In Sheffield Children's NHS Foundation Trust, we already did this in 2013/4 and found that a total position read depth of 18 was the minimum at which one should be reporting [edit: germline] variants.

The general workflow was:

1. obtain a few dozen patient samples that had matched NGS and Sanger data over our regions of interest
2. downsample the aligned BAMs using Picard's DownsampleSam - I believe we chose 75%, 50%, and 25% random reads
3. check the last known position read depth at which all Sanger-confirmed variants were called

That was it. To obtain better precision, one could generate even more downsampled BAMs. Had we had time to publish, my plan was to downsample in 5% decrements, from 100% to 5%.

It was through this process that we also inadvertently 'recovered' the missed GATK variants, i.e., we would frequently encounter Sanger-confirmed variants, not in the original BAM, but in one of the downsampled BAMs.

Example for 75% random reads:

java -jar "${Picard_root}"picard.jar DownsampleSam \
  INPUT=Aligned_Sorted_PCRDuped_FiltMAPQ.bam \ 
  OUTPUT=Aligned_Sorted_PCRDuped_FiltMAPQ_75pcReads.bam \
  RANDOM_SEED=50 PROBABILITY=0.75 \
  VALIDATION_STRINGENCY=SILENT ;

"${SAMtools_root}"samtools index Aligned_Sorted_PCRDuped_FiltMAPQ_75pcReads.bam` ;

Kevin