Notes on the Maximum Likelihood Estimation of Haplotype Frequencies

Inferring linkage disequilibrium from non-random samples

BACKGROUND

Linkage disequilibrium (LD) plays a fundamental role in population genetics and in the current surge of studies to screen for subtle genetic variants affecting complex traits. Methods widely implemented in LD analyses require samples to be randomly collected, which, however, are usually ignored and thus raise the general question to the LD community of how the non-random sampling affects statistical inference of genetic association. Here we propose a new approach for inferring LD using a sample un-randomly collected from the population of interest.

RESULTS

Simulation study was conducted to mimic generation of samples with various degrees of non-randomness from the simulated populations of interest. The method developed in the paper outperformed its rivals in adequately estimating the disequilibrium parameters in such sampling schemes. In analyzing a 'case and control' sample with beta-thalassemia, the current method presented robustness to non-random sampling in contrast to two commonly used methods.

CONCLUSIONS

Through an intensive simulation study and analysis of a real dataset, we demonstrate the robustness of the proposed method to non-randomness in sampling schemes and the significant improvement of the method to provide accurate estimates of the disequilibrium parameter. This method provides a route to improve statistical reliability in association studies.

Cubic exact solutions for the estimation of pairwise haplotype frequencies: implications for linkage disequilibrium analyses and a web tool 'CubeX'

BACKGROUND

The frequency of a haplotype comprising one allele at each of two loci can be expressed as a cubic equation (the 'Hill equation'), the solution of which gives that frequency. Most haplotype and linkage disequilibrium analysis programs use iteration-based algorithms which substitute an estimate of haplotype frequency into the equation, producing a new estimate which is repeatedly fed back into the equation until the values converge to a maximum likelihood estimate (expectation-maximisation).

RESULTS

We present a program, "CubeX", which calculates the biologically possible exact solution(s) and provides estimated haplotype frequencies, D', r2 and chi2 values for each. CubeX provides a "complete" analysis of haplotype frequencies and linkage disequilibrium for a pair of biallelic markers under situations where sampling variation and genotyping errors distort sample Hardy-Weinberg equilibrium, potentially causing more than one biologically possible solution. We also present an analysis of simulations and real data using the algebraically exact solution, which indicates that under perfect sample Hardy-Weinberg equilibrium there is only one biologically possible solution, but that under other conditions there may be more.

CONCLUSION

Our analyses demonstrate that lower allele frequencies, lower sample numbers, population stratification and a possible |D'| value of 1 are particularly susceptible to distortion of sample Hardy-Weinberg equilibrium, which has significant implications for calculation of linkage disequilibrium in small sample sizes (eg HapMap) and rarer alleles (eg paucimorphisms, q < 0.05) that may have particular disease relevance and require improved approaches for meaningful evaluation.

Whole genome association study of rheumatoid arthritis using 27 039 microsatellites

A major goal of current human genome-wide studies is to identify the genetic basis of complex disorders. However, the availability of an unbiased, reliable, cost efficient and comprehensive methodology to analyze the entire genome for complex disease association is still largely lacking or problematic. Therefore, we have developed a practical and efficient strategy for whole genome association studies of complex diseases by charting the human genome at 100 kb intervals using a collection of 27,039 microsatellites and the DNA pooling method in three successive genomic screens of independent case-control populations. The final step in our methodology consists of fine mapping of the candidate susceptible DNA regions by single nucleotide polymorphisms (SNPs) analysis. This approach was validated upon application to rheumatoid arthritis, a destructive joint disease affecting up to 1% of the population. A total of 47 candidate regions were identified. The top seven loci, withstanding the most stringent statistical tests, were dissected down to individual genes and/or SNPs on four chromosomes, including the previously known 6p21.3-encoded Major Histocompatibility Complex gene, HLA-DRB1. Hence, microsatellite-based genome-wide association analysis complemented by end stage SNP typing provides a new tool for genetic dissection of multifactorial pathologies including common diseases.