Solving genetic heterogeneity in extended families by identifying sub-types of complex diseases

The study of genetic properties of a disease requires the collection of information concerning the subjects in a set of pedigrees. The main focus of this study was the detection of susceptible genes. However, even with large pedigrees, the heterogeneity of phenotypes in complex diseases such as Schizophrenia, Bipolar and Autism, makes the detection of susceptible genes difficult to accomplish. This is mainly due to a genetic heterogeneity: many genes phenomena are involved in the disease. In order to reduce this heterogeneity, our idea consists in sub-typing the disease and in partitioning the population into more alike sub-groups. We developed a probabilistic model based on a Latent Class Analysis (LCA) that takes into account the familial dependence inside a pedigree, even for large pedigrees. It also takes into account individuals with missing and partially missing measurements. Estimation of model parameters is performed by an EM algorithm, and computations for the E step inside a pedigree are achieved using a pedigree peeling algorithm. When more than one model are fitted, we use model selection strategies such as cross-validation or/and BIC approaches to choose the suitable model among a set of candidates. Moreover, we present a simulation based on a genetic disease class model and we show that our model leads to better individual classification than the model that assumes independence among subjects. An application of our model to a Schizophrenia-Bipolar pedigree data set from Eastern Quebec is also performed.