12 research outputs found
A non-Markovian model for cell population growth: speed of convergence and central limit theorem
No full textAbstractIn De Gunst (1989) a stochastic model was developed for the growth of a batch culture of plant cells. In this paper the mathematical properties of the model are considered. We investigate the asymptotic behaviour of the population growth as predicted by the model when the initial cell number of population members tends to infinity. In particular it is shown that the total cell number, which is a non-Markovian counting process, converges almost surely, uniformly on the real line to a non-random function and the rate of convergence is established. Moreover, a central limit theorem is proved. Computer simulations illustrate the behaviour of the process. The model is graphically compared with experimental data
A non-Markovian model for cell population growth: speed of convergence and central limit theorem
No full textIn De Gunst (1989) a stochastic model was developed for the growth of a batch culture of plant cells. In this paper the mathematical properties of the model are considered. We investigate the asymptotic behaviour of the population growth as predicted by the model when the initial cell number of population members tends to infinity. In particular it is shown that the total cell number, which is a non-Markovian counting process, converges almost surely, uniformly on the real line to a non-random function and the rate of convergence is established. Moreover, a central limit theorem is proved. Computer simulations illustrate the behaviour of the process. The model is graphically compared with experimental data.stochastic model population growth non-Markovian counting process almost sure converegence rate of convergence central limit theorem
Wild Bootstrap for Counting Process-Based Statistics
No full textThe wild bootstrap is a popular resampling method in the context of
time-to-event data analyses. Previous works established the large sample
properties of it for applications to different estimators and test statistics.
It can be used to justify the accuracy of inference procedures such as
hypothesis tests or time-simultaneous confidence bands. This paper consists of
two parts: in Part~I, a general framework is developed in which the large
sample properties are established in a unified way by using martingale
structures. The framework includes most of the well-known non- and
semiparametric statistical methods in time-to-event analysis and parametric
approaches. In Part II, the Fine-Gray proportional sub-hazards model
exemplifies the theory for inference on cumulative incidence functions given
the covariates. The model falls within the framework if the data are
censoring-complete. A simulation study demonstrates the reliability of the
method and an application to a data set about hospital-acquired infections
illustrates the statistical procedure.Comment: 2 parts, 115 pages, 2 figures, 13 table
A Non-Markovian Model for Cell Population Growth: Tail Behavior and Duration of the Growth Process
No full textInference via Wild Bootstrap and Multiple Imputation under Fine-Gray Models with Incomplete Data
No full textFine-Gray models specify the subdistribution hazards for one out of multiple
competing risks to be proportional. The estimators of parameters and cumulative
incidence functions under Fine-Gray models have a simpler structure when data
are censoring-complete than when they are more generally incomplete. This paper
considers the case of incomplete data but it exploits the above-mentioned
simpler estimator structure for which there exists a wild bootstrap approach
for inferential purposes. The present idea is to link the methodology under
censoring-completeness with the more general right-censoring regime with the
help of multiple imputation. In a simulation study, this approach is compared
to the estimation procedure proposed in the original paper by Fine and Gray
when it is combined with a bootstrap approach. An application to a data set
about hospital-acquired infections illustrates the method.Comment: 32 pages, 2 figures, 1 tabl
Identification of context-specific gene regulatory networks with GEMULA--Gene Expression Modeling Using LAsso
No full textMotivation: Gene regulatory networks, in which edges between nodes describe interactions between transcriptional regulators and their target genes, determine the coordinated spatiotemporal expression of genes. Especially in higher organisms, context-specific combinatorial regulation by transcription factors (TFs) is believed to determine cellular states and fates. TF-target gene interactions can be studied using high-throughput techniques such as ChIP-chip or ChIP-Seq. These experiments are time and cost intensive, and further limited by, for instance, availability of high affinity TF antibodies. Hence, there is a practical need for methods that can predict TF-TF and TF-target gene interactions in silico, i.e. from gene expression and DNA sequence data alone. We propose GEMULA, a novel approach based on linear models to predict TF-gene expression associations and TF-TF interactions from experimental data. GEMULA is based on linear models, fast and considers a wide range of biologically plausible models that describe gene expression data as a function of predicted TF binding to gene promoters. Results: We show that models inferred with GEMULA are able to explain roughly 70% of the observed variation in gene expression in the yeast heat shock response. The functional relevance of the inferred TF-TF interactions in these models are validated by different sources of independent experimental evidence. We also have applied GEMULA to an in vitro model of neuronal outgrowth. Our findings confirm existing knowledge on gene regulatory interactions underlying neuronal outgrowth, but importantly also generate new insights into the temporal dynamics of this gene regulatory network that can now be addressed experimentally. © The Author 2011. Published by Oxford University Press. All rights reserved
