Intermediate methods in observational epidemiology 2008 Confounding - II

Total <65 Mort. (%) No. dths Pop.Mort. (%) No. dths Pop. Age Age as a confounding variable UnexposedExposed

Total <65 Mort. (%) No. dths Pop.Mort. (%) No. dths Pop. Age Age as a confounding variable Age Different distributions between the groups UnexposedExposed

Total <65 Mort. (%) No. dths Pop.Mort. (%) No. dths Pop. Age Age as a confounding variable Age Different distributions between the groups AND Associated with mort. (older ages have >mort.) UnexposedExposed

Total <65 Mort. (%) No. dths NMort. (%) No. dths N Age Age as a confounding variable Relative Risk UNADJUSTED = 21% / 22%= 0.95 UnexposedExposed

Direct Adjustment Create a standard population

Standard Population Options 1)Easiest: Sum the number of persons in each stratum Total <65 Stand Pop ExposedUnexp. Groups Age Total <65 Mort (%) No. dths NMort (%) No. dths N ExposedUnexposed Age

Total [400 x 75]/[ ]= [100 x 425]/[ ]= <65 Stand. Pop. (minimum variance) ExposedUnexp Groups Age Standard Population Options 2. Minimum Variance Method: Useful when the sample sizes are small (variance of adjusted rates is minimized): Wi= [nA i x nB i ] / [nA i + nB i ] Total <65 Mort (%) No. dths NMort (%) No. dths N ExposedUnexposed Age

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. Direct Adjustment

500 Total <65 Mort. (%) Pop.Mort. (%) Pop. Age Age as a confounding variable UnexposedExposed

144 Total <65 Mort. (%) Std pop Mort. (%) Std pop Age Age as a confounding variable UnexposedExposed

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. Direct Adjustment

144 Total 4063 x.40= x.25= x.18= x.10= 881<65 Mort. (%) Expected No. of deaths Std pop Mort. (%) Expected No. of deaths Std pop ExposedUnexposed Age Age as a confounding variable Total <65 Mort (%) No. dths NMort (%) No. dths N ExposedUnexposed Age

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 Direct Adjustment

Total 4063 x.40= x.25= x.18= x.10= 881<65 Mort. (%) Expected No. of deaths Std pop Mort. (%) Expected No. of deaths Std pop ExposedUnexposed Age Age as a confounding variable Age-Adjusted Mortality Rates Unexposed: [24 / 144] x 100= 16.7% Exposed: [40 / 144] x 100= 27.8% Relative Risk= 27.8% / 16.7%= 1.7

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

Example of Calculation of Sunburn Score-Adjusted Mean Number of New Nevi in Each Group Sunscreen GroupControl Group Sunburn score Standard Weights (1)* Mean No. of New Nevi (2) Calculation (2) × (1) Mean No. of New Nevi (3) Calculation (3) × (1) Low × 230= × 230= High × 228= × 228= total = = Sunburn- adjusted score means /458= /458= 69.9 *Sum of the two groups’ sample sizes Difference - Crude= Adjusted= 30.0 (Szklo M. Arch Dermatol 2000;136:1544-6)

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., 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

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

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

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

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

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

Adjustment and Interaction RRs are the same, but AR exp ’s are different Additive interaction

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

Mantel-Haenszel Formula for Calculation of Adjusted Odds Ratios = = Thus, the OR MH is a weighted average of stratum-specific ORs (OR i ), with weights equal to each stratum’s:

CHDNo CHD Post-menopausal OR POOLED = 4.5 Pre-menopausal

Stratum 1Post3141OR 1 = 2.5 Ages 45-49Pre Stratum 2Post14684OR 2 = 2.6 Ages 50-54Pre Stratum 3Post OR 3 = 4.0 Ages 55-59Pre Stratum 4Post OR 4 = 1.2* Ages 60-64Pre CHDNo CHD Post-menopausal OR POOLED = 4.5 Pre-menopausal *1.0 was added to each cell Variable to be adjusted for in the outside stub Main variable of interest in the inside stub

Stratum 1Post3141OR 1 = 2.5 Ages 45-49Pre Stratum 2Post14684OR 2 = 2.6 Ages 50-54Pre Stratum 3Post OR 3 = 4.0 Ages 55-59Pre Stratum 4Post OR 4 = 1.2* Ages 60-64Pre *1.0 was added to each cell

Stratum 1Post3141OR 1 = 2.5 Ages 45-49Pre Stratum 2Post14684OR 2 = 2.6 Ages 50-54Pre Stratum 3Post OR 3 = 4.0 Ages 55-59Pre Stratum 4Post OR 4 = 1.2* Ages 60-64Pre *1.0 was added to each cell

