Semiparametric method for estimating paleodemographic profiles from age indicator data.

This paper addresses the problem of estimating an age-at-death distribution or paleodemographic profile from osteological data. It is demonstrated that the classical two-stage procedure whereby one first constructs estimates of age-at-death of individual skeletons and then uses these age estimates to obtain a paleodemographic profile is not a correct approach. This is a consequence of Bayes' theorem. Instead, we demonstrate a valid approach that proceeds from the opposite starting point: given skeletal age-at-death, one first estimates the probability of assigning the skeleton into a specific osteological age-indicator stage. We show that this leads to a statistically valid method for obtaining a paleodemographic profile, and moreover, that valid individual age estimation itself requires a demographic profile and therefore is done subsequent to its construction. Individual age estimation thus becomes the last rather than the first step in the estimation procedure. A central concept of our statistical approach is that of a weight function. A weight function is associated with each osteological age-indicator stage or category, and provides the probability that a specific age indicator stage is observed, given age-at-death of the individual. We recommend that weight functions be estimated nonparametrically from a reference data set. In their entirety, the weight functions characterize the relevant stochastic properties of a chosen age indicator. For actual estimation of the paleodemographic profile, a parametric age distribution in the target sample is assumed. The maximum likelihood method is used to identify the unknown parameters of this distribution. As some components are estimated nonparametrically, one then has a semiparametric model. We show how to obtain valid estimates of individual age-at-death, confidence regions, and goodness-of-fit tests. The methods are illustrated with both real and simulated data.     

Multi-type Galton-Watson process as a model for proliferating human tumour cell populations derived from stem cells: estimation of stem cell self-renewal probabilities in human ovarian carcinomas

A mathematical model for proliferation of tumour cell populations is developed. The cell population is assumed to be organized in a hierarchy of decreasing proliferative potential and increasing degree of differentiation. Using some elements of the theory of Multi-type Galton-Watson processes, a method is proposed for the estimation of Psr, the probability of self-renewal of tumour stem cells, from the experimental distribution of clonal unit sizes obtained in cell culture studies. Six data sets from patients with advanced adenocarcinoma of the ovary are used to demonstrate the method. Reasonable estimates are obtained, and the theoretical colony size distributions predicted by the model appear to be in good qualitative agreement with the experimental ones, and lend support to a stem cell model of tumour growth. The possible significance of Psr as a prognostic factor is briefly discussed.     

The application of kinematic equations for the study of cell turnover

Cell turnover in renewing populations is accompanied by cell displacement from a site where cells are formed to a location where they are eliminated. Cell displacement reflects genuine streaming, proceeding along a trajectory denominated as tissue radius. In the sagittally sectioned gastro-intestinal crypt the radius extends along one of its cell columns. In each column the cell locations are numbered so that the crypt origin resides at location 1. Since the cell proceeds from the first location and outward, given two locations i and j such that j greater than i, the cell at j is older or more differentiated than the cell at location i, or more generally, state j represents the future state of i while state i represents a past stage for j. Cell displacement on the radius depends solely upon cell production and the acceleration of a cell through location i equals the cell production rate there. Its velocity may be represented by kinematic equations which in the present context acquire dual meaning: either describing cell displacement, or cell production associated with cell displacement. Cell velocities may be derived by following a labelled cell with time or from density distributions of labelled cells along the tissue radius. The first approach is essentially kinematic, while the second regards the density distribution as an analog of mechanical work and since work involves displacement, velocity (and cell production) is derivable from the density distribution. The two estimates are denominated here as time and space estimates. The second approach is essentially morphological, and may be applied during routine examination of histopathological slide and even be computerized.(ABSTRACT TRUNCATED AT 250 WORDS)     

Multi-Type Galton-Watson Process As A Model For Proliferating Human Tumour Cell Populations Derived From Stem Cells: Estimation of Stem Cell Self-Renewal Probabilities In Human Ovarian Carcinomas

Abstract. A mathematical model for proliferation of tumour cell populations is developed. the cell population is assumed to be organized in a hierarchy of decreasing proliferative potential and increasing degree of differentiation. Using some elements of the theory of Multi-type Galton-Watson processes, a method is proposed for the estimation of P_sr, the probability of self-renewal of tumour stem cells, from the experimental distribution of clonal unit sizes obtained in cell culture studies. Six data sets from patients with advanced adenocarcinorna of the ovary are used to demonstrate the method. Reasonable estimates are obtained, and the theoretical colony size distributions predicted by the model appear to be in good qualitative agreement with the experimental ones, and lend support to a stem cell model of tumour growth. the possible significance of P_sr as a prognostic factor is briefly discussed.     

