BACKGROUND Linkage disequilibrium (LD) is the non-random association between alleles at different loci and remains important for disease mapping studies in humans. A common measure of LD is the sample correlation between indicator variables for alleles at the 2 loci. Knowledge of LD estimate precision may help inform biomedical decisions based on those estimates. OBJECTIVES AND METHODS Variance formulae are obtained for correlation measures of LD in 4 scenarios. These scenarios include data in the form of gametic and genotypic counts, with different assumptions used to simplify the analysis. RESULTS The formulae are expressed as polynomials (or ratios of polynomials) in higher-order disequilibrium coefficients with constants which are functions of the allele frequencies and Hardy-Weinberg disequilibrium coefficients. With genotypic data, the variance is the same as with gametic data when the phase is known and there is random mating. When the phase is unknown, the correlation LD has variance which is twice as large. CONCLUSIONS Symbolic computation proved to be effective in facilitating algebraic derivations which would otherwise have been intractable.

中文翻译：

---

连锁不平衡相关度量的方差公式。

背景技术连锁不平衡（LD）是在不同基因座的等位基因之间的非随机关联，并且对于人类疾病作图研究仍然很重要。LD的常见度量是两个基因座等位基因的指标变量之间的样本相关性。LD估计精度的知识可能有助于基于这些估计的生物医学决策。目的和方法获得方差公式用于LD在4种情况下的相关性度量。这些方案包括配子和基因型计数形式的数据，并使用不同的假设来简化分析。结果公式以高阶不平衡系数的多项式（或多项式的比率）表示，常数是等位基因频率和Hardy-Weinberg不平衡系数的函数。有了基因型数据，当阶段已知且存在随机交配时，方差与配子数据相同。当相位未知时，相关性LD的方差是两倍。结论事实证明，符号计算可有效地简化本来就难以处理的代数推导。