## Abstract

In a registry of volunteer bone marrow donors, the relation between registry size and probability of finding an exact or partial match for a random recipient cannot be theoretically derived because it depends on specifics of the human leukocyte antigen (HLA) haplotype frequencies in the donor and recipient populations. The relation must be explicitly calculated using empirically determined HLA haplotype frequency data for all possible pairings between a donor and a recipient population. This report describes a general solution to this problem. The method shows that the relation of the probability of matching to registry size is sigmoidal, with small increases in probability at the extremes of registry size and a middle range of registry size within which the probability of matching increases most sharply. This range determines the approximate size of the most cost-effective registry. In addition, for any pairing of donor and recipient populations, there is a maximum probability of identifying a match of a given quality for a random recipient, which cannot be exceeded even if registry size were infinite. This upper limit is a function of the frequency of blank (or unknown) alleles in the donor and recipient populations; the higher that frequency, the lower the maximum probability of achieving any given quality of match. The determinants of the probability of achieving a given quality of match with a given registry size are (1) the genetic heterogeneity within the recipient and donor populations, which increases the registry size required to achieve a given probability of matching, and (2) the degree of genetic homology between the donor and recipient populations, which increases the maximum probability of matching and also lowers registry size requirements. The method described here can be used to estimate donor pool size requirements using any donor and recipient populations for which HLA frequency data are available.

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