The Clustering of Infected SIV Cells in Lymphatic Tissue

Here we investigate the clustering of simian immunodeficiency virus (SIV)–infected cells in a lymphatic tissue sample taken from a rhesus macaque to test a spatial proximity model of the spread of infection. We see that standard methods for analysis of the clustering of point processes are not entirely satisfactory for this application, so we define a novel statistic to understand the clustering in the data. This statistic examines how events spread out from certain points deemed cluster centers. Using this statistic, we can demonstrate the statistical significance of the clustering and examine over what distances this clustering is witnessed. We use Bayesian methods to fully assess the uncertainty in the estimation of this statistic by positing a model for the process. (We assume the process is a nonhomogeneous Poisson process with an intensity that is a linear combination of Gaussian densities.) We see that the distances at which clustering is present are consistent with a simple model of SIV spread within the lymph node.

[1]  M. S. Bartlett,et al.  The spectral analysis of two-dimensional point processes , 1964 .

[2]  M. Dietrich,et al.  Immunohistochemical, electron microscopic and in situ hybridization evidence for the involvement of lymphatics in the spread of HIV-1. , 1988, AIDS.

[3]  A. Baddeley,et al.  A cautionary example on the use of second-order methods for analyzing point patterns , 1984 .

[4]  J. MacQueen.  Some methods for classification and analysis of multivariate observations , 1967 .

[5]  J. Ord,et al.  Spatial and temporal analysis in ecology , 1981 .

[6]  T. Mattfeldt.  Stochastic Geometry and Its Applications , 1996 .

[7]  A. F. Smith,et al.  Statistical analysis of finite mixture distributions , 1986 .

[8]  Mike Rees,et al.  5. Statistics for Spatial Data , 1993 .

[9]  B. Ripley.  The Second-Order Analysis of Stationary Point Processes , 1976 .

[10]  Yosihiko Ogata,et al.  Likelihood analysis of spatial inhomogeneity for marked point patterns , 1988 .

[11]  A. Haase,et al.  Tracking Members of the Simian Immunodeficiency Virus deltaB670 Quasispecies Population In Vivo at Single-Cell Resolution , 1998, Journal of Virology.

[12]  A. F. Smith,et al.  Statistical analysis of finite mixture distributions , 1986 .

[13]  A. Raftery,et al.  Model-based Gaussian and non-Gaussian clustering , 1993 .

[14]  Andrew B. Lawson,et al.  On tests for spatial trend in a non-homogeneous Poisson process , 1988 .

[15]  B. Ripley.  Statistical inference for spatial processes , 1990 .

[16]  D. Richman,et al.  Sexual transmission and propagation of SIV and HIV in resting and activated CD4+ T cells. , 1999, Science.

[17]  A. Haase,et al.  Population biology of HIV-1 infection: viral and CD4+ T cell demographics and dynamics in lymphatic tissues. , 1999, Annual review of immunology.

[18]  Robert Haining,et al.  Statistics for spatial data: by Noel Cressie, 1991, John Wiley & Sons, New York, 900 p., ISBN 0-471-84336-9, US $89.95 , 1993 .

[19]  Daryl J. Daley,et al.  An Introduction to the Theory of Point Processes , 2013 .

[20]  A. Gelman,et al.  Estimating the Electoral Consequences of Legislative Redistricting , 1990 .

[21]  É. Oksenhendler,et al.  HIV and T cell expansion in splenic white pulps is accompanied by infiltration of HIV-specific cytotoxic T lymphocytes , 1994, Cell.

[22]  D. Rubin,et al.  Inference from Iterative Simulation Using Multiple Sequences , 1992 .

[23]  D. Rubin,et al.  A method for calibrating false-match rates in record linkage , 1995 .

[24]  G. C. Tiao,et al.  A bayesian approach to some outlier problems. , 1968, Biometrika.

[25]  Z. Grossman,et al.  Multiple modes of cellular activation and virus transmission in HIV infection: a role for chronically and latently infected cells in sustaining viral replication. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[26]  Julian Besag,et al.  The Detection of Clusters in Rare Diseases , 1991 .

[27]  A. Perelson,et al.  HIV-1 Dynamics in Vivo: Virion Clearance Rate, Infected Cell Life-Span, and Viral Generation Time , 1996, Science.