OBJECTIVE We analyze data sets consisting of pedigrees with age at onset of colorectal cancer (CRC) as phenotype. The occurrence of familial clusters of CRC suggests the existence of a latent, inheritable risk factor. We aimed to compute the probability of a family possessing this risk factor as well as the hazard rate increase for these risk factor carriers. Due to the inheritability of this risk factor, the estimation necessitates a costly marginalization of the likelihood. METHODS We propose an improved EM algorithm by applying factor graphs and the sum-product algorithm in the E-step. This reduces the computational complexity from exponential to linear in the number of family members. RESULTS Our algorithm is as precise as a direct likelihood maximization in a simulation study and a real family study on CRC risk. For 250 simulated families of size 19 and 21, the runtime of our algorithm is faster by a factor of 4 and 29, respectively. On the largest family (23 members) in the real data, our algorithm is 6 times faster. CONCLUSION We introduce a flexible and runtime-efficient tool for statistical inference in biomedical event data with latent variables that opens the door for advanced analyses of pedigree data.

中文翻译：

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用和积算法对谱系数据进行有效的最大似然估计。

目的我们分析以大肠癌（CRC）发病表型的家谱为特征的数据集。CRC家族簇的出现表明存在潜在的，可遗传的危险因素。我们旨在计算一个家庭拥有该危险因素的可能性，以及这些危险因素携带者的危险率增加。由于该风险因素的可继承性，因此估算必须将可能性的成本边缘化。方法我们通过在E步骤中应用因子图和求和积算法，提出了一种改进的EM算法。这将计算复杂度从家族成员的数量从指数级降低到线性级。结果我们的算法与CRC风险的模拟研究和真实家庭研究中的直接似然最大化一样精确。对于大小为19和21的250个模拟族，我们算法的运行时间分别快了4倍和29倍。在实际数据中最大的家族（23个成员）上，我们的算法快6倍。结论我们引入了一种灵活且运行时高效的工具，可对具有潜在变量的生物医学事件数据进行统计推断，从而为谱系数据的高级分析打开了方便之门。