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PubMed2004

Conflicting phylogenies of balsaminoid families and the polytomy in Ericales: combining data in a Bayesian framework.

The balsaminoid Ericales, namely Balsaminaceae, Marcgraviaceae, Tetrameristaceae, and Pellicieraceae have been confidently placed at the base of Ericales, but the relations among these families have been resolved differently in recent analyses. Sister to this basal group is a large polytomy comprising all other families of Ericales, which is associated with short internodes. Because there are more than 13 kb of sequences for a large sampling of representatives, a thorough examination of the available data with novel methods seemed in place. Because of its computational speed, Bayesian phylogenetics allows for the use of parameter-rich models that can accommodate differences in the evolutionary process between partitions in a simultaneous analysis. In addition, there are recently proposed Bayesian strategies of assessing incongruence between partitions. We have applied these methods to the current problems in Ericales phylogeny, taking into account reported pitfalls in Bayesian analysis such as model selection uncertainty. Based on our results we infer several, previously unresolved relationships in the order Ericales. In balsaminoid families, we find that the closest relatives of Balsaminaceae are Marcgraviaceae. In the Ericales polytomy, we find strong support for Pentaphylacaceae sensu APG II as the sister group of Maesaceae. In addition, Symplocaceae receive a position as sister to Theaceae and these families form a monophyletic group together with Styracaceae-Diapensiaceae. At the base of this clade are Actinidiaceae and Clethraceae. The positions of Ebenaceae and Lecythidaceae remain uncertain.

Balsaminaceae↗
PubMed2006

Likelihood ratio tests in behavioral genetics: problems and solutions.

The likelihood ratio test of nested models for family data plays an important role in the assessment of genetic and environmental influences on the variation in traits. The test is routinely based on the assumption that the test statistic follows a chi-square distribution under the null, with the number of restricted parameters as degrees of freedom. However, tests of variance components constrained to be non-negative correspond to tests of parameters on the boundary of the parameter space. In this situation the standard test procedure provides too large p-values and the use of the Akaike Information Criterion (AIC) or the Bayesian Information Criterion (BIC) for model selection is problematic. Focusing on the classical ACE twin model for univariate traits, we adapt existing theory to show that the asymptotic distribution for the likelihood ratio statistic is a mixture of chi-square distributions, and we derive the mixing probabilities. We conclude that when testing the AE or the CE model against the ACE model, the p-values obtained from using the chi(2)(1 df) as the reference distribution should be halved. When the E model is tested against the ACE model, a mixture of chi(2)(0 df), chi(2)(1 df) and chi(2)(2 df) should be used as the reference distribution, and we provide a simple formula to compute the mixing probabilities. Similar results for tests of the AE, DE and E models against the ADE model are also derived. Failing to use the appropriate reference distribution can lead to invalid conclusions.

Analysis of Variance↗
PubMedDate not supplied

Estimation of markov chain transition probabilities and rates from fully and partially observed data: uncertainty propagation, evidence synthesis, and model calibration.

Markov transition models are frequently used to model disease progression. The authors show how the solution to Kolmogorov's forward equations can be exploited to map between transition rates and probabilities from probability data in multistate models. They provide a uniform, Bayesian treatment of estimation and propagation of uncertainty of transition rates and probabilities when 1) observations are available on all transitions and exact time at risk in each state (fully observed data) and 2) observations are on initial state and final state after a fixed interval of time but not on the sequence of transitions (partially observed data). The authors show how underlying transition rates can be recovered from partially observed data using Markov chain Monte Carlo methods in WinBUGS, and they suggest diagnostics to investigate inconsistencies between evidence from different starting states. An illustrative example for a 3-state model is given, which shows how the methods extend to more complex Markov models using the software WBDiff to compute solutions. Finally, the authors illustrate how to statistically combine data from multiple sources, including partially observed data at several follow-up times and also how to calibrate a Markov model to be consistent with data from one specific study.

Calibration↗
PubMedDate not supplied

Markov chain Monte Carlo estimation of a multiparameter decision model: consistency of evidence and the accurate assessment of uncertainty.