Stratum 1Post3141OR 1 = 2.5 Ages 45-49Pre Stratum 2Post14684OR 2 = 2.6 Ages 50-54Pre Stratum 3Post OR 3 = 4.0 Ages 55-59Pre Stratum 4Post OR 4 = 1.2* Ages 60-64Pre OR MZ = Weighted average= 3.04 Is this weighted average representative of the OR in this stratum? *1.0 was added to each cell

Stratum 1Post3141OR 1 = 2.5 Ages 45-49Pre Stratum 2Post14684OR 2 = 2.6 Ages 50-54Pre Stratum 3Post OR 3 = 4.0 Ages 55-59Pre Report the OR separately for age group Stratum 4Post OR 4 = 1.2* Ages 60-64Pre Calculate the MH- adjusted OR for these 3 (relatively) homogeneous age groups and… *1.0 was added to each cell

Stratum 1Post3141OR 1 = 2.5 Ages 45-49Pre Stratum 2Post14684OR 2 = 2.6 Ages 50-54Pre Stratum 3Post OR 3 = 4.0 Ages 55-59Pre Report the OR separately for age group Stratum 4Post OR 4 = 1.2* Ages 60-64Pre Calculate the MH- adjusted OR for these 3 (relatively) homogeneous age groups and… *1.0 was added to each cell

MenCasesControls Exposed205OR= 4.75 Unexposed Women Exposed1025OR= 0.33 Unexposed Does an OR MH = 1.0 properly characterize the relationship of the exposure to the disease in this study population? NO A MORE DRAMATIC EXAMPLE

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

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

Main Variable of Interest: Menopausal Status AgeMenopausal?CasesContls 45-49Pre Post 50-54Pre Post 55-59Pre Post 60-64Pre Post Main Variable of Interest: Age Menopausal?AgeCasesContls Pre Post

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).

Odds Ratio Type of confounding: Positive Negative 3.0 TRUE, UNCONFOUNDED 5.0 OBSERVED, CRUDE x x x x x ? QUALITATIVE CONFOUNDING 1/3.3= 1/2.5=

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)

Directions of the Associations of the Confounder with the Exposure and the Disease, and Expectation of Change of Estimate with Adjustment (Assume a Direct Relationship Between the Exposure and the Disease, i.e., Odds Ratio > 1.0 (in Case-Based Control Studies), or Relative Risk > 1.0 (in Case-Cohort Studies) Association of Exposure with Confounder is Association of Confounder with Disease is Type of confounding Expectation of Change from Unadjusted to Adjusted OR Direct* Positive#Unadjusted > Adjusted Direct*Inverse**Negative##Unadjusted < Adjusted Inverse**Direct*Positive#Unadjusted > Adjusted Inverse** Negative##Unadjusted < Adjusted *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 CONFOUNDING EFFECT IN CASE-CONTROL STUDIES (Szklo M & Nieto FJ, Epidemiology: Beyond the Basics, Jones & Bartlett, 2 nd Edition, 2007, p. 176)

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

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

Residual Confounding: Relationship Between Natural Menopause and Prevalent CHD (prevalent cases v. normal controls), ARIC Study, Ages Years, ModelOdds Ratio (95% CI) 1Crude4.54 (2.67, 7.85) 2Adjusted for age: Vs. 55+ (Mantel-Haenszel) 3.35 (1.60, 6.01) 3Adjusted for age: 45-49, 50-54, 55-59, (Mantel-Haenszel) 3.04 (1.37, 6.11) 4Adjusted for age: continuous (logistic regression) 2.47 (1.31, 4.63)

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

How to control (“adjust”) with no calculations? - Examine the effect of varying one variable, holding all other variables “constant” (fixed). Relationship Between Serum Cholesterol Levels and Risk of Coronary Heart Disease by Age and Sex, Framingham Study, 12-year Follow-up

(Truett et al, J Chronic Dis 1967;20:511) Examine the effect of varying one variable, holding all other variables “constant” (fixed). Example: effect of sex, holding serum cholesterol and age constant

(Truett et al, J Chronic Dis 1967;20:511) Examine the effect of varying one variable, holding all other variables “constant” (fixed). Example: effect of serum cholesterol, holding sex and age constant

(Truett et al, J Chronic Dis 1967;20:511) Examine the effect of varying one variable, holding all other variables “constant” (fixed). Example: effect of age, holding sex and serum cholesterol constant.