Eliciting Dirichlet and Gaussian copula prior distributions for multinomial models

In this paper, we propose novel methods of quantifying expert opinion about prior distributions for multinomial models. Two different multivariate priors are elicited using median and quartile assessments of the multinomial probabilities. First, we start by eliciting a univariate beta distribution for the probability of each category. Then we elicit the hyperparameters of the Dirichlet distribution, as a tractable conjugate prior, from those of the univariate betas through various forms of reconciliation using least-squares techniques. However, a multivariate copula function will give a more flexible correlation structure between multinomial parameters if it is used as their multivariate prior distribution. So, second, we use beta marginal distributions to construct a Gaussian copula as a multivariate normal distribution function that binds these marginals and expresses the dependence structure between them. The proposed method elicits a positive-definite correlation matrix of this Gaussian copula. The two proposed methods are designed to be used through interactive graphical software written in Java

Mesenchymal Stromal Cells Derived from the Bone Marrow of Acute Lymphoblastic Leukemia Patients Show Altered BMP4 Production: Correlations with the Course of Disease

The relevance of tumor microenvironment for the development and progression of tumor cells in hematological malignancies has been extensively reported. Identification of factors involved in the information exchange between the malignant cells and the bone marrow mesenchymal stem cells (BM-MSCs) and the knowledge on their functioning may provide important information to eliminate leukemic cells from protective BM niches. We evaluated changes in BM-MSCs obtained from children with acute lymphoblastic leukemia (ALL) at different times in the course of disease. Whereas ALL-MSCs did not exhibit phenotypic changes compared to BM-derived MSCs isolated from healthy donors, they exhibited increased adipogenic capacity. In addition, the viability of healthy CD34+ hematopoietic progenitors was significantly reduced when co-cultured with ALL-MSCs. ALL-MSCs grow less efficiently, although gradually recover normal growth with treatment. Accordingly, proliferation is particularly low in MSCs obtained at diagnosis and in the first days of treatment (+15 days), recovering to control levels after 35 days of treatment. Correlating these results with bone morphogenetic protein 4 (BMP4) production, a molecule demonstrated to affect MSC biology, we found higher production of BMP4 in ALL-MSCs derived from patients over the course of disease but not in those free of leukemia. However, no significant differences in the expression of different members of the BMP4 signaling pathway were observed. Furthermore, an inverse correlation between high levels of BMP4 production in the cultures and MSC proliferation was found, as observed in MSCs derived from patients at diagnosis that produce high BMP4 levels. In addition, co-culturing ALL-MSC with the REH leukemia cell line, but not CD34+ hematopoietic progenitors, powerfully enhanced BMP4 production, suggesting an intimate crosstalk among ALL-MSCs isolated from BM colonized by ALL cells that presumably also occurs in situ conditions. Our data may support the participation of BMP4 in BM niche, but the mechanism remains to be elucidated