determining confounding effect in multi-categorical exposure variable?

[Danah Abdul]

Hello,
I am running a fixed effect multivariable conditional logistic regression for the association between the exposure ethnicity (entails 12 categories) and death (binary outcome). I would like to adjust for confounders, and have set a 10% change in the odds ratio as a threshold.
But I don't know does the 10% change have to apply to all categories of ethnicity or any category? or is there another way to determine confounders for primary exposure variable with multiple categories (not ordinal)?

[Mike Lacy]

First, note that you are talking about "mediator" variables between ethnicity and death, since most disciplines would define a "confounder" as causally *prior* to an exposure. I can't imagine how you could have any variables in your model that cause ethnicity.

You don't say why you want to set a "threshold," but I'd presume your idea is omit from the model any mediator that doesn't represent a substantial mediation path. If that is your idea, I'd be inclined to include variables that are interesting mediators for any category of ethnicity: "Variable X appears to mediate the effect of Ethnicity Category 1, but not the effects for categories 2, 3, ... ." I would discourage the idea of thinking in terms of "this mediation effect occurs or doesn't occur," and instead think of "I want to estimate the mediation effect, big or small, as it exists for each ethnic category." Perhaps your "either/or" threshold here might be appropriate for a true confounder, but I would even question it in that case. Also, if you have a large enough sample to be able to use 12 ethnicity categories in a model, then I would not be so worried about having to set an arbitrary threshold for leaving out a predictor, as I'd guess your events/variable ratio is likely not a problem.

As for estimating mediation effects with a conditional logit model: As you may know, there is considerable controversy about whether mediation or confounding can be properly estimated with a logit model. That being said, I'd say your best bet in Stata would be to use the -khb- community contributed program, available at SSC. I also understand that the developers of that program also may have some newer related methods and software.

[Danah Abdul]

May thanks Mike Lacy for your reply and elaboration.
the factor (e.g. self-harm) I guess is more of a confounder (being statistically significantly associated with both the exposure and outcome) than a mediator (decedent of exposure and ancestor of outcome); hence the 10% rule for changing a risk when added to the model is a part of confounder criteria. By all means, I got your point of looking at the effect of the factor per category rather than all or non. Thank you for that.
May I ask what do you mean by the -khb- community?

Kind regards
Danah

[Mike Lacy]

One of the standard and well-liked features of Stata is its accommodation of what are called "community-contributed" or "user-written" commands. You can learn about this feature of Stata in the PDF documentation available through -help ssc- . -khb- (See -ssc describe khb-) is such a command, whose purpose is to offer mediation estimates for logit and related models, enabling estimates of direct and indirect effects.

I do understand that some sources refer to as confounders variables that are *not* causally prior to the exposure. However, I'd say that any variable that is associated with ethnicity in this context would be an *effect* of ethnicity, though perhaps through a complicated chain of causation. (I'd be willing to comment on counterexamples, and be corrected as appropriate.)

Many contemporary commentators about causal inference caution about controlling for mediators unless you're specifically going to parse out direct and indirect effects. To take a prosaic example: Income is likely a confounder (according to your definition) in relation to the association of ethnicity and death. If one controls for income and examines the relation of ethnicity to death, there would presumably be a much smaller effect estimate for ethnicity, but this will *not* be because ethnicity has a small impact on death rate, but rather because much of ethnicity's effect happens to proceed through its effect on income. To make a reductio ad absurdem argument: If one was clever enough to control all the variables through which ethnicity has an effect on death, one could get a 0 estimate for the effect of ethnicity, when in fact a better description would be that it has a large effect that proceeds through many paths. This is why, from the point of view of causal inference, I'd say that it's important to regard the goal here as to identify all the mediated (indirect) effects of ethnicity. Treating income, health behaviors, access to food, medical care, tobacco use, etc. as having distorting effects on the estimate of the effect of the ethnicity on the risk of death would be strange, I'd say.

One possible counterexample that occurs to me is that in some countries, ethnicity and region of residence are strongly correlated. I suppose one might want to regard region as a cause (or at least not an effect) of ethnicity, in which case perhaps region is a confounder in the sense I'd use the term.

