Efficient Maximum Likelihood Estimation for Pedigree Data with the Sum-Product Algorithm

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.

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.

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.

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.