Nonlinear Dual Reconstruction of SPECT Activity and Attenuation Images

In single photon emission computed tomography (SPECT), accurate attenuation maps are needed to perform essential attenuation compensation for high quality radioactivity estimation. Formulating the SPECT activity and attenuation reconstruction tasks as coupled signal estimation and system parameter identification problems, where the activity distribution and the attenuation parameter are treated as random variables with known prior statistics, we present a nonlinear dual reconstruction scheme based on the unscented Kalman filtering (UKF) principles. In this effort, the dynamic changes of the organ radioactivity distribution are described through state space evolution equations, while the photon-counting SPECT projection data are measured through the observation equations. Activity distribution is then estimated with sub-optimal fixed attenuation parameters, followed by attenuation map reconstruction given these activity estimates. Such coupled estimation processes are iteratively repeated as necessary until convergence. The results obtained from Monte Carlo simulated data, physical phantom, and real SPECT scans demonstrate the improved performance of the proposed method both from visual inspection of the images and a quantitative evaluation, compared to the widely used EM-ML algorithms. The dual estimation framework has the potential to be useful for estimating the attenuation map from emission data only and thus benefit the radioactivity reconstruction.     

Cell kinetics in a tumour cord

In some tumours, the viable cells grow around blood vessels forming cylindrical structures called tumour cords, which are surrounded by regions of necrosis. In the present paper, we propose a mathematical model for the cell kinetics in a tumour cord at the stationary state. Both proliferating cells and quiescent cells are considered, and the proliferating cell population is structured by age. Cell migration towards cord periphery is accounted for from a continuum viewpoint. The age distribution of proliferating cells, the fraction of cells in S phase, the growth fraction and the velocity along the cord radius are computed. The predictions of the model are compared with literature data obtained from two experimental rat hepatomas. The model was used to compute the profile of the oxygen tension within the cord. Possible modifications and extensions are also presented.     

Small area estimation for semicontinuous skewed spatial data: An application to the grape wine production in Tuscany

Linear‐mixed models are frequently used to obtain model‐based estimators in small area estimation (SAE) problems. Such models, however, are not suitable when the target variable exhibits a point mass at zero, a highly skewed distribution of the nonzero values and a strong spatial structure. In this paper, a SAE approach for dealing with such variables is suggested. We propose a two‐part random effects SAE model that includes a correlation structure on the area random effects that appears in the two parts and incorporates a bivariate smooth function of the geographical coordinates of units. To account for the skewness of the distribution of the positive values of the response variable, a Gamma model is adopted. To fit the model, to get small area estimates and to evaluate their precision, a hierarchical Bayesian approach is used. The study is motivated by a real SAE problem. We focus on estimation of the per‐farm average grape wine production in Tuscany, at subregional level, using the Farm Structure Survey data. Results from this real data application and those obtained by a model‐based simulation experiment show a satisfactory performance of the suggested SAE approach.     

Identification of a multihit model for nonhomogeneous cell population]

A generalized multihit-multitarget model for a nonhomogeneous, with respect to radiosensitivity, population of irradiated cells is presented. The least squares and the maximum likelihood estimation of the model parameters is given. The estimates quality is evaluated by the computer-based study. The results obtained show the possibility of the parametric identification of cell radiosensitivity distribution according to the "dose-response" data.     

Analysis of number, size and distribution patterns of lipid vacuoles in benign and malignant mesothelial cells

A quantitative analysis of the lipid vacuoles in benign hypertrophic and neoplastic mesothelial cells, using a size-independent distribution index, showed that computer-assisted image analysis for distribution patterns of cytoplasmic components can aid in distinguishing benign from malignant cells. Benign mesothelial cells had fewer lipid vacuoles, which were smaller and predominantly found around the nuclei. It is argued that, due to the high surface tension in the lipid vacuoles, the largest vacuoles are found in the center of the cells, which is the least flattened part of the air-dried mesothelial cells. It seems likely that the distribution pattern of rigid substructures, such as lipid vacuoles, varies between histologic and cytologic material as well as between cells processed by different cytologic methods with various cell-flattening artifacts. The study of the distribution of cytoplasmic components that differ in size was enhanced by using the defined size-independent distribution index, which incorporates the radius of the cell, the radius of the vacuoles and their respective centers of gravity.     

