Michael A. Newton Peter Guttorp Sandra Catlin Renato Assunção Janis L. Abkowitz
1995 Journal of the American Statistical Association, 90, 1146--1155.
J. L. Abkowitz and colleagues at the University of Washington have developed an experimental method for studying the kinetics of early hematopoiesis in a hybrid cat. The essence of the method is to analyze G6PD, an enzyme linked to the X-chromosome. The G6PD type of a cell forms a binary marker that is passed down to all its descendant cells. Data record time series of proportions of one G6PD type in cells from the bone marrow, providing information about the number and lifetime of unobservable stem cells. Studies were performed after the autologous transplantation of G6PD heterozygous cats with limited numbers of hematopoietic stem cells. Preliminary analysis of the observed proportions indicates that under these circumstances the proportion of cells with one type of G6PD is not constant over time. A simple stochastic model is used to quantify the relationship between observed proportions and unobserved stem cell populations. The model has a hidden-Markov structure. We develop parameter estimates, confidence sets, and goodness-of-fit tests for this model.
For our simple model, a recursive updating algorithm allows computation of the multi-modal likelihood functions. A similar algorithm produces estimates of the realized Markov process. The parametric bootstrap is used to calibrate likelihood-based confidence sets and to perform simple goodness-of-fit tests. We address the question of whether stem cells have a constant proliferative potential between cats, and we discuss criticisms of the simple model.
Keywords: stem cells, clonal succession, glucose phosphate dehydrogenase, hidden Markov model, recursive updating, parametric bootstrap, overdispersion.