Quantifying uncertainty, variability and likelihood for ordinary differential equation models

<p>Abstract</p> <p>Background</p> <p>In many applications, ordinary differential equation (ODE) models are subject to uncertainty or variability in initial conditions and parameters. Both, uncertainty and variability can be quantified in terms of a probability density function on the state and parameter space.</p> <p>Results</p> <p>The partial differential equation that describes the evolution of this probability density function has a form that is particularly amenable to application of the well-known method of characteristics. The value of the density at some point in time is directly accessible by the solution of the original ODE extended by a single extra dimension (for the value of the density). This leads to simple methods for studying uncertainty, variability and likelihood, with significant advantages over more traditional Monte Carlo and related approaches especially when studying regions with low probability.</p> <p>Conclusions</p> <p>While such approaches based on the method of characteristics are common practice in other disciplines, their advantages for the study of biological systems have so far remained unrecognized. Several examples illustrate performance and accuracy of the approach and its limitations.</p

The NANOGrav 12.5-Year Data Set: Dispersion Measure Mis-Estimation with Varying Bandwidths

Noise characterization for pulsar-timing applications accounts for interstellar dispersion by assuming a known frequency-dependence of the delay it introduces in the times of arrival (TOAs). However, calculations of this delay suffer from mis-estimations due to other chromatic effects in the observations. The precision in modeling dispersion is dependent on the observed bandwidth. In this work, we calculate the offsets in infinite-frequency TOAs due to mis-estimations in the modeling of dispersion when using varying bandwidths at the Green Bank Telescope. We use a set of broadband observations of PSR J1643-1224, a pulsar with an excess of chromatic noise in its timing residuals. We artificially restricted these observations to a narrowband frequency range, then used both data sets to calculate residuals with a timing model that does not include short-scale dispersion variations. By fitting the resulting residuals to a dispersion model, and comparing the ensuing fitted parameters, we quantify the dispersion mis-estimations. Moreover, by calculating the autocovariance function of the parameters we obtained a characteristic timescale over which the dispersion mis-estimations are correlated. For PSR J1643-1224, which has one of the highest dispersion measures (DM) in the NANOGrav pulsar timing array, we find that the infinite-frequency TOAs suffer from a systematic offset of ~22 microseconds due to DM mis-estimations, with correlations over ~1 month. For lower-DM pulsars, the offset is ~7 microseconds. This error quantification can be used to provide more robust noise modeling in NANOGrav's data, thereby increasing sensitivity and improving parameter estimation in gravitational wave searches.Comment: 15 pages, 7 figure

Human Tumor Cell Proliferation Evaluated Using Manganese-Enhanced MRI

Tumor cell proliferation can depend on calcium entry across the cell membrane. As a first step toward the development of a non-invasive test of the extent of tumor cell proliferation in vivo, we tested the hypothesis that tumor cell uptake of a calcium surrogate, Mn(2+) [measured with manganese-enhanced MRI (MEMRI)], is linked to proliferation rate in vitro.Proliferation rates were determined in vitro in three different human tumor cell lines: C918 and OCM-1 human uveal melanomas and PC-3 prostate carcinoma. Cells growing at different average proliferation rates were exposed to 1 mM MnCl(2) for one hour and then thoroughly washed. MEMRI R(1) values (longitudinal relaxation rates), which have a positive linear relationship with Mn(2+) concentration, were then determined from cell pellets. Cell cycle distributions were determined using propidium iodide staining and flow cytometry. All three lines showed Mn(2+)-induced increases in R(1) compared to cells not exposed to Mn(2+). C918 and PC-3 cells each showed a significant, positive correlation between MEMRI R(1) values and proliferation rate (p≤0.005), while OCM-1 cells showed no significant correlation. Preliminary, general modeling of these positive relationships suggested that pellet R(1) for the PC-3 cells, but not for the C918 cells, could be adequately described by simply accounting for changes in the distribution of the cell cycle-dependent subpopulations in the pellet.These data clearly demonstrate the tumor-cell dependent nature of the relationship between proliferation and calcium influx, and underscore the usefulness of MEMRI as a non-invasive method for investigating this link. MEMRI is applicable to study tumors in vivo, and the present results raise the possibility of evaluating proliferation parameters of some tumor types in vivo using MEMRI

