Confounding

A plot of the population of Oldenburg at the end of each year against the number of storks observed in that year, Ornitholigische Monatsberichte 1936;44(2)

Mortality rate in six countries in the Americas, 1986 Question: Are people living in Costa Rica or Venezuela at lower risk of mortality than people in Canada or the US? Yes No  (assuming vital statistics are correct)

Mortality rate in six countries in the Americas, 1986 Next question: Is the observed association causal in nature, i.e., is there something about living in Costa Rica or Venezuela that makes the population have lower risk of death than the population of Canada or the US? Yes No 

Mortality Country ? Age distribution

N=14,054 middle age adults from 4 US communities Comparing risk profile according to known CVD risk factors:  Low Risk individuals (n=623): - Never smokers - Total cholesterol <200 mg/dL - HDL cholesterol >65mg/dL - LDL cholesterol <100 mg/dL - Triglycerides <170 mg/dL - Glycemia <140 mg/dL - BP<140/90 mm Hg, no Rx - No Hx of CVD, htn, diabetes, high cholesterol  Rest (n=13,431): at least one of the above.

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Disease Outcome Exposure ? Confounder Common feature of previous examples

A variable can be a confounder if all the following conditions are met: It is associated with the exposure of interest (causally or not). It is causally related to the outcome. AND... It is not part of the exposure  outcome causal pathway

Ways to assess if confounding is present: 1) Does the variable meet the criteria to be a confounder (relation with exposure and outcome)? 2) If the effect of that variable (on exposure and outcome) is controlled for (e.g., by stratification or adjustment) does the association change?

Strategy #1: Does the variable meet the criteria to be a confounder? Hypothetical case-control study of risk factors for malaria. 150 cases, 150 controls; gender distribution. Question: Is male gender causally related to the risk of malaria? Yes No Further study is needed  OR= [88 x 82] ÷ [68 x 62] = 1.71

Malaria Male gender ? Confounder for a male gender-malaria association? ?

Malaria Male gender ? Confounder for a male gender-malaria association? Outdoor occupation

Malaria Male gender ? Outdoor occupation ? First criterion: Is the putative confounder associated with exposure?

. Question: Is outdoor occupation associated with male gender? Yes No  OR=7.8 First criterion: Is the putative confounder associated with exposure?

Malaria Male gender ? Outdoor occupation ? Second criterion: Is the putative confounder associated with the outcome (case-control status)?

. Question: Is outdoor occupation (or something for which this variable is a marker of --e.g., exposure to mosquitoes) causally related to malaria? Yes No  OR=5.3 Malaria Second criterion: Is the putative confounder associated with case-control status?

Third criterion: Is the putative confounder in the causal pathway exposure  outcome?. Malaria Male gender ? Outdoor occupation ? Yes, it could be Probably not  Note: Judgment and knowledge about the socio-cultural context are critical to answer this question

Question: Provided that: Crude association between male gender and malaria: OR=1.71 and... Outdoor occupation is more frequent among males, and... Outdoor occupation is associated with greater risk of malaria … What would be the expected magnitude of the association between male gender and malaria after controlling for occupation (i.e., assuming the same degree of outdoor occupation in males and females)? The (adjusted) association estimate will be smaller than 1.71  The (adjusted) association estimate will =1.71 The (adjusted) association estimate will greater than 1.71

Strategy #2: Does controlling for the putative confounder change the magnitude of the exposure-outcome association? OR=1.71 OR=1.06 OR=1.00 Outdoor occupation Indoor occupation Malaria

Ways to control for confounding During the design phase of the study: –Randomized trial –Matching –Restriction During the analysis phase of the study: –Stratification –Adjustment

M F RestLR Examples of stratification OR=1.71 OR=1.06 OR=1.00 Outdoor occupation Indoor occupation Malaria

Note that confounding is present when: RR/OR pooled different from RR/OR stratified and RR/OR 1 = RR/OR 2 = …= RR/OR z

