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PubMed1997

A flexible approach to time-varying coefficients in the Cox regression setting.

Research on methods for studying time-to-event data (survival analysis) has been extensive in recent years. The basic model in use today represents the hazard function for an individual through a proportional hazards model (Cox, 1972). Typically, it is assumed that a covariate's effect on the hazard function is constant throughout the course of the study. In this paper we propose a method to allow for possible deviations from the standard Cox model, by allowing the effect of a covariate to vary over time. This method is based on a dynamic linear model. We present our method in terms of a Bayesian hierarchical model. We fit the model to the data using Markov chain Monte Carlo methods. Finally, we illustrate the approach with several examples.

Bayes Theorem↗
PubMed2006

A bivariate quantitative genetic model for a threshold trait and a survival trait.

Many of the functional traits considered in animal breeding can be analyzed as threshold traits or survival traits with examples including disease traits, conformation scores, calving difficulty and longevity. In this paper we derive and implement a bivariate quantitative genetic model for a threshold character and a survival trait that are genetically and environmentally correlated. For the survival trait, we considered the Weibull log-normal animal frailty model. A Bayesian approach using Gibbs sampling was adopted in which model parameters were augmented with unobserved liabilities associated with the threshold trait. The fully conditional posterior distributions associated with parameters of the threshold trait reduced to well known distributions. For the survival trait the two baseline Weibull parameters were updated jointly by a Metropolis-Hastings step. The remaining model parameters with non-normalized fully conditional distributions were updated univariately using adaptive rejection sampling. The Gibbs sampler was tested in a simulation study and illustrated in a joint analysis of calving difficulty and longevity of dairy cattle. The simulation study showed that the estimated marginal posterior distributions covered well and placed high density to the true values used in the simulation of data. The data analysis of calving difficulty and longevity showed that genetic variation exists for both traits. The additive genetic correlation was moderately favorable with marginal posterior mean equal to 0.37 and 95% central posterior credibility interval ranging between 0.11 and 0.61. Therefore, this study suggests that selection for improving one of the two traits will be beneficial for the other trait as well.

Bayes Theorem↗
PubMed2001

Evaluation of five commercial enzyme immunoassays for the detection of human cytomegalovirus-specific IgM antibodies in the absence of a commercially available gold standard.

In the recent years the number of commercially available immunoassays for the detection of human cytomegalovirus (HCMV)-specific immunoglobulin M (IgM) antibodies has rapidly increased. The aim of the present study was to evaluate five commercial immunoassays for the serological diagnosis of HCMV-infection. These methods, namely the IMx CMV IgM assay, the AxSYM CMV IgM assay (both Abbott), the Gull CMV IgM, the CMV-IgM-ELA test PCS Medac and the Biotest Anti-HCMV recombinant IgM ELISA, were compared for their diagnostic effectiveness and interference with substances eventually producing cross-reactions with HCMV-IgM (Epstein-Barr-virus (EBV)-IgM, rheumatoid factor (RF)). In addition, repeated measurements on samples from kidney and heart transplant recipients with active HCMV infection were examined to compare the temporal development of the HCMV-IgM measured with the five assay systems. Since there is no commercially available gold standard, it was assumed that the true classification, of whether the patient sample is HCMV-IgM positive or negative, was unknown. Hence sensitivity and specificity were assessed based on a maximum likelihood approach using a "latent class" model. The cross-reactions were quantified by a Bayesian statistical model using prior information for the expected prevalences in the EBV-IgM and rheumatoid factor sample groups. The results of the study demonstrated that there are great differences in sensitivity and specificity as well as in cross-reactions with EBV-IgM and RF between the tested ELISAs.

Adolescent↗
PubMed2006

Bayesian item fit analysis for unidimensional item response theory models.

Assessing item fit for unidimensional item response theory models for dichotomous items has always been an issue of enormous interest, but there exists no unanimously agreed item fit diagnostic for these models, and hence there is room for further investigation of the area. This paper employs the posterior predictive model-checking method, a popular Bayesian model-checking tool, to examine item fit for the above-mentioned models. An item fit plot, comparing the observed and predicted proportion-correct scores of examinees with different raw scores, is suggested. This paper also suggests how to obtain posterior predictive p-values (which are natural Bayesian p-values) for the item fit statistics of Orlando and Thissen that summarize numerically the information in the above-mentioned item fit plots. A number of simulation studies and a real data application demonstrate the effectiveness of the suggested item fit diagnostics. The suggested techniques seem to have adequate power and reasonable Type I error rate, and psychometricians will find them promising.