Decision models are usually populated 1 parameter at a time, with 1 item of information informing each parameter. Often, however, data may not be available on the parameters themselves but on several functions of parameters, and there may be more items of information than there are parameters to be estimated. The authors show how in these circumstances all the model parameters can be estimated simultaneously using Bayesian Markov chain Monte Carlo methods. Consistency of the information and/or the adequacy of the model can also be assessed within this framework. Statistical evidence synthesis using all available data should result in more precise estimates of parameters and functions of parameters, and is compatible with the emphasis currently placed on systematic use of evidence. To illustrate this, WinBUGS software is used to estimate a simple 9-parameter model of the epidemiology of HIV in women attending prenatal clinics, using information on 12 functions of parameters, and to thereby compute the expected net benefit of 2 alternative prenatal testing strategies, universal testing and targeted testing of high-risk groups. The authors demonstrate improved precision of estimates, and lower estimates of the expected value of perfect information, resulting from the use of all available data.

AIDS Serodiagnosis↗
PubMed2003

Analysis of the evolutionary relationships of HIV-1 and SIVcpz sequences using bayesian inference: implications for the origin of HIV-1.

The most plausible origin of HIV-1 group M is an SIV lineage currently represented by SIVcpz isolated from the chimpanzee subspecies Pan troglodytes troglodytes. The origin of HIV-1 group O is less clear. Putative recombination between any of the HIV-1 and SIVcpz sequences was tested using bootscanning and Bayesian-scanning plots, as well as a new method using a Bayesian multiple change-point (BMCP) model to infer parental sequences and crossing-over points. We found that in the case of highly divergent sequences, such as HIV-1/SIVcpz, Bayesian scanning and BMCP methods are more appropriate than bootscanning analysis to investigate spatial phylogenetic variation, including estimating the boundaries of the regions with discordant evolutionary relationships and the levels of support of the phylogenetic clusters under study. According to the Bayesian scanning plots and BMCP method, there was strong evidence for discordant phylogenetic clustering throughout the genome: (1) HIV-1 group O clustered with SIVcpzANT/TAN in middle pol, and partial vif/env; (2) SIVcpzGab1 clustered with SIVcpzANT/TAN in 3'pol/vif, and middle env; (3) HIV-1 group O grouped with SIVcpzCamUS and SIVcpzGab1 in p17/p24; (4) HIV-1 group M was more closely related to SIVcpzCamUS in 3'gag/pol and in middle pol, whereas in partial gp120 group M clustered with group O. Conditionally independent phylogenetic analysis inferred by maximum likelihood (ML) and Bayesian methods further confirmed these findings. The discordant phylogenetic relationships between the HIV-1/SIVcpz sequences may have been caused by ancient recombination events, but they are also due, at least in part, to altered rates of evolution between parental SIVcpz lineages.

Animals↗
PubMed2002

Handling non-negativity in deconvolution of physiological signals: a nonlinear stochastic approach.

A stochastic interpretation of Tikhonov regularization has been recently proposed to attack some open problems of deconvolution when dealing with physiological systems, i.e., in addition to ill-conditioning, infrequent and nonuniform sampling and necessity of having credible confidence intervals. However, the possible violation of the non-negativity constraint cannot be dealt with on firm statistical grounds, since the model of the unknown signal is compatible with negative realizations. In this paper, we propose a new model of the unknown input which excludes negative values. The model is embedded within a Bayesian estimation framework to calculate, by resorting to a Markov chain Monte Carlo algorithm, a nonlinear estimate of the unknown input given by its a posteriori expected value. Applications to simulated and real hormone secretion/pharmacokinetic problems are presented which show that this nonlinear approach is more accurate than the linear one. In addition, more realistic confidence intervals are obtained.

Algorithms↗
PubMed2002

Detecting recombination with MCMC.

