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Evaluation of HIV-1 kinetic models using quantitative discrimination analysis.

MOTIVATION: Since the identification of human immunodeficiency virus (HIV) over twenty years ago, many mathematical models of HIV dynamics have been proposed. The purpose of this study was to evaluate intracellular and intercellular scale HIV models that best described the dynamics of viral and cell titers of a person, where parameters were determined using typically available patient data. In this case, 'best' was defined as the model most capable of describing experimental patient data and was determined by Bayesian-based model discrimination analysis and the ability to provide realistic results. RESULTS: Twenty models of HIV-1 viral dynamics were initially evaluated to determine whether parameters could be obtained from readily available clinical data from established HIV-1 patients with stable disease. Based on this analysis, three models were chosen for further examination and comparison. Parameters were estimated using experimental data from a cohort of 338 people monitored for up to 2484 days. The models were evaluated using a Bayesian technique to determine which model was most probable. The model ultimately selected as most probable was overwhelmingly favored relative to the remaining two models, and it accounted for uninfected cells, infected cells and cytotoxic T lymphocyte dynamics. The authors developed a fourth model for comparison purposes by combining the features of the original three models. Parameters were estimated for the new model and the statistical analysis was repeated for all four models. The model that was initially favored was selected again upon model discrimination analysis. CONTACT: srivasta@engr.uconn.edu.

Cohort Studies↗

A Bayesian space varying parameter model applied to estimating fertility schedules.

We propose a spatial generalized linear model (GLM) to analyse the vital rates for small areas. In each small area, we have a response vector and covariates to explain its variability. The statistical methodology is based on a spatial Bayesian approach and it allows the covariates' parameters of the generalized linear model to vary smoothly on space. Hence, the effect of a covariate on the response varies depending on the random variables measurement location. Our model is an extension of disease mapping models allowing the space-covariate interaction to be modelled in a natural way and giving space a position of intrinsic interest. We introduce the model in the context of fertility curve estimation. In each small area, we have a curve describing the variation of fertility rates by age modelled by Coale's fertility model, which implies a GLM in each area. A simulation shows the advantages of our approach. In addition, the paper applies the procedure to census data used to study the diffusion of low fertility behaviour in Brazil.

Adolescent↗

Assessment and monitoring in clinical trials when survival curves have distinct shapes: a Bayesian approach with Weibull modelling.

The comparison of Weibull distributions with unequal shape parameters, in the case of right censored survival data obtained from independent samples, is considered within the framework of Bayesian statistical methodology. The procedures are illustrated with the example of a mortality study where a new treatment is compared to a placebo. The posterior distributions about relevant parameters, which may provide support for a conclusion of clinical superiority of the treatment, and the predictive distributions, which may guide decision about early stopping at an interim analysis, are considered for a class of appropriate priors.

Amiodarone↗

Bayesian regression methodology for estimating a receiver operating characteristic curve with two radiologic applications: prostate biopsy and spiral CT of ureteral stones.

RATIONALE AND OBJECTIVES: The authors evaluated two Bayesian regression models for receiver operating characteristic (ROC) curve analysis of continuous diagnostic outcome data with covariates. MATERIALS AND METHODS: Full and partial Bayesian regression models were applied to data from two studies (n = 180 and 100, respectively): (a) The diagnostic value of prostate-specific antigen (PSA) levels (outcome variable) for predicting disease after radical prostatectomy (gold standard) was evaluated for three risk groups (covariates) based on Gleason scores. (b) Spiral computed tomography was performed on patients with proved obstructing ureteral stones. The predictive value of stone size (outcome) was evaluated along with two treatment options (gold standard), as well as stone location (in or not in the ureterovesical junction [UVJ]) and patient age (covariates). Summary ROC measures were reported, and various prior distributions of the regression coefficients were investigated. RESULTS: (a) In the PSA example, the ROC areas under the full model were 0.667, 0.769, and 0.703, respectively, for the low-, intermediate-, and high-risk groups. Under the partial model, the area beneath the ROC curve was 0.706. (b) The ROC areas for patients with ureteral stones in the UVJ decreased dramatically with age but otherwise were close to that under the partial model (ie, 0.774). The prior distribution had greater influence in the second example. CONCLUSION: The diagnostic tests were accurate in both examples. PSA levels were most accurate for staging prostate cancer among intermediate-risk patients. Stone size was predictive of treatment option for all patients other than those 40 years or older and with a stone in the UVJ.

Adult↗

Multiple-trait Gibbs sampler for animal models: flexible programs for Bayesian and likelihood-based (co)variance component inference.

