Confounding

Question 1

What is Confounding?

Answer 1

–Confounding is bias in the estimation of the effect of exposure on disease occurrence, due to a lack of comparability between exposed and unexposed population.

–Occurs when the substitute population is NOT equivalent to the counterfactual condition.

(AKA, the substitute population does not show the outcome in the exposed population WITHOUT the exposure.)

Question 2

How do we Identify and Control for Empirical Manifestations of Confounding?

Answer 2

Practically, there is no empirical method for directly examining the correctness of the comparability assumption

We search for differences in the distributions of risk factors among the exposure groups = confounding variables

Question 3

Interaction

Example : smoking, lung cancer, and asbestos

Answer 3

Occurs when the association between the exposure and the disease varies by levels of a third factor

ie when the magnitude of effect is “modified” by varying levels of a 3rd factor

Ex: the association btwn smoking + lung cancer varies by exposure to asbestos.
—(risk is much higher and smoking + asbestos exposures are present together)

Question 4

Example of Confounding

smoking, lung cancer, and age

Answer 4

If smokers are older than non-smokers, how would we know whether the observed association between smoking + lung cancer is due to smoking or to age?

(if we have adequately measured confounders in all subjects, we can correct or control for their distorting effect in the analysis)

Question 5

Comparability-based confounding

Answer 5

The observed value of the outcome measure in the exposed group is compared with the expected value that would have been observed in the exposure group if it had not been exposed.

The unexposed group’s actual outcome is used as a proxy for the exposed group’s unobserved value. When the two groups experiences differ, the groups are noncomparable
=confounding occurs

Question 6

Collapsibility-based confounding

Answer 6

Confounding is a failure of the estimate for an adjusted effect parameter to equal the estimate for the crude parameter that is obtained when a covariate is ignored (collapsed).

Confounding is equated with non-collapsibility (or change in the estimated parameter)

Question 7

Properties of a Confounder

Answer 7

1. A confounder must be the cause of the disease
2. A confounder must be associated with the exposure in the base population
3. A confounder must not be affected by the exposure or the disease

Question 8

Property 1:
A Confounder must be the cause of the disease

Meaning?

Answer 8

Covariate must be a risk factor for the disease in the unexposed base population.
OR, it can be a marker for another, often unmeasured risk factor.

Meaning: the association can be observed in the unexposed group in both cohort and case-control studies.

C is not a confounder if:

• -its association with D is due to chance/bias
• -association is due to the effect of D on C
• -the effect of C on D in the base pop. is not independent of the exposure

Question 9

Property 2:

A confounder must be associated with the exposure in the base population

Answer 9

Covariate must be associated with exposure status in the total base population.

• -Cohort study: association can be observed in the total sample.
• -Case-control study: association can be observed in controls, assuming that it reflects the association in the base population.
• C-E association should be known prior to study, or else we may have to assume that the observed C-E association reflects this association in the base population

Question 10

Property 1 and 2 depend on:

Answer 10

–Prior knowledge of covariate associations or effects in the base population, which may conflict with associations observed in the data

Question 11

Property 3:

A confounder must not be affected by the exposure or the disease

Answer 11

C is not a confounder if its association with E in the base population is due entirely to the effect of E on C –even if C is a proxy/risk factor for D

C is not a confounder if:

• C is an intermediate variable in the causal pathway between E + D
• both C + D are affected by the same unmeasured risk factors and C is affected by E
• both C and D are affected by another unmeasured risk factor

*often requires prior knowledge

Question 12

Positive v Negative Confounding

Answer 12

When X is a Risk Factor:

• -If Ba* Bb are > 0, bias is away from the null (positive)
• -If Ba* Bb < 0, bias is toward the null (negative)

When X is a Protective Factor:

• -If Ba* Bb > 0, bias is toward the null (negative)
• -If Ba* Bb <0, bias is away from the null (positive)

Positive confounding: crude OR/RR > Adjusted OR/RR
Negative confounding: crude OR/RR < Adjusted OR/RR

Question 13

Stratification Methods:

Mantel-Haenszel method

Answer 13

1. Stratify data by the level (i) of a confounder
2. Calculate a weighted average of the stratum specific estimates (adjusting)
3. Compare crude vs. adj estimates

Question 14

Advantages and Disadvantages of Stratification Methods

Answer 14

Advantage:
-easy to understand and compute

Disadvantage:

• cannot handle a large number of variables (problematic if there are sparse data in some strata or too many variables to adjust for)
• each calculation requires a rearrangement of tables
• limited to categorical confounders

Question 15

How to Identify a Confounder

Answer 15

1. Prior knowledge
2. Change-In-Estimate strategy
   Collapsibility-based confounding:
   –when the estimate for adjusted effect measure does not equal the estimate for crude effect measure (which is obtained when covariate is ignored/collapsed)

Question 16

Identifying a Confounder: Prior Knowledge

Answer 16

Prior knowledge of a causal relationship from previous empirical studies, biologic plausibility, or theories/models

existing DAG’s

Question 17

Identifying a Confounder: Change in Estimate Strategy

Answer 17

A crude effect estimate is compared to the adjusted effect estimate.

1. Stratify effect estimates by variable
2. If the difference after adjustment is >= 10%, then the variable in question is a confounder
   * provided stratum specific measures are homogenous

Magnitude of confounding = (crude - adjusted / adjusted)

Question 18

Methods of Controlling for Confounding

Answer 18

1. Design and conduct of a study (randomization, matching)
2. Analytic methods of adjustment
   (DAG’s)

Question 19

Controlling for Confounding:

Design and Conduct of a Study

Answer 19

1. Randomization (experiments):
   - -controls for all confounders, including those that are unmeasured or unrecognized.
   - -since there is no guarantee that randomization has eliminated all bias, especially with small sample bias, other options are used to control for confounding.
2. Restricting the eligibility of subjects according to values of potential confounders (in any type of study).
   - -commonly used in observational studies to control for known confounders.