Volunteer Bias in Recruitment, Retention, and Blood Sample Donation in a Randomised Controlled Trial Involving Mothers and Their Children at Six Months and Two Years: A Longitudinal Analysis

BACKGROUND: The vulnerability of clinical trials to volunteer bias is under-reported. Volunteer bias is systematic error due to differences between those who choose to participate in studies and those who do not. METHODS AND RESULTS: This paper extends the applications of the concept of volunteer bias by using data from a trial of probiotic supplementation for childhood atopy in healthy dyads to explore 1) differences between a) trial participants and aggregated data from publicly available databases b) participants and non-participants as the trial progressed 2) impact on trial findings of weighting data according to deprivation (Townsend) fifths in the sample and target populations. 1) a) Recruits (n = 454) were less deprived than the target population, matched for area of residence and delivery dates (n = 6,893) (mean [SD] deprivation scores 0.09[4.21] and 0.79[4.08], t = 3.44, df = 511, p<0.001). b) i) As the trial progressed, representation of the most deprived decreased. These participants and smokers were less likely to be retained at 6 months (n = 430[95%]) (OR 0.29,0.13-0.67 and 0.20,0.09-0.46), and 2 years (n = 380[84%]) (aOR 0.68,0.50-0.93 and 0.55,0.28-1.09), and consent to infant blood sample donation (n = 220[48%]) (aOR 0.72,0.57-0.92 and 0.43,0.22-0.83). ii) Mothers interested in probiotics or research or reporting infants' adverse events or rashes were more likely to attend research clinics and consent to skin-prick testing. Mothers participating to help children were more likely to consent to infant blood sample donation. 2) In one trial outcome, atopic eczema, the intervention had a positive effect only in the over-represented, least deprived group. Here, data weighting attenuated risk reduction from 6.9%(0.9-13.1%) to 4.6%(-1.4-+10.5%), and OR from 0.40(0.18-0.91) to 0.56(0.26-1.21). Other findings were unchanged. CONCLUSIONS: Potential for volunteer bias intensified during the trial, due to non-participation of the most deprived and smokers. However, these were not the only predictors of non-participation. Data weighting quantified volunteer bias and modified one important trial outcome. TRIAL REGISTRATION: This randomised, double blind, parallel group, placebo controlled trial is registered with the International Standard Randomised Controlled Trials Register, Number (ISRCTN) 26287422. Registered title: Probiotics in the prevention of atopy in infants and children

Comparative transcriptome analyses indicate molecular homology of zebrafish swimbladder and mammalian lung

10.1371/journal.pone.0024019PLoS ONE68

Rationale, design, methodology and sample characteristics for the family partners for health study: a cluster randomized controlled study

