Nicola G. Best

Dynamic conditional independence models and Markov chain Monte Carlo methods

Abstract In dynamic statistical modeling situations, observations arise sequentially, causing the model to expand by progressive incorporation of new data items and new unknown parameters. For example, in clinical monitoring, patients and data arrive sequentially, and new patient-specific parameters are introduced with each new patient. Markov chain Monte Carlo (MCMC) might be used for continuous updating of the evolving posterior distribution, but would need to be restarted from scratch at each expansion stage. Thus MCMC methods are often too slow for real-time inference in dynamic contexts. By combining MCMC with importance resampling, we show how real-time sequential updating of posterior distributions can be effected. The proposed dynamic sampling algorithms use posterior samples from previous updating stages and exploit conditional independence between groups of parameters to allow samples of parameters no longer of interest to be discarded, such as when a patient dies or is discharged. We apply the ...

Spatial Poisson Regression for Health and Exposure Data Measured at Disparate Resolutions

Abstract Ecological regression studies are widely used to examine relationships between disease rates for small geographical areas and exposure to environmental risk factors. The raw data for such studies, including disease cases, environmental pollution concentrations, and the reference population at risk, are typically measured at various levels of spatial aggregation but are accumulated to a common geographical scale to facilitate statistical analysis. In this traditional approach, heterogeneous exposure distributions within the aggregate areas may lead to biased inference, whereas individual attributes such as age, gender, and smoking habits must either be summarized to provide area-level covariate values or used to stratify the analysis. This article presents a spatial regression analysis of the effect of traffic pollution on respiratory disorders in children. The analysis features data measured at disparate, nonnested scales, including spatially varying covariates, latent spatially varying risk factors, and case-specific individual attributes. The problem of disparate discretizations is overcome by relating all spatially varying quantities to a continuous underlying random field model. Case-specific individual attributes are accommodated by treating cases as a marked point process. Inference in these hierarchical Poisson/gamma models is based on simulated samples drawn from Bayesian posterior distributions, using Markov chain Monte Carlo methods with data augmentation.

Commissioned analysis of surgical performance using routine data: lessons from the Bristol inquiry

The public inquiry into paediatric cardiac surgery at the Bristol Royal Infirmary commissioned the authors to design and conduct analyses of routine data sources to compare surgical outcomes between centres. Such analyses are necessarily complex in this context but were further hampered by the inherent inconsistencies and mediocre quality of the various sources of data. Three levels of analysis of increasing sophistication were carried out. The reasonable consistency of the results arising from different sources of data, together with a number of sensitivity analyses, led us to conclude that there had been excess mortality in Bristol in open heart operations on children under 1 year of age. We consider criticisms of our analysis and discuss the role of statisticians in this inquiry and their contribution to the final report of the inquiry. The potential statistical role in future programmes for monitoring clinical performance is highlighted.

Estimation of population pharmacokinetics using the Gibbs sampler

Quantification of the average and interindividual variation in pharmacokinetic behavior within the patient population is an important aspect of drug development. Population pharmacokinetic models typically involve large numbers of parameters related nonlinearly to sparse, observational data, which creates difficulties for conventional methods of analysis. The nonlinear mixed-effects method implemented in the computer program NONMEM is a widely used approach to the estimation of population parameters. However, the method relies on somewhat restrictive modeling assumptions to enable efficient parameter estimation. In this paper we describe a Bayesian approach to population pharmacokinetic analysis which used a technique known as Gibbs sampling to simulate values for each model parameter. We provide details of how to implement the method in the context of population pharmacokinetic analysis, and illustrate this via an application to gentamicin population pharmacokinetics in neonates.

