A new study (link to study itself) which estimates about 400,000 deaths from war related causes plus another 55,000 from related migration in the Iraq War has been published. It gives a lower figure than the previous 2006 study which estimated a death toll of about 655,000. Various government and conservative sources dispute these studies and give much lower figures but lack scientific methodology.
These studies are made by attempting in a sophisticated way to get a good sample of surviving families or relatives and asking about lost family members. That process can be done well but the results cannot include families that are entirely wiped out or otherwise disappear. This means that the prior study is an underestimate to that degree. The prior study did not correct for this effect.
The new study being made by sampling and interviewing after more years have passed is more subject to the problem of not interviewing families which are no longer represented in the sample area. They have attempted in the study to correct for the effect in two ways. First, they estimated a number of households not included because of out migration. They have figures for total out migration and assumed that the households not included were of average size and average probability of migrating. The is a very doubtful assumption in that households who lost members would be made more likely to migrate by the loss itself and by correlated damage to the household in other ways. The size of the household would also be reduced by the loss.
The second correction is to the portion of the study based on interviewing siblings. They used a methodology to allow for sibling sets that were completely wiped out but gave no link to the definition of the methodology in the study. It was stated in the study that 3.7 missing siblings were added to the 2,531 deaths of sibling that the study found. That is a miniscule correction. It must be based on an unlikely assumption that the probabilities of death and other removal from the sample set are independent within each set of siblings.
In my opinion, the reduction in the estimate from the prior study is due to the passage of years making the sample less representative and not due to some improvement in accuracy. I still think that the true number of war deaths from the Iraq War is more than 700,000.