I would like advice on pooling the calibration plots/statistics after multiple imputation. In the setting of developing statistical models in order to predict a future event (e.g. using data from hospital records to predict post hospital discharge survival or events), one can imagine there is some to a lot of missing information. Multiple imputation is a way of handling such a situation, but results in the need to pool the tests statistics from each imputation dataset taking into account the additional variability due to the inherent uncertainty of imputation.
I understand there are multiple calibration statistics (hosmer-lemeshow, Harrell's Emax, estimated calibration index, etc.), for which the 'regular' Rubin's rules for pooling might apply.
However, these statistics often are overall measures of calibration which do not show specific miss-calibrated regions of the model. For this reason, I'd rather look at a calibration plot. Regrettably, I am clueless as to how to 'pool' the plots or the data behind them (predicted probabilities per individual and observed outcome per individual), and can't find much in the biomedical literature (the field I am familiar with), or here, on CrossValidated. Of course, looking at each imputation dataset's calibration plot could be an answer, but could become quite bothersome (to present) when a lot of imputation sets are created.
I would therefore like to ask whether there are techniques which would result in a calibration plot, pooled after multiple imputation(?)