MOTIVATION: We present a statistical method for detecting recombination, whose objective is to accurately locate the recombinant breakpoints in DNA sequence alignments of small numbers of taxa (4 or 5). Our approach explicitly models the sequence of phylogenetic tree topologies along a multiple sequence alignment. Inference under this model is done in a Bayesian way, using Markov chain Monte Carlo (MCMC). The algorithm returns the site-dependent posterior probability of each tree topology, which is used for detecting recombinant regions and locating their breakpoints. RESULTS: The method was tested on a synthetic and three real DNA sequence alignments, where it was found to outperform the established detection methods PLATO, RECPARS, and TOPAL.

Algorithms↗
PubMed2006

Population pharmacokinetics of high-dose methotrexate in children with acute lymphoblastic leukaemia.

OBJECTIVE: To develop and a priori validate a methotrexate population pharmacokinetic model in children with acute lymphoblastic leukaemia (ALL), receiving high-dose methotrexate followed by folinic acid rescue, identifying the covariates that could explain part of the pharmacokinetic variability of methotrexate. METHODS: The study was carried out in 49 children (aged 6 months to 17 years) who received high-dose methotrexate (3 g/m(2) per course) in long-term treatment. In an index group (37 individuals; 1236 methotrexate plasma concentrations), a population pharmacokinetic model was developed using a nonlinear mixed-effects model. The remaining patients' data (12 individuals; 278 methotrexate plasma concentrations) were used for model validation. Age, sex, total bodyweight (TBW), height, body surface area, lowest urine pH during infusion, serum creatinine, ALT, AST, folinic acid dose and length of rescue were analysed as possible covariates. The final predictive performance of the pharmacokinetic model was tested using standardised mean prediction errors. RESULTS: The final population pharmacokinetic model (two-compartmental) included only age and total bodyweight as influencing clearance (CL) and volume of distribution of central compartment (V(1)). For children aged < or =10 years: CL (L/h) = 0.287 . TBW(0.876); V(1) (L) = 0.465 . TBW, and for children aged >10 years: CL (L/h) = 0.149 . TBW; V(1) (L) = 0.437 . TBW. From the base to the final model, the inter-individual variabilities for CL and V(1) were significantly reduced in both age groups (30-50%). The coefficients of variation of the pharmacokinetic parameters were <30%, while residual and inter-occasional coefficients maintained values close to 40%. Validation of the proposed model revealed the suitability of the model. CONCLUSION: A methotrexate population pharmacokinetic model has been developed for ALL children. The proposed model could be used in Bayesian algorithms with a limited sampling strategy to estimate the systemic exposure of individual patients to methotrexate and adapt both folinic acid rescue and methotrexate dosing accordingly.

Adolescent↗
PubMed2004

An interstitial compartment is necessary to link the pharmacokinetics and pharmacodynamics of mivacurium.

BACKGROUND AND OBJECTIVE: The time course of action of mivacurium does not correlate with its rapid breakdown by plasma cholinesterase. Pharmacokinetic-pharmacodynamic (PK-PD) modelling was applied to obtain more insight in the concentration-effect relationship. METHODS: Fourteen patients between 25 and 55yr, undergoing non-major surgery, American Society of Anesthesiologists Grade I-II, were included. All patients received thiopentone/fentanyl/isoflurane/oxygen/nitrous oxide anaesthesia. Neuromuscular block was monitored mechanomyographically using single twitch stimulation (0.1 Hz). Mivacurium was administered as a short-term infusion, mean (standard deviation) duration 4.7 (1.0) min and dose 145 (33) microg kg(-1). Arterial blood samples were obtained, and plasma was analysed using high performance liquid chromatography. PK-PD modelling was performed using an iterative Bayesian two-stage approach, assuming that the trans-trans and cis-trans isomers are equally potent. RESULTS: A PK-PD model with an effect compartment linked to plasma did not fit to the data satisfactorily. A model using an interstitial space compartment between plasma and effect compartment fitted significantly better. Parameters (mean (percentage coefficient of variation)) of the best fitting model were: k(ip) 0.374 min(-1) (46%), k(ei) 0.151 min(-1) (36%), EC50 98 microg L(-1) (29%) and gamma 3.7 (22%). CONCLUSIONS: The PK-PD behaviour of mivacurium could be described using a model with an interstitial space compartment interposed between plasma and effect compartment. This model shows that the time course of mivacurium is mainly governed by the concentration decline in this interposed compartment and only indirectly related to the rapid plasma clearance.

