search

pzivich / Delicatessen

Delicatessen: the Python one-stop sandwich (variance) shop 🥪
https://deli.readthedocs.io/en/latest/index.html
MIT License
22 stars 2 forks source link

Estimating Equation: Regression Calibration #49

Closed pzivich closed 3 months ago

pzivich commented 5 months ago

Is your feature request related to a problem? Please describe.

Regression calibration is a method to correct for measurement error in the exposure. It actually is pretty easily to implement (and fairly intuitive). Basically, one fits a regression model for the true exposure and a outcome model with the mismeasured exposure. The coefficient from the mismeasured exposure is rescaled using the first model.

As estimating equations, this is fairly simple to implement. Basically, you have two regression models and that's it. So, the entire thing can be built using ee_regression. M-estimation and the sandwich variance are particularly valuable, since it automates the whole process (regression calibration can be annoying otherwise).

One caution is that regression calibration assumes measurement error is non-differential. So, that is a limitation. MIME still works in that context.

Describe the solution you'd like

Extend measurement.py to include regression calibration as a built-in equation. This is a nice complement to Rogan-Gladen, which deals with outcome measurement error. From that perspective, I cover two major types of measurement error.

Two (?) design matrices would be the inputs, one outcome variable. I should use ee_glm as the backbone for the outcome model to allow for maximum flexibility in that model specification. For the calibration model, I can just use linear regression (that is the current standard).

Describe alternatives you've considered

None.

Additional context

Some references

Boe, L. A., Shaw, P. A., Midthune, D., Gustafson, P., Kipnis, V., Park, E., ... & of the STRATOS Initiative, O. B. O. T. M. E. A. M. T. G. (2023). Issues in Implementing Regression Calibration Analyses. American Journal of Epidemiology, 192(8), 1406-1414.

https://academic.oup.com/aje/article-abstract/132/4/734/102293?redirectedFrom=fulltext&login=false

https://onlinelibrary.wiley.com/doi/10.1002/sim.4780080905

https://academic.oup.com/aje/article-abstract/136/11/1400/79365?redirectedFrom=fulltext&login=false

pzivich commented 5 months ago

More references

https://academic.oup.com/aje/article/184/3/249/2237540

https://www.degruyter.com/document/doi/10.1515/ijb-2012-0039/html

pzivich commented 5 months ago

Actually more relevant that previous two

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2800300/

pzivich commented 3 months ago

Related https://academic.oup.com/aje/article/193/5/798/7452857