Bivariate gamma-geometric law and its induced Levy process

In this article we introduce a three-parameter extension of the bivariate exponential-geometric (BEG) law (Kozubowski and Panorska, 2005) [4]. We refer to this new distribution as the bivariate gamma-geometric (BGG) law. A bivariate random vector (X, N) follows the BGG law if N has geometric distribution and X may be represented (in law) as a sum of N independent and identically distributed gamma variables, where these variables are independent of N. Statistical properties such as moment generation and characteristic functions, moments and a variance-covariance matrix are provided. The marginal and conditional laws are also studied. We show that BBG distribution is infinitely divisible, just as the BEG model is. Further, we provide alternative representations for the BGG distribution and show that it enjoys a geometric stability property. Maximum likelihood estimation and inference are discussed and a reparametrization is proposed in order to obtain orthogonality of the parameters. We present an application to a real data set where our model provides a better fit than the BEG model. Our bivariate distribution induces a bivariate Levy process with correlated gamma and negative binomial processes, which extends the bivariate Levy motion proposed by Kozubowski et al. (2008) [6]. The marginals of our Levy motion are a mixture of gamma and negative binomial processes and we named it BMixGNB motion. Basic properties such as stochastic self-similarity and the covariance matrix of the process are presented. The bivariate distribution at fixed time of our BMixGNB process is also studied and some results are derived, including a discussion about maximum likelihood estimation and inference. (C) 2012 Elsevier Inc. All rights reserved.

Transplantation for Autoimmune Diseases in North and South America: A Report of the Center for International Blood and Marrow Transplant Research

Hematopoietic cell transplantation (HCT) is an emerging therapy for patients with severe autoimmune diseases (AID). We report data on 368 patients with AID who underwent HCT in 64 North and South American transplantation centers reported to the Center for International Blood and Marrow Transplant Research between 1996 and 2009. Most of the HCTs involved autologous grafts (n = 339); allogeneic HCT (n = 29) was done mostly in children. The most common indications for HCT were multiple sclerosis, systemic sclerosis, and systemic lupus erythematosus. The median age at transplantation was 38 years for autologous HCT and 25 years for allogeneic HCT. The corresponding times from diagnosis to HCT were 35 months and 24 months. Three-year overall survival after autologous HCT was 86% (95% confidence interval [CI], 81%-91%). Median follow-up of survivors was 31 months (range, 1-144 months). The most common causes of death were AID progression, infections, and organ failure. On multivariate analysis, the risk of death was higher in patients at centers that performed fewer than 5 autologous HCTs (relative risk, 3.5; 95% CI, 1.1-11.1; P = .03) and those that performed 5 to 15 autologous HCTs for AID during the study period (relative risk, 4.2; 95% CI, 1.5-11.7; P = .006) compared with patients at centers that performed more than 15 autologous HCTs for AID during the study period. AID is an emerging indication for HCT in the region. Collaboration of hematologists and other disease specialists with an outcomes database is important to promote optimal patient selection, analysis of the impact of prognostic variables and long-term outcomes, and development of clinical trials. Biol Blood Marrow Transplant 18: 1471-1478 (2012) (C) 2012 Published by Elsevier Inc. on behalf of American Society for Blood and Marrow Transplantation