Effect of Variable Selection Strategy on the Performance of Prognostic Models When Using Multiple Imputation

BACKGROUND: Variable selection is an important issue when developing prognostic models. Missing data occur frequently in clinical research. Multiple imputation is increasingly used to address the presence of missing data in clinical research. The effect of different variable selection strategies with multiply imputed data on the external performance of derived prognostic models has not been well examined. METHODS AND RESULTS: We used backward variable selection with 9 different ways to handle multiply imputed data in a derivation sample to develop logistic regression models for predicting death within 1 year of hospitalization with an acute myocardial infarction. We assessed the prognostic accuracy of each derived model in a temporally distinct validation sample. The derivation and validation samples consisted of 11524 patients hospitalized between 1999 and 2001 and 7889 patients hospitalized between 2004 and 2005, respectively. We considered 41 candidate predictor variables. Missing data occurred frequently, with only 13% of patients in the derivation sample and 31% of patients in the validation sample having complete data. Regardless of the significance level for variable selection, the prognostic model developed using only the complete cases in the derivation sample had substantially worse performance in the validation sample than did the models for which variables were selected using the multiply imputed versions of the derivation sample. The other 8 approaches to handling multiply imputed data resulted in prognostic models with performance similar to one another. CONCLUSIONS: Ignoring missing data and using only subjects with complete data can result in the derivation of prognostic models with poor performance. Multiple imputation should be used to account for missing data when developing prognostic models

Three dimensional optical imaging of blood volume and oxygenation in the neonatal brain

Optical methods provide a means of monitoring cerebral oxygenation in newborn infants at risk of brain injury. A 32-channel optical imaging system has been developed with the aim of reconstructing three-dimensional images of regional blood volume and oxygenation. Full image data sets were acquired from 14 out of 24 infants studied; successful images have been reconstructed in 8 of these infants. Regional variations in cerebral blood volume and tissue oxygen saturation are present in healthy preterm infants. In an infant with a large unilateral intraventricular haemorrhage, a corresponding region of low oxygen saturation was detected. These results suggest that optical tomography may provide an appropriate technique for investigating regional cerebral haemodynamics and oxygenation at the cotside. (c) 2006 Elsevier Inc. All rights reserved

Regulatory control and the costs and benefits of biochemical noise

Experiments in recent years have vividly demonstrated that gene expression can be highly stochastic. How protein concentration fluctuations affect the growth rate of a population of cells, is, however, a wide open question. We present a mathematical model that makes it possible to quantify the effect of protein concentration fluctuations on the growth rate of a population of genetically identical cells. The model predicts that the population's growth rate depends on how the growth rate of a single cell varies with protein concentration, the variance of the protein concentration fluctuations, and the correlation time of these fluctuations. The model also predicts that when the average concentration of a protein is close to the value that maximizes the growth rate, fluctuations in its concentration always reduce the growth rate. However, when the average protein concentration deviates sufficiently from the optimal level, fluctuations can enhance the growth rate of the population, even when the growth rate of a cell depends linearly on the protein concentration. The model also shows that the ensemble or population average of a quantity, such as the average protein expression level or its variance, is in general not equal to its time average as obtained from tracing a single cell and its descendants. We apply our model to perform a cost-benefit analysis of gene regulatory control. Our analysis predicts that the optimal expression level of a gene regulatory protein is determined by the trade-off between the cost of synthesizing the regulatory protein and the benefit of minimizing the fluctuations in the expression of its target gene. We discuss possible experiments that could test our predictions.Comment: Revised manuscript;35 pages, 4 figures, REVTeX4; to appear in PLoS Computational Biolog

