Although estimator is complex, some nice properties arise from the construction: in particular, we can examine distribution of cumulative weights across subjects, like in single-timepoint weighting

Cross-world"ness" --> nuances in identification and estimation

- ID: Need strong seq. rand., but still possible w/out positivity
- Est: new EIF for doubly robust estimator involves additional term w/ covariate density ratio across the target regimes

These fx are

- "Cross-world"
- "Mechanism-relevant" (they target mean diff in POs we care about)
- **Not** "policy-relevant" (they're not implementable)

This tradeoff arises elsewhere (mediation, censoring by death). Ours is another example:

What you want to know != what you can implement

We show that contrasts in flip effects yield WATEs when t=1 and non-baseline weighting for t>1

We also give some new doubly robust estimation results:
1. typical multiply robust estimator is twice as robust as people had thought
2. new sequentially doubly robust style estimator

Flip ints are built from a target tx and a weight (eg overlap wt, trimming indicator):

1. If subject would take target tx, do nothing
2. O/w flip subject to target with prob equal to the weight

Allows you to target any regime (eg, always treated) while adjusting to pos violations as needed

@idiaz.bsky.social et al. 2020

arxiv.org/pdf/2006.01366

Generalizes to a large class of ints. Also gives great review of other innovations from 2010s

Bonus: for identification, it uses an NPSEM -- an alternative to SWIGs. NPSEMs come from do-why lit; great for discussing asmps w/ practitioners

2) Young et al. 2014 pmc.ncbi.nlm.nih.gov/articles/PMC...

Ints that depend on natural value of trtment. Very easy-to-read! Appendix B is great on ID.

Further reading: the SWIG papers; primer first (stats.ox.ac.uk/~evans/uai13/Richardson.pdf), and original (R&R '13) when you're feeling brave!

1) Robins et al. 2004 www.jstor.org/stable/pdf/r...

Addresses or foreshadows lots of subsequent work on time-varying data. The data analysis in Section 6 helped me build intuition for earlier parts of the paper.

Not a 2024 paper, but new to me in 2024: www.sciencedirect.com/science/arti...

Cool results about estimation with extreme prop scores; limiting dists and inference even w/out CLT. Nicely resolved some q's I was thinking abt, before I spent too much time thinking about them (the perfect situation!)

We analyze the effect of mothers’ smoking on infant birthweight, and see that accounting for uncertainty in estimating M alters CIs for ATE.

This was fun work with Edward and Zach Branson (sites.google.com/site/zjbrans...) and was a great project to finish my PhD!

9/9

We incorporate M into our “calibrated” sensitivity models. Generically:

U <= GM

where G is sensitivity parameter.

We outline many choices for U and M and develop three specific models. Then identify bounds on ATE and give estimators that account for uncertainty in estimating M.

8/9

Often calibration is somewhat informal w/out accounting for uncertainty in M. However, statistical error in estimating M is first order and can alter confidence intervals! Indeed, if calibration is goal, more intuitive to put M directly in model.

We explore ramifications of this reframing!

7/9