Re: st: Appropriate modelling - testing which set of exposures are more important

[David Hoaglin <dchoaglin@gmail.com>]

Dear Amal,

As Maarten Buis explains, a thorough answer to your question may not
be simple.  I need to study the article that he cited (submitted to
the Stata Journal).  A few less-sophisticed comments may be helpful.

The coefficients in the model in Step 3 tell you about the effects of
SEP on the outcome, adjusting for ethnicity (and the confounders) AND
the effects of ethnicity on the outcome, adjusting for SEP (and the
confounders).  SEP and ethnicity are on an equal footing in that
model.

The predictors in Step 4 should include the "main effects" of
ethnicity and SEP, not just the interaction effects.  You can use the
## operator on those factor variables.

If those interaction effects (in the revised Step 4) are statistically
significant, you will need to interpret the effects of SEP separately
for each category of ethnicity and the effects of ethnicity separately
for each category of SEP.  A transformation of the outcome variable
(or a suitable choice of link function) may remove or reduce
interactions if they are present.

If interactions are not an issue, a simple (simplistic?) approach to
assessing the relative "importance" of ethnicity and SEP would fit the
model in Step 2 and the corresponding model that contains SEP and not
ethnicity, and then look at the difference in R^2 between the model of
Step 3 and each of those two models.  That is one way of assessing the
contribution of SEP after accounting for ethnicity and the
contribution of ethnicity after accounting for SEP.  It may be
instructive to compare the values of R^2 for the two Step 2 models
against the R^2 of the model that contains neither ethnicity nor SEP.

It may be important to understand the relations between the potential
confounders and ethnicity and SEP --- in a diagram for the causal
model.

If your data are observational, it is more accurate to say "adjusting
for" instead of "controlling for."  In an observational study, the
potential confounders are not actually controlled.

David Hoaglin

On Thu, Sep 27, 2012 at 1:46 PM, Amal Khanolkar <Amal.Khanolkar@ki.se> wrote:
> Hello all,
>
> I need some advice on the following approach:
>
> I have two main exposures; maternal ethnicity and maternal socioeconomic position (SEP).
>
> I want to test which of the above two exposures are more important in determining maternal pregnancy outcomes.
>
> 1. I plan to use linear regression, as my outcome of interest is continuous.
> 2. Initially, the first model will test the effect of ethnicity on the outcome, controlling for potential confounders as follows:
>
> xi: regress outcome i.ethnicity confounder1 confounder2 i.confounder3
>
> 3. In the next step, I introduce the second main exposure, maternal SEP:
>
> xi: regress outcome i.ethnicity confounder1 confounder2 i.confounder3 i.SEP
>
> 4. I test for an interaction as follows:
>
> xi: regress outcome i.ethnicity*i.SEP confounder1 confounder2 i.confounder3
>
> Questions: If the effects of ethnicity on my outcome of interest change from step2 to step3, controlling for the same confounders in both models, is this enough evidence of one exposure being more important than the other? (I assume, this isn't completely right, as in essense the model in step 3 is the effect of SEP on the otcome adjusting for ethnicity). But I hope the model with the interaction test solves this to some extent, as I will be able to see if socieconomically disadvantaged mothers of certain ethnicites  have a worse outcome compared to other disadvantaged mothers belonging to other ethnic groups.
>
> If there are any better ways to improve the above approache - please let me know.
>
> Regards,
>
> /Amal.

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