A set of FORTRAN programs to implement a multiple-trait Gibbs sampling algorithm for (co)variance component inference in animal models (MTGSAM) was developed. The MTGSAM programs are available to the public. The programs support models with correlated genetic effects and arbitrary numbers of covariates, fixed effects, and independent random effects for each trait. Any combination of missing traits is allowed. The programs were used to estimate variance components for 50 replicates of simulated data. Each replicate consisted of 50 animals of each sex in each of four generations, for 400 animals in each replicate for two traits. For MTGSAM, informative prior distributions for variance components were inverted Wishart random variables with 10 df and means equal to the simulation parameters. A total of 15,000 Gibbs sampling rounds were completed for each replicate, with 2,000 rounds discarded for burn-in. For multiple-trait derivative free restricted maximum likelihood (MTDFREML), starting values for the variance components were the simulation parameters. Averages of posterior mean of variance components estimated using MTGSAM with informative and flat prior distributions for variance components and REML estimates obtained using MTDFREML indicated that all three methods were empirically unbiased. Correlations between estimates from MTGSAM using flat priors and MTDFREML all exceeded .99.

Algorithms↗

A population-based Bayesian approach to the minimal model of glucose and insulin homeostasis.

The minimal model was proposed in the late 1970s by Bergman et al. (Am. J. Physiol. 1979; 236(6):E667) as a powerful model consisting of three differential equations describing the glucose and insulin kinetics of a single individual. Considering the glucose and insulin simultaneously, the minimal model is a highly ill-posed estimation problem, where the reconstruction most often has been done by non-linear least squares techniques separately for each entity. The minimal model was originally specified for a single individual and does not combine several individuals with the advantage of estimating the metabolic portrait for a whole population. Traditionally it has been analysed in a deterministic set-up with only error terms on the measurements. In this work we adopt a Bayesian graphical model to describe the coupled minimal model that accounts for both measurement and process variability, and the model is extended to a population-based model. The estimation of the parameters are efficiently implemented in a Bayesian approach where posterior inference is made through the use of Markov chain Monte Carlo techniques. Hereby we obtain a powerful and flexible modelling framework for regularizing the ill-posed estimation problem often inherited in coupled stochastic differential equations. We demonstrate the method on experimental data from intravenous glucose tolerance tests performed on 19 normal glucose-tolerant subjects.

Adult↗

Nonconjugate Bayesian analysis of variance component models.

We consider the usual normal linear mixed model for variance components from a Bayesian viewpoint. With conjugate priors and balanced data, Gibbs sampling is easy to implement; however, simulating from full conditionals can become difficult for the analysis of unbalanced data with possibly nonconjugate priors, thus leading one to consider alternative Markov chain Monte Carlo schemes. We propose and investigate a method for posterior simulation based on an independence chain. The method is customized to exploit the structure of the variance component model, and it works with arbitrary prior distributions. As a default reference prior, we use a version of Jeffreys' prior based on the integrated (restricted) likelihood. We demonstrate the ease of application and flexibility of this approach in familiar settings involving both balanced and unbalanced data.

Algorithms↗

Risk factors associated with incident clinical vertebral and nonvertebral fractures in postmenopausal women: the Canadian Multicentre Osteoporosis Study (CaMos).

Utilizing data from the Canadian Multicentre Osteoporosis Study (CaMos), we examined the association between potential risk factors and incident vertebral and nonvertebral fractures. A total of 5,143 postmenopausal women were enrolled. Information collected during the study included data from the CaMos baseline and annually mailed fracture questionnaires, the Short Form 36 (SF-36), the Health Utilities Index, and physical measurements. Participants were followed for 3 years. Postmenopausal women were classified into four groups according to their incident fracture status since baseline: those without a new fracture; those with a new clinically recognized vertebral fracture; those with an incident nonvertebral fracture at the wrist, hip, humerus, pelvis, or ribs (main nonvertebral fracture group); and those with any new nonvertebral fracture (any-nonvertebral-fracture group). We performed multivariate Cox proportional hazard analysis using all possible risk factors to determine the association between risk factors and the time to the first minimal trauma fracture. Best predictive models were also determined using variables that were included in the full models. The Bayesian information criterion was used for model selection. For all analyses, relative risks and associated 95% confidence intervals were calculated. During the follow-up period, 34, 163, and 280 women developed a vertebral, a main nonvertebral, or any nonvertebral fracture, respectively. The best predictive models indicated that a five point lower quality of life as measured by the SF-36 physical component summary score was associated with relative risks of 1.21 (95% CI, 1.02 to 1.44), 1.17 (95% CI, 1.07 to 1.28), and 1.19 (95% CI, 1.11 to 1.27) for incident vertebral, main nonvertebral, and all nonvertebral fractures, respectively. In addition, for a one standard deviation (SD=0.12) lower femoral neck BMD, the relative risks for incident vertebral, main nonvertebral, and any nonvertebral fractures increased by 2.73 (95% CI, 1.74 to 4.28), 1.39 (95% CI, 1.06 to 1.82), and 1.34 (95% CI, 1.09 to 1.65), respectively. Furthermore, various anthropometric measures, disease conditions, and medications are associated with a new fracture. Identifying postmenopausal women at risk is important given that fracture prevention therapies are now available.

