Synthetic Confounding Simulation

[chathasphere]

At three positions in each patients sequence, we insert either special codes X and Y. So there are four possible combinations: XX, XY, YX, and YY.

If the first position is X, then set P(T = 1) = 0.2.
If the first position is Y, then set P(T = 1) = 0.8.

If the second position is X, then set E[Y | T=1] = 0.1 and E[Y | T = 0] = 0.3.
If the second position is Y, then set E[Y | T = 1] = 0.7 and E[Y | T = 0] = 0.9.

Therefore, the relative ordering and presence of X and Y are confounders.

[chathasphere]

@jeff-regier This might be simple, but it seems like a reasonable place to start

[chathasphere]

I could set these probabilities based on the presence of two special ICD codes in actual Optum Data sequences, but these choices would be pretty arbitrary, most likely. I will keep thinking of a clever motivating example in the meantime.

[jeff-regier]

Yep, seems like a fine way to start

…

On Thu, May 5, 2022 at 1:55 PM Prayag Chatha ***@***.***> wrote: @jeff-regier <https://github.com/jeff-regier> This might be simple, but it seems like a reasonable place to start — Reply to this email directly, view it on GitHub <#132 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ACEJ4CZPDRZVQ3DLAFDKN5TVIQDRZANCNFSM5VF2BIOA> . You are receiving this because you were mentioned.Message ID: ***@***.***>

[chathasphere]

As a generalization of this approach, it might be interesting to have a set of variables that affect outcome but are not confounders and to show empirically that the AIPW does better when propensity score is estimated on a "minimal" set of covariates