ORDERING GENES - CONTROLLING THE DECISION-ERROR PROBABILITIES

Determination of the relative gene order on chromosomes is of critical importance in the construction of human gene maps. In this paper we d evelop a sequential algorithm for gene ordering. We start by comparing three sequential procedures to order three genes on the basis of Baye sian posterior probabilities, maximum-likelihood ratio, and minimal re combinant class. In the second part of the paper we extend sequential procedure based on the posterior probabilities to the general case of g genes. We present a theorem that states that the predicted average p robability of committing a decision error, associated with a Bayesian sequential procedure that accepts the hypothesis of a gene-order confi guration with posterior probability equal to or greater than pi, is s maller than 1 - pi. This theorem holds irrespective of the number of genes, the genetic model, and the source of genetic information. The t heorem is an extension of a classical result of Wald, concerning the s um of the actual and the nominal error probabilities in the sequential probability ratio test of two hypotheses. A stepwise strategy for ord ering a large number of genes, with control over the decision-error pr obabilities, is discussed. An asymptotic approximation is provided, wh ich facilitates the calculations with existing computer software for g ene mapping, of the posterior probabilities of an order and the error probabilities. We illustrate with some simulations that the stepwise o rdering is an efficient procedure.