How one can know the unknowable in observational research
IntroductionProblem Setup2.1. Causal Graph2.2. Mannequin With and With out Z2.3. Energy of Z as a ConfounderSensitivity Analysis3.1. Goal3.2. Robustness ValuePySensemakrConclusionAcknowledgementsReferences
The specter of unobserved confounding (aka omitted variable bias) is a infamous downside in observational research. In most observational research, until we will fairly assume that remedy project is as-if random as in a pure experiment, we will by no means be actually sure that we managed for all doable confounders in our mannequin. Consequently, our mannequin estimates could be severely biased if we fail to regulate for an essential confounder–and we wouldn’t even realize it for the reason that unobserved confounder is, effectively, unobserved!
Given this downside, it is very important assess how delicate our estimates are to doable sources of unobserved confounding. In different phrases, it’s a useful train to ask ourselves: how a lot unobserved confounding would there must be for our estimates to drastically change (e.g., remedy impact now not statistically vital)? Sensitivity evaluation for unobserved confounding is an energetic space of analysis, and there are a number of approaches to tackling this downside. On this publish, I’ll cowl a easy linear methodology [1] based mostly on the idea of partial R² that’s broadly relevant to a big spectrum of circumstances.
It is a frequent setting in lots of observational research the place the researcher is keen on realizing whether or not the remedy of curiosity has an impact on the result after controlling for doable treatment-outcome confounders.
In our hypothetical setting, the connection between these variables are such that X and Z each have an effect on D and Y, however D has no impact on Y. In different phrases, we’re describing a state of affairs the place the true remedy impact is null. As will turn into clear within the subsequent part, the aim of sensitivity evaluation is having the ability to motive about this remedy impact when we’ve got no entry to Z, as we usually received’t because it’s unobserved. Determine 1 visualizes our setup.
Determine 1: Drawback Setup
2.2. Mannequin With and With out Z
To reveal the issue that our unobserved Z may cause, I simulated some information according to the issue setup described above. You’ll be able to discuss with this pocket book for the main points of the simulation.
Since Z could be unobserved in actual life, the one mannequin we will usually match to information is Y~D+X. Allow us to see what outcomes we get if we run that regression.
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