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# Inappropriate Statistical Testing for Confounding

## Examining a Known Confounder

Testing for statistically significant differences (adjustment) between crude and adjusted measures is inappropriate when:

Factor is a known confounder.

• e.g., examining an association for which a factor is a known confounder
• age in the association between hypertension (HTN) and coronary artery disease (CAD)
Why don’t we just apply a statistical test to see if the difference between the crude and adjusted measure of association is significant? This is a bad idea. Even if you wanted to perform a statistical test, they are actually not available in software packages.

## Small Sample Size

Testing for statistically significant differences (adjustment) between crude and adjusted measures is inappropriate when:

The study has a small sample size, even large differences between crude and adjusted measures may not be statistically different.

• Yet, we know confounding is present.
• Therefore, the difference between crude and adjusted measures cannot be ignored as merely chance.
• Bias must be prevented: the difference must be reported as confounding.
Why is statistical testing for confounding inappropriate?
• Say you are working with a variable that you know is a confounder in every prior instance it was examined, like age in the evaluation of the relationship between hypertension and coronary artery disease.
What if you happened to have a small sample size in your study?
• Then even large differences between the crude and adjusted measures of association might not be statistically significant.
• What are you going to do?
• Throw out age and just go with crude estimate of the relationship between hypertension and CAD?
• Of course, you won’t do this because you know that confounding is present!
You cannot ignore differences between crude and adjusted measures just because they are not statistically significant.
• In other words, when protecting against bias, you have to do whatever you can regardless of statistical significance.
• We have to live with what we see as differences between crude and adjusted regardless of the statistics.

## Issue of Confounding Is Bias

The issue of confounding is one of bias, not of sampling error.

• We must live with whatever effects we see after adjustment for a factor for which there is a strong a priori belief about confounding.
• We’re not concerned that sampling error is causing confounding and therefore we don’t have to worry about testing for role of chance
• The exception to this are variables for which we are not sure a priori are confounders. For such variables, we need to weigh bias versus variance tradeoffs.
Caveat: there may be a penalty in statistical precision when controlling for potential confounders. See the study of spermicide use and Down Syndrome.