Confounding Involving Several Risk Factors

Abstract

This lesson considers how the assessment of confounding gets somewhat more complicated when controlling for more than one risk factor. In particular, when several risk factors are being controlled, we may find that considering all risk factors simultaneously may not lead to the same conclusion as when considering risk factors separately. We have previously (Lesson 10) argued that the assessment of confounding is not appropriate for variables that are effect modifiers of the exposure-disease relationship under study. Consequently, throughout this lesson, our discussion of confounding will assume that none of the variables being considered for control are effect modifiers (i.e., there is no interaction between exposure and any variable being controlled).

Appendices

Homework

1.1 ACE-Identifying Risk Factors for Control

Suppose you carry out a cohort study to assess the relationship between a dichotomous exposure variable and a dichotomous disease variable. You identify and measure three risk factors f1, f2 and f3 that you want to control for in assessing the E-D relationship. Suppose further that the analysis of your data gives the following estimates of effect:

• aRR( f1, f2, f3 ) = 4.1  cRR = 1.3

• aRR( f1, f2 ) = 2.5  aRR( f1 ) = 2.1

• aRR( f2, f3 ) = 4.0  aRR( f2 ) = 4.0

• aRR( f1, f3 ) = 2.9  aRR( f3 ) = 2.8

Assuming no interaction of any kind and that all of the above estimates are very precise, answer the following questions:

• a. Is there confounding? Explain

• b. How should you decide on which of the above variables need to be controlled? (You are being asked for a strategy, not a conclusion.)

• c. Which of the variables are not confounders. Explain

• d. What conclusions can you make about which variables should be controlled in this study?

• e. If you strictly use a 10 % change rule to determine whether an adjusted estimate differs from the gold standard adjusted estimate, what conclusions do you draw about which variables should be controlled in this study?

• f. If you strictly use a 20 % change rule to determine whether an adjusted estimate differs from the gold standard adjusted estimate, what conclusions do you draw about which variables should be controlled in this study?

1.2 ACE-2. Variable Selection

Suppose you carry out a case-control study to assess the relationship between a dichotomous exposure variable and a dichotomous disease variable. You identify and measure four risk factors f1 (previous history of mental disorder), f2 (personality type), f3 (age), and f4 (gender) that you want to control for in assessing the E-D relationship. Suppose further that the analysis of your data gives the following estimates of effect:

• a0R( f1, f2, f3, f4 ) = 1.68

• aOR( f2, f3, f4 ) = 1.20

• aOR( f1, f3, f4 ) = 1.20

• aOR( f1, f2, f4 )

• aOR( f1, f2, f3 ) = 1.18

• aOR( f3, f4 ) = 1.69

• aOR( f1, f4 ) = 2.78

• aOR( f1, f3 ) = 1.68

• aOR( f2, f4 ) = 1.70

• aOR( f2, f3 ) = 5.88

• aOR ( f1, f2 ) = 5.95

• aOR ( f4 ) = 2.75

• aOR ( f3 ) = 5.85

• aOR ( f2 ) = 1.20

• aOR ( f1 ) = 1.69

Given the above information and assuming no interaction of any kind, use a 10 % change rule to determine which variables should be included to correct for confounding. How might precision play a role in terms of which variables are selected for control?

1.3 ACE-3. Joint and Marginal Confounding

A case-control study was carried out to evaluate whether alcohol consumption was a risk factor for the development of breast cancer in women. The exposure variable was denoted as ALC and categorized into 3 groups (1 = no alcohol intake, 2 = small to moderate alcohol intake, and 3 = high alcohol intake. Three risk factors were considered as control variables, AGE (1 = under 50, 2 = race 50), SMK status(1 = ever, 2 = never), and OBESITY (0 = No, 1 = Yes). The following adjusted odds ratio were obtained comparing moderate drinkers (ALC = 1) to non-drinkers (ALC = 0) and heavy drinkers (ALC = 2) to non-drinkers (ALC = 0):

Variables Controlled aOR( 1 to 0 ) aOR( 2 to 0 )

None 4.5 6.0

AGE 3.4 5.1

SMK 2.0 2.8

OBESITY 2.9 4.1

AGE, SMK 1.8 3.3

AGE, OBESITY 4.6 5.6

SMK, OBESITY 3.2 5.4

AGE, SMK, OBESITY 1.9 3.1

Assuming no interaction of any of the control variables with ALC and using a 10 % change rule to determine a meaningful difference in adjusted odds ratios, answer the following questions:

• a. Is there confounding? Justify your answer.