Blood Cyclosporine Concentrations And Cytomegalovirus Infection Following Heart Transplantation

We have attempted to identify major risk factors for cytomegalovirus (CMV) infection and disease following heart transplantation, with emphasis on the degree and type of immunosuppression used. One hundred and eleven consecutive heart transplant recipients were studied for the first 4 months. Data from the 95 who survived at least 1 month were analyzed using multiple Cox regression. Blood cyclosporine concentrations (CsAbc) > 550 micrograms L-1 were associated with a 4.4-fold increase in risk of CMV infection during the next week (95% confidence interval = 1.2-16.2). Other significant risk factors for CMV infection included antirejection treatment in the past 14 days, a drop in white blood cell count, receiving a CMV antibody-positive donor organ, and primary diagnosis other than cardiomyopathy. We found that patients experiencing a CMV infection were at 3 times the risk of subsequently developing symptomatic CMV disease (95% confidence interval = 1.1-9.7). In addition, the proportion of patients developing symptomatic CMV disease was significantly higher amongst those with a median CsAbc > 550 micrograms L-1 for at least 1 week (29% vs. 10%; P = 0.02) or who had been treated for rejection more frequently than once every 6 weeks (31% vs. 12%; P = 0.04) during the first 4 months. CMV antibody-negative recipients of antibody-positive donor organs had a higher rate of symptomatic CMV disease than did other serological combinations (67% vs. 10%; P = 0.0001). We conclude that the risk of CMV infection and symptomatic disease following heart transplantation may be critically influenced by early management of immunosuppression as well as by donor serology.

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.

Pharmacodynamics of cyclosporine in heart and heart-lung transplant recipients. I: Blood cyclosporine concentrations and other risk factors for cardiac allograft rejection.

We have attempted to quantify the optimal clinical use of cyclosporine during the first 3 months after heart-lung transplantation. We used multiple logistic regression to investigate the influence of blood cyclosporine concentrations and other potential risk factors on histologically confirmed acute lung rejection in 50 heart-lung transplant recipients. A 50% increase in cyclosporine concentration was associated with a 25% reduction in risk of rejection in the subsequent 5 days (P=0.008). Increasing oral corticosteroid dose also protected against rejection (P=0.006). Rejection was over 4 times more likely to occur during the first 20 postoperative days (P=0.002). After 20 days, an FEV1 < or = 70% of the age-, sex-, and height-adjusted expected score was associated with a 4-fold increase in risk of rejection (P=0.01). Patients who had multiple previous rejection episodes were also predisposed to further rejection (P=0.005). An investigation of threshold levels for the cyclosporine concentration-effect relationship suggested that cyclosporine concentrations above 500 microg L(-1) provide optimal protection against acute lung allograft rejection. This result provides an objectively defined therapeutic threshold for targeting early cyclosporine concentrations following heart-lung transplantation.

Modeling the Impact of Traffic-Related Air Pollution on Childhood Respiratory Illness

Epidemiological studies of the health effects of outdoor air pollution have suffered from a number of methodological difficulties. These include major problems of estimating exposure; confounding due to socioeconomic deprivation and other factors; failure to account for possible spatial dependence induced by unmeasured covariates with smooth spatial variation; and the potential for bias arising from approximation and aggregation in the data. We present a flexible modeling framework using recently developed Bayesian spatial regression methods to address some of these issues. We apply this approach to a study of the relation of London traffic pollution to the incidence of respiratory ailments in infants using the recently available Hospital Episodes Statistics (HES) dataset.

Hepatitis B: a case study in MCMC

This chapter features a worked example using Bayesian graphical modelling and the most basic of MCMC techniques, the Gibbs sampler, and serves to introduce ideas that are developed more fully in other chapters. This case study first appeared in Gilks, Richardson and Spiegelhalter (1996), and frequent reference is made to other chapters in that book.

A Bayesian approach to estimate the prevalence of low height-for-age from the prevalence of low weight-for-age

Victora et al. (1998) proposed the use of low weight-for-age prevalence to estimate the prevalence of height-for-age deficit in Brazilian children. This procedure was justified by the need to simplify methods used in the context of community health programs. From the same perspective, the present article broadens this proposal by using a Bayesian approach (based on Markov Chain Monte Carlo (MCMC) methods) to deal with the imprecision resulting from Victora et al.s model. In order to avoid invalid estimated prevalence values which can occur with the original linear model, truncation or a logit transformation of the prevalences are suggested. The Bayesian approach is illustrated using a community study as an example. Imprecision arising from methodological complexities in the community study design, such as multi-stage sampling and clustering, is easily handled within the Bayesian framework by introducing a hierarchical or multilevel model structure. Since growth deficit was also evaluated in the community study, the article may also serve to validate the procedure proposed by Victora et al.