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PubMed1997

Predictive model selection for repeated measures random effects models using Bayes factors.

The random effects model fit to repeated measures data is an extremely common model and data structure in current biostatistical practice. Modern data analysis often involves the selection of models within broad classes of prespecified models, but for models beyond the generalized linear model, few model-selection tools have been actively studied. In a Bayesian analysis, Bayes factors are the natural tool to use to explore these classes of models. In this paper, we develop a predictive approach for specifying the priors of a repeated measures random effects model with emphasis on selecting the fixed effects. The advantage of the predictive approach is that a single predictive specification is used to specify priors for all models considered. The methodology is applied to a pediatric pain data analysis.

Bayes Theorem↗
PubMed2002

Dynamic conditionally linear mixed models for longitudinal data.

We develop a new class of models, dynamic conditionally linear mixed models, for longitudinal data by decomposing the within-subject covariance matrix using a special Cholesky decomposition. Here 'dynamic' means using past responses as covariates and 'conditional linearity' means that parameters entering the model linearly may be random, but nonlinear parameters are nonrandom. This setup offers several advantages and is surprisingly similar to models obtained from the first-order linearization method applied to nonlinear mixed models. First, it allows for flexible and computationally tractable models that include a wide array of covariance structures; these structures may depend on covariates and hence may differ across subjects. This class of models includes, e.g., all standard linear mixed models, antedependence models, and Vonesh-Carter models. Second, it guarantees the fitted marginal covariance matrix of the data is positive definite. We develop methods for Bayesian inference and motivate the usefulness of these models using a series of longitudinal depression studies for which the features of these new models are well suited.

Antidepressive Agents↗
PubMed2001

Properties of phylogenetic trees generated by Yule-type speciation models.

We investigate some discrete structural properties of evolutionary trees generated under simple null models of speciation, such as the Yule model. These models have been used as priors in Bayesian approaches to phylogenetic analysis, and also to test hypotheses concerning the speciation process. In this paper we describe new results for three properties of trees generated under such models. Firstly, for a rooted tree generated by the Yule model we describe the probability distribution on the depth (number of edges from the root) of the most recent common ancestor of a random subset of k species. Next we show that, for trees generated under the Yule model, the approximate position of the root can be estimated from the associated unrooted tree, even for trees with a large number of leaves. Finally, we analyse a biologically motivated extension of the Yule model and describe its distribution on tree shapes when speciation occurs in rapid bursts.

Animals↗
PubMed2006

Prediction of postoperative mortality in elderly patients with colorectal cancer.

PURPOSE: This study was designed to develop a model for predicting postoperative mortality in elderly patients undergoing surgery for colorectal cancer. METHODS: This multicenter study was conducted by using routinely collected clinical data, assessing patients older than aged 80 years, with 30-day operative mortality as the primary end point. Data were collected from The Association of Coloproctology of Great Britain and Ireland database, encompassing 8,077 newly diagnosed colorectal cancer patients undergoing resectional surgery in 79 hospitals between April 2000 to March 2002, The Association of Coloproctology Malignant Bowel Obstruction Study, encompassing 1,046 patients with malignant bowel obstruction in 148 hospitals, between April 1998 to March 1999, and The Wales-Trent audit, encompassing 3,522 newly diagnosed colorectal cancer patients, between July 1992 to June 1993. A multilevel logistic regression model was developed to adjust for case-mix and to accommodate the variability of outcomes between the three study populations. The model was internally validated using a Bayesian resampling technique and tested using measures of discrimination, calibration, and subgroup analysis. RESULTS: A total of 2,533 patients satisfied the inclusion criteria, with a 30-day mortality of 15.6 percent. Multivariate analysis identified the following independent risk factors: age (odds ratio for 85-90, 90-95, >95 vs. 80-85 = 1.1, 1.8, 2.9), American Society of Anesthesiology grade (odds ratio for Grade III, IV vs. I-II = 2.7, 6.1), operative urgency (odds ratio for emergency vs. elective = 1.9), no cancer excision vs. resection (odds ratio = 1.2), and metastatic disease (odds ratio for metastases vs. no metastases = 1.9). The model offered adequate discrimination (area under receiver operator curve = 0.732) and excellent agreement between observed and predicted outcomes during eight colorectal procedures (P = 0.885). CONCLUSIONS: The elderly colorectal cancer model can accurately estimate 30-day mortality in patients older than aged 80 years undergoing surgery for colorectal cancer. Because the mortality can be considerable, this may have important implications when determining management for this group of patients.

Age Factors↗
PubMed2005

A Bayesian Neural Network approach to estimating the Energy Equivalent Speed.

