Numerous statistical methods have been developed to explore genomic imprinting and maternal effects, which are causes of parent-of-origin patterns in complex human diseases. However, most of them either only model one of these two confounded epigenetic effects, or make strong yet unrealistic assumptions about the population to avoid over-parameterization. A recent partial likelihood method (LIME) can identify both epigenetic effects based on case-control family data without those assumptions. Theoretical and empirical studies have shown its validity and robustness. However, because LIME obtains parameter estimation by maximizing partial likelihood, it is interesting to compare its efficiency with full likelihood maximizer. To overcome the difficulty in over-parameterization when using full likelihood, in this study we propose a Monte Carlo Expectation Maximization (MCEM) method to detect imprinting and maternal effects jointly. Those unknown mating type probabilities, the nuisance parameters, can be considered as latent variables in EM algorithm. Monte Carlo samples are used to numerically approximate the expectation function that cannot be solved algebraically. Our simulation results show that though this MCEM algorithm takes longer computational time, and can give higher bias in some simulations compared to LIME, it can generally detect both epigenetic effects with higher power and smaller standard error which demonstrates that it can be a good complement of LIME method.

翻译：许多统计方法已被开发用于探索基因组印记和母体效应——这两种是复杂人类疾病中亲本起源模式的成因。然而，大多数方法要么仅对这两种混淆的表观遗传效应中的一种进行建模，要么为避免过度参数化而对群体做出强烈且不切实际的假设。近期一种基于偏似然的方法（LIME）可在无需这些假设的情况下，利用病例-对照家庭数据识别这两种表观遗传效应。理论和实证研究已证明其有效性和稳健性。然而，由于LIME通过最大化偏似然来获取参数估计，将其效率与全似然最大化方法进行比较具有重要价值。为克服使用全似然时过度参数化的难题，本研究提出一种蒙特卡洛期望最大化（MCEM）方法，用于联合检测印记效应与母体效应。那些未知的婚配类型概率（即冗余参数）可在EM算法中被视为潜在变量。通过蒙特卡洛样本对无法代数求解的期望函数进行数值近似。仿真结果表明，尽管与LIME相比，该MCEM算法计算时间更长，且在某些模拟中偏差更大，但其通常能以更高的统计检验力和更小的标准误检测两种表观遗传效应，证明其可作为LIME方法的有力补充。