Examples of adjustment OR=1.71 OR=1.06 OR=1.00 Outdoor occupation Indoor occupation Adjusted OR * = 1.01 *Using the Mantel-Haenszel method, to be discussed. *Adjusted by direct method using the 1960 population of Latin America as the standard population. Malaria

Further issues for discussion Types of confounding Confounding is not an “all or none” phenomenon Residual confounding Confounder might be a “constellation” of variables or characteristics Considering an intermediary variable as a “confounder” for examining pathways Confounding: a type of bias? Statistical significance and confounding

Types of confounding Positive confounding When the confounding effect results in an overestimation of the effect (i.e., the crude 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 effect (i.e., the crude estimate is closer to 1.0 than it would be if confounding were not present).

Relative risk Type of confounding: PositiveNegative UNCONFOUNDED OBSERVED, CRUDE      ? “Qualitative confounding”

Example of positive confounding OR=1.71 OR=1.06 OR=1.00 Outdoor occupation Indoor occupation Adjusted OR= 1.01 Malaria

Example of negative confounding An occupational study in which workers exposed to a certain carcinogen are younger than those not exposed. If the risk of cancer increases with age, the crude association between exposure and cancer will underestimate the unconfounded (adjusted) association. Age: negative confounder.

M F RestLR Examples of qualitative confounding *Adjusted by direct method using the 1960 population of Latin America as the standard population. Rate ratio US/Mex =

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 Residual confounding Controlling for one of several confounding variables does not guarantee that confounding is 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 may reflect a “constellation” of variables/characteristics –E.g., Occupation (SES, physical activity, exposure to environmental risk factors) –Healthy life style (diet, physical activity)

Low CHD ERT (adjusted)* ? Other factors? *Adjusted for family history, type of menopause, smoking, hypertension, diabetes, OC use, high cholesterol, age, obesity.

(Matthews KA et al. Prior to use of estrogen replacement therapy, are users healthier than nonusers? Am J Epidemiol 1996;143: )

JAMA 1998;280: Estrogen-Progestin Placebo Kaplan-Meier estimates of the cumulative incidence of primary coronary heart disease events.

Circulation 1996;94:922-7.

Treating an intermediary variable as a confounder (i.e., ignoring “the 3 rd rule”) Under certain circumstances, it might be of interest to treat an hypothesized intermediary variable acting as a mechanism for the [risk factor  outcome] association as if it were a confounder (for example, adjusting for it) in order to explore the possible existence of additional mechanisms/pathways. This is done by comparing the adjusted with the unadjusted values.

EXAMPLE: It has been argued that obesity is not a risk factor of mortality. The observed association between obesity and mortality in many studies might just be the product of the confounding effect of hypertension. Mortality Obesity ? Hypertension

HOWEVER, Hypertension is probably not a real confounder but rather a mechanism whereby obesity causes hypertension.* Mortality Obesity Hypertension *Manson JE et al: JAMA 1987;257:353-8.

EVEN IF HYPERTENSION IS A MECHANISM LINKING OBESITY TO MORTALITY, it may be of interest to conduct analyses that control for hypertension, to assess whether alternative mechanisms may causally link obesity and mortality. Mortality Obesity Hypertension alternative mechanism(s)? Block by adjustment

EXAMPLE: Is maternal smoking a risk factor of perinatal death? Is the association confounded by low birth weight? Perinatal mortality Maternal smoking ? Low birth weight

OR RATHER: Is low birth weight the reason why maternal smoking is associated to higher risk of perinatal death? Perinatal mortality Maternal smoking Low birth weight

BUT THERE COULD BE AN ADDITIONAL QUESTION: Does maternal smoking cause perinatal death by mechanisms other than low birth weight? Perinatal mortality Maternal smoking Low birth weight Direct toxic effect? Block by adjustment

Statistical significance should not be used to assess confounding effects Age (years)5556 Odds Ratio [age 56/age 55] = 60/40 ÷ 50/50 = 1.5

% post-menopausal Age (years)5556 Odds Ratio [cases/controls] = 60/40 ÷ 50/50 = 1.5 Statistical significance should not be used to assess confounding effects

The main strategy must be to evaluate whether the difference in the confounder is large enough to explain the association.