To reduce the number and the gravity of accidents, it is necessary to analyse and reconstruct them. Accident modelling requires the modelling of the impact which in turn requires the estimation of the deformation energy. There are several tools available to evaluate the deformation energy absorbed by a vehicle during an impact. However, there is a growing demand for more precise and more powerful tools. In this work, we express the deformation energy absorbed by a vehicle during a crash as a function of the Energy Equivalent Speed (EES). The latter is a difficult parameter to estimate because the structural response of the vehicle during an impact depends on parameters concerning the vehicle, but also parameters concerning the impact. The objective of our work is to design a model to estimate the EES by using an original approach combining Bayesian and Neural Network approaches. Both of these tools are complementary and offer significant advantages, such as the guarantee of finding the optimal model and the implementation of error bars on the computed output. In this paper, we present the procedure for implementing this Bayesian Neural Network approach and the results obtained for the modelling of the EES: our model is able to estimate the EES of the car with a mean error of 1.34 m s(-1). Furthermore, we built a sensitivity analysis to study the relevance of model's inputs.

Accidents, Traffic↗
PubMed2003

Sequential Bayesian decoding with a population of neurons.

Population coding is a simplified model of distributed information processing in the brain. This study investigates the performance and implementation of a sequential Bayesian decoding (SBD) paradigm in the framework of population coding. In the first step of decoding, when no prior knowledge is available, maximum likelihood inference is used; the result forms the prior knowledge of stimulus for the second step of decoding. Estimates are propagated sequentially to apply maximum a posteriori (MAP) decoding in which prior knowledge for any step is taken from estimates from the previous step. Not only do we analyze the performance of SBD, obtaining the optimal form of prior knowledge that achieves the best estimation result, but we also investigate its possible biological realization, in the sense that all operations are performed by the dynamics of a recurrent network. In order to achieve MAP, a crucial point is to identify a mechanism that propagates prior knowledge. We find that this could be achieved by short-term adaptation of network weights according to the Hebbian learning rule. Simulation results on both constant and time-varying stimulus support the analysis.

Bayes Theorem↗
PubMed2004

Phylogenetic inference in Rafflesiales: the influence of rate heterogeneity and horizontal gene transfer.

BACKGROUND: The phylogenetic relationships among the holoparasites of Rafflesiales have remained enigmatic for over a century. Recent molecular phylogenetic studies using the mitochondrial matR gene placed Rafflesia, Rhizanthes and Sapria (Rafflesiaceae s. str.) in the angiosperm order Malpighiales and Mitrastema (Mitrastemonaceae) in Ericales. These phylogenetic studies did not, however, sample two additional groups traditionally classified within Rafflesiales (Apodantheaceae and Cytinaceae). Here we provide molecular phylogenetic evidence using DNA sequence data from mitochondrial and nuclear genes for representatives of all genera in Rafflesiales. RESULTS: Our analyses indicate that the phylogenetic affinities of the large-flowered clade and Mitrastema, ascertained using mitochondrial matR, are congruent with results from nuclear SSU rDNA when these data are analyzed using maximum likelihood and Bayesian methods. The relationship of Cytinaceae to Malvales was recovered in all analyses. Relationships between Apodanthaceae and photosynthetic angiosperms varied depending upon the data partition: Malvales (3-gene), Cucurbitales (matR) or Fabales (atp1). The latter incongruencies suggest that horizontal gene transfer (HGT) may be affecting the mitochondrial gene topologies. The lack of association between Mitrastema and Ericales using atp1 is suggestive of HGT, but greater sampling within eudicots is needed to test this hypothesis further. CONCLUSIONS: Rafflesiales are not monophyletic but composed of three or four independent lineages (families): Rafflesiaceae, Mitrastemonaceae, Apodanthaceae and Cytinaceae. Long-branch attraction appears to be misleading parsimony analyses of nuclear small-subunit rDNA data, but model-based methods (maximum likelihood and Bayesian analyses) recover a topology that is congruent with the mitochondrial matR gene tree, thus providing compelling evidence for organismal relationships. Horizontal gene transfer appears to be influencing only some taxa and some mitochondrial genes, thus indicating that the process is acting at the single gene (not whole genome) level.

Bayes Theorem↗
PubMed2006

Pharmacodynamics of antiretroviral agents in HIV-1 infected patients: using viral dynamic models that incorporate drug susceptibility and adherence.