Application of Most-Probable-Number Statistics to Direct Enumeration of Microorganisms

A novel method for rapid determination of total microbial cell numbers was investigated. The method involves the application of most-probable-number estimation statistics to direct microscopic counting of microbial cells by using a particle sizing graticule. Its accuracy and reliability were tested with computer simulations of bacterial cell distributions encountered in ecological studies. Good estimates of cell numbers were obtained when the cell density varied from 3 to 6,000 cells per field, i.e., over 3 orders of magnitude. Low levels of contagion did not markedly influence cell estimates, although high levels, corresponding to discrete scattered microcolonies, did. However, these could be recognized visually. Estimates of cell numbers in Breed smears confirmed its speed and good correlation with the standard quadrat counting technique under real experimental conditions.     

Predicting global abundance of a threatened species from its occurrence: implications for conservation planning

Aim Global abundance is an important characteristic of a species that is correlated with geographical distribution and body size. Despite its importance these estimates are not available since reliable field estimates are either expensive or difficult to obtain. Based on the relationship between a species’ local abundance and distribution, some authors propose that abundance can be obtained through spatial distribution data from maps plotted at different scales. This has never been tested over the entire geographical range of a species. Thus, the aim of this study was to estimate global abundance of the Neotropical primate Brachyteles hypoxanthus (northern muriqui) and compare the results with available field estimates. Location From southern Bahia to Minas Gerais and Espírito Santo states, in the Brazilian Atlantic rain forest. Methods We compiled 25 recent occurrence localities of B. hypoxanthus and plotted them in grid cells of five different sizes (1, 25, 50, 75 and 100 km per side) to evaluate the performance and accuracy of abundance estimates over a wide range of scales. The abundance estimates were obtained by the negative binomial distribution (NBD) method and corrected by average group size to take into account primate social habits. To assess the accuracy of the method, the predicted abundances were then compared to recent independent field estimates. Results The NBD estimates were quite accurate in predicting B. hypoxanthus global abundance, once the gregarious habits of this species are taken into account. The predicted abundance estimates were not statistically different from those obtained from field estimates. Main conclusions The NBD method seems to be a quick and reliable approach to estimate species abundance once several limiting factors are taken into account, and can greatly impact conservation planning, but further applications in macroecological and ecological theory testing needs improvement of the method.     

Hidden population size estimation and diagnostics using two respondent-driven samples with applications in Armenia

Estimating the size of hidden populations is essential to understand the magnitude of social and healthcare needs, risk behaviors, and disease burden. However, due to the hidden nature of these populations, they are difficult to survey, and there are no gold standard size estimation methods. Many different methods and variations exist, and diagnostic tools are needed to help researchers assess method-specific assumptions as well as compare between methods. Further, because many necessary mathematical assumptions are unrealistic for real survey implementation, assessment of how robust methods are to deviations from the stated assumptions is essential. We describe diagnostics and assess the performance of a new population size estimation method, capture–recapture with successive sampling population size estimation (CR-SS-PSE), which we apply to data from 3 years of studies from three cities and three hidden populations in Armenia. CR-SS-PSE relies on data from two sequential respondent-driven sampling surveys and extends the successive sampling population size estimation (SS-PSE) framework by using the number of individuals in the overlap between the two surveys and a model for the successive sampling process to estimate population size. We demonstrate that CR-SS-PSE is more robust to violations of successive sampling assumptions than SS-PSE. Further, we compare the CR-SS-PSE estimates to population size estimations using other common methods, including unique object and service multipliers, wisdom of the crowd, and two-source capture–recapture to illustrate volatility across estimation methods.     