<p>Abstract</p> <p>Background</p> <p>Young children who are overweight are at increased risk of becoming obese and developing type 2 diabetes and cardiovascular disease later in life. Therefore, early intervention is critical. This paper describes the rationale, design, methodology, and sample characteristics of a 5-year cluster randomized controlled trial being conducted in eight elementary schools in rural North Carolina, United States.</p> <p>Methods/Design</p> <p>The first aim of the trial is to examine the effects of a two-phased intervention on weight status, adiposity, nutrition and exercise health behaviors, and self-efficacy in overweight or obese 2nd, 3 rd, and 4th grade children and their overweight or obese parents. The primary outcome in children is stabilization of BMI percentile trajectory from baseline to 18 months. The primary outcome in parents is a decrease in BMI from baseline to 18 months. Secondary outcomes for both children and parents include adiposity, nutrition and exercise health behaviors, and self-efficacy from baseline to 18 months. A secondary aim of the trial is to examine in the experimental group, the relationships between parents and children's changes in weight status, adiposity, nutrition and exercise health behaviors, and self-efficacy. An exploratory aim is to determine whether African American, Hispanic, and non-Hispanic white children and parents in the experimental group benefit differently from the intervention in weight status, adiposity, health behaviors, and self-efficacy.</p> <p>A total of 358 African American, non-Hispanic white, and bilingual Hispanic children with a BMI ≥ 85th percentile and 358 parents with a BMI ≥ 25 kg/m²have been inducted over 3 1/2 years and randomized by cohort to either an experimental or a wait-listed control group. The experimental group receives a 12-week intensive intervention of nutrition and exercise education, coping skills training and exercise (Phase I), 9 months of continued monthly contact (Phase II) and then 6 months (follow-up) on their own. Safety endpoints include adverse event reporting. Intention-to-treat analysis will be applied to all data.</p> <p>Discussion</p> <p>Findings from this trial may lead to an effective intervention to assist children and parents to work together to improve nutrition and exercise patterns by making small lifestyle pattern changes.</p> <p>Trial registration</p> <p><a href="http://www.clinicaltrials.gov/ct2/show/NCT01378806">NCT01378806</a>.</p

The NANOGrav Nine-year Data Set:Observations, Arrival Time Measurements, and Analysis of 37 Millisecond Pulsars

We present high-precision timing observations spanning up to nine years for 37 millisecond pulsars monitored with the Green Bank and Arecibo radio telescopes as part of the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) project. We describe the observational and instrumental setups used to collect the data, and methodology applied for calculating pulse times of arrival; these include novel methods for measuring instrumental offsets and characterizing low signal-to-noise ratio timing results. The time of arrival data are fit to a physical timing model for each source, including terms that characterize time-variable dispersion measure and frequency-dependent pulse shape evolution. In conjunction with the timing model fit, we have performed a Bayesian analysis of a parameterized timing noise model for each source, and detect evidence for excess low-frequency, or "red," timing noise in 10 of the pulsars. For 5 of these cases this is likely due to interstellar medium propagation effects rather than intrisic spin variations. Subsequent papers in this series will present further analysis of this data set aimed at detecting or limiting the presence of nanohertz-frequency gravitational wave signals

Suitability of external controls for drug evaluation in Duchenne muscular dystrophy

OBJECTIVE: To evaluate the suitability of real-world data (RWD) and natural history data (NHD) for use as external controls in drug evaluations for ambulatory Duchenne muscular dystrophy (DMD). METHODS: The consistency of changes in the 6-minute walk distance (Δ6MWD) was assessed across multiple clinical trial placebo arms and sources of NHD/RWD. Six placebo arms reporting 48-week Δ6MWD were identified via literature review and represented 4 sets of inclusion/exclusion criteria (n = 383 patients in total). Five sources of RWD/NHD were contributed by Universitaire Ziekenhuizen Leuven, DMD Italian Group, The Cooperative International Neuromuscular Research Group, ImagingDMD, and the PRO-DMD-01 study (n = 430 patients, in total). Mean Δ6MWD was compared between each placebo arm and RWD/NHD source after subjecting the latter to the inclusion/exclusion criteria of the trial for baseline age, ambulatory function, and steroid use. Baseline covariate adjustment was investigated in a subset of patients with available data. RESULTS: Analyses included ∼1,200 patient-years of follow-up. Differences in mean Δ6MWD between trial placebo arms and RWD/NHD cohorts ranged from -19.4 m (i.e., better outcomes in RWD/NHD) to 19.5 m (i.e., worse outcomes in RWD/NHD) and were not statistically significant before or after covariate adjustment. CONCLUSIONS: We found that Δ6MWD was consistent between placebo arms and RWD/NHD subjected to equivalent inclusion/exclusion criteria. No evidence for systematic bias was detected. These findings are encouraging for the use of RWD/NHD to augment, or possibly replace, placebo controls in DMD trials. Multi-institution collaboration through the Collaborative Trajectory Analysis Project rendered this study feasible