Algorithms↗
PubMed2005

AUC-guided dosing of tacrolimus prevents progressive systemic overexposure in renal transplant recipients.

BACKGROUND: Tacrolimus has a narrow therapeutic window, and bioavailability is known to vary considerably between renal transplant recipients. Most centers still rely on measurement of trough levels, but there are conflicting reports on the correlation between tacrolimus trough levels and systemic exposure, as measured by the area-under-the-concentration-over-time curve (AUC((0-12h))). METHODS: We developed and validated a two-compartmental population-based pharmacokinetic model with Bayesian estimation of tacrolimus systemic exposure. Subsequently, we used this model to apply prospectively AUC-guided dosing of tacrolimus in 15 consecutive renal transplant recipients. The main objective was to study intrapatient variability in the course of time. RESULTS: Bayesian forecasting with a two-point sampling strategy, a trough level, and a second sample obtained between two and four hours post-dose significantly improved the squared correlation with the AUC((0-12h)) (r(2)= 0.94). Compared with trough level monitoring only, this approach reduced the 95%-prediction interval by 50%. The Bayesian approach proved to be feasible in clinical practice, and provided accurate information about systemic tacrolimus exposure in individual patients. In the AUC-guided dosing cohort the apparent clearance of tacrolimus decreased gradually over time, which was not reflected in corresponding trough levels. CONCLUSION: This simple, flexible method provides the opportunity to tailor immunosuppression, and should help minimize tacrolimus-related toxicity, such as nephrotoxicity and post-transplant diabetes mellitus.

Adult↗
PubMed2003

Prediction of community prevalence of human onchocerciasis in the Amazonian onchocerciasis focus: Bayesian approach.

OBJECTIVE: To develop a Bayesian hierarchical model for human onchocerciasis with which to explore the factors that influence prevalence of microfilariae in the Amazonian focus of onchocerciasis and predict the probability of any community being at least mesoendemic (>20% prevalence of microfilariae), and thus in need of priority ivermectin treatment. METHODS: Models were developed with data from 732 individuals aged > or =15 years who lived in 29 Yanomami communities along four rivers of the south Venezuelan Orinoco basin. The models' abilities to predict prevalences of microfilariae in communities were compared. The deviance information criterion, Bayesian P-values, and residual values were used to select the best model with an approximate cross-validation procedure. FINDINGS: A three-level model that acknowledged clustering of infection within communities performed best, with host age and sex included at the individual level, a river-dependent altitude effect at the community level, and additional clustering of communities along rivers. This model correctly classified 25/29 (86%) villages with respect to their need for priority ivermectin treatment. CONCLUSION: Bayesian methods are a flexible and useful approach for public health research and control planning. Our model acknowledges the clustering of infection within communities, allows investigation of links between individual- or community-specific characteristics and infection, incorporates additional uncertainty due to missing covariate data, and informs policy decisions by predicting the probability that a new community is at least mesoendemic.

Adolescent↗
PubMed2001

Bayesian inference for categorical traits with an application to variance component estimation.

We implemented statistical models of Bayesian inference that included direct and maternal genetic effects for genetic parameter estimation of categorical traits by Gibbs sampling. The estimation errors and variances of estimates of animal versus sire and maternal grandsire models, of linear versus threshold models, of single-trait versus multiple-trait models, and of treating herd-year-season as fixed versus random effects in the model were compared. The results indicated that linear models yielded biased estimates of genetic parameters for categorical traits. The animal model was improper for analysis of categorical traits using a threshold model and the Gibbs sampler. Moreover, linear versus threshold models and animal versus sire-maternal grandsire models resulted in larger Monte Carlo errors and increased auto-correlations among posterior samples. Treating herd-year-seasons as random effects in the threshold models decreased the Monte Carlo error, auto-correlations, and the variances of estimates. Efficiency of the single-trait threshold sire model, as measured by the variance of the estimates, was lower than for a multiple-trait model that included a correlated continuous trait, but both estimates were unbiased. Therefore, the threshold single-trait sire and maternal grandsire model is a feasible alternative to the multiple-trait model for analysis of variance components of categorical traits affected by direct and maternal genetic factors.

Animals↗
PubMed1997

Large sample Bayesian inference on the parameters of the proportional hazard models.

