Bayesian inference in a hidden stochastic two-compartment model for feline hematopoiesis.

In this paper, we describe a hidden two-compartment stochastic process used to model the kinetics of feline hematopoietic stem cells (HSCs) in continuous time. Because of the experimental design and data collection scheme, the inferential task presents numerous challenges. While the hematopoietic process evolves in continuous time, the observations are collected only at discrete irregular times and are a probabilistic function of the state of the process. In addition, the animals go through an experimental procedure such that their reserve of HSCs is severely depleted at the start of the observation period. This impedes any approximation of the hematopoietic process with a continuous state-space process (normal approximation of the transition probabilities would be inaccurate when the state of the process, i.e. the number of stem cells, is small). We implement a Markov chain Monte Carlo algorithm that allows us to estimate the posterior distribution of the parameters of the hematopoietic process while maintaining its state-space discrete (i.e. without using any approximation). We show the performance of the algorithm on simulated data. Finally, we apply the algorithm to data on multiple experimental cats and provide estimates of the rates of the fates of feline HSCs. The obtained estimates are in agreement with the estimates obtained with different methods published in the medical literature. However, the proposed approach makes a more efficient use of the data and hence the parameter estimates are much more accurate than the one obtained with the methods previously proposed.

Statistical inference in a two-compartment model for hematopoiesis.

We present a method for parameter estimation in a two-compartment hidden Markov model of the first two stages of hematopoiesis. Hematopoiesis is the specialization of stem cells into mature blood cells. As stem cells are not distinguishable in bone marrow, little is known about their behavior, although it is known that they have the ability to self-renew or to differentiate to more specialized (progenitor) cells. We observe progenitor cells in samples of bone marrow taken from hybrid cats whose cells contain a natural binary marker. With data consisting of the changing proportions of this binary marker over time from several cats, estimates for stem cell self-renewal and differentiation parameters are obtained using an estimating equations approach.

In vivo kinetics of murine hemopoietic stem cells.

We used stochastic modeling and computer simulation to study the replication, apoptosis, and differentiation of murine hemopoietic stem cells (HSCs) in vivo. This approach allows description of the behavior of an unobserved population (ie, HSCs) on the basis of the behavior of observed progeny cells (ie, granulocytes and lymphocytes). The results of previous limiting-dilution, competitive-repopulation studies in 44 mice were compared with the results of simulated transplantation studies to identify parameters that led to comparable outcomes. Using this approach, we estimated that murine HSCs replicate (on average) once every 2.5 weeks and that the frequency of murine HSCs is 8 per 10(5) nucleated marrow cells. If it is assumed that short-term repopulating cells are distinct from HSCs, that they contribute to hemopoiesis early after transplantation, and that they are independently regulated, a frequency of 4 HSCs per 10(5) nucleated marrow cells also allows simulations that best approximate the observed data. When stochastic modeling and computer simulation were applied to limiting-dilution, autologous-transplantation studies in cats heterozygous for glucose-6-phosphate-dehydrogenase, different estimates of HSC replication rate (1 per 8.3-10 weeks) and frequency (6 per 10(7) cells) were derived. Therefore, it appears that these parameters vary inversely with increased longevity, size, or both. An implication of these data is that human HSCs may be less frequent and replicate more slowly. These findings on cell kinetics have several implications.

A preliminary statistical examination of the effects of uncertainty and variability on environmental regulatory criteria for ozone.

Basing the quantitative expression of environmental regulatory standards and associated compliance criteria on statistical principles has recently received attention in Europe, most visibly in a study by the UK Royal Commission on Environmental Pollution. These issues are timely for consideration in the USA, where a recent periodic review of National Ambient Air Quality Standards (NAAQS) has led to revision of the regulatory standards for ambient ozone and particulate matter. Salient statistical issues include accounting for errors of the first and second kind due to sampling and measurement error. These issues appear routine statistically and also may seem absent from regulations, but neither is necessarily the case. This paper is directed towards developing a methodology for examining the problem of dealing with uncertainty and variation in environmental regulations and compliance criteria. Our approach is illustrated through statistical analysis of the (old) 1 hour and the (new) 8 hour standards for ambient ozone, based on intensive monitoring in California's San Joaquin Valley during summer 1990 performed under the SARMAP Project. This paper presents preliminary findings based on quantifying measurement error or precision in terms of small-scale spatial and temporal variability, laying the groundwork for future work.

An X chromosome gene regulates hematopoietic stem cell kinetics.

