I think that the impact on the variance of target parameters of using a class of variables in the imputation will be stronger for the class of adjunct variables than for the class of causally prior covariates in the target model. Parallel or alternate outcomes are particularly good examples of this. People who favor nesting variables with nonresponse within flags for missingness as an alternative to imputation fail to realize these gains in precision and possibly in bias reduction. (Obviously, they cannot include parallel outcomes in their analytic models.)
It harkens back to one of the central themes in the debate between imputation and ANCOVA. The imputer frequently has access to a richer set of auxiliary information than does the downstream analyst. If we are shy about using that information in the imputation, then we have surrendered most of the advantage of imputation over the alternatives. To give an example from my own work, I had a longitudinal sample of 8th graders with parent interviews for the fall of the normative freshman year of college. Parent nonresponse was high with the 4.5 year gap. The primary outcome of interest was college admission. We matched students to administrative datasets about college going. We could not report the administrative data directly because of known biases (e.g. no coverage of children from families who do not require financial aid). Using the match status as an adjunct variable in imputation of the parent responses, however, had a huge impact on the final estimates. In addition to strong variance reduction, we also discovered that parent nonresponse was strongly nonignorable. Those whose children did not go to college were far less likely to respond to the survey. I would send you a reference but unfortunately the evaluation was cancelled without a report. --Dave Judkins Sent from my iPhone On Apr 16, 2013, at 8:52 AM, "Hunsicker, Lawrence" <[email protected]<mailto:[email protected]>> wrote: Many thanks to Drs. Judkins, VonHippel, and Raghunathan: We seem to have a consensus that inclusion of auxillary variables is legitimate. Frank Harrell also concurs in a separate e-mail, and I have just read a piece by Paul Allison that comes to the same conclusion. But it is nice to have the Meng reference to document that it is mathematically correct. I appreciate also Raghu’s suggestion that where it is likely that data will be missing, the data collection plans should deal with this prospectively by collecting data on potentially useful auxiliary covariates. There seem to me to be two ways to think about whether “the auxiliary variable helps a little or a lot.” If one’s metric is the accuracy of the imputation, it seems pretty likely to me that the accuracy of the imputation will be improved by including a strongly correlated auxiliary variable. One could check this by checking the correlation of the values predicted by the imputation model with the actually observed values. But the real issue is how much inclusion of the auxiliary variables in the imputation model improves the results of the actual final analysis. This has to be a function of how strongly the covariate with missing values correlates with (predicts) the final outcome variable, and with the amount of missing data. The analysis that I posed in my original post is not a particularly good one for asking this question, as the amount of missing data for the current PRA is only about 3%, and the impact of current PRA on graft survival is not particularly strong. It was a convenient straw man to permit me to ask the question coherently. But I agree that it would be worthwhile asking the question about how much inclusion of an auxiliary variable helps using an appropriate data set. I’ll think about this and see if I can construct some data sets that permit a test of this question. Again, thanks to all. Larry Hunsicker Prof. Internal Medicine U. Iowa College of Medicine From: Paul von Hippel [mailto:[email protected]] Sent: Tuesday, April 16, 2013 5:57 AM To: Hunsicker, Lawrence; [email protected]<mailto:[email protected]> Subject: Re: "Accessory" variables in imputation You may be right. From Larry's point of view the important thing is that inclusion of auxiliary variables is legitimate but not mandatory. Larry: if you like you could fit the imputation model with and without the auxiliary variable, analyze the data both ways, and report back how much smaller your standard error is when you use the auxiliary variable. Of course, you're under no obligation to do that, but it would be interesting to know if this is a situation where the auxiliary variable helps a little or a lot. On Mon, Apr 15, 2013 at 7:21 PM, David Judkins <[email protected]<mailto:[email protected]>> wrote: I would say that it all depends. In Hunsicker's example, peak PRA sounds like it was excluded from the outcome space because of colinearity issues. This makes it an ideal adjunct variable to the imputation process. --Dave Judkins Sent from my iPhone On Apr 15, 2013, at 7:13 PM, "Paul von Hippel" <[email protected]<mailto:[email protected]>> wrote: Let me correct my first sentence: What I meant to say is that Meng showed that MI imputation is still valid of auxiliary variables have been included in the imputation model. So it's a legitimate practice and, if its' not too much trouble, why not. But it probably won't make much difference. ________________________________ From: Paul von Hippel <[email protected]<mailto:[email protected]>> To: [email protected]<mailto:[email protected]> Sent: Monday, April 15, 2013 4:39 PM Subject: Re: "Accessory" variables in imputation Meng showed that MI imputation is still valid if auxiliary variables have been included in the analysis. In theory auxiliary variables can improve the estimates, but in practice they rarely help much. See the recent paper by Sarah Mustillo in Sociological Methods & Research. On Mon, Apr 15, 2013 at 4:27 PM, Hunsicker, Lawrence <[email protected]<mailto:[email protected]>> wrote: Good afternoon, all: A question about the use of "accessory" variables in imputation. Consider for a moment a kidney transplant survival model in which one has data (among other things) on peak panel reactive antibody (peak PRA) and the PRA at the time of the actual transplant (current PRA). These actually measure different things, but they are obviously strongly correlated. Data are missing of some fraction of these covariates, but most of the time one or the other is available. Current PRA is considered to be the stronger predictor of transplant outcomes. One is developing a model in which one wants to limit the model df. So it has been decided that the final model will include current PRA but not peak PRA. I understand that the imputation model must include the outcome variable and also all of the covariates that will be used in the final analysis model. The question is whether one can/should include additional covariates (such as peak PRA) in the imputation model that WON'T be in the final analysis model. It would seem that inclusion of peak PRA in the imputation model might improve considerably the prediction of current PRA, the covariate that will be included in the final analysis model. Is this legitimate? Thanks in advance to any guidance from the listserv members. Larry Hunsicker Prof. Internal Medicine U. Iowa College of Medicine ________________________________ Notice: This UI Health Care e-mail (including attachments) is covered by the Electronic Communications Privacy Act, 18 U.S.C. 2510-2521, is confidential and may be legally privileged. If you are not the intended recipient, you are hereby notified that any retention, dissemination, distribution, or copying of this communication is strictly prohibited. Please reply to the sender that you have received the message in error, then delete it. Thank you. ________________________________ -- Best wishes, Paul von Hippel Assistant Professor LBJ School of Public Affairs Sid Richardson Hall 3.251 University of Texas, Austin 2315 Red River, Box Y Austin, TX 78712 (512) 537-8112 ________________________________ This message may contain privileged and confidential information intended solely for the addressee. Please do not read, disseminate or copy it unless you are the intended recipient. If this message has been received in error, we kindly ask that you notify the sender immediately by return email and delete all copies of the message from your system. -- Best wishes, Paul von Hippel Assistant Professor LBJ School of Public Affairs Sid Richardson Hall 3.251 University of Texas, Austin 2315 Red River, Box Y Austin, TX 78712 (512) 537-8112 ________________________________ Notice: This UI Health Care e-mail (including attachments) is covered by the Electronic Communications Privacy Act, 18 U.S.C. 2510-2521, is confidential and may be legally privileged. If you are not the intended recipient, you are hereby notified that any retention, dissemination, distribution, or copying of this communication is strictly prohibited. Please reply to the sender that you have received the message in error, then delete it. Thank you. ________________________________ ________________________________ This message may contain privileged and confidential information intended solely for the addressee. Please do not read, disseminate or copy it unless you are the intended recipient. If this message has been received in error, we kindly ask that you notify the sender immediately by return email and delete all copies of the message from your system.