Question 20

Matching

Answer 20

Method used to control for confounders in observational studies
- Restrict eligibility of unexposed subjects by making them similar/comparable to exposed subjects with respect to matching variables (confounders)

Question 21

Matching in Cohort Studies

Answer 21

• -Unexposed subjects are matched to exposed subjects
• -used to prevent confounding due to the matching factors
• -if there is no source of bias other than confounding by the matching factors, statistical adjustment (modeling) for these factors may be unnecessary to remove bias

Question 22

Matching in Case-Control Studies

Answer 22

Matching is more common in case-control studies, because there is more likely to be a relative shortage of cases than there is to be a shortage of controls

Controls are matched to the cases

• -used to increase statistical efficiency when a subsequent procedure (stratification) is used to adjust for confounding but introduces bias
• -statistical adjustment/modeling for the matching factors may be necessary to remove bias even if they were not originally confounders

Question 23

Types of Matching:

Answer 23

Individual matching

Frequency matching

Question 24

Individual Matching

Answer 24

• –One or more unexposed subjects are selected separately for each exposed subject
• —such that each set of unexposed subjects is made similar to the corresponding exposed group on one or more matching variables

Question 25

Methods for selecting Comparison (Unexposed) Subjects

Answer 25

1. Category matching: each set of comparison subjects is selected (preferably randomly) from the same matching category (stratum) to which the exposed subjects belong (ex white males aged 30-34)
2. Caliper matching: each set of comparison subjects is selected to have values on the matching variable that are close to the corresponding value of the index subject
   –fixed caliper: the tolerance for eligibility is the same for all matched set
   –variable caliper: tolerance for eligibility varies among matched sets
   (practical -can avoid not getting a match for certain exposed subjects, or can get the best possible match)

Question 26

Frequency Matching

Answer 26

The total comparison group is selected in such a way as to make the joint distribution of one or matching variables in the unexposed and exposed groups similar

Unexposed subjects are not selected until after all exposed subjects are identified

Ex: freq. matching on age and sex
If 20% of cases are females age 50-54, then controls are selected so that 20% are also females aged 50-54. Must wait for cases to accumulate before controls are selected

Question 27

Why Match?

Answer 27

In a case-control study, matching on a variable generally introduces selection bias, which must be controlled in data analysis–even if matching factor is not a risk factor for the disease
–so it’s not the matching but the analysis that controls for confounding

In a cohort study, matching does not usually introduce bias, but it reduces confounding by the matching variables.
Adjustment for matching factors is unnecessary if there are not other biases

Question 28

Matching + Small Sample Size

Answer 28

We use matching to control for confounding more effective when sample size is small

–without matching, controlling for confounding in analysis will result in many strata with sparse data
–balancing the distribution across strata of a matching variable, the effect estimates will be more stable
(smaller standard errors, narrower CI)

Question 29

Reasons for Matching in Case-Control Studies

Answer 29

The major advantage of matching in case control studies is to make the adjusted estimate of effect for precise for a given sample size

This gain in precision occurs when the matching variable is associated with both exposure and disease in the base population, so we must control for M as a confounder

The major statistical reason for matching is therefore not to control for confounders (done in analysis) but to control for confounding more efficiently than if we had not matched

You need BALANCED STRATA

Question 30

Matching and Selection Bias in Case Control Studies

Answer 30

In case control studies, selection bias introduced by the matching process can occur whether or not there is confounding by the matched factors in the base population

If there is confounding in the base population, the process of matching will superimpose a selection bias over the initial confounding

Bias generally toward the null, because matching selects controls who are more like cases with respect to exposure than randomly selected controls

Question 31

Why matching in a case control study introduces bias

Answer 31

If controls are selected to match the cases on a factor that is correlated with the exposure, then the crude exposure frequency in controls will be distorted in direction of similarity to cases

Matched controls are identical to cases with respect to the matched variables. If the matching variable were perfectly correlated with the exposure, the exposure distribution of controls would be identical to that of the cases, therefore crude OR would = 1

So matching usually doesn’t control confounding, but adds a selection bias on top of the existing confounding

Question 32

How to Maximize Efficiency of Matching

Answer 32

In Cohort Studies - the potential gain in size efficacy from matching is usually greater when the association between the matching variables and exposure status is stronger (because unexposed are matched to exposed)

In Case Control Studies - the potential gain in size efficiency from matching is usually greater when the association btwn matching variable + disease in stronger (bc controls are matched to cases)

Question 33

Analysis of Matched Data

1. General stratified analysis

Answer 33

Must take matching into consideration through some form of stratification

1. General stratified analysis (Mantel Haenszel): most efficient strategy for estimating the effect
   - ignore matched sets and re-stratify on all matching variables in the analysis

MH estimates are robust and not affected by small numbers in specific strata
-hard/impossible to control for factors other than matching factors if some strata involve small numbers

Question 34

Analysis of Matched Data

2. Matched analysis

Answer 34

With caliper matching or a mixture of caliper and category matching, we usually conduct a special type of (matched) stratified analysis

• -treat each matched set as a separate stratum.
• -then estimate and test exposure effect using MH method or model-fitting techniques
• -Preserves the matched sets