Oxygen diffusivity in gel beads containing viable cells

This article proposes a simple steady-state method for measuring the effective diffusion coefficient of oxygen (D(e)) in gel beads entrapping viable cells. We applied this method to the measurement of D(e) in Ca- and Ba-alginate gel beads entrapping Saccharomyces cerevisiae and Pseudomonas ovalis. The diffusivity of oxygen through gel beads containing viable cells was measured within an accuracy of +/-7% and found not to be influenced by cell density (0-30 g/L gel), cell type, and cell viability in gel beads. The oxygen diffusivity in the Ca-alginate gel beads was superior to that of the Ba-alginate gel beads, and the D(e) in the Ca-alginate gel beads nearly equalled the molecular diffusion coefficient in the liquid containing the gel beads. The oxygen concentration profile in a single Ca-alginate gel bead was calculated and compared to the distribution of mycelia of Aspergillus awamori grown in that gel bead. This procedure indicated that the oxygen concentration profile is useful for the estimation of the thickness of the cell layer in a gel bead. Numerical investigation revealed that high effectiveness factors, greater than 0.8, could be obtained using microgel beads with a radius of 0.25 mm.     

Suitability of flow cytometry for estimating bacterial biovolume in natural plankton samples: comparison with microscopy data

The relationship between flow cytometry data and epifluorescence microscopy measurements was assessed in bacterioplankton samples from 80 lakes to estimate bacterial biovolume and cell size distribution. The total counts of 4',6'-diamidino-2-phenylindole-stained cells estimated by both methods were significantly related, and the slope of their linear regression was not significantly different from 1, indicating that both methods produce very similar estimates of bacterial abundance. The relationships between side scatter (SSC) and 4',6'-diamidino-2-phenylindole fluorescence and cell volume (microscopy values) were improved by binning of the data in three frequency classes for each, but further increases in the number of classes did not improve these relationships. Side scatter was the best cell volume predictor, and significant relationships were observed between the SSC classes and the smallest (R2 = 0.545, P < 0.001, n = 80) and the largest (R2 = 0.544, P < 0.001, n = 80) microscopy bacterial-size classes. Based on these relationships, a reliable bacterial biomass estimation was obtained from the SSC frequency classes. Our study indicates that flow cytometry can be used to properly estimate bacterioplankton biovolume, with an accuracy similar to those of more time-consuming microscopy methods.     

Comparison of analytical and inverse finite element approaches to estimate cell viscoelastic properties by micropipette aspiration

The viscoelastic properties of cells are important in predicting cell deformation under mechanical loading and may reflect cell phenotype or pathological transition. Previous studies have demonstrated that viscoelastic parameters estimated by finite element (FE) analyses of micropipette aspiration (MA) data differ from those estimated by the analytical half-space model. However, it is unclear whether these differences are statistically significant, as previous studies have been based on average cell properties or parametric analyses that do not reflect the inherent experimental and biological variability of real experimental data. To determine whether cell material parameters estimated by the half-space model are significantly different from those predicted by the FE method, we implemented an inverse FE method to estimate the viscoelastic parameters of a population of primary porcine aortic valve interstitial cells tested by MA. We found that inherent differences between the analytical and inverse FE estimation methods resulted in statistically significant differences in individual cell properties. However, in cases with small pipette to cell radius ratios and short loading periods, model-dependent differences were masked by experimental and cell-to-cell variability. Analytical models that account for finite cell-size and loading rate further relaxed the experimental conditions for which accurate cell material parameter estimates could be obtained. These data provide practical guidelines for analysis of MA data that account for the wide range of conditions encountered in typical experiments.     

Estimating species trees using approximate Bayesian computation

Development of methods for estimating species trees from multilocus data is a current challenge in evolutionary biology. We propose a method for estimating the species tree topology and branch lengths using approximate Bayesian computation (ABC). The method takes as data a sample of observed rooted gene tree topologies, and then iterates through the following sequence of steps: First, a randomly selected species tree is used to compute the distribution of rooted gene tree topologies. This distribution is then compared to the observed gene topology frequencies, and if the fit between the observed and the predicted distributions is close enough, the proposed species tree is retained. Repeating this many times leads to a collection of retained species trees that are then used to form the estimate of the overall species tree. We test the performance of the method, which we call ST-ABC, using both simulated and empirical data. The simulation study examines both symmetric and asymmetric species trees over a range of branch lengths and sample sizes. The results from the simulation study show that the model performs very well, giving accurate estimates for both the topology and the branch lengths across the conditions studied, and that a sample size of 25 loci appears to be adequate for the method. Further, we apply the method to two empirical cases: a 4-taxon data set for primates and a 7-taxon data set for yeast. In both cases, we find that estimates obtained with ST-ABC agree with previous studies. The method provides efficient estimation of the species tree, and does not require sequence data, but rather the observed distribution of rooted gene topologies without branch lengths. Therefore, this method is a useful alternative to other currently available methods for species tree estimation.     