Adult↗
PubMed1997

Multimodality Bayesian algorithm for image reconstruction in positron emission tomography: a tissue composition model.

The use of anatomical information to improve the quality of reconstructed images in positron emission tomography (PET) has been extensively studied. A common strategy has been to include spatial smoothing within boundaries defined from the anatomical data. We present an alternative method for the incorporation of anatomical information into PET image reconstruction, in which we use segmented magnetic resonance (MR) images to assign tissue composition to PET image pixels. We model the image as a sum of activities for each tissue type, weighted by the assigned tissue composition. The reconstruction is performed as a maximum a posteriori (MAP) estimation of the activities of each tissue type. Two prior functions, defined for tissue-type activities, are considered. The algorithm is tested in realistic simulations employing a full physical model of the PET scanner.

Algorithms↗
PubMed2004

An extended general location model for causal inferences from data subject to noncompliance and missing values.

Noncompliance is a common problem in experiments involving randomized assignment of treatments, and standard analyses based on intention-to-treat or treatment received have limitations. An attractive alternative is to estimate the Complier-Average Causal Effect (CACE), which is the average treatment effect for the subpopulation of subjects who would comply under either treatment (Angrist, Imbens, and Rubin, 1996, Journal of American Statistical Association 91, 444-472). We propose an extended general location model to estimate the CACE from data with noncompliance and missing data in the outcome and in baseline covariates. Models for both continuous and categorical outcomes and ignorable and latent ignorable (Frangakis and Rubin, 1999, Biometrika 86, 365-379) missing-data mechanisms are developed. Inferences for the models are based on the EM algorithm and Bayesian MCMC methods. We present results from simulations that investigate sensitivity to model assumptions and the influence of missing-data mechanism. We also apply the method to the data from a job search intervention for unemployed workers.

Algorithms↗
PubMed1985

A computer simulation of medical decision strategy performance.

This study demonstrates a computer model which can be used to compare the effects of errors in probability and utility estimation on the performance of Bayesian and alternative medical decision strategies. The model task requires choosing one of three treatments for a patient with one of three diseases based on the patient's state with respect to five binary cues and estimates of the prior probabilities of disease, the conditional probabilities of the cues and the utilities of the treatments. A classic decision analytic strategy uses Bayes' formula to calculate posterior probabilities of disease and chooses treatments based on maximization of expected value. Alternative strategies use likelihood ratios to calculate disease scores for each patient state and choose the treatment with highest payoff for the disease with the highest score. Two strategies with different cutoffs for the ratios are compared with a random strategy and a classic decision analytic strategy. The simulation results show that the payoffs for all strategies except the random strategy decline with increasing estimation error. The decision analytic strategy has the highest mean payoff at all levels of error. The differences between this optical strategy and the alternatives, however, decrease as estimation error increases, and the frequency with which the strategies based on simple diagnostic scoring rules outperform the formal Bayesian strategy increases.

Bayes Theorem↗
PubMed2004

An empirical comparison of information-theoretic selection criteria for multivariate behavior genetic models.

Information theory provides an attractive basis for statistical inference and model selection. However, little is known about the relative performance of different information-theoretic criteria in covariance structure modeling, especially in behavioral genetic contexts. To explore these issues, information-theoretic fit criteria were compared with regard to their ability to discriminate between multivariate behavioral genetic models under various model, distribution, and sample size conditions. Results indicate that performance depends on sample size, model complexity, and distributional specification. The Bayesian Information Criterion (BIC) is more robust to distributional misspecification than Akaike's Information Criterion (AIC) under certain conditions, and outperforms AIC in larger samples and when comparing more complex models. An approximation to the Minimum Description Length (MDL; Rissanen, J. (1996). IEEE Transactions on Information Theory 42:40-47, Rissanen, J. (2001). IEEE Transactions on Information Theory 47:1712-1717) criterion, involving the empirical Fisher information matrix, exhibits variable patterns of performance due to the complexity of estimating Fisher information matrices. Results indicate that a relatively new information-theoretic criterion, Draper's Information Criterion (DIC; Draper, 1995), which shares features of the Bayesian and MDL criteria, performs similarly to or better than BIC. Results emphasize the importance of further research into theory and computation of information-theoretic criteria.

