Age as a confounding variable Unexposed Exposed Relative RiskUNADJUSTED= 21% / 22%= 0.95

  6. Direct Adjustment • Create a standard population

  7. Age Unexposed Exposed N No. dths Mort (%) N No. dths Mort (%) <65 100 10 10 425 77 18 65+ 400 100 25 75 30 40 Total 500 110 22 500 107 21 Age Groups StandPop Unexp. Exposed <65 100 425 525 65+ 400 75 475 Total 500 500 1000 Standard Population Options • Easiest: Sum the • number of persons • in each stratum

  8. Standard Population Options Age Unexposed Exposed N No. dths Mort (%) N No. dths Mort (%) <65 100 10 10 425 77 18 65+ 400 100 25 75 30 40 Age Groups Stand. Pop. (minimum variance) Total 500 110 22 500 107 21 Unexp Exposed <65 100 425 [100 x 425]/[100 + 425]= 81 65+ 400 75 [400 x 75]/[400 + 75]= 63 Total 500 500 144 2. Minimum Variance Method: Useful when the sample sizes are small (variance of adjusted rates is minimized): Wi= [nAi x nBi] / [nAi + nBi]

  9. Direct Adjustment • Create a standard population • Replace each population with the standard population. • Calculate the expected number of events in each age group, using the true age-specific rates and the standard population for each age group.

  10. Age as a confounding variable Age Unexposed Exposed Pop. Mort. (%) Pop. Mort. (%) <65 100 10 425 18 65+ 400 25 75 40 Total 500 500

  11. Age as a confounding variable Age Unexposed Exposed Std pop Mort. (%) Std pop Mort. (%) <65 81 10 81 18 65+ 63 25 63 40 Total 144 144

  12. Direct Adjustment • Create a standard population • Replace each population with the standard population. • Calculate the expected number of events in each age category, using the true age-specific rates and the standard population for each age group.

  13. Age Unexposed Exposed N No. dths Mort (%) N No. dths Mort (%) Age Unexposed Exposed <65 100 10 10 425 77 18 Std pop Expected No. of deaths Mort. (%) Std pop Expected No. of deaths Mort. (%) 65+ 400 100 25 75 30 40 Total 500 110 22 500 107 21 <65 81 81 x .10= 8 10 81 81 x .18= 15 18 65+ 63 63 x .25= 16 25 63 63 x .40= 25 40 Total 144 144 Age as a confounding variable

  14. Direct Adjustment • Create a standard population • Replace each group with the standard population • Calculate the expected number of events in each age group, using the true age-specific rates and the standard population for each age group • Sum up the total number of events in each age category for each group, and divide by the total standard population to calculate the age-adjusted rates

  15. Age Unexposed Exposed Std pop Expected No. of deaths Mort. (%) Std pop Expected No. of deaths Mort. (%) <65 81 81 x .10= 8 10 81 81 x .18= 15 18 65+ 63 63 x .25= 16 25 63 63 x .40= 25 40 Total 144 24 144 40 Age-Adjusted Mortality Rates Unexposed: [24 / 144] x 100= 16.7% Exposed: [40 / 144] x 100= 27.8% Age as a confounding variable Relative Risk= 27.8% / 16.7%= 1.7

  16. No additive interaction Example of direct adjustment when the outcome is continuous

  17. Example of Calculation of Sunburn Score-Adjusted Mean Number of New Nevi in Each Group (Szklo M. Arch Dermatol 2000;136:1544-6) *Sum of the two groups’ sample sizes Difference - Crude= 8.5 - Adjusted= 30.0

  18. Assumptions when adjusting • Rates are uniform within each stratum (for example, age category--- i.e, age-specific rates are the same for all ages included in each age category, e.g., 25-29 years). • If assumption not true:residual confounding • There is a uniform difference (absolute or relative) in the age-specific rates between the groups under comparison. • If assumption not true:interaction

  19. W < B Breast Cancer Incidence Rates, USA, SEER, 1973-77 (*Using Black Women as the Standard Population)

  20. W > B Breast Cancer Incidence Rates, USA, SEER, 1973-77 (*Using Black Women as the Standard Population)

  21. Interaction between age and ethnic background “cross-over” WW Breast Cancer Incidence Rates BW 40 Age (years)

  22. ARs are the same, but • RR’s are different Multiplicative interaction Adjustment and Interaction

  23. When ABSOLUTE differences (ATTRIBUTABLE RISKS IN EXPOSED) are homogeneous, adjusted ARexp is the same regardless of standard population

  24. When ABSOLUTE differences (ATTRIBUTABLE RISKS IN EXPOSED) are homogeneous, adjusted ARexp is the same regardless of standard population

  25. When ABSOLUTE differences (ATTRIBUTABLE RISKS IN EXPOSED) are homogeneous, adjusted ARexp is the same regardless of standard population

