Reduction of bias in estimating the frequency of recessive genes

Abstract

The standard approach to estimating the frequency of a completely recessive autosomal gene is to use the maximum-likelihood estimator (MLE), q = square root q2. Since the expectation oof Q using MLE is systematically less than the true value, this estimator always gives a negatively biased estimate of q. Here we describe the bias associated the MLE over a range of q and N values, explore some of the properties of this estimator, and propose new estimators which reduce the bias. We also describe some of the new estimators' properties, as well as the remaining bias associated with them for varying q and N values. We further propose one of these estimators as the one which most effectively reduces bias over a specific q value range of approximately .005 to .05, and which is less biased than JLE over essentially all q and N values. The proposed estimator also is directly compared with MLE in calculating various available estimates of q, demonstrating the percentage of reduction in bias achieved. This reduction varies from negligible for estimates of q above .3 and N greater than 100, to a 23% reduction in bias for a q value of .09 and an N value of 215.