MLEP: an R package for exploring the maximum likelihood estimates of penetrance parameters

Abstract

Background: Linkage analysis is a useful tool for detecting genetic variants that regulate a trait of interest, especially genes associated with a given disease. Although penetrance parameters play an important role in determining gene location, they are assigned arbitrary values according to the researcher's intuition or as estimated by the maximum likelihood principle. Several methods exist by which to evaluate the maximum likelihood estimates of penetrance, although not all of these are supported by software packages and some are biased by marker genotype information, even when disease development is due solely to the genotype of a single allele.

Findings: Programs for exploring the maximum likelihood estimates of penetrance parameters were developed using the R statistical programming language supplemented by external C functions. The software returns a vector of polynomial coefficients of penetrance parameters, representing the likelihood of pedigree data. From the likelihood polynomial supplied by the proposed method, the likelihood value and its gradient can be precisely computed. To reduce the effect of the supplied dataset on the likelihood function, feasible parameter constraints can be introduced into maximum likelihood estimates, thus enabling flexible exploration of the penetrance estimates. An auxiliary program generates a perspective plot allowing visual validation of the model's convergence. The functions are collectively available as the MLEP R package.

Conclusions: Linkage analysis using penetrance parameters estimated by the MLEP package enables feasible localization of a disease locus. This is shown through a simulation study and by demonstrating how the package is used to explore maximum likelihood estimates. Although the input dataset tends to bias the likelihood estimates, the method yields accurate results superior to the analysis using intuitive penetrance values for disease with low allele frequencies. MLEP is part of the Comprehensive R Archive Network and is freely available at http://cran.r-project.org/web/packages/MLEP/index.html.

Figure 1

Perspective plot of the log likelihood surface of the simulation pedigree data with γ = 0.188. The simulated pedigree dataset is generated assuming penetrance values 0.95, 0.7, and 0, and disease allele frequency 0.0001. The likelihood of the simulated pedigree data is evaluated with frequency assigned to 0.0001, and the penetrances are estimated by the MLEP package. Fixing γ at its estimate 0.188, the log likelihood surface is drawn on a limited region reflecting the parameter constraint α ≥ β. The maximum appears near those of the other two maximum likelihood estimates (α,β) = (0.970,0.943).

Figure 2

Perspective plot of the log likelihood surface of the simulation pedigree data with γ = 0.003. The same likelihood polynomial as that of Figure 1 is plotted with the γpenetrance estimate fixed at 0.003. The penetrance estimates are evaluated employing a parameter constraint 0 ≤ γ ≤ 0.01. The maximum appears near those of the other two estimates (α,β) = (0.875,0.759).