[Danah Abdul]

Many thanks Mike Lacy for the clarification and interesting discussion about causal inferences.

If you may please allow me to comment and enquire further more about this topic.

If we are to take "gender" for example and how it alters the association between ethnicity & death: in such instance, how can gender be an effect of ethnicity in the sense you described?

Moreover, with regards to the example provided about ethnicity, death and income- In a regression model, when adjusting for income, the adjusted odds ratio will reflect the "direct effect" of ethnicity on death after controlling for income, but *not* the "total effect" I assume. Am I correct in that? Are you suggesting that the khb model will allow us to assess the total effect (direct and indirect)?

[Mike Lacy]

If you have a study population in which for some reason reason why ethnicity is substantially correlated with gender, I think I'd have to know more about how that relationship arises to say how I'd think about it. If, for example, there were features of social life w/in ethnic group that led to differential death rates by gender, changing the sex ratio within ethnic group, then there's something more complicated going on.

Yes, separating the total/direct/indirect effects is actually what -khb- tries to do. Again, the extent to which that can be validly done by any method is somewhat controversial, but -khb- and its methods are well-regarded, if not universally so.

[Danah Abdul]

Mike Lacy I can see that now. Thank you very much for the insight and suggestion. I shall discuss that with our research team.

Kindest regards
Danah

[Danah Abdul]

Mike Lacy
Hello Mike, back to an old discussion related to ethnicity and the risk of suicide #2
I became very inclined to believe that covariates in the relationship between ethnicity and suicide are mediators rather than confounders.
I am using KHB to assess the indirect effect of self-harm and mental illness on the association between ethnicity and suicide. But ethnic groups in the sample differ from one another with regards to age and gender (p<0.0001). This may probably be a "result" of ethnicity on age and gender (hence age and gender are yet considered as mediators).
Nevertheless, when assessing the the mediated effect of self-harm and mental illness, do you advice using the "concomitant" option for age and gender to ensure that ethnic groups are similar with regards to age and gender when comparing the mediated effect?

I also found it hard to interpret results. I will demonstrate one result (odds ratio) for ethnicity X compared to White (had to change details for confidentiality).


Reduced: 0.70
Full: 0.87
Diff: 0.86

Summary of confounding:
Conf_ratio: 2.04
Conf_pct: 41.2

Components of Difference:
self-harm:
coef: -0.08
Std_Err: .0019
P_Diff: 31.41
P_Reduced: 14.57

How would we interpret the results for indirect effect, Conf_pct and component of difference?
Would it be correct to say that:
self-harm and mental illness contribute to 24% [(1-0.86)*100] reduction in the odds of suicide amongst ethnicity X compared to White which means that 41.2% (Conf_pct) of the total risk was related to self-harm and mental illness. Self-harm alone contributed to 31.41% (P_Diff) of the reduction in odds.
Also the negative sign before the coef is puzzling.

Sorry for the long enquiry, but I am a yet jumbled and would very much appreciate your kind help.

Kindest regards
Danah

[Mike Lacy]

My short answer here is that I can't offer a helpful response to your question as posed.

Longer answer: First of all, on StataList, directing a question to one person is not usually a good idea. Doing so discourages other people from responding who might well have helpful or different ideas. Second, without seeing all the results and most importantly, the actual command(s) you gave to Stata, I (and others) don't know enough about what you did to understand the context of your question. Finally, I'd say that the answer to your questions will depend in part on one having substantive knowledge of your research area and your specific study. I and others *might* have some knowledge there, but not knowing the meaning of "self-harm," "mental illness," or "ethnicity" in your research context, that would be difficult. I'd want to know the nature of the data collection, the country and time in it was collected, and the meaning of the variables. You've also now turned the focus toward suicide in particular, rather than death in general, which might well matter. As for study design, I might guess that what you have comes from a case-control study, but I don't know.

[Danah Abdul]

Mike Lacy Thank you for taking the time to reply.
I posted the question in the general forum, hopefully I get a reply/replies.
I also see your point about the research details which brought about insight. thank you.

[Mike Lacy]

There was nothing wrong with continue to post in this thread. The issue was that you directed it to one person, which more or less says "I only want this one person to answer my question." However, posting a new question, with a different subject, might be helpful.