We developed a novel HIV-1 dynamic model with consideration of pharmacokinetics, drug adherence and drug susceptibility to link plasma drug concentration to the long-term changes in HIV-1 RNA observation after initiation of therapy. A Bayesian approach is proposed to fit this model to clinical data from ACTG A5055, a study of two dosage regimens of indinavir (IDV) with ritonavir (RTV) in subjects failing their first protease inhibitor treatment. The HIV RNA testing was completed at days 0, 7, 14, 28, 56, 84, 112, 140, and 168. An intensive pharmacokinetic (PK) evaluation was performed on day 14 and multiple trough concentrations were subsequently collected. Pill counts were used to monitor adherence. IC(50) for IDV and RTV were determined at baseline and at virologic failure. Viral dynamic model fitting residuals were used to assess the significance of covariate effects on long-term virologic response. As univariate predictors, none of the four PK parameters C(trough), C(12 hour), C(max), and AUC was significantly related to virologic response (p > 0.05). By including drug susceptibility (IC(50)), or IC(50) and adherence measured by pill counts together, C(trough), C(12 hour), C(max) and AUC were each significantly correlated to long-term virologic response (p = 0.0055,0.0002,0.0136,0.0002 with IC(50) and adherence measured by pill counts considered). The IC(50) and adherence measured by pill counts alone were not related to the virologic response. In predicting virologic response adherence measured by pill counts did not provide any additional information to PK parameters (p = 0.064), to drug susceptibility IC(50) (p = 0.086), and to their combination (p = 0.22). Simple regression approaches did not detect any significant pharmacodynamic (PD) relationships. Any single factor of PK, adherence measured by pill counts and drug susceptibility did not contribute to long-term virologic response. But their combinations in viral dynamic modeling significantly predicted virologic response. The HIV dynamic modeling can appropriately capture complicated nonlinear relationships and interactions among multiple covariates.

Algorithms↗
PubMed2005

Population pharmacokinetic studies in pediatrics: issues in design and analysis.

The current review addresses the following 3 frequently encountered challenges in the design and analysis of population pharmacokinetic studies in pediatrics: (1) body size adjustments during the development of pharmacostatistical models, (2) design and validation of limited sampling strategies, and (3) the integration of historical priors in data analysis and trial simulation. Size adjustments with empiric approaches based on body weight or body surface area have frequently proven as a pragmatic tool to overcome large size differences in a pediatric study population. Allometric size adjustments, however, provide a more mechanistic, physiologically based approach that, if used a priori, allows delineation of the effect of size from that of other covariates that show a high degree of collinearity. The frequent lack of dense data sets in pediatric clinical pharmacology because of ethical and logistic constraints in study design can be overcome with the application of D-optimality-based limited sampling schemes in combination with Bayesian and nonlinear mixed-effects modeling approaches. Empirically based dose selection and clinical trial designs for pediatric clinical pharmacology studies can be improved by applying clinical trial simulation techniques, especially if they integrate adult and pediatric in vitro and/or in vivo data as historic priors. Although integration of these concepts and techniques in population pharmacokinetic analyses is not only limited to pediatric research, their application allows researchers to overcome some major hurdles frequently encountered in pharmacokinetic studies in pediatrics and, thus, provides the basis for additional clinical pharmacology research in this previously insufficiently studied fraction of the general population.

Humans↗
PubMed2006

Temporal transferability and updating of zonal level accident prediction models.

This paper examines the temporal transferability of the zonal accident prediction models by using appropriate evaluation measures of predictive performance to assess whether the relationship between the dependent and independent variables holds reasonably well across time. The two temporal contexts are the years 1996 and 2001, with updated 1996 models being used to predict 2001 accidents in each traffic zone of the City of Toronto. The paper examines alternative updating methods for temporal transfer by imagining that only a sample of 2001 data is available. The sensitivity of the performance of the updated models to the 2001 sample size is explored. The updating procedures examined include the Bayesian updating approach and the application of calibration factors to the 1996 models. Models calibrated for the 2001 samples were also explored, but were found to be inadequate. The results show that the models are not transferable in a strict statistical sense. However, relative measures of transferability indicate that the transferred models yield useful information in the application context. Also, it is concluded that the updated accident models using the calibration factors produce better results for predicting the number of accidents in the year 2001 than using the Bayesian approach.

Accidents, Traffic↗
PubMed2005

Modeling long-term HIV dynamics and antiretroviral response: effects of drug potency, pharmacokinetics, adherence, and drug resistance.