• b. What subsets of variables give the same adjusted odds ratio as the gold standard adjusted odds ratio? Justify your answer.

• c. How would you consider precision to determine which subset of variables to control?

• d. Suppose no meaningful gain in precision is made when controlling for a proper subset of all three control variables. Which variables would you control? Justify your answer.

1.4 ACE-4. Marginal Confounding

The accompanying Table provides the results of a stratified analysis of data collected in a case-control study. The outcome variable is dichotomous and is labeled A. The predictor variables are labeled 1 through 10 with variable 1 the exposure variable of interest. Variables 2 through 10 are control variables.

Results of Stratified Analysis in Examination of the Association Between Variable 1 and the Outcome (Variable A)

Risk Variable Controlled	Sub-Strata estimated OR		Adjusted ORM-H	95 % Confidence Interval	Breslow-Day Test of Homogeneity (p-value)
	Stratum 1	Stratum 2
Variable 2	1.550	2.360	1.998	(1.070, 3.730)	0.522
Variable 3	5.758	1.840	3.083	(1.517, 6.268)	0.136
Variable 4	3.300	1.875	2.040	(1.088, 3.822)	0.534
Variable 5	1.250	3.829	2.711	(1.357, 5.415)	0.151
Variable 6	0.563	2.972	1.813	(.984, 3.341)	0.022
Variable 7	2.000	1.648	1.711	(0.889, 3.293)	0.819
Variable 8	1.125	2.134	2.032	(1.082, 3.819)	0.603
Variable 9	1.333	2.146	1.964	(1.044, 3.693)	0.570
Variable 10	1.9028	1.950	1.931	(1.026, 3.632)	0.970

1. cOR for Variable 1 vs. Variable A (outcome) = 2.022 (1.084 - 3.772)

• a. Assuming no interaction of any kind, how would you assess whether or not there is confounding? Has enough information been provided in the above table to allow you to answer this question?

• b. Again, assuming no interaction, is there marginal confounding due to any of the control variables? Explain.

• c. Again, assuming no interaction, how would you determine which variables to control? What is the primary reason why you can’t answer this question based on the data provided above (assuming no interaction)?

• d. Assuming that there is interaction of variables 9 and 10 with the exposure (variable 1), how would you modify your answer to part c to determine which variables to control?

Answers to Study Questions and Quizzes

2.1 Q11.1

• 1. The adjusted estimate that simultaneously controls for all 4 risk factors under consideration.

• 2. Confounding might not be controlled if there is not a subset of potential confounders that yields (essentially) the same adjusted estimate as obtained when all confounders are controlled.

• 3. Yes, provided the subset yields essentially the same adjusted estimate as the gold standard.

• 4. Adjusting for a smaller number of variables may increase precision. Also, such a subset provides a more parsimonious description of the exposure-disease relationship.

2.2 Q11.2

• 1. Yes, the cRR of 1.5 differs from the aRR(age, smoking) of 2.4 that controls for both potential confounders.

• 2. No, the cRR of 1.5 is essentially equal to the aRR(age, smoking) of 1.4 that controls for both potential confounders.

• 3. No, the cRR of 1.5 differs from the aRR(age, smoking) of 2.4, which controls for all potential confounders. This is evidence of joint confounding.

• 4. No, since the cRR of 1.5 is approximately equal to the aRR(age) of 1.4, there is no evidence of marginal confounding due to age.

• 5. Not necessarily. Our conclusions regarding confounding should be based on the joint control of all risk factors.

• 6. Yes. Controlling for smoking alone gives us the same result as controlling for both risk factors. We might still wish to evaluate the precision of the estimates before making a final conclusion.

• 7. There may be so many risk factors in our list relative to the amount of data available that the adjusted estimate cannot be estimated with any precision at all.

• 8. Then we may be forced to make decisions by using a subset of this large initial set of risk factors.