Adult↗

A test of geographic assignment using isotope tracers in feathers of known origin.

We used feathers of known origin collected from across the breeding range of a migratory shorebird to test the use of isotope tracers for assigning breeding origins. We analyzed deltaD, delta13C, and delta15N in feathers from 75 mountain plover (Charadrius montanus) chicks sampled in 2001 and from 119 chicks sampled in 2002. We estimated parameters for continuous-response inverse regression models and for discrete-response Bayesian probability models from data for each year independently. We evaluated model predictions with both the training data and by using the alternate year as an independent test dataset. Our results provide weak support for modeling latitude and isotope values as monotonic functions of one another, especially when data are pooled over known sources of variation such as sample year or location. We were unable to make even qualitative statements, such as north versus south, about the likely origin of birds using both deltaD and delta13C in inverse regression models; results were no better than random assignment. Probability models provided better results and a more natural framework for the problem. Correct assignment rates were highest when considering all three isotopes in the probability framework, but the use of even a single isotope was better than random assignment. The method appears relatively robust to temporal effects and is most sensitive to the isotope discrimination gradients over which samples are taken. We offer that the problem of using isotope tracers to infer geographic origin is best framed as one of assignment, rather than prediction.

Animal Migration↗

NMR and Bayesian regularized neural network regression for impurity determination of 4-aminophenol.

A method for the determination of 4-aminophenol as an impurity in paracetamol (N-(4-hydroxyphenyl)-acetamide) by proton nuclear magnetic resonance ((1)H-NMR) spectroscopy has been developed. The (13)C-satellite from the protons in the ortho position from the hydroxyl group in paracetamol was used as an internal standard, although these peaks interfered with the peaks from the protons in 4-aminophenol. Because of interference in the spectra and non-linearity over a wide calibration range, a Bayesian regularized neural network model was used for calibration. Various kinds of data preprocessing were examined: zero filling, multiplication by a negative exponential function (line broadening), followed by Fourier transformation of the free induction decay (FID). The NMR spectral data were automatically phased and shift-adjusted by means of a genetic algorithm. Multiplicative scatter correction and data compression by wavelets and sequential zeroing of weights variable selection were performed to obtain an optimal calibration model. Neither zero filling of the FID nor line broadening improved the calibration models with regard to error of prediction, so these processes were excluded in the final model. The generated Bayesian regularized network model was evaluated with an independent test set. Four different models with different test sets were constructed to explore the quality of the calibration. The mean error of the optimal calibration model was 25.3 x 10(-6) weight of 4-aminophenol per weight paracetamol. The method is characterized by being relative fast, simple and sufficient sensitive for typical pharmaceutical impurity determinations.

Acetaminophen↗

Investigation of bacteriophage MS2 viral dynamics using model discrimination analysis and the implications for phage therapy.

Lytic phages infect their bacterial hosts, use the host machinery to replicate, and finally lyse and kill their hosts, releasing progeny phages. Various mathematical models have been developed that describe these phage-host viral dynamics. The aim of this study was to determine which of these models best describes the viral dynamics of lytic RNA phage MS2 and its host Escherichia coli C-3000. Experimental data consisted of uninfected and infected bacterial cell densities, free phage density, and substrate concentration. Parameters of various models were either determined directly through other experimental techniques or estimated using regression analysis of the experimental data. The models were evaluated using a Bayesian-based model discrimination technique. Through model discrimination it was shown that phage-resistant cells inhibited the growth of phage population. It was also shown that the uninfected bacterial population was a quasispecies consisting of phage-sensitive and phage-resistant bacterial cells. When there was a phage attack the phage-sensitive cells died out and the phage-resistant cells were selected for and became the dominant strain of the bacterial population.

Cell Proliferation↗

Genomic prediction and genome-wide association study for liver abscesses in crossbred beef cattle.

