What is the Bias due to omitted confounders relationship for Conditional Logistic Regression and Generalized Estimating Equations?

Question

I'm trying to work out the differences between conditional logistic regression and generalized estimating equations GEEs for repeated measures binary data. GEEs seem to be far more popular and I'm not sure why.

I ran a simulation with repeated measures on the same subject where I omitted a subject-specific confounding variable from the model for both the conditional logistic regression and the GEE logistic regression. Conditional logistic regression gave me unbiased estimates of the effect of interest while GEE logistic regression yield biased (but ultimately consistent) estimates.

I'm struggling to understand why conditional logistic regression is superior to GEE for reducing this omitted variable bias.

Answer 1

Found my own answer, I assumed the GEE would control for cluster-level confounding, which is not true. Conditional logistic regression conditions out the cluster-specific effects entirely so it yields unbiased estimates in the face of omitted cluster-level confounders. In my simulation the GEE did reduce the bias by about 60%, but still produced biased estimates.

The method I found to produce unbiased estimates using GEE was to include the cluster mean of the confounded dependent variable as a co-variate. It serves as a proxy for the omitted cluster-level effect. I believe there are some more complicated solutions as well.

For reference:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4320764/#b4

http://link.springer.com/article/10.1023/A:1025897811143

https://books.google.ca/books?id=w0fxBwAAQBAJ&pg=PA77&lpg=PA77&dq=Effect+of+Confounding+and+Other+Misspecification+in+Models+for+Longitudinal+Data&source=bl&ots=I7QD46U6Ov&sig=mSEFtrxU28mapRdcDRoQOPAje5M&hl=en&sa=X&ved=0ahUKEwiBwduyl7XPAhWHWh4KHVaLB1AQ6AEILTAD#v=onepage&q=Effect%20of%20Confounding%20and%20Other%20Misspecification%20in%20Models%20for%20Longitudinal%20Data&f=false