The what and where of adding channel noise to the Hodgkin-Huxley equations

One of the most celebrated successes in computational biology is the Hodgkin-Huxley framework for modeling electrically active cells. This framework, expressed through a set of differential equations, synthesizes the impact of ionic currents on a cell's voltage -- and the highly nonlinear impact of that voltage back on the currents themselves -- into the rapid push and pull of the action potential. Latter studies confirmed that these cellular dynamics are orchestrated by individual ion channels, whose conformational changes regulate the conductance of each ionic current. Thus, kinetic equations familiar from physical chemistry are the natural setting for describing conductances; for small-to-moderate numbers of channels, these will predict fluctuations in conductances and stochasticity in the resulting action potentials. At first glance, the kinetic equations provide a far more complex (and higher-dimensional) description than the original Hodgkin-Huxley equations. This has prompted more than a decade of efforts to capture channel fluctuations with noise terms added to the Hodgkin-Huxley equations. Many of these approaches, while intuitively appealing, produce quantitative errors when compared to kinetic equations; others, as only very recently demonstrated, are both accurate and relatively simple. We review what works, what doesn't, and why, seeking to build a bridge to well-established results for the deterministic Hodgkin-Huxley equations. As such, we hope that this review will speed emerging studies of how channel noise modulates electrophysiological dynamics and function. We supply user-friendly Matlab simulation code of these stochastic versions of the Hodgkin-Huxley equations on the ModelDB website (accession number 138950) and http://www.amath.washington.edu/~etsb/tutorials.html.Comment: 14 pages, 3 figures, review articl

Master equation simulation analysis of immunostained Bicoid morphogen gradient

<p>Abstract</p> <p>Background</p> <p>The concentration gradient of Bicoid protein which determines the developmental pathways in early <it>Drosophila </it>embryo is the best characterized morphogen gradient at the molecular level. Because different developmental fates can be elicited by different concentrations of Bicoid, it is important to probe the limits of this specification by analyzing intrinsic fluctuations of the Bicoid gradient arising from small molecular number. Stochastic simulations can be applied to further the understanding of the dynamics of Bicoid morphogen gradient formation at the molecular number level, and determine the source of the nucleus-to-nucleus expression variation (noise) observed in the Bicoid gradient.</p> <p>Results</p> <p>We compared quantitative observations of Bicoid levels in immunostained <it>Drosophila </it>embryos with a spatially extended Master Equation model which represents diffusion, decay, and anterior synthesis. We show that the intrinsic noise of an autonomous reaction-diffusion gradient is Poisson distributed. We demonstrate how experimental noise can be identified in the logarithm domain from single embryo analysis, and then separated from intrinsic noise in the normalized variance domain of an ensemble statistical analysis. We show how measurement sensitivity affects our observations, and how small amounts of rescaling noise can perturb the noise strength (Fano factor) observed. We demonstrate that the biological noise level in data can serve as a physical constraint for restricting the model's parameter space, and for predicting the Bicoid molecular number and variation range. An estimate based on a low variance ensemble of embryos suggests that the steady-state Bicoid molecular number in a nucleus should be larger than 300 in the middle of the embryo, and hence the gradient should extend to the posterior end of the embryo, beyond the previously assumed background limit. We exhibit the predicted molecular number gradient together with measurement effects, and make a comparison between conditions of higher and lower variance respectively.</p> <p>Conclusion</p> <p>Quantitative comparison of Master Equation simulations with immunostained data enabled us to determine narrow ranges for key biophysical parameters, which for this system can be independently validated. Intrinsic noise is clearly detectable as well, although the staining process introduces certain limits in resolution.</p

Entrepreneurs’ age, institutions, and social value creation goals: a multi-country study

This study explores the relationship between an entrepreneur's age and his/her social value creation goals. Building on the lifespan developmental psychology literature and institutional theory, we hypothesize a U-shaped relationship between entrepreneurs’ age and their choice to create social value through their ventures, such that younger and older entrepreneurs create more social value with their businesses while middle age entrepreneurs are relatively more economically and less socially oriented with their ventures. We further hypothesize that the quality of a country’s formal institutions in terms of economic, social, and political freedom steepen the U-shaped relationship between entrepreneurs’ age and their choice to pursue social value creation as supportive institutional environments allow entrepreneurs to follow their age-based preferences. We confirm our predictions using multilevel mixed-effects linear regressions on a sample of over 15,000 entrepreneurs (aged between 18 and 64 years) in 45 countries from Global Entrepreneurship Monitor data. The findings are robust to several alternative specifications. Based on our findings, we discuss implications for theory and practice, and we propose future research directions