This paper considers large sample Bayesian analysis of the proportional hazards model when interest is in inference on the parameters and estimation of the log relative risk for specified covariate vectors rather than on prediction of the survival function. We use a normal prior distribution for the parameters and make inferences based on the derived posterior distribution. The suggested approach is much simpler than alternative Bayesian analyses previously suggested for the proportional hazards models. Using simulated data we compare estimates obtained from the Bayesian analysis with those obtained from the full proportional hazards model and the reduced model after backwards elimination. We show that under a wider range of assumptions, the Bayesian analysis provides reduced estimation errors and improved rejection of noise variables. Finally, we illustrate the methodology using data from a large study of prognostic markers in breast cancer.

Bayes Theorem↗
PubMed2006

Mapping malaria transmission in West and Central Africa.

We have produced maps of Plasmodium falciparum malaria transmission in West and Central Africa using the Mapping Malaria Risk in Africa (MARA) database comprising all malaria prevalence surveys in these regions that could be geolocated. The 1846 malaria surveys analysed were carried out during different seasons, and were reported using different age groupings of the human population. To allow comparison between these, we used the Garki malaria transmission model to convert the malaria prevalence data at each of the 976 locations sampled to a single estimate of transmission intensity E, making use of a seasonality model based on Normalized Difference Vegetation Index (NDVI), temperature and rainfall data. We fitted a Bayesian geostatistical model to E using further environmental covariates and applied Bayesian kriging to obtain smooth maps of E and hence of age-specific prevalence. The product is the first detailed empirical map of variations in malaria transmission intensity that includes Central Africa. It has been validated by expert opinion and in general confirms known patterns of malaria transmission, providing a baseline against which interventions such as insecticide-treated nets programmes and trends in drug resistance can be evaluated. There is considerable geographical variation in the precision of the model estimates and, in some parts of West Africa, the predictions differ substantially from those of other risk maps. The consequent uncertainties indicate zones where further survey data are needed most urgently. Malaria risk maps based on compilations of heterogeneous survey data are highly sensitive to the analytical methodology.

Africa, Central↗
PubMed2007

Bayesian analysis of latent variable models with non-ignorable missing outcomes from exponential family.

To provide a comprehensive framework for analysing complex non-normal medical and biological data, we propose a Bayesian approach for a non-linear latent variable model with covariates, and non-ignorable missing data, under the exponential family of distributions. The non-ignorable missing mechanism is defined via a logistic regression model. Based on conjugate prior distributions, full conditional distributions for the implementation of Markov chain Monte Carlo methods in simulating observations from the joint posterior distribution are derived. These observations are used in computing the Bayesian estimates, as well as in implementing a path sampling procedure to evaluate the Bayes factor for model comparison. The proposed methods are illustrated using real data from a study on the non-adherence of hypertension patients.

Antihypertensive Agents↗
PubMed2000

Vancomycin pharmacokinetics and Bayesian estimation in pediatric patients.

The vancomycin pharmacokinetic profile was characterized in six pediatric patients and the potential of nonlinear mixed effects modeling and Bayesian forecasting for vancomycin monitoring was explored using NONMEM V (1.1). Based on steady state serial vancomycin concentrations, the estimates of mean t1/2, Vd, and Cl derived by the Sawchuk and Zaske method (1) were 3.52 hours, 0.57 L/kg, and 0.12 L/h per kg, respectively. NONMEM analysis demonstrated that a weight-adjusted two-compartment model described individual patients' data better than a comparable one-compartment model. The two-compartment estimates of mean t1/2alpha, t1/2beta, Vss, and Cl were 0.80 hour, 5.63 hours, 0.63 L/kg, and 0.11 L/h per kg, respectively. The relatively long mean t1/2alpha suggests that peak vancomycin concentrations measured earlier than 4 hours postdose do not reflect postdistributional serum concentrations. NONMEM population modeling revealed that a weight-adjusted two-compartment model provided a better fit than a comparable one-compartment model. The resulting population parameters and variances were fixed in NONMEM to obtain Bayesian predictions of individual vancomycin serum concentrations. Bayesian estimation with either a single midinterval or trough sample has the potential to provide accurate and precise predictions of vancomycin concentrations. This should be evaluated using a vancomycin population pharmacokinetic model based on a larger sample of pediatric patients.

Anti-Bacterial Agents↗
PubMed1994

The hierarchical Bayesian approach to population pharmacokinetic modelling.