Liver abscesses are a concern in feedlot cattle, and little is known about the role of genetics in their development. This study aimed to estimate genetic parameters and to identify single-nucleotide polymorphisms (SNPs) associated with liver abscesses. Crossbred cattle representing 18 breeds in the U.S. Meat Animal Research Center Germplasm Evaluation Program were phenotyped for liver abscesses at slaughter (n&#x2005;=&#x2005;9,044). Seventeen percent of cattle had liver abscesses. These cattle had genotypes that were imputed to sequence variant genotypes. After filtering and quality control, 340,723 SNPs were used in the analysis. Liver abscess prevalence was modeled with a single-step genomic best linear unbiased prediction (ssGBLUP) threshold model using a Bayesian framework. The model included contemporary group (sex, treatment group, and slaughter date), additive genomic, and residual effects. Genomic heritability was 0.039 (95% highest posterior density&#x2005;=&#x2005;0.005, 0.081), which was very small. To assess prediction quality, a 5-fold random cross-validation structure was used. Method Linear Regression was used to assess accuracy, bias, and dispersion by comparing estimated breeding values (EBV) from full and reduced analyses. Cross-validation metrics showed EBV based on genotypes had 0.05 reliability (SD&#x2005;<&#x2005;0.01) with no bias relative to EBV based on genotypes and phenotypes. For the genome-wide association study, SNP effects were back calculated from the EBV solutions from ssGBLUP. No SNPs were associated with liver abscesses at a Benjamini-Hochberg adjusted 0.05 significance level. Although a large dataset was used, this result was because of the low genomic heritability and imprecise EBV used to calculate SNP effects. Based on these results, environmental factors contribute to most of the variation in liver abscesses. Genetic selection to reduce liver abscesses would be slow because of the low genomic heritability, measurement late in life, and inability to measure breeding animals. A faster approach would be finding additional environmental interventions that maintain animal performance.

Animals↗

Disposition of phenytoin in critically ill trauma patients.

Estimates of phenytoin pharmacokinetic variables and protein binding were determined in 10 adult critically ill trauma patients. Each study subject received phenytoin sodium as an intravenous loading dose of 15 mg/kg, followed by an initial intravenous maintenance dose of 6 mg/kg/day. Serial blood samples were obtained throughout the seven-day study period and analyzed for total and unbound serum phenytoin concentrations. The concentration data for each patients were fitted to a one-compartment model with elimination defined by the Michaelis-Menten constant Km and the maximum rate of metabolism (Vmax) and to a one-compartment model with first-order elimination. The Michaelis-Menten model used Bayesian parameter estimation while the linear model used weighted non-linear least-squares regression analysis. Unbound phenytoin fraction ranged from 0.073 to 0.25. Free fraction increased 7% to 108% in 9 of 10 patients (median increase 29%) from day 1 to day 7 of therapy. Variable estimates using the Michaelis-Menten model were as follows: volume of distribution, 0.76 +/- 0.15 L/kg (0.58-1.01 L/kg); Vmax, 568 +/- 197 mg/day (350-937 mg/day); and Km, 4.5 +/- 1.8 mg/L (1.8-6.2 mg/L). These estimates fell within the wide range of values obtained in studies using stable patients or healthy volunteers. The Michaelis-Menten model was significantly less biased and more precise than the linear model. Three of four patients who continued to receive their study maintenance dose had substantially lower measured total serum concentrations of phenytoin than predicted using the study variable estimates.(ABSTRACT TRUNCATED AT 250 WORDS)

Adult↗

Bayesian synthesis of a pathogen growth model: Listeria monocytogenes under competition.

The Bayesian synthesis method is applied to data from two studies of Listeria monocytogenes grown in broth monocultures to draw inferences about the joint distribution of two Baranyi growth model parameters-lag time and maximum specific growth rate. The resultant joint distribution is then combined with prior distributions for the initial and maximum pathogen density parameters under competitive growth conditions. Finally, the pathogen growth model is updated using the Sampling/Importance Resampling (SIR) algorithm with data on L. monocytogenes growth in competition with natural microflora in fish. Although the latter data provide no information on the stationary phase to directly estimate the maximum pathogen density parameter, combining them with relevant prior information provides a means to characterize L. monocytogenes growth in a food with mixed microbial populations. Based on a specified tolerance for L. monocytogenes growth, the updated model provides a storage time limit for fish held at 5 degrees C, pH 6.8, 43% CO(2), 57% N(2).

Animals↗

A Bayesian hierarchical approach to comparative audit for carotid surgery.