Females are natural mosaics for X chromosome-linked genes. As X chromosome inactivation occurs randomly, the ratio of parental phenotypes among blood cells is approximately 1:1. Recently, however, ratios of greater than 3:1 have been observed in 38-56% of women over age 60. This could result from a depletion of hematopoietic stem cells (HSCs) with aging (and the maintenance of hematopoiesis by a few residual clones) or from myelodysplasia (the dominance of a neoplastic clone). Each possibility has major implications for chemotherapy and for transplantation in elderly patients. We report similar findings in longitudinal studies of female Safari cats and demonstrate that the excessive skewing that develops with aging results from a third mechanism that has no pathologic consequence, hemizygous selection. We show that there is a competitive advantage for all HSCs with a specific X chromosome phenotype and, thus, demonstrate that an X chromosome gene (or genes) regulates HSC replication, differentiation, and/or survival.

Strategies for hematopoietic stem cell gene therapy: insights from computer simulation studies.

We simulated gene therapy using parameters derived from the analysis of autologous transplantation studies in glucose-6-phosphate dehydrogenase heterozygous cats to determine how hematopoietic stem cell (HSC) biology might influence outcomes. Simulation illustrates that a successful experiment can result by chance and may not be the repeated outcome of a specific protocol design or technical approach. As importantly, in many simulated gene therapy experiments where 1, 2, or 6 of 30 transplanted HSC were labeled, there was significant variation in the contribution from marked clones over time. Variability was minimized in simulations in which large numbers of HSC were transplanted. Strategies that may permit consistent clinically successful results are presented. Taken together, these simulation studies demonstrate that the in vivo behavior of HSC must be considered when optimizing approaches to gene therapy in large animals, and perhaps by extension, in humans.

Modelling non-stationary spatial covariance structure from space-time monitoring data.

Accurate interpolation of soil and climate variables at fine spatial scales is necessary for precise field management. Interpolation is needed to produce the input variables necessary for crop modelling. It is also important when deciding on regulations to limit environmental impacts from processes such as nitrate leaching. Non-stationarity may arise due to many factors, including differences in soil type, or heterogeneity in chemical concentrations. Many geostatistical methods make stationarity assumptions. Substantial improvements in interpolation or in the estimation of standard errors may be obtained by using non-stationary models of spatial covariances. This paper presents recent methodological developments for an approach to modelling non-stationary spatial covariance structure through deformations of the geographic coordinate system. This approach was first introduced by Sampson & Guttorp, although the estimation approach is updated in more recent papers. They compute a deformation of the geographic plane so that the spatial covariance structure can be considered stationary in terms of a new spatial coordinate system. This provides a non-stationary model for the spatial covariances between sampled locations and prediction locations. In this paper, we present a cross-validation procedure to avoid over-fitting of the sample dispersions. Results concerning the variability of the spatial covariance estimates are also presented. An example of the modelling of the spatial correlation field of rainfall at small regional scale is presented. Other directions in methodological development, including modelling temporally varying spatial correlation, and approaches to model temporal and spatial correlation are mentioned. Future directions for methodological development are indicated, including the modelling of multivariate processes and the use of external spatially dense covariables. Such covariates are frequently available in precision agriculture.

Evidence that hematopoiesis may be a stochastic process in vivo.

To study the behavior of hematopoietic stem cells in vivo, hematopoiesis was simulated by assuming that all stem cell decisions (that is, replication, apoptosis, initiation of a differentiation/maturation program) were determined by chance. Predicted outcomes from simulated experiments were compared with data obtained in autologous marrow transplantation studies of glucose 6-phosphate dehydrogenase (G6PD) heterozygous female Safari cats. With this approach, we prove that stochastic differentiation can result in the wide spectrum of discrete outcomes observed in vivo, and that clonal dominance can occur by chance. As the analyses also suggest that the frequency of feline hematopoietic stem cells is only 6 per 10(7) nucleated marrow cells, and that sem cells do not replicate on average more frequently than once every three weeks, these large-animal data challenge clinical strategies for marrow transplantation and gene therapy.

Simulation of hematopoiesis: implications for the gene therapy of lysosomal enzyme disorders.

Although the hematopoietic stem cell is an attractive target for gene transfer, little is known about its biology in vivo in large animals (including humans). We have studied the in vivo behavior of hematopoietic stem cells in glucose-6-phosphate dehydrogenase heterozygous (female Safari) cats, and demonstrated that clonal instability persists for up to 4.5 years after autologous marrow transplantation. This contrasts with the 2-6 months of clonal disequilibrium reported in comparable murine studies. Our data also suggest that hematopoietic stem cells do not self-renew more than once every 3 weeks. These data may have relevance for strategies to optimize gene therapy in large animals and, by extension, in humans.