Compartmental models are widely used to model the profile of drug concentrations versus time from administration in an individual subject. Observed concentrations are then modelled as noisy departures from the underlying profile, the latter characterised for each individual by a small number of 'individual parameters'. When a population of individuals is studied, inter-individual variation is modelled by assuming that the individual profile parameters are drawn from a population distribution, the latter characterised by 'population parameters' describing, in effect, a mean population profile and individual variation around it. From a Bayesian statistical perspective, such models fit exactly into the so-called hierarchical modelling framework, which provides a coherent basis for individual and population inferences and prediction, as well as for decision-making (for example, the design of dosage regimens). This paper outlines the hierarchical model framework and describes how the required computations can be carried out in a straightforward manner by a Markov chain Monte Carlo technique known as Gibbs sampling, even when models involve mean-variance relationships and outliers.

Bayes Theorem↗
PubMed2000

Bayesian analysis of an epidemiologic model of Plasmodium falciparum malaria infection in Ndiop, Senegal.

Plasmodium falciparum has a complex transmission cycle. Public health planning and research would benefit from the ability of a calibrated model to predict the epidemiologic characteristics of populations living in areas of malaria endemicity. This paper describes the application of Bayesian calibration to a malaria transmission model using longitudinal data gathered from 176 subjects in Ndiop, Senegal, from July 1, 1993, to July 31, 1994. The model was able to adequately predict P. falciparum parasitemia prevalence in the study population. Further insight into the dynamics of malaria in Ndiop was provided. During the dry season, the estimated fraction of nonimmune subjects goes down to 20% and then increases up to 80%. The model-predicted time-weighted average incidences contributed by nonimmune and immune individuals are 0.52 cases per day and 0.47 cases per day, respectively. The median times needed to acquire infection (conversion delay) for nonimmune and immune individuals are estimated at 39 days and 285 days, respectively.

Adolescent↗
PubMed2001

Genetic and dietary factors affecting human metabolism of 1,3-butadiene.

The objective of this project was to determine the factors associated with differences in butadiene (BD) inhalation uptake and the rate of metabolism for BD to epoxy butene by monitoring exhaled breath during and after a brief exposure to BD in human volunteers. A total of 133 subjects (equal males and females; four racial groups) provided final data. Volunteers gave informed consent and completed a questionnaire including diet and alcohol use. A venous blood sample was collected for genotyping CYP2E1. Subjects received a 20 min exposure to 2.0 ppm of BD, followed by a 40 min washout period. The total administered dose was 0.6 ppm*h, which is in the range of everyday exposures. Ten, 1 or 2 min exhaled breath samples (five during and five after exposure) were collected using an optimized strategy. BD was determined by GC-FID analysis. Breathing activity (minute ventilation, breath frequency and tidal volume) was measured to estimate alveolar ventilation. After the washout period, 250 mg of chlorzoxazone were administered and urine samples collected for 6 h to measure 2E1 phenotype. The total BD uptake during exposure (inhaled BD minus exhaled) was estimated. A three-compartment PBPK model was fitted to each subject's breath measurements to estimate personal and population model parameters, including in-vivo BD metabolic rate. A hierarchical Bayesian PBPK model was fit by Monte Carlo simulations to estimate model parameters. Regression and ANOVA analyses were performed. Earlier data analysis showed wide ranges for both total uptake BD and metabolic rate. Both varied significantly by sex and age, and showed suggestive differences by race, with Asians having the highest rates. The analyses reported here found no correlation between total BD uptake and metabolic rate. No significant differences were found for oxidation rates by 2E1 genotype or phenotype, but the rates showed trends consistent with reported differences by genotype and phenotype for chlorzoxazone metabolism. No effects on metabolic rate were observed for long-term alcohol consumption, or consumption in the past 24 h. Overall, neither dietary factors nor genetic differences explained much of the wide variability in metabolic rates. Population characteristics, age, sex, and race, were the most important explanatory variables, but a large fraction of the total variability in metabolism remains to be explained.

Administration, Inhalation↗
PubMed2004

Population pharmacokinetic modelling of tramadol with application of the NPEM algorithms.