  26. RRs are the same, but • ARexp’s are different Additive interaction Adjustment and Interaction

  27. When RELATIVE RISKS are homogeneous, adjusted RR is the same, regardless of standard population

  28. When RELATIVE RISKS are homogeneous, adjusted RR is the same, regardless of standard population

  29. When RELATIVE RISKS are homogeneous, adjusted RR is the same, regardless of standard population

  30. = = Thus, the ORMHis a weighted average of stratum-specific ORs (ORi), with weights equal to each stratum’s: Mantel-Haenszel Formula for Calculation of Adjusted Odds Ratios

  31. Variable to be adjusted for in the outside stub Main variable of interest in the inside stub *1.0 was added to each cell

  32. *1.0 was added to each cell

  33. *1.0 was added to each cell

  34. Is this weighted average representative of the OR in this stratum? ORMZ = Weighted average= 3.04 *1.0 was added to each cell

  35. Calculate the MH-adjusted OR for these 3 (relatively) homogeneous age groups and… *1.0 was added to each cell

  36. Calculate the MH-adjusted OR for these 3 (relatively) homogeneous age groups and… *1.0 was added to each cell

  37. A MORE DRAMATIC EXAMPLE Does an ORMH= 1.0 properly characterize the relationship of the exposure to the disease in this study population? NO

  38. Stratification Methods • Advantages • Easy to understand and compute • Allow simultaneous assessment of interaction • Disadvantages • Cannot handle a large number of variables • Each calculation requires a rearrangement of tables

  39. Stratification Methods • Advantages • Easy to understand and compute • Allow simultaneous assessment of interaction • Disadvantages • Cannot handle a large number of variables • Each calculation requires a rearrangement of tables

  40. Types of confounding • Positive confounding When the confounding effect results in an overestimation of the magnitude of the association (i.e., the crude OR estimate is further away from 1.0 than it would be if confounding were not present). • Negative confounding When the confounding effect results in an underestimation of the magnitude of the association (i.e., the crude OR estimate is closer to 1.0 than it would be if confounding were not present).

  41. 3.0 TRUE, UNCONFOUNDED 3.0 5.0 OBSERVED, CRUDE 2.0 0.3 0.4 0.7 0.4 0.7 3.0 x ? Type of confounding: PositiveNegative x x 1/3.3= x 1/2.5= x QUALITATIVE CONFOUNDING 1 0.1 10 Odds Ratio

  42. Confounding is not an “all or none” phenomenon A confounding variable may explain the whole or just part of the observed association between a given exposure and a given outcome. • Crude OR=3.0 … Adjusted OR=1.0 • Crude OR=3.0 … Adjusted OR=2.0 The confounding variable may reflect a “constellation” of variables/characteristics • E.g., Occupation (SES, physical activity, exposure to environmental risk factors) • Healthy life style (diet, physical activity)

  43. CONFOUNDING EFFECT IN CASE-CONTROL STUDIES *Direct association: presence of the confounder is related to an increased odds of the exposure or the disease **Inverse association: presence of the confounder is related to a decreased odds of the exposure or the disease #Positive confounding: when the confounding effect results in an unadjusted odds ratio further away from the null hypothesis than the adjusted estimate ##Negative confounding” when the confounding effect results in an unadjusted odds ratio closer to the null hypothesis than the adjusted estimate (Szklo M & Nieto FJ, Epidemiology: Beyond the Basics, Jones & Bartlett, 2nd Edition, 2007, p. 176)

  44. Residual confounding • Controlling for one of several confounding variables does not guarantee that confounding be completely removed. • Residual confounding may be present when: • The variable that is controlled for is an imperfect surrogate of the true confounder, • Other confounders are ignored, • The units of the variable used for adjustment/stratification are too broad • - The confounding variable is misclassified

  45. Residual confounding • Controlling for one of several confounding variables does not guarantee that confounding be completely removed. • Residual confounding may be present when: • The variable that is controlled for is an imperfect surrogate of the true confounder, • Other confounders are ignored, • The units of the variable used for adjustment/stratification are too broad • - The confounding variable is misclassified

  46. Residual Confounding: Relationship Between Natural Menopause and Prevalent CHD (prevalent cases v. normal controls), ARIC Study, Ages 45-64 Years, 1987-89

  47. CONTROLLING FOR CONFOUNDING WITHOUT ADJUSTMENT (Truett et al, J Chronic Dis 1967;20:511)

  48. Relationship Between Serum Cholesterol Levels and Risk of Coronary Heart Disease by Age and Sex, Framingham Study, 12-year Follow-up How to control (“adjust”) with no calculations? - Examine the effect of varying one variable, holding all other variables “constant” (fixed). (Truett et al, J Chronic Dis 1967;20:511)

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