Bayes Theorem↗
PubMed2004

Bayesian Monte Carlo uncertainty analysis of human health risks from animal antimicrobial use in a dynamic model of emerging resistance.

Recent qualitative analyses warn of potential future human health risks from emergence of antibiotic resistance in food-borne pathogens due to the use of similar antimicrobial drugs in both food animals and human medicine. While historical data suggest that human health risks from some animal antimicrobials, such as virginiamycin (VM), have remained low (McDonald et al., 2001), there is a widespread concern that "resistance epidemics" or endemics could arise in the future. How reassuring is the past about the future? This article applies quantitative risk assessment methods to help find out, using human health risks from VM and the nearly identical human antimicrobial quinupristin-dalfopristin (QD) as a case study. A dynamic simulation model is used to predict the risks of emerging resistance to human antimicrobials in human populations from given input assumptions. Bayesian Monte Carlo uncertainty analysis allows past data to constrain and inform selection of input parameter values, and thus to predict the possible future resistance patterns that are consistent with historical data. The results show that health risks from VM use in food animals are highly sensitive to the human prescription rate of QD. For realistic prescription rates, quantitative risks are less than 1 x 10(-6) even for members of the most-threatened (ICU patient) population, while societal risks are <1 excess statistical death per year for the whole U.S. population. Such quantitative estimates complement more qualitative assessments that discuss the possibility of future "resistance epidemics" (or endemics) without quantifying their probabilities.

Animals↗
PubMed2003

Uising WinBUGS to fit nonlinear mixed models with an application to pharmacokinetic modelling of insulin response to glucose challenge in sheep exposed antenatally to glucocorticoids.

Many chronic diseases of adulthood, such as hypertension and diabetes, are now believed to have at least some of their origins before birth. Extensive studies in animal models have identified antenatal exposure to excess glucocorticoids as a leading candidate for the physiological cause of fetal compromise. The resulting adverse intra-uterine environment appears to "program" the individual for higher risk of subsequent disease. We present an analysis of blood glucose and insulin concentrations collected during glucose tolerance tests at 6 and 12 months postnatal age in a cohort of sheep that were treated antenatally with injections of betamethasone (a synthetic glucocorticoid) which, when injected into the mother, cross the placenta to the fetus. A simple pharmacokinetic model, essentially a modification of the single compartment model with first-order absorption and elimination, is developed to describe the time course of glucose concentration and the associated insulin response. The resulting nonlinear mixed model is implemented in a Bayesian framework using the Markov chain Monte Carlo technique Gibbs Sampling via the software package BUGS. This sampling process allows inferences to be made directly about derived quantities with an immediate physical interpretation, such as the maximum insulin concentration in response to glucose challenge. At 6 months postnatal age, sheep treated with antenatal injections of synthetic glucocorticoids had raised insulin concentration in comparison to controls after bolus administration of glucose. This effect persisted to 12 months postnatal age only in the sheep that received multiple doses of glucocorticoids. Moreover, the raised insulin concentration in sheep that received direct injections of synthetic glucocorticoid as fetuses is accompanied by better glucose clearance than in those sheep that received only saline injections, a phenomenon that is not observed in the animals that received maternal injections. It is argued that the fitting of an appropriate statistical model to complex physiological data does not necessarily proclude a result that has a clear interpretation for clinical scientists.

Animals↗
PubMed2006

Outdoor NOx and stroke mortality: adjusting for small area level smoking prevalence using a Bayesian approach.

