Limited and optimal sampling strategies for etoposide and etoposide catechol in children with leukemia

Etoposide is used to treat childhood malignancies, and its plasma pharmacokinetics have been related to pharmacodynamic endpoints. Limiting the number of samples should facilitate the assessment of etoposide pharmacokinetics in children. We compared limited sampling strategies using multiple linear regression of plasma concentrations and clearance with Bayesian methods of estimating clearance using compartmental pharmacokinetic models. Optimal sampling times were estimated in the multiple linear regression method by determining the combination of two samples which maximized the correlation coefficient, and in the Bayesian estimation approach by minimizing the variance in estimates of clearance. Clearance estimates were compared to the actual clearances from Monte Carlo-simulated data and predicted clearances estimated using all available plasma concentrations in clinical data from children with acute lymphoblastic leukemia. Multiple linear regression poorly predicted clearance (mean bias 8.3%, precision 17.5%), but improved if plasma concentrations were logarithmically transformed (mean bias 1.4%, precision 12.5%). Bayesian estimation methods with optimal samples gave the best overall prediction (mean bias 2.5%, precision 6.8%) and also performed better than regression methods for abnormally high or low clearances. We conclude that Bayesian estimation with limited sampling gives the best estimates of etoposide clearance.     

Population toxicokinetic analysis of 2,3,7,8-tetrachlorodibenzo-p-dioxin using Bayesian techniques

Understanding the kinetics of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) concentrations in humans is an important step for TCDD cancer risk assessment. In this paper longitudinal series of serum TCDD concentration measurements on U.S. veterans of the Vietnam war, who were exposed to dioxin during herbicide-spraying operations, are studied. The overall aim is to use these data to infer the dynamics of TCDD concentrations in humans. This is done by identifying a kinetic model describing the dioxin time course at the individual level. The individual toxicokinetic model is then expanded into a population model within a Bayesian hierarchical framework which allows residual variations across subjects that cannot be explained by observed covariates. Other complications in the data, such as unknown exposure histories, are also resolved implicitly through the hierarchical model. Moreover, the choice of a Bayesian approach enables the accumulation of external source of information in the form of prior distributions. The model is subjected to various diagnostic checks and analyses of sensitivity to distributional assumptions showing a good fit in terms of both the population and the kinetic features.     

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.     

HIV testing and retesting for men and women in Switzerland

This study was conducted to describe voluntary HIV testing in the general population in Switzerland and to estimate yearly HIV test incidence. In 1994, a representative telephone survey of individuals aged 17 to 45 years obtained self-reported information on HIV testing. In addition to describing cumulative HIV test incidence, yearly HIV test incidence over time was estimated by a Bayesian hurdle model allowing for the plausible scenario of test consumption differing between first test and subsequent retests. Overall, 33% of the Swiss population (age 17 to 45 years) has been tested at some time for HIV on a voluntary basis (30% men, 36% women). For the time period 1990–1994, the result showed for 35-year-old individuals with supposedly low risk behavior, that 1) annual test incidence (first test or retest) showed a greater increase for men (4.2 to 5.9%) than for women (5.0 to 6.0% 2) annual first test incidence increased moderately and differed for men and women (2.9 to 3.4% for men, 4.6 to 5.2% for women), and 3) annual retest incidence was twice as high for men (17.6%) as for women (8.6%). In conclusion, a substantial part of the Swiss population has been tested at some stage for HIV on a voluntary basis, and differences exist for testing and retesting between men and women.     

The probability of failing in detecting an infectious disease at entry points into a country

In a group of N individuals, carrying an infection with prevalence pi, the exact probability P of failing in detecting the infection is evaluated when a diagnostic test of sensitivity s and specificity s' is carried out on a sample of n individuals extracted without replacement from the group. Furthermore, the minimal number of individuals that must be tested if the probability P has to be lower than a fixed value is determined as a function of pi. If all n tests result negative, confidence intervals for pi are given both in the frequentistic and Bayesian approach. These results are applied to recent data for severe acute respiratory syndrome (SARS). The conclusion is that entry screening with a diagnostic test is rarely an efficacious tool for preventing importation of a disease into a country.     

Bayesian inference on the patient population size given list mismatches

In applying capture-recapture methods for closed populations to epidemiology, one needs to estimate the total number of people with a certain disease in a certain research area by using several lists with information of patients. Problems of lists error often arise due to mistyping or misinformation. Adopting the concept of tag-loss methodology in animal populations, Seber et al. (Biometrics 2000; 56:1227-1232) proposed solutions to a two-list problem. This article reports an interesting simulation study, where Bayesian point estimates based on improper constant and Jeffreys prior for unknown population size N could have smaller frequentist standard errors and MSEs compared to the estimates proposed in Seber et al. (2000). The Bayesian credible intervals based on the same priors also have super frequentist coverage probabilities while some of the frequentist confidence intervals procedures have drastically poor coverage. Seber's real data set on gestational diabetics is analysed with the proposed new methods.     

