Confounding, Precision, Effect Modification
QUESTION:
I'm still somewhat confused about the difference between confounding, effect modification, and precision variables.
My understanding is that precision variables are associated with the outcome
but not the POI, and that confounders are associated with both outcome and POI
(but not in the causal pathway of interest), and that effect modifiers are
associated with both outcome and POI, *in* the causal pathway of interest.
My query is: how can we tell the difference?
ANSWER:
You are basically right on the confounders and precision variables. The only
thing I would note is that the association between the confounder and the POI
is an association in the sample. The association between the confounder or
precision variable and the response needs to be
- causal in the real world,
- independent of any association with the POI, AND
- (as you note) not in the causal pathway of interest for the association
between the POI and response.
(These three criteria are somewhat overlapping, but I give them all because we
think about it in different ways at different times.)
This is the main point we are discussing so far. The effect modifier is
something different than your description.
I have not fully discussed the way to detect the difference between confounders
and precision variables and effect modifiers in class (that comes a bit later),
but for the nonce:
Effect modifiers define subgroups in which the association between the response
and POI is different.
I note that sometimes we choose to ignore effect modification. This seems a
surprising statement, but it is true.
-- In epidemiology, we often consider incidence rates for disease across
countries. We know that countries have different age distributions, and we know
that disease has different incidence at different ages. We also suspect that
the difference in incidence between countries might be different for each age
group. But we use standardized rates and forge ahead. This is akin to:
-- In political science, we are interested in who will win for president. We
know that different sexes, ages, ethnic groups vote differently. But we average
across those groups in the proportion they represent in the (voting)
population, in order to predict who will win.
But, presuming that we do want to tell the difference between effect
modification, confounding, and precision, how do we do it?
I think about it in three stages, first thinking about effect modification,
then discriminating between precision and confounding.
So if Y is response, X is predictor of interest, and W is the other variable,
then
***** Examine the association between Y and X when W=0, and examine the
association between Y and X when W=1. (If you have more levels of W, we would
consider all the levels.)
1) Do you get markedly different answers? If so, you have effect modification.
(There will always be a slight difference due to random chance, we try to
decide if there is a big difference beyond what is possible by chance.)
2) Do you get the same answer? Then this could be either confounding or
precision or neither, and we advance to the next stage:
***** Does W causally affect Y independent of X (and its potential causal
pathway of interest)? This is usually a thought experiment based on previous
knowledge. We would address this by thinking about whether there was a causal
association between Y and W when X is held constant. Sometimes we examine the
data for associations between Y and W when, say, X=0, but to decide about
causation we only have our prior beliefs.
1) If not, then W is neither a confounder or precision variable. Since we
already have decided it is not an effect modifier in the first stage, get rid
of W. Fast.
2) If so, we advance to the next stage:
***** Is W associated with X in the sample? (I note for future reference that a
hypothesis test is completely irrelevant for this question. Descriptive
statistics are only real tool. More on this later.)
1) If so, then W is a confounder.
2) If not, then W is a precision variable.
I note that in the above, we do have to decide how we define "an association".
One common way is by seeing whether some summary measure (mean, median, odds,
hazard...) is different between groups. (We can use a difference or a ratio.)
Scott
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Scott S. Emerson, M.D., Ph.D. Biost Dept: (O) 206-543-1044
Professor of Biostatistics (F) 206-543-3286
Department of Biostatistics Box 357232 ROC: (O) 206-221-4185
University of Washington (F) 206-543-0131
Seattle, Washington 98195 semerson@u.washington.edu
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