Arman Oganisian

When it comes to likelihood-based inference, it’s not that we are “treating X as fixed” it’s just that we implicitly assume that F_{Y|X} and F_{X} have distinct parameters so that contributions from F_{X} are ignorable.

Teaching regression in my Bayes class and one thing I don’t like is language about whether we “treat X as fixed” or “treat X as random”.

Both X and Y are random draws from a joint F_{X,Y}. It’s just that we factorize it as F_{X,Y}= F_{Y|X} F_{X} w/interest in E[Y|X] = ∫y dF_{Y|X}.

Having got into causal from econometrics, this paper is giving me flashbacks. Everything was about endogeneity wrt an error term in a linear/additive outcome model.

I also don't think an observational study should be published or not based on how sensitivity results are to unmeasured confounding. A main point and interval estimate accompanied by a tipping point analysis is still a valid and useful contribution.

The critique of unmeasured confounding is often levied in a lazy/broad way. It is trivially true in any observational study. But if the critic can't think of a plausible such confounder and posit a reasonable direction/magnitude of its bias then they're not doing productive science.

We really do need to get away from the binary. It should be "is there unmeasured confounding or not." Almost certainty there is - it's a matter of how much and what direction.

I would say experts I work with more like the "tipping point" style of reasoning (e.g. in the slides). That is, how much/in what direction would unmeasured confounding have to be to make my non-null result null. Or make my null result non-null.

So these are pretty mainstream, "establishment" folks in causal working on this stuff over decades.

As a field, one reason causal inference is obsessed with stating untestable assumptions with precision is because now you can reason about effects of their violations in an equally precise way.

At least among methodologists sensitivity analyses are embraced and developed. E.g. the approach with the Delta(a,l) is straight from Jamie Robins' "confounding function" - thought he Bayesian spin is new. Another example from Brumback, Hernan, Haneuse, and Robins: pubmed.ncbi.nlm.nih.gov/14981673/

Delta is just the amount of residual confounding remaining even after controlling for L.

The approach in the slide is different and does posit one “composite” confounder - more akin to the e-value approach of vanderwheele

The approach in the paper is agnostic to the number of unmeasured confounders. Unmeasured confounders implies that Delta(a,l) = E[ Y(a) | L=l] - E[ Y(a) | A=a, L=l] =\= 0

Agnostic to whether this is due to 1 or 10 unmeasured confounders. You put a prior on Delta directly.

Lately peer review has just involved fighting the erroneous notion that “all bayesian causal inference is a posterior predictive exercise in which we impute each subject’s missing counterfactual”

As a result I’m sympathetic to the argument that you go to school to get skills that make you valued in the labor market and get a high ROI. That intangible enrichment outside of that is great but a second order priority.

I’m sure we’re between utopia and societal collapse ;)

I’ve just seen too many people get screwed into decades of college debt because some philosophy professor told them that “true education” is debating Kant.

I came from a very low income family and never had the luxury of thinking this way.

Equality is another story sure. But absent a commensurate increase in demand, wages will fall and dissuade subsequent entrants rather than societal collapse.

Also fwiw law salaries are extremely bimodal - skewed up by top firms. A big chunk don’t make much money

www.nalp.org/salarydistri...

I’m not sure because the supply-demand dynamics may simply shift. If everyone suddenly goes into a very high paying job, the increased supply may just lower wages.

I also give an example in Part 2 of a summer instute course I teach slides/code available here:
github.com/stablemarket...

Relevant slides posted here.

E.g. Figure 3B shows mean/CI for causal effect across various priors for Delta - the amount of unmeasured confounding (UC).

First from Left: point-mass at 0 encodes strong prior belief of no UC.

Second: Gaussian encodes prior belief of UC in either direction symmetrically - widening the interval.

I survey a bunch of papers along these lines in Section 5 of this paper and give an implementation example.

doi.org/10.1002%2Fsi...

here's arxiv version in case there's access issues: arxiv.org/abs/2004.07375

Imo this adds (not subtracts) from the hype as there's a large body of work on causal sensitivity analyses for such cases.

All methods will involve untestable assumptions - e.g. at-random compliance. We can widen our intervals appropriately to account for our uncertainty their violations.

100% prediction interval

Related is this excellent post by gelman about studies that are “dead on arrival.” Roughly: questions around true effect sizes that are tiny but estimated using data that are noisy. It’s a long post but I screenshotted the tldr.

statmodeling.stat.columbia.edu/2016/06/26/2...

What exactly is the paradox? Nearly every aspect of the knowledge production pipeline - grant funding decisions, peer-review, replication and falsification, dissemination - involves community exchange. The goal is still to produce knowledge.

Similarly I don’t think one can encode unit-level assumptions like exclusion restrictions cleanly on a DAG - since these are structural assumptions about potential outcomes, not their distributions. Nor can we (explicitly) encode cross-world identification assumptions.

I agree. DAGs are visual representations of conditional dependencies (arrows) in a joint distribution of variables (nodes). So they can encode exchangeability (a conditional independence statement) but not parallel trends (an equality of expected differences).

I think to distinguish, pearl’s generalization is sometimes referred to as non-parametric structural equation models with independent errors NPSEM-IE

See eg csss.uw.edu/files/workin...

This paper is now out in final form and is open-access!

journals.lww.com/epidem/fullt...

It follows that what we are really after is flagging subgroups with high P(Y^1 < Y^0 | X_i) - ie a high probability of benefiting from treatment. Unlike P(Y=1 | X_i) this involves potential outcomes Y^1 and Y^0 and so is an exercise in heterogenous treatment effect estimation.

We train a model for relapse Y on “risk factors” X then flag patients with high P(Y=1 | X_i) for intervention. But consider that some of these subjects may still relapse whether treated or not - wasting resources.

This is a really nice post - and productive way of avoiding doomscrolling!

In my view, prediction models that are used to inform a decision may be implicitly causal.

Suppose we want to build a prediction model for relapse, with the goal of flagging patients in high-risk subgroups for treatment