Single patient (n-of-1) trials with binary treatment preference

The use of a fully parametric Bayesian method for analysing single patient trials based on the notion of treatment 'preference' is described. This Bayesian hierarchical modelling approach allows for full parameter uncertainty, use of prior information and the modelling of individual and patient sub-group structures. It provides updated probabilistic results for individual patients, and groups of patients with the same medical condition, as they are sequentially enrolled into individualized trials using the same medication alternatives. Two clinically interpretable criteria for determining a patient's response are detailed and illustrated using data from a previously published paper under two different prior information scenarios.     

How vague is vague? A simulation study of the impact of the use of vague prior distributions in MCMC using WinBUGS

There has been a recent growth in the use of Bayesian methods in medical research. The main reasons for this are the development of computer intensive simulation based methods such as Markov chain Monte Carlo (MCMC), increases in computing power and the introduction of powerful software such as WinBUGS. This has enabled increasingly complex models to be fitted. The ability to fit these complex models has led to MCMC methods being used as a convenient tool by frequentists, who may have no desire to be fully Bayesian.Often researchers want 'the data to dominate' when there is no prior information and thus attempt to use vague prior distributions. However, with small amounts of data the use of vague priors can be problematic. The results are potentially sensitive to the choice of prior distribution. In general there are fewer problems with location parameters. The main problem is with scale parameters. With scale parameters, not only does one have to decide the distributional form of the prior distribution, but also whether to put the prior distribution on the variance, standard deviation or precision.We have conducted a simulation study comparing the effects of 13 different prior distributions for the scale parameter on simulated random effects meta-analysis data. We varied the number of studies (5, 10 and 30) and compared three different between-study variances to give nine different simulation scenarios. One thousand data sets were generated for each scenario and each data set was analysed using the 13 different prior distributions. The frequentist properties of bias and coverage were investigated for the between-study variance and the effect size.The choice of prior distribution was crucial when there were just five studies. There was a large variation in the estimates of the between-study variance for the 13 different prior distributions. With a large number of studies the choice of prior distribution was less important. The effect size estimated was not biased, but the precision with which it was estimated varied with the choice of prior distribution leading to varying coverage intervals and, potentially, to different statistical inferences. Again there was less of a problem with a larger number of studies. There is a particular problem if the between-study variance is close to the boundary at zero, as MCMC results tend to produce upwardly biased estimates of the between-study variance, particularly if inferences are based on the posterior mean.The choice of 'vague' prior distribution can lead to a marked variation in results, particularly in small studies. Sensitivity to the choice of prior distribution should always be assessed.     

Extending logistic regression to model diffuse interactions

In an observational study focussed on association between a health outcome and numerous explanatory variables, the question of interactions can be problematic. Commonly, logistic regression of the outcome on the explanatory variables might be employed. Such modelling often includes an attempt to select some pairwise product interaction terms, from amongst the many such possible pairs. For several reasons, however, this can be unsatisfying. Here we consider a different approach based on a parsimonious extension of a logistic regression model without interaction terms. This extension permits an overall synergism or antagonism in how the explanatory variables combine to associate with the outcome, without any attempt to identify specific variables which give rise to interactive behaviour. We call this diffuse interaction. We elucidate some simple properties of the diffuse interaction model, and give an example of its application to epidemiological data. We also consider asymptotic behaviour in a restricted case of the model, to gain some insight into how well this kind of interaction can be detected from data.     

Spline-based non-parametric regression for periodic functions and its application to directional tuning of neurons

The activity of neurons in the brain often varies systematically with some quantitative feature of a stimulus or action. A well-known example is the tendency of the firing rates of neurons in the primary motor cortex to vary with the direction of a subject's arm or wrist movement. When this movement is constrained to vary in only two dimensions, the direction of movement may be characterized by an angle, and the neuronal firing rate can be written as a function of this angle. The firing rate function has traditionally been fit with a cosine, but recent evidence suggests that departures from cosine tuning occur frequently. We report here a new non-parametric regression method for fitting periodic functions and demonstrate its application to the fitting of neuronal data. The method is an extension of Bayesian adaptive regression splines (BARS) and applies both to normal and non-normal data, including Poisson data, which commonly arise in neuronal applications. We compare the new method to a periodic version of smoothing splines and some parametric alternatives and find the new method to be especially valuable when the smoothness of the periodic function varies unevenly across its domain.