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I'm using the MICE package to generate 10 imputed datasets. After that, I know I should perform analysis on each dataset (propensity score matching, Chi-square, and Cox-regression in my case) and report the pooled results. However, how do you generate a pooled descriptive frequency table from the imputed datasets? For instance, if I have missing variables in my Gender variable, the proportion of males and females would differ between each imputed dataset.

To be more concrete, let's say of 5 imputed datasets of size 100, dataset 1 has 70M:30F, dataset 2 has 72M:27F, datset 3 has 69M:31F, dataset 4 has 71M:29F, and dataset 5 has 68M:32F. In this case, how do you generate the final Gender frequency and count from all the imputed datasets, keeping the dataset size to the original 100?

Also, how would you combine the Kaplan-Meier curves from each dataset into one final Kaplan-Meier curve? I have seen this question here before, but no one has posted a single accepted answer.

I'm referencing this paper from Lancet, which claims to have done propensity score matching and Cox regression, as well as generate a Kaplan-Meier survival curve, after multiple imputation:


Lancet Oncol. 2016 Jul;17(7):966-975. doi: 10.1016/S1470-2045(16)30050-X. Epub 2016 May 17.

Preoperative or postoperative radiotherapy versus surgery alone for retroperitoneal sarcoma: a case-control, propensity score-matched analysis of a nationwide clinical oncology database.


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    $\begingroup$ To your first question, the paper you referenced to notes, for Tables 1 and 2, "Percentages were calculated after excluding missing cases from the denominator". I'm not sure that imputed statistics are customarily reported in summary tables. $\endgroup$ Commented May 14, 2018 at 23:52
  • $\begingroup$ Multiple imputation was designed for inferential purposes, not for descriptive purposes (see Daniel Klein's last answer on the thread statalist.org/forums/forum/general-stata-discussion/general/…). From this point of view, it makes more sense to report the amount of missigness present in each variable in the original data set and compute descriptive statistics from the original data set. $\endgroup$ Commented May 15, 2018 at 1:48
  • $\begingroup$ Thank you for the responses. I did not quite see the fine print on that Table in the paper. In regards to fitting a Kaplan-Meier curve after imputation, I'm doing the analysis on survminer in R. My proposed strategy is extract the Kaplan-Meier survival probabilities from each imputed dataset after propensity score matching and then calculate the average survival probability per individual. Would this be a valid method? Also, does the survminer package allow the user to define his own survival probability, so I can conduct a log-rank test from the averaged survival probability? $\endgroup$ Commented May 15, 2018 at 13:56
  • $\begingroup$ *Edit: after some quick playing in R, I found out that you can indeed define your own survival probabilities with fit[["surv"]], so that issue is solved. Also, per this paper ("Prostate cancer: net survival and cause-specific survival rates after multiple imputation"), you can log transform survival probabilities from each imputed set, average the probabilities, and back-transform the average probabilities to yield a final single set of pooled probabilities. Apparently this follows Rubin's rules. Would you do the same for the confidence intervals, and is this a widely accepted approach? $\endgroup$ Commented May 15, 2018 at 14:59

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There is a similar topic: "Is this way of pooling Kaplan-Meier estimates correct? Example made with R mice::pool_scalar" that may be useful to you. The author shows how to pool the KM estimates and calculate the pooled confidence intervals for them. The log(-log(1-Surv)) transformation is for the survival probability, and log(-log(Surv)) for the CDF = CIF = 1-KM.

Contrary to one of the comments below you question, there is nothing wrong is pooling KM estimates to observe how close is the result AFTER the imputation to the complete observed data. One must not forget that imputation CAN distort the original distribution if the method imputation model is misspecified and the analysis model is not congenial with the imputation model. This is easy to fail under the chained multiple imputation with more than single variable. Nobody should be surprised that applying a misspecified imputation will lead to biased estimates.

Then, one of the mandatory assessments after the imputation is to observe both post-imputation and pooled distributions against the observed one. Of course discrepancies may exist, as the imputation is at MAR (conditional to the predictor), BUT if the pooled and empirical distributions vary a lot, then evidently something happened to your imputation and this must be explained. It doesn't necessarily mean something "bad", it's just something you should explore further to be able to answer the question why is the observed estimate so different from the post-imputed one?

And for this the pooling process is mandatory.

Not to mention, that KM is not just a descriptive method. It's a valid non-parametric cross-product estimator and can be used for inferential purposes as well, similarly to survival estimate at each timepoint along with it's pointwise confidence interval.

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