Control of Confounding Variables Randomization Matching Adjustment –Direct –Indirect –Mantel-Haenszel Multiple Regression –Linear –Logistic –Poisson –Cox Stratified methods

Control of Confounding Variables Randomization Matching Adjustment –Direct –Indirect –Mantel-Haenszel Multiple Regression –Linear –Logistic –Poisson –Cox Stratified methods

Mantel-Haenszel Technique for Adjustment of the Odds Ratios and Rate Ratios Nathan Mantel and William Haenszel were two very productive statisticians: –Test for homogeneity of stratified OR’s (see Schlesselman, pp , or Kahn & Sempos, pp ): for the assessment of multiplicative interaction –Mantel-Haenszel test for trend

Mantel-Haenszel Technique for Adjustment of Odds Ratios-- Example (Israeli Study, see Kahn & Sempos, pp. 105) OR= 1.88 Is the association causal? Is it due to a third (confounding) variable (e.g., age)? BP MI ? Age A variable is only a confounder if dual association is present

OR= 3.0 OR= 3.4 Does age meet the criteria to be a confounder? Yes

Age Increased odds of systolic hypertension (“exposure”) Increased odds of myocardial infarction (“outcome”)

Blood Pressure MI Risk Is it appropriate to calculate an adjusted OR MH ? NO Odds Ratios not homogeneous These findings fail to meet Mantel-Haenszel adjustment approach’s main assumption: that odds ratios are homogeneous (no multiplicative interaction).

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: =

OR POOLED = 4.5 OR 1 = 2.5 OR 2 = 2.6 OR 3 = 4.0 OR 4 =1.2* (*adding 1.0 to each cell)

Ages 45-64

Stratum-specific odds ratios: 2.5, 2.6, 4.0, 1.2 Average= 3.04 ?

OR POOLED = 4.5 OR 1 = 2.5 OR 2 = 2.6 OR 3 = 4.0 OR 4 =1.2* (*adding 1.0 to each cell)

Ages 45-59

Stratum-specific odds ratios: 2.5, 2.6, 4.0 Average= OR MH 2.83

There is an analogous procedure to obtain an adjusted Rate Ratio from stratified data in a prospective study (see Kahn & Sempos, pp )

Mortality of Individuals with High and Low Vitamin C/Beta-Carotene Intake Index, by Smoking Status, Western Electric Company Study (Pandey et al, Am J Epidemiol 1995;142: ) Vitamin C/Beta Carotene Index No. deaths No. of Person- years Stratified Rate Ratio Non-smokersHigh RR= 0.77 Low Total9403 SmokersHigh RR= 0.83 Low Total12680

Formulas for calculating confidence intervals for the OR MH are available (Schlesselman, p. 184, Szklo & Nieto, Appendix A.8)

If OR Pooled ~ ~ (OR Z=1 ~ ~ OR Z=2 ~ ~ OR Z=3, …) Z is not a confounder: report crude OR (OR Pooled ) Z is a confounder: report OR Pooled and adjusted OR If OR Pooled (OR Z=1 ~ ~ OR Z=2 ~ ~ OR Z=3, …) # IfOR Z=1 OR Z=2 OR Z=3, … # # Z is an effect modifier. Do not adjust: report Z-specific ORs

Correspondence between the “matched” odds ratios and the Mantel-Haenszel method (Adapted from Heinone et al, Lancet 2:675, 1974) OR= 45/23= 1.96 OR??

OR= 45/23= 1.96 Reserpine Use and Breast Cancer

Stratification Methods Advantages –Easy to understand and compute –Allow simultaneous assessment of interaction Disadvantages –Cannot handle a large number of variables (zero cells are problematic in direct adjustment) –Each calculation requires a rearrangement of tables