LLM3D: a log-linear modeling-based method to predict functional gene regulatory interactions from genome-wide expression data
No full textAll cellular processes are regulated by condition-specific and time-dependent interactions between transcription factors and their target genes. While in simple organisms, e.g. bacteria and yeast, a large amount of experimental data is available to support functional transcription regulatory interactions, in mammalian systems reconstruction of gene regulatory networks still heavily depends on the accurate prediction of transcription factor binding sites. Here, we present a new method, log-linear modeling of 3D contingency tables (LLM3D), to predict functional transcription factor binding sites. LLM3D combines gene expression data, gene ontology annotation and computationally predicted transcription factor binding sites in a single statistical analysis, and offers a methodological improvement over existing enrichment-based methods. We show that LLM3D successfully identifies novel transcriptional regulators of the yeast metabolic cycle, and correctly predicts key regulators of mouse embryonic stem cell self-renewal more accurately than existing enrichment-based methods. Moreover, in a clinically relevant in vivo injury model of mammalian neurons, LLM3D identified peroxisome proliferator-activated receptor γ (PPARγ) as a neuron-intrinsic transcriptional regulator of regenerative axon growth. In conclusion, LLM3D provides a significant improvement over existing methods in predicting functional transcription regulatory interactions in the absence of experimental transcription factor binding data. © 2011 The Author(s)
Genetic study of the height and weight process during infancy.
No full textLongitudinal height and weight data from 4649 Dutch twin pairs between birth and 2.5 years of age were analyzed. The data were first summarized into parameters of a polynomial of degree 4 by a mixed-effects procedure. Next, the variation and covariation in the parameters of the growth curve (size at one year of age, growth velocity, deceleration of growth, rate of change in deceleration [i.e., jerk] and rate of change in jerk [i.e., snap]) were decomposed into genetic and nongenetic sources. Additionally, the variation in the estimated size at birth and at 2 years of age interpolated from the polynomial was decomposed into genetic and nongenetic components. Variation in growth was best characterized by a genetic model which included additive genetic, common environmental and specific environmental influences, plus effects of gestational age. The effect of gestational age was largest for size at birth, explaining 39% of the variance. The differences between monozygotic and dizygotic twin correlations were largest for size at 1 and 2 years of age and growth velocity of weight, which suggests that these parameters are more influenced by heritability than size at birth, deceleration and jerk. The percentage of variance explained by additive genetic influences for height at 2 years of age was 52% for females and 58% for males. For weight at 2 years of age, heritability was approximately 58% for both sexes. Variation in snap height for males was also mainly influenced by additive genetic factors, while snap for females was influenced by both additive genetic and common environmental factors. The correlations for the additive genetic and common environmental factors for deceleration and snap are large, indicating that these parameters are almost entirely under control of the same additive genetic and common environmental factors. Female jerk and snap, and also female height at birth and height at 2 years of age, are mostly under control of the same additive genetic factor
Identification of candidate transcriptional modulators involved in successful regeneration after nerve injury
No full textSuccessful regeneration of injured neurons requires a complex molecular response that involves the expression, modification and transport of a large number of proteins. The identity of neuronal proteins responsible for the initiation of regenerative neurite outgrowth is largely unknown. Dorsal root ganglion (DRG) neurons display robust and successful regeneration following lesion of their peripheral neurite, whereas outgrowth of central neurites is weak and does not lead to functional recovery. We have utilized this differential response to gain insight in the early transcriptional events associated with successful regeneration. Surprisingly, our study shows that peripheral and central nerve crushes elicit very distinct transcriptional activation, revealing a large set of novel genes that are differentially regulated within the first 24 h after the lesion. Here we show that Ankrd1, a gene known to act as a transcriptional modulator, is involved in neurite outgrowth of a DRG neuron-derived cell line as well as in cultured adult DRG neurons. This gene, and others identified in this study, may be part of the transcriptional regulatory module that orchestrates the onset of successful regeneration
