CONFOUNDING INVOLVING SEVERAL RISK FACTORS
Issue: how do deal with several risk factors that may confound an E→D relationship
Assumption: no risk factors are effect modifiers
Two Fundamental Principles for Confounding with Two or More Risk Factors
1. Joint control of 2+ variables may give different results from controlling each variable separately. The adjusted estimate that controls for all risk factors is the “standard” for which conclusions of confounding are based.
2. Not all variables may need to be controlled.
Data-based joint confounding – meaningful difference between crude and adjusted effect when controlling for all potential confounders
aRR(age, smoking) = 2.4
cRR = 1.5
Data-based marginal confounding – meaningful difference between crude and adjusted effect controlling for only one confounder
cRR = 1.5 aRR(age) = 1.5
aRR(smoking) = 2.4
Considering principle 2, an adjusted estimate for a subset of risk factors may adequately control for confounding.
Example: cRR = 2; aRR(K, L) = 1.0; aRR(K) = 1.0; aRR(L) = 1.0
Why not always control for all potential confounders? Validity vs. Precision
Identifying a subset of confounders giving a precise estimate (yet still “valid”) is important enough to make such examination worthwhile.
Study Questions (Q11.7)
A clinical trial to determine effectiveness of a treatment.
1. The cRR = 6.28 and the aRR(AGE, SERH, TSZ, INSG) = 8.24. Confounding?
Four subsets shown below.
2. What criteria may we use to reduce the number of candidate subsets? Note the answer there is +/- 10% around adjusted estimate.
Below are the results from the gold standard and the 4 candidate subsets whose aRR is within 10% of the gold standard:
3. The most valid estimate results from controlling which covariates?
4. The most precise estimate results from controlling which covariates?
5. Which covariates do you think are most appropriate to control?
A valid estimate of effect is most important.
Consider the trade-off between controlling for enough risk factors to maintain validity and loss in precision from control of too many variables.
Study Designs by Bias
Comparison of study designs for assessing exposure-disease relationships
Clinical Trial Cohort Case-Control Cross-Sectional
√ √√ √√√ √√√
Loss to Follow-up Berkson’s Survival
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E→D E→D E←D E↔D
Unlikely √√ √√ √√
Note: Sampling Error
Affects all designs; can reduce by increasing sample size