Effect of promoter architecture on the cell-to-cell variability in gene expression

According to recent experimental evidence, the architecture of a promoter, defined as the number, strength and regulatory role of the operators that control the promoter, plays a major role in determining the level of cell-to-cell variability in gene expression. These quantitative experiments call for a corresponding modeling effort that addresses the question of how changes in promoter architecture affect noise in gene expression in a systematic rather than case-by-case fashion. In this article, we make such a systematic investigation, based on a simple microscopic model of gene regulation that incorporates stochastic effects. In particular, we show how operator strength and operator multiplicity affect this variability. We examine different modes of transcription factor binding to complex promoters (cooperative, independent, simultaneous) and how each of these affects the level of variability in transcription product from cell-to-cell. We propose that direct comparison between in vivo single-cell experiments and theoretical predictions for the moments of the probability distribution of mRNA number per cell can discriminate between different kinetic models of gene regulation.Comment: 35 pages, 6 figures, Submitte

Role of mitochondrial raft-like microdomains in the regulation of cell apoptosis

Lipid rafts are envisaged as lateral assemblies of specific lipids and proteins that dissociate and associate rapidly and form functional clusters in cell membranes. These structural platforms are not confined to the plasma membrane; indeed lipid microdomains are similarly formed at subcellular organelles, which include endoplasmic reticulum, Golgi and mitochondria, named raft-like microdomains. In addition, some components of raft-like microdomains are present within ER-mitochondria associated membranes. This review is focused on the role of mitochondrial raft-like microdomains in the regulation of cell apoptosis, since these microdomains may represent preferential sites where key reactions take place, regulating mitochondria hyperpolarization, fission-associated changes, megapore formation and release of apoptogenic factors. These structural platforms appear to modulate cytoplasmic pathways switching cell fate towards cell survival or death. Main insights on this issue derive from some pathological conditions in which alterations of microdomains structure or function can lead to severe alterations of cell activity and life span. In the light of the role played by raft-like microdomains to integrate apoptotic signals and in regulating mitochondrial dynamics, it is conceivable that these membrane structures may play a role in the mitochondrial alterations observed in some of the most common human neurodegenerative diseases, such as Amyotrophic lateral sclerosis, Huntington's chorea and prion-related diseases. These findings introduce an additional task for identifying new molecular target(s) of pharmacological agents in these pathologies

The aging Canadian population and hospitalizations for acute myocardial infarction: projection to 2020

<p>Abstract</p> <p>Background</p> <p>The risk of experiencing an acute myocardial infarction (AMI) increases with age and Canada's population is aging. The objective of this analysis was to examine trends in the AMI hospitalization rate in Canada between 2002 and 2009 and to estimate the potential increase in the number of AMI hospitalizations over the next decade.</p> <p>Methods</p> <p>Aggregated data on annual AMI hospitalizations were obtained from the Canadian Institute for Health Information for all provinces and territories, except Quebec, for 2002/03 and 2009/10. Using these data in a Poisson regression model to control for age, gender and year, the rate of AMI hospitalizations was extrapolated between 2010 and 2020. The extrapolated rate and Statistics Canada population projections were used to estimate the number of AMI hospitalizations in 2020.</p> <p>Results</p> <p>The rates of AMI hospitalizations by gender and age group showed a decrease between 2002 and 2009 in patients aged ≥ 65 years and relatively stable rates in those aged < 64 years in both males and females. However, the total number of AMI hospitalizations in Canada (excluding Quebec) is projected to increase by 4667 from 51847 in 2009 to 56514 in 2020, a 9.0% increase. Inflating this number to account for the unavailable Quebec data results in an increase of approximately 6200 for the whole of Canada. This would amount to an additional cost of between $46 and$54 million and sensitivity analyses indicate that it could be between $36 and$65 million.</p> <p>Conclusions</p> <p>Despite projected decreasing or stable rates of AMI hospitalization, the number of hospitalizations is expected to increase substantially as a result of the aging of the Canadian population. The cost of these hospitalizations will be substantial. An increase of this extent in the number of AMI hospitalizations and the ensuing costs would significantly impact the already over-stretched Canadian healthcare system.</p