multiple imputation for missing not at random data: binary outcomes

[Laura Myles]

Hi listers,

I am exploring options for sensitivity analyses to test the robustness of the results based on multiple imputation, if data were MNAR. In previous threads, I found this paper recommended: https://pubmed.ncbi.nlm.nih.gov/29679317/

The approach suggested appears interesting, but in my case I have a binary outcome (disease vs. no disease). I am not sure the approach can be implemented and was wondering if other approaches could be used for MNAR sensitivity analyses in my case.

Thanks!

[Carlo Lazzaro]

Laura:
you might be interested in: https://pubmed.ncbi.nlm.nih.gov/10204197/

[Laura Myles]

Thanks Carlo, the paper suggests the use of an adjustment; however, it is done on a continuous variable and I am not sure how this can be applied to binary variables. If I were to assume missing data = worse outcome (more likely to develop disease), I am not sure how I can adjust the results from the MAR-based MI model to reflect this.

[Carlo Lazzaro]

Laura:
you're right: my previous reference focuses on blood pressure (a continuous variable indeed).
I do hope this one can be more useful: https://pubmed.ncbi.nlm.nih.gov/21225900/.
Unfortunately, when it comes to MNAR, the usual fast and hard rule is to impute as if the mechanism were MAR and then do sensitivity analysis (that is, dealing with delta).

[Laura Myles]

Thanks Carlo,

Based on the papers you recommended which discuss the delta-adjustment for continuous variables. Assuming I were expecting those patients with missing data to be (e.g. 20%) less likely to recover, I am wondering if I could apply a delta-adjustment to the imputed data assuming MAR.

I created a dummy dataset and code, which would need to then be extended when used on mi set data and it seems to work fine. Before I extend the code to apply to my MI dataset, I wanted to check if this looks like a reasonable approach to you.

* Set up data
clear

set seed 12345

set obs 20

g id = _n
g arm = runiform()<0.5
g miss = 0 // missing data indicator
replace miss = 1 if id>=11

g out = runiform()<0.5 if miss==0 //observed outcome

g out_imputed = runiform()<0.5 //imputed outcome

* NMAR sensitivity - assuming 20% less recoveries in those with missing data
capture drop randid
bysort id: g double randid = runiform()

g flag = miss==1 & out_imputed==1

capture drop out_adju
g out_adju = 0
bysort flag (randid): replace out_adju = (_n <= round(_N * (.8),1)) if flag==1
drop randid

[Carlo Lazzaro]

Laura:
pargaraph 2 of that paper ought to give some hints about imputing binary data too.
That said, In think your approach makes sense, proviso that you're going to present different scenarios with different delta-adjustements to your audience.
As usual, it would be great if some reference in your research field could justify the different delta-adjustements you apply,

[Laura Myles]

Hi Carlo,
Thanks for taking the time to answer my questions and your suggestions!