Estimating the size of the dividing stem cell pool after allogeneic bone marrow transplantation

Currently the problem of estimation of the number of pluripotent stem cells reconstituting marrow grafts following bone marrow transplantation, or studies looking at questions of clonal dominance in hematopoietic cell populations, rely on indirect measurement and a simple application of the formula for the sampling variation of a binomial proportion. This approach, from a statistical viewpoint, can be seen to be flawed. It is very easily remedied though and only requires appropriate use of variance stabilizing transformations. These lead to a very simple estimator for the number of hematopoietic stem cells involved in repopulating the marrow and require little in the way of additional calculation. We give the distribution theory for this estimator as well as simple approximations for practical application. As an illustration we rework data recently gathered to address the question as to whether or not reconstitution of marrow grafts in the clinical setting is oligoclonal.