A new strategy for estimating two-locus recombination fractions under some natural inequality restrictions

Abstract

Linkage analysis is now being widely used to map markers on each chromosome in the human genome, to map genetic diseases, and to identify genetic forms of common diseases. Two-locus linkage analysis and multi-locus analysis have been investigated comprehensively, and many computer programs have been developed to perform linkage analysis. Yet there exists a shortcoming in traditional methods, i.e., the parameter space of two-locus recombination fractions has not been emphasized sufficiently in the usual analyses. In this paper, we propose a new strategy for estimating the two-locus recombination fractions based on data of backcross family in the framework of some natural and necessary parameter restrictions. The new strategy is based on a restricted projection algorithm, which can provide fast reasonable estimates of recombination fraction, and can therefore serve as a superior alternative algorithm. Results obtained from both real and simulated data indicate that the new algorithm performs well in the estimation of recombination fractions and outperforms current methods.

A simple route to maximum-likelihood estimates of two-locus recombination fractions under inequality restrictions

“…We provide in table 1 the resulting parameter estimates and log-likelihood values, plus comparable results from the two methods described by Zhou et al (2008Zhou et al ( , 2011. What is noticeable is that the log-likelihood values achieved by those two methods appear to be very slightly inferior to that found here by constrOptim, although it has to be pointed out that those apparently inferior values were computed from the estimates given to four significant figures by Zhou et al (2008Zhou et al ( , 2011; likelihood values are not given by Zhou Table 1.…”

“…Subsequently, Zhou et al (2011) have described another proposal, a restricted projection algorithm, which also solves the problem subject to the constraints, and converges at quadratic rate. Both methods appear to require for their application considerable mathematical and coding effort; see, for instance, the lengthy and detailed derivations of Zhou et al (2008, p. 4-5) and Zhou et al (2011, p. 277).…”

“…We implement our proposal on the same data as considered by Zhou et al (2008Zhou et al ( , 2011, and compare our parameter estimates and maximized loglikelihood with their results.…”

“…With the starting values g 11 = 0.1 and g 10 = g 01 = 0.2, we used constrOptim to fit the model to the data on a backcross of mice appearing in Clemens et al (2000) and analysed by Zhou et al (2008Zhou et al ( , 2011; i.e., to the counts n = (21, 17, 14, 15). (Note that constrOptim requires starting values to lie in the interior of the feasible set.)…”

“…It requires fewer than 15 lines of R code. Zhou et al (2008Zhou et al ( , 2011 describe, and present two solutions of, a statistical estimation problem arising in genetics which can be summarized briefly as follows. Consider three biallelic loci A, B and C, in that order.…”