We propose a long-term HIV-1 dynamic model by considering drug potency, drug exposure, and drug susceptibility. Using a Bayesian approach, HIV-1 dynamic parameters were estimated by fitting the model to viral load data from a phase 1/2 randomized clinical study of 2 indinavir (IDV)/ritonavir (RTV)-containing highly active antiretroviral (ARV) therapy regimens in HIV-infected subjects who had previously failed protease inhibitor-containing ARV therapies. A large between-subject variation in estimated viral dynamic parameters was observed, even after accounting for variations in drug exposure and drug susceptibility, suggesting that characteristics of HIV-1 dynamics are host dependent. Significant correlations of baseline factors such as HIV-1 RNA levels and CD4 cell counts with viral dynamic parameters were found. These correlations coincide with biologic interaction mechanisms between HIV and the host immune system and also provide an explanation for the correlations between the baseline viral load and phase 1 viral decay rate, for which inconsistent results have been reported in the literature. The relations between viral dynamic parameters and virologic response were established, and these results suggest that viral dynamic parameters may play an important role in determining treatment success or failure. In particular, we estimated a drug efficacy threshold for each patient that can be used to assess whether an ARV regimen is potent enough to suppress HIV viruses in the individual patient. Our findings indicate that it is necessary to individualize the ARV regimen to treat HIV-1-infected patients. The proposed mathematic models and statistical techniques may provide a framework to simulate and predict antiviral response for individual patients.

Anti-HIV Agents↗
PubMed2005

Seasonal variation of air pollution index: Hong Kong case study.

Air pollution is an important and popular topic in Hong Kong as concerns have been raised about the health impacts caused by vehicle exhausts in recent years. In Hong Kong, sulphur dioxide SO2, nitrogen dioxide (NO2), nitric oxide (NO), carbon monoxide (CO), and respirable suspended particulates (RSP) are major air pollutants caused by the dominant usage of diesel fuel by goods vehicles and buses. These major pollutants and the related secondary pollutant, e.g., ozone (O3), become and impose harmful impact on human health in Hong Kong area after the northern shifting of major industries to Mainland China. The air pollution index (API), a referential parameter describing air pollution levels, provides information to enhance the public awareness of air pollutions in time series since 1995. In this study, the varying trends of API and the levels of related air pollutants are analyzed based on the database monitored at a selected roadside air quality monitoring station, i.e., Causeway Bay, during 1999-2003. Firstly, the original measured pollutant data and the resultant APIs are analyzed statistically in different time series including daily, monthly, seasonal patterns. It is found that the daily mean APIs in seasonal period can be regarded as stationary time series. Secondly, the auto-regressive moving average (ARMA) method, implemented by Box-Jenkins model, is used to forecast the API time series in different seasonal specifications. The performance evaluations of the adopted models are also carried out and discussed according to Bayesian information criteria (BIC) and root mean square error (RMSE). The results indicate that the ARMA model can provide reliable, satisfactory predictions for the problem interested and is expecting to be an alternative tool for practical assessment and justification.

Air Pollutants↗
PubMed2001

Interpreting results from trials of pneumococcal conjugate vaccines: a statistical test for detecting vaccine-induced increases in carriage of nonvaccine serotypes.

Conjugate vaccines against Streptococcus pneumoniae (pneumococcus) protect against nasopharyngeal carriage of serotypes included in the vaccine. However, in several clinical trials, vaccinees have shown increased carriage of nonvaccine serotypes of pneumococcus. These increases may be due to serotype replacement, if vaccine-induced protection against carriage of vaccine serotypes increases susceptibility to carriage of nonvaccine serotypes. Alternatively, observed increases may be an artifact of "unmasking," in which nonvaccine serotypes are more readily detected among vaccinees than among controls because vaccine serotypes are not present. In this paper, a statistical test for distinguishing serotype replacement from unmasking is described. The test attempts to reject a null model of unmasking alone; serotype replacement is inferred if the observed increase in detectable nonvaccine serotype carriage among vaccinees is significantly greater than that expected under the null model. Significance is assessed using the Bayesian "posterior predictive p value" as modified by Robins et al. (J Am Stat Assoc 2000;95:1143-56). Analysis of data from a South African trial suggests that replacement may have occurred in the study, but results do not reach the conventional level of significance in rejecting the null hypothesis of unmasking (p = 0.074). The author performs sensitivity analyses for the prior and for unmeasured confounding by differences in susceptibility to pneumococcus carriage. The implications of the findings and the assumptions and limitations of this technique are then discussed.

Bayes Theorem↗
PubMed1986

Familial aggregation in Alzheimer dementia--II. Clinical genetic implications of age-dependent onset.

