Robust conditional logistic regression with rstanarm::stan_clogit?

Interfaces rstanarm
1

Dear all,

We’re (still, I’ve posted a few comments already) preparing a case-control study in which we’d like to use stan_clogit to estimate the effect of some exposure on mortality. We have quite some patients who are controls for many cases, so my supervisor asked if it might be feasible to use robust errors in the estimation (he’s not a Bayesian). Our data set is fairly large with some 25k patients in total.

To the best of my knowledge, the way to render the model robust in a Bayesian framework might be to use e.g. student_t priors to regularise the parameter estimation (e.g. Prior choices recommendations) or add an intermediate step in the likelihood function (DBA3 p. 438, ch. “Models for robust inference”).

I was considering going for the student_t priors on the coefficients and was curious if others have done something similar of might be able to provide some guidance for alternative/better approaches, ideally sticking with stan_clogit.

Cheers,
Ben

2

You can use student_t priors with stan_clogit or a bunch of other things besides the default normals. But I doubt that corresponds to whatever your supervisor means by “robust errors” or whether whatever your supervisor means by “robust errors” corresponds to anything Bayesian.

3

I think he’s referring to robust standard errors, but using those seems a bad idea in GLMs (except when linear, but then they’re not generalised anymore anyway) because the point estimate isn’t consistent (e.g. this post).

His point, I believe, was to not let outliers pull the effect sizes unduly, and these robust (standard) errors would supposedly alleviate this. That’s why I thought student_t would be an appropriate way to (try and) address this in a Bayesian manner. We won’t really know until we see the results, I guess, but since we’re writing up a detailed protocol, I wanted to include at least some considerations.

Thanks for you your replies, @bgoodri! I really appreciate it.

Cheers,
Ben