Estimating effect sizes of differentially expressed genes for power and sample-size assessments in microarray experiments

Summary In microarray screening for differentially expressed genes using multiple testing, assessment of power or sample size is of particular importance to ensure that few relevant genes are removed from further consideration prematurely. In this assessment, adequate estimation of the effect sizes of differentially expressed genes is crucial because of its substantial impact on power and sample‐size estimates. However, conventional methods using top genes with largest observed effect sizes would be subject to overestimation due to random variation. In this article, we propose a simple estimation method based on hierarchical mixture models with a nonparametric prior distribution to accommodate random variation and possible large diversity of effect sizes across differential genes, separated from nuisance, nondifferential genes. Based on empirical Bayes estimates of effect sizes, the power and false discovery rate (FDR) can be estimated to monitor them simultaneously in gene screening. We also propose a power index that concerns selection of top genes with largest effect sizes, called partial power. This new power index could provide a practical compromise for the difficulty in achieving high levels of usual overall power as confronted in many microarray experiments. Applications to two real datasets from cancer clinical studies are provided.     

Robust estimation of mean and dispersion functions in extended generalized additive models

Generalized linear models are a widely used method to obtain parametric estimates for the mean function. They have been further extended to allow the relationship between the mean function and the covariates to be more flexible via generalized additive models. However, the fixed variance structure can in many cases be too restrictive. The extended quasilikelihood (EQL) framework allows for estimation of both the mean and the dispersion/variance as functions of covariates. As for other maximum likelihood methods though, EQL estimates are not resistant to outliers: we need methods to obtain robust estimates for both the mean and the dispersion function. In this article, we obtain functional estimates for the mean and the dispersion that are both robust and smooth. The performance of the proposed method is illustrated via a simulation study and some real data examples.     

Elevated substitution rates estimated from ancient DNA sequences

Ancient DNA sequences are able to offer valuable insights into molecular evolutionary processes, which are not directly accessible via modern DNA. They are particularly suitable for the estimation of substitution rates because their ages provide calibrating information in phylogenetic analyses, circumventing the difficult task of choosing independent calibration points. The substitution rates obtained from such datasets have typically been high, falling between the rates estimated from pedigrees and species phylogenies. Many of these estimates have been made using a Bayesian phylogenetic method that explicitly accommodates heterochronous data. Stimulated by recent criticism of this method, we present a comprehensive simulation study that validates its performance. For datasets of moderate size, it produces accurate estimates of rates, while appearing robust to assumptions about demographic history. We then analyse a large collection of 749 ancient and 727 modern DNA sequences from 19 species of animals, plants and bacteria. Our new estimates confirm that the substitution rates estimated from ancient DNA sequences are elevated above long-term phylogenetic levels.     

Broader utilization of origins of DNA replication in cancer cell lines along a 78 kb region of human chromosome 2q34

Human DNA replication depends on the activation of thousands of origins distributed within the genome. The actual distribution of origins is not known, nor whether this distribution is unique to a cell type, or if it changes with the proliferative state of the cell. In this study, we have employed a real‐time PCR‐based nascent strand DNA abundance assay, to determine the location of origins along a 78 kb region on Chr2q34. Preliminary studies using nascent DNA strands isolated from either HeLa and normal skin fibroblast cells showed that in both cell lines peaks of high origin activity mapped in similar locations. However, the overall origin profile in HeLa cells corresponded to broad origin activation zones, whereas in fibroblasts a more punctuated profile of origin activation was observed. To investigate the relevance of this differential origin profile, we compared the origin distribution profiles in breast cancer cell lines MDA‐MB‐231, BT‐474, and MCF‐7, to their normal counterpart MCF‐10A. In addition, the CRL7250 cell line was also used as a normal control. Our results validated our earlier observation and showed that the origin profile in normal cell lines exhibited a punctuated pattern, in contrast to broader zone profiles observed in the cancer cell lines. A quantitative analysis of origin peaks revealed that the number of activated origins in cancer cells is statistically larger than that obtained in normal cells, suggesting that the flexibility of origin usage is significantly increased in cancer cells compared to their normal counterparts. J. Cell. Biochem. 113: 132–140, 2012. © 2011 Wiley Periodicals, Inc.