OBJECTIVES: the aim of this study was to illustrate how a Bayesian hierarchical modelling approach can aid the reliable comparison of outcome rates between surgeons. DESIGN: retrospective analysis of prospective and retrospective data. MATERIALS: binary outcome data (death/stroke within 30 days), together with information on 15 possible risk factors specific for CEA were available on 836 CEAs performed by four vascular surgeons from 1992-99. The median patient age was 68 (range 38-86) years and 60% were men. METHODS: the model was developed using the WinBUGS software. After adjusting for patient-level risk factors, a cross-validatory approach was adopted to identify "divergent" performance. A ranking exercise was also carried out. RESULTS: the overall observed 30-day stroke/death rate was 3.9% (33/836). The model found diabetes, stroke and heart disease to be significant risk factors. There was no significant difference between the predicted and observed outcome rates for any surgeon (Bayesian p -value>0.05). Each surgeon had a median rank of 3 with associated 95% CI 1.0-5.0, despite the variability of observed stroke/death rate from 2.9-4.4%. After risk adjustment, there was very little residual between-surgeon variability in outcome rate. CONCLUSIONS: Bayesian hierarchical models can help to accurately quantify the uncertainty associated with surgeons' performance and rank.

Adult↗

Lansoprazole compared with histamine2-receptor antagonists in healing gastric ulcers: a meta-analysis.

To compare the gastric ulcer healing rates of lansoprazole with histamine2-receptor antagonists (H2RAs) (ranitidine, famotidine, cimetidine, and roxatidine), a meta-analysis was performed using data from five published and eight unpublished randomized controlled trials. Analyses were performed using (1) both evaluable patients (n = 1527) and all randomized patients (n = 1655) (assuming that patients lost to follow-up were treatment failures); (2) all studies and a subset of studies that received high methodologic quality scores; and (3) fixed-effects, random-effects, and Bayesian statistical models. In all cases, lansoprazole was associated with a significantly higher rate of endoscopic healing at both 4 and 8 weeks compared with the H2RAs. When the most conservative Bayesian statistical model and intent-to-treat analysis were used, lansoprazole was associated with a 33% higher healing rate at 4 weeks (risk ratio = 1.33; 95% confidence interval [CI] = 1.19 to 1.49) and a 12% higher healing rate at 8 weeks (risk ratio = 1.12; 95% CI = 1.06 to 1.19) than were the H2RA agents. Similar results were obtained when the meta-analysis was performed on evaluable rather than all randomized patients and using the three different analytical techniques noted above. Slightly lower, though still highly significant, improvement in ulcer healing rates was obtained when the meta-analysis was performed using a subset of six studies that received high methodologic quality scores. These results support the conclusion that lansoprazole heals ulcers more quickly than do the H2RAs and also achieves higher overall rates of healing. The eradication of Helicobacter pylori associated with gastric ulcers was not assessed in individual studies.

2-Pyridinylmethylsulfinylbenzimidazoles↗

Population pharmacokinetic modeling of oral cyclosporin using NONMEM: comparison of absorption pharmacokinetic models and design of a Bayesian estimator.

There have been very few population pharmacokinetic (PopPK) studies and Bayesian forecasting methods dealing with cyclosporin (CsA) so far, probably because of the difficulty of modeling the particular absorption profiles of CsA. The present study was conducted in stable renal transplant patients treated with Neoral and employed the NONMEM program. Its goals were (1) to develop a population pharmacokinetic model for CsA based on an Erlang frequency distribution (which describes asymmetric S-shaped absorption profiles) combined with a 2-compartment model; (2) to compare this model with models combining a time-lag parameter and either a zero-order or first-order rate constant and with a model based on a Weibull distribution; and (3) to develop a PK Bayesian estimator for full AUC estimation based on that "Erlang model." The PopPK model was developed in an index set of 70 patients, and then individual PK parameters and AUC were estimated in 10 other patients using Bayesian estimation. The "Erlang" model best described the data, with mean absorption time (MAT), apparent clearance (CL/F), and apparent volume of the central compartment (Vc/F) of 0.78 hours, 26.3 L/h, and 76 L, respectively (interindividual variability CV = 33, 30, and 48%). Bayesian estimation allowed accurate prediction of systemic exposure using only 3 samples collected at 0, 1, and 3 hours. Regression analysis found no significant difference between the predicted and observed concentrations (10 per patient), and AUC(0-12) were estimated with a nonsignificant bias (0.6 to 8.7%) and good precision (RMSE = 5.3%). In conclusion, the Erlang distribution best described CsA absorption profiles, and a Bayesian estimator developed using this model and a mixed-effect PK modeling program provided accurate estimates of CsA systemic exposure using only 3 blood samples.

Area Under Curve↗