Behavior of hematopoietic stem cells in a large animal.

To study the behavior of hematopoietic stem cells in vivo, we transplanted glucose-6-phosphate dehydrogenase (G6PD) heterozygous (female Safari) cats with small amounts of autologous marrow. The G6PD phenotypes of erythroid burst-forming units and granulocyte/macrophage colony-forming units were repeatedly assayed for 3.5-6 years after transplantation to track contributions of stem cell clones to the progenitor cell compartment. Two phases of stem cell kinetics were observed, which were similar to the pattern reported in comparable murine studies. Initially there were significant fluctuations in contributions of stem cell clones. Later clonal contributions to hematopoiesis stabilized. The initial phase of clonal disequilibrium, however, extended for 1-4.5 years (and not 2-6 months as seen in murine experiments). After this subsided, all progenitor cells from some animals expressed a single parental G6PD phenotype, suggesting that blood cell production could be stably maintained by the progeny of one (or a few) cells. As the hematopoietic demand of a cat (i.e., number of blood cells produced per lifetime) is over 600 times that of a mouse, this provides evidence that an individual hematopoietic stem cell has a vast self-renewal and/or proliferative capacity. The long phase of clonal instability may reflect the time required for stem cells to replicate sufficiently to reconstitute a large stem cell reserve.

Behavior of feline hematopoietic stem cells years after busulfan exposure.

The kinetics of hematopoietic stem cells were investigated in glucose-6-phosphate dehydrogenase (G-6-PD) heterozygous cats treated with dimethylbusulfan. Because of X-chromosome inactivation during embryogenesis, each somatic cell from these animals contains either maternal- or paternal-type G-6-PD. Therefore, all hematopoietic progenitor cells carry the G-6-PD phenotype of the most primitive cell (stem cell) from which they originate. For up to 6.5 years after dimethylbusulfan therapy, we determined the percentages of erythroid and granulocyte/macrophage progenitor cells with each G-6-PD phenotype. Significant variations were seen in studies from five of six cats, showing that the population of stem cells contributing to hematopoiesis was neither large nor constant. With mathematical analyses, we estimated that the proliferative potential of residual stem cells was much less than that of normal stem cells reduced in number by autologous transplantation (Abkowitz et al, Proc Natl Acad Sci USA 87:9062, 1990). There was no evidence for the regeneration of a normal stem cell reserve over time; rather, damage was most pronounced years after dimethylbusulfan exposure. These data may help explain the high clinical incidence of aplastic anemia and myelodysplasia after alkylating agent therapies.

Evidence for the maintenance of hematopoiesis in a large animal by the sequential activation of stem-cell clones.

To test if hematopoiesis can be maintained by the sequential activation of stem-cell clones, we performed autologous marrow transplantations with limited numbers of cells in cats heterozygous for the X chromosome-linked enzyme glucose-6-phosphate dehydrogenase (G6PD) and observed the G6PD phenotypes of erythroid and granulocyte/macrophage progenitors over time. The animals were the female offspring of Geoffroy male and domestic female cats. In repeated studies of marrow from control animals (n = 5) or experimental animals prior to transplantation (n = 3), the percent of progenitors with domestic-type G6PD did not vary. After transplantation, the peripheral blood counts, marrow morphologies, frequencies of progenitors, and progenitor cell cycle kinetics returned to normal. However, abrupt and significant fluctuations were seen in the G6PD type of progenitors from each cat during the 1-1.5 years of observation. These data cannot be explained if there were either a large or constant population of active stem cells and thus imply, in a large-animal system, that hematopoiesis was maintained through clonal succession. A stochastic model was developed to estimate the numbers of active clones and their mean lifetimes.

A stochastic model for haematopoiesis in cats.

Haematopoiesis is the process by which progenitor cells differentiate into competent mature blood cells. Only those cells in the latter stages of haematopoiesis can be observed in vitro, so theories about the early stages of the process cannot be tested directly. Experimental data of bone marrow samples from Safari cats provides evidence for the clonal succession hypothesis of early haematopoiesis. In this paper, a hidden Markov model is constructed to quantify this support. Recursive updating techniques are derived and are used to calculate the likelihood and to construct fitted values for the model. Inference is based on multimodal likelihood surfaces.