BACKGROUND AND OBJECTIVE: Although the kinetic behaviour of tramadol has been described, the present study is the first to our knowledge, to report specifically on the population pharmacokinetic modelling of tramadol hydrochloride. METHODS: The parametric Iterative Two-stage Bayesian Population Model (IT2B) program followed by the Non-parametric Expectation Maximization Population Model (NPEM2) program was used to determine population pharmacokinetic parameter values of tramadol in 138 postoperative orthopaedic Malaysian patients. All patients had received a 100 mg intravenous dose of tramadol, infused over 2-3 min, as their first postoperative analgesic. Blood was sampled at 0 min and subsequently at 15, 30 min, 1, 2, 4, 8, 16, 20 and 24 h for serum tramadol high-performance liquid chromatography analysis. RESULTS AND DISCUSSION: The one-compartmental model pharmacokinetic parameters--volume of distribution (Vd), elimination rate constant (kel) and the total clearance rates (ClT)--found were: mean Vd = 167.6 +/- 63.84 L; median Vd = 161.48 L; mean kel = 0.1241 +/- 0.056 h(-1); median kel = 0.1138 h(-1); ClT = 19.57 +/- 9.51 L/h; median ClT =18.12 L/h. The interindividual coefficient of variation of ClT (48.56%) was higher than that of Vd (38.09%), indicating the presence of other possible influencing factors on tramadol's ClT such as CYP2D6 polymorphism, gender and age. Overall, NPEM2 suggested more diversity in the population than did IT2B.

Adolescent↗
PubMed2006

Refining a probabilistic model for interpreting verbal autopsy data.

OBJECTIVE: To build on the previously reported development of a Bayesian probabilistic model for interpreting verbal autopsy (VA) data, attempting to improve the model's performance in determining cause of death and to reassess it. DESIGN: An expert group of clinicians, coming from a wide range geographically and in terms of specialization, was convened. Over a four-day period the content of the previous probabilistic model was reviewed in detail and adjusted as necessary to reflect the group consensus. The revised model was tested with the same 189 VA cases from Vietnam, assessed by two local clinicians, that were used to test the preliminary model. RESULTS: The revised model contained a total of 104 indicators that could be derived from VA data and 34 possible causes of death. When applied to the 189 Vietnamese cases, 142 (75.1%) achieved concordance between the model's output and the previous clinical consensus. The remaining 47 cases (24.9%) were presented to a further independent clinician for reassessment. As a result, consensus between clinical reassessment and the model's output was achieved in 28 cases (14.8%); clinical reassessment and the original clinical opinion agreed in 8 cases (4.2%), and in the remaining 11 cases (5.8%) clinical reassessment, the model, and the original clinical opinion all differed. Thus overall the model was considered to have performed well in 170 cases (89.9%). CONCLUSIONS: This approach to interpreting VA data continues to show promise. The next steps will be to evaluate it against other sources of VA data. The expert group approach to determining the required probability base seems to have been a productive one in improving the performance of the model.

Autopsy↗
PubMed2006

Comparative performance of Bayesian and AIC-based measures of phylogenetic model uncertainty.

Reversible-jump Markov chain Monte Carlo (RJ-MCMC) is a technique for simultaneously evaluating multiple related (but not necessarily nested) statistical models that has recently been applied to the problem of phylogenetic model selection. Here we use a simulation approach to assess the performance of this method and compare it to Akaike weights, a measure of model uncertainty that is based on the Akaike information criterion. Under conditions where the assumptions of the candidate models matched the generating conditions, both Bayesian and AIC-based methods perform well. The 95% credible interval contained the generating model close to 95% of the time. However, the size of the credible interval differed with the Bayesian credible set containing approximately 25% to 50% fewer models than an AIC-based credible interval. The posterior probability was a better indicator of the correct model than the Akaike weight when all assumptions were met but both measures performed similarly when some model assumptions were violated. Models in the Bayesian posterior distribution were also more similar to the generating model in their number of parameters and were less biased in their complexity. In contrast, Akaike-weighted models were more distant from the generating model and biased towards slightly greater complexity. The AIC-based credible interval appeared to be more robust to the violation of the rate homogeneity assumption. Both AIC and Bayesian approaches suggest that substantial uncertainty can accompany the choice of model for phylogenetic analyses, suggesting that alternative candidate models should be examined in analysis of phylogenetic data. [AIC; Akaike weights; Bayesian phylogenetics; model averaging; model selection; model uncertainty; posterior probability; reversible jump.].

Bayes Theorem↗
PubMed2004

Bayesian experimental design for nonlinear mixed-effects models with application to HIV dynamics.

Bayesian experimental design is investigated for Bayesian analysis of nonlinear mixed-effects models. Existence of the posterior risk for parameter estimation is shown. When the same prior distribution is used for both design and inference, existence of the preposterior risk for design is also proven. If the prior distribution used in design is different from that used for inference, sufficient conditions are established for existence of the preposterior risk for design. A case study of design for an experiment in population HIV dynamics is provided.

Bayes Theorem↗