There is increasing evidence, mainly from daily time series studies, linking air pollution and stroke. Small area level geographical correlation studies offer another means of examining the air pollution-stroke association. Populations within small areas may be more homogeneous than those within larger areal units, and census-based socioeconomic information may be available to adjust for confounding effects. Data on smoking from health surveys may be incorporated in spatial analyses to adjust for potential confounding effects but may be sparse at the small area level. Smoothing, using data from neighbouring areas, may be used to increase the precision of smoking prevalence estimates for small areas. We examined the effect of modelled outdoor NOx levels on stroke mortality using a Bayesian hierarchical spatial model to incorporate random effects, in order to allow for unmeasured confounders and to acknowledge sampling error in the estimation of smoking prevalence. We observed an association between NOx and stroke mortality after taking into account random effects at the small area level. We found no association between smoking prevalence and stroke mortality at the small area level after modelling took into account imprecision in estimating smoking prevalence. The approach we used to incorporate smoking as a covariate in a single large model is conceptually sound, though it made little difference to the substantive results.

Age Factors↗
PubMed2006

Multivariable modeling of radiotherapy outcomes, including dose-volume and clinical factors.

PURPOSE: The probability of a specific radiotherapy outcome is typically a complex, unknown function of dosimetric and clinical factors. Current models are usually oversimplified. We describe alternative methods for building multivariable dose-response models. METHODS: Representative data sets of esophagitis and xerostomia are used. We use a logistic regression framework to approximate the treatment-response function. Bootstrap replications are performed to explore variable selection stability. To guard against under/overfitting, we compare several analytical and data-driven methods for model-order estimation. Spearman's coefficient is used to evaluate performance robustness. Novel graphical displays of variable cross correlations and bootstrap selection are demonstrated. RESULTS: Bootstrap variable selection techniques improve model building by reducing sample size effects and unveiling variable cross correlations. Inference by resampling and Bayesian approaches produced generally consistent guidance for model order estimation. The optimal esophagitis model consisted of 5 dosimetric/clinical variables. Although the xerostomia model could be improved by combining clinical and dose-volume factors, the improvement would be small. CONCLUSIONS: Prediction of treatment response can be improved by mixing clinical and dose-volume factors. Graphical tools can mitigate the inherent complexity of multivariable modeling. Bootstrap-based variable selection analysis increases the reliability of reported models. Statistical inference methods combined with Spearman's coefficient provide an efficient approach to estimating optimal model order.

Carcinoma, Non-Small-Cell Lung↗
PubMed2006

The effect of ignoring individual heterogeneity in Weibull log-normal sire frailty models.

The objective of this study was, by means of simulation, to quantify the effect of ignoring individual heterogeneity in Weibull sire frailty models on parameter estimates and to address the consequences for genetic inferences. Three simulation studies were evaluated, which included 3 levels of individual heterogeneity combined with 4 levels of censoring (0, 25, 50, or 75%). Data were simulated according to balanced half-sib designs using Weibull log-normal animal frailty models with a normally distributed residual effect on the log-frailty scale. The 12 data sets were analyzed with 2 models: the sire model, equivalent to the animal model used to generate the data (complete sire model), and a corresponding model in which individual heterogeneity in log-frailty was neglected (incomplete sire model). Parameter estimates were obtained from a Bayesian analysis using Gibbs sampling, and also from the software Survival Kit for the incomplete sire model. For the incomplete sire model, the Monte Carlo and Survival Kit parameter estimates were similar. This study established that when unobserved individual heterogeneity was ignored, the parameter estimates that included sire effects were biased toward zero by an amount that depended in magnitude on the level of censoring and the size of the ignored individual heterogeneity. Despite the biased parameter estimates, the ranking of sires, measured by the rank correlations between true and estimated sire effects, was unaffected. In comparison, parameter estimates obtained using complete sire models were consistent with the true values used to simulate the data. Thus, in this study, several issues of concern were demonstrated for the incomplete sire model.

Animals↗