• 9. The use of marginal confounding may be the only alternative.

2.3 Q11.3

• 1. Joint confounding should be used, whenever possible, as the baseline from which all other confounding issues should be examined.

• 2. No, the two stratum-specific RRs that compare F with not F are equal and the two stratum-specific RRs that compare G with not G are equal.

• 3. Yes, the second fundamental principal of confounding states that “not all variables in a given list of risk factors my need to be controlled”; it is possible that different subsets of such variables can alternatively correct for confounding.

• 4. No, controlling for either of these risk factors separately yields the same results as the crude data. It is only in the joint control of these factors that we observe confounding.

2.4 Q11.4

• 1. True – There is interaction because the risk ratio estimated in one stratum (F₀G₁) is 0.3, which is quite different from the stratum-specific risk ratios of 3.0 in the other strata.

• 2. True – The presence of strong interaction may preclude the assessment of confounding. Also, the value of an adjusted estimate may vary depending on the weights chosen for the different strata.

• 3. False – The RR for F₁ and F₀ at level G₀ are both 3.0. These differ from the overall RR at level G₀ of 1.0. Therefore, at level G₀, there is confounding due to factor F.

• 4. True

• 5. False – There is interaction and possibly confounding. At level F₀, the RR for G₁ and G₀ are very different, and both are very different from the overall risk ratio at level F₀.

• 6. True

• 7. False – Both confounding and interaction are present and each should be addressed.

2.5 Q11.5

• 1. You may wish to control for the variable(s) that yield(s) the most precise estimate.

• 2. Yes, you may wish to control for both if you do not gain anything regarding precision by dropping one. Although these results may be the same, if you drop a variable from analysis, it is not clear to a reviewer that you controlled for both.

• 3. No; the results when controlling for L alone differ from the results controlling for both K and L, the standard on which all conclusions about confounding must be based.

• 4. Controlling for K yields the same results as controlling for both factors K and L simultaneously.

• 5. Yes, if you do not gain anything regarding precision from dropping L.

2.6 Q11.6

• 1. Controlling for fewer variables will likely increase the precision of the results.

• 2. The two that provide the most precise adjusted estimate.

• 3. Controlling for any of these three factors alone yields different results than controlling for all three, which is the standard on which our conclusions should be based.

• 4. Yes

• 5. Yes

• 6. No

• 7. Yes

2.7 Q11.7

• 1. Yes, the cRR differs from the aRR controlling for all potential confounders, which is the gold standard.

• 2. We may choose to only consider those results within 10 % of the gold standard. In this case, that would be 8.24 ± 0.82 which is a range of values between 7.42 and 9.06.

• 3. Controlling for all the covariates provides the most valid estimate. It is the gold standard.

• 4. Controlling for both INSG and AGE provides the narrowest confidence interval and hence is the most precise.

• 5. Debatable: Controlling for SERH alone yields an almost identical aRR as the gold standard, increases precision, and is the stingiest subset. Controlling for INSG and AGE provides a slightly larger increase in precision (than controlling for SERH only) and its aRR is within 10 % of the standard. Consider the trade-off between parsimony and political/scientific implications of not controlling for all risk factors, and more precision from controlling for fewer risk factors.

2.8 Q11.8

• 1. True

• 2. True

• 3. False – Variable G does not need to be controlled since aOR(F,G) = aOR(F). In other words, controlling for F alone yields the same results as the gold standard, controlling for both F and G.

• 4. False – Variable H is not a risk factor in this study, and therefore should not be considered a confounding.

• 5. True

• 6. Yes – The cRR of 1.02 differs from the standard RR of 4.10 that controls for all potential confounders.

• 7. #3, #5, #7

• 8. #1 – The most valid estimate controls for all risk factors measured.

• 9. Yes – Candidate subgroups 1 and 7 are equally precise.

• 10. #1 – The gold standard is the most valid estimate; has the same precision as obtained for candidate 7. No precision is gained by dropping any risk factors so it can be argued the gold standard is the ‘political’ choice for it controls for all considered risk factors. Controlling only for SMK is the best choice for it gives the smallest, most precise subset of variables.

Author Query

AQ1: Please provide citations for Kleinbaum et al. 1982 in the text if applicable.