A biomathematical genetic model for the age-specific risk of Alzheimer Dementia (AD) was applied to two problems in the clinical genetics of this disorder. In a test of the ability of a clinical marker specifically to identify genetic AD, cases grouped by the phenotype of amnesia with aphasia or apraxia (aaa) were shown to have familial risk that suggested a pure genetic illness, and differed significantly (p = 0.006) from cases without this phenotype. The model was also used in a Bayesian paradigm to assess the probability that individual cases had hereditary disease, given their family history. Here the results were surprisingly ambiguous: Even with no affected relatives, there is a substantial likelihood that many AD cases may have a genetic illness. Hence, one cannot reliably classify individual cases as "familial" or "sporadic" from family history alone. The phenotype of aaa (or other suitable marker) appears to be more reliable than the degree of manifest familial aggregation as an indicator of genetic AD.

Age Factors↗
PubMedDate not supplied

[Bayesian prediction of chloramphenicol blood levels in children with sepsis and malnutrition].

OBJECTIVE: To validate the population pharmacokinetic parameters of chloramphenicol in pediatric patients with sepsis and malnutrition (PPSM) using a bayesian forecasting program. DESIGN: Retrospective evaluation of predictive performance of a bayesian program in PPSM. SETTING: Tertiary care center. PATIENTS: Fifteen MPSP and ten NMPSP that receiving treatment with chloramphenicol. METHODS AND MAIN RESULTS: In the first part of the study, the medical records of 10 MPSP and 10 NMPSP who had received treatment with chloramphenicol were reviewed. The population pharmacokinetic parameter values for each group were estimated using a nonparametric expectation maximization algorithm (NPEM). In the second part, data gathered from five other MPSP receiving chloramphenicol were entered into a bayesian program. Chloramphenicol pharmacokinetic values for each of these five patients were estimated, first using the values of NMPSP as a priori distribution and then repeating the analysis using the MPSP values. The bayesian serum chloramphenicol concentrations predicted for each population model were compared with the actual peaks and troughs. The specific model for MPSP permitted forecasting the peak and trough serum chloramphenicol concentrations with less bias and a better precision compared with the NMPSP population model. CONCLUSIONS: These data indicate that chloramphenicol pharmacokinetics in PPSM can be predicted with minimal bias and good precision using a bayesian forecasting program, allowing a better control of the chloramphenicol serum concentrations. In addition, the limited number of samples required by the bayesian method may represent an important economical benefit for the patient.

Anti-Bacterial Agents↗
PubMed2003

Efficient and accurate experimental design for enzyme kinetics: Bayesian studies reveal a systematic approach.

In areas such as drug development, clinical diagnosis and biotechnology research, acquiring details about the kinetic parameters of enzymes is crucial. The correct design of an experiment is critical to collecting data suitable for analysis, modelling and deriving the correct information. As classical design methods are not targeted to the more complex kinetics being frequently studied, attention is needed to estimate parameters of such models with low variance. We demonstrate that a Bayesian approach (the use of prior knowledge) can produce major gains quantifiable in terms of information, productivity and accuracy of each experiment. Developing the use of Bayesian Utility functions, we have used a systematic method to identify the optimum experimental designs for a number of kinetic model data sets. This has enabled the identification of trends between kinetic model types, sets of design rules and the key conclusion that such designs should be based on some prior knowledge of K(M) and/or the kinetic model. We suggest an optimal and iterative method for selecting features of the design such as the substrate range, number of measurements and choice of intermediate points. The final design collects data suitable for accurate modelling and analysis and minimises the error in the parameters estimated.

Bayes Theorem↗
PubMed2003

Generalized common spatial factor model.

There are often two types of correlations in multivariate spatial data: correlations between variables measured at the same locations, and correlations of each variable across the locations. We hypothesize that these two types of correlations are caused by a common spatially correlated underlying factor. Under this hypothesis, we propose a generalized common spatial factor model. The parameters are estimated using the Bayesian method and a Markov chain Monte Carlo computing technique. Our main goals are to determine which observed variables share a common underlying spatial factor and also to predict the common spatial factor. The model is applied to county-level cancer mortality data in Minnesota to find whether there exists a common spatial factor underlying the cancer mortality throughout the state.

Bayes Theorem↗
PubMed1999

Naive Bayesian-based nomogram for prediction of prostate cancer recurrence.

This paper introduces a schema with naive-Bayesian classifier and patient weighting technique to develop a prostate cancer recurrence prediction model from patient data. We propose the graphical presentation of naive-Bayesian classifier with a nomogram, which can be used both for prediction or can provide means to data analysis. The resulting model was experimentally evaluated; the results were favorable both in terms of interpretability and predictive accuracy.

Bayes Theorem↗