Anthony N. Pettitt

Overcrowding and understaffing in modern health-care systems: Key determinants in meticillin-resistant Staphylococcus aureus transmission

Recent decades have seen the global emergence of meticillin-resistant Staphylococcus aureus (MRSA), causing substantial health and economic burdens on patients and health-care systems. This epidemic has occurred at the same time that policies promoting higher patient throughput in hospitals have led to many services operating at, or near, full capacity. A result has been limited ability to scale services according to fluctuations in patient admissions and available staff, and hospital overcrowding and understaffing. Overcrowding and understaffing lead to failure of MRSA control programmes via decreased health-care worker hand-hygiene compliance, increased movement of patients and staff between hospital wards, decreased levels of cohorting, and overburdening of screening and isolation facilities. In turn, a high MRSA incidence leads to increased inpatient length of stay and bed blocking, exacerbating overcrowding and leading to a vicious cycle characterised by further infection control failure. Future decision making should use epidemiological and economic evidence to evaluate the effect of systems changes on the incidence of MRSA infection and other adverse events.

Estimation of Parameters for Macroparasite Population Evolution Using Approximate Bayesian Computation

We estimate the parameters of a stochastic process model for a macroparasite population within a host using approximate Bayesian computation (ABC). The immunity of the host is an unobserved model variable and only mature macroparasites at sacrifice of the host are counted. With very limited data, process rates are inferred reasonably precisely. Modeling involves a three variable Markov process for which the observed data likelihood is computationally intractable. ABC methods are particularly useful when the likelihood is analytically or computationally intractable. The ABC algorithm we present is based on sequential Monte Carlo, is adaptive in nature, and overcomes some drawbacks of previous approaches to ABC. The algorithm is validated on a test example involving simulated data from an autologistic model before being used to infer parameters of the Markov process model for experimental data. The fitted model explains the observed extra-binomial variation in terms of a zero-one immunity variable, which has a short-lived presence in the host.

A Conditional Autoregressive Gaussian Process for Irregularly Spaced Multivariate Data with Application to Modelling Large Sets of Binary Data

A Gaussian conditional autoregressive (CAR) formulation is presented that permits the modelling of the spatial dependence and the dependence between multivariate random variables at irregularly spaced sites so capturing some of the modelling advantages of the geostatistical approach. The model benefits not only from the explicit availability of the full conditionals but also from the computational simplicity of the precision matrix determinant calculation using a closed form expression involving the eigenvalues of a precision matrix submatrix. The introduction of covariates into the model adds little computational complexity to the analysis and thus the method can be straightforwardly extended to regression models. The model, because of its computational simplicity, is well suited to application involving the fully Bayesian analysis of large data sets involving multivariate measurements with a spatial ordering. An extension to spatio-temporal data is also considered. Here, we demonstrate use of the model in the analysis of bivariate binary data where the observed data is modelled as the sign of the hidden CAR process. A case study involving over 450 irregularly spaced sites and the presence or absence of each of two species of rain forest trees at each site is presented; Markov chain Monte Carlo (MCMC) methods are implemented to obtain posterior distributions of all unknowns. The MCMC method works well with simulated data and the tree biodiversity data set.

Use of stochastic epidemic modeling to quantify transmission rates of colonization with methicillin-resistant Staphylococcus aureus in an intensive care unit.

OBJECTIVE To consider statistical methods for estimating transmission rates for colonization of patients with methicillin-resistant Staphylococcus aureus (MRSA) in an intensive care unit (ICU) from three different sources: background contamination, non-isolated patients, and isolated patients. METHODS We developed statistical methods that allowed for the analysis of interval-censored, routine surveillance data and extended the general epidemic model for the flow of patients through the ICU. RESULTS Within this ICU, the rate of transmission to susceptible patients from a background source of MRSA (0.0092 case per day; 95% confidence interval [CI95], 0.0062-0.0126) is approximately double the rate of transmission from a non-isolated patient (0.0052 case per day; CI95, 0.0013-0.0096) and six times the rate of transmission from an isolated patient (0.0015 case per day; CI95, 0.0001-0.0043). We used the methodology to investigate whether transmission rates vary with workload. CONCLUSION Our methodology has general application to infection by and transmission of pathogens in a hospital setting and is appropriate for quantifying the effect of infection control interventions.

Bayesian inference in hidden Markov random fields for binary data defined on large lattices.

Hidden Markov random fields represent a complex hierarchical model, where the hidden latent process is an undirected graphical structure. Performing inference for such models is difficult primarily because the likelihood of the hidden states is often unavailable. The main contribution of this article is to present approximate methods to calculate the likelihood for large lattices based on exact methods for smaller lattices. We introduce approximate likelihood methods by relaxing some of the dependencies in the latent model, and also by extending tractable approximations to the likelihood, the so-called pseudolikelihood approximations, for a large lattice partitioned into smaller sublattices. Results are presented based on simulated data as well as inference for the temporal-spatial structure of the interaction between up- and down-regulated states within the mitochondrial chromosome of the Plasmodium falciparum organism. Supplemental material for this article is available online.

Variational Bayes for estimating the parameters of a hidden Potts model

Hidden Markov random field models provide an appealing representation of images and other spatial problems. The drawback is that inference is not straightforward for these models as the normalisation constant for the likelihood is generally intractable except for very small observation sets. Variational methods are an emerging tool for Bayesian inference and they have already been successfully applied in other contexts. Focusing on the particular case of a hidden Potts model with Gaussian noise, we show how variational Bayesian methods can be applied to hidden Markov random field inference. To tackle the obstacle of the intractable normalising constant for the likelihood, we explore alternative estimation approaches for incorporation into the variational Bayes algorithm. We consider a pseudo-likelihood approach as well as the more recent reduced dependence approximation of the normalisation constant. To illustrate the effectiveness of these approaches we present empirical results from the analysis of simulated datasets. We also analyse a real dataset and compare results with those of previous analyses as well as those obtained from the recently developed auxiliary variable MCMC method and the recursive MCMC method. Our results show that the variational Bayesian analyses can be carried out much faster than the MCMC analyses and produce good estimates of model parameters. We also found that the reduced dependence approximation of the normalisation constant outperformed the pseudo-likelihood approximation in our analysis of real and synthetic datasets.

Bayesian Indirect Inference Using a Parametric Auxiliary Model

Indirect inference (II) is a methodology for estimating the parameters of an intractable (generative) model on the basis of an alternative parametric (auxiliary) model that is both analytically and computationally easier to deal with. Such an approach has been well explored in the classical literature but has received substantially less attention in the Bayesian paradigm. The purpose of this paper is to compare and contrast a collection of what we call parametric Bayesian indirect inference (pBII) methods. One class of pBII methods uses approximate Bayesian computation (referred to here as ABC II) where the summary statistic is formed on the basis of the auxiliary model, using ideas from II. Another approach proposed in the literature, referred to here as parametric Bayesian indirect likelihood (pBIL), we show to be a fundamentally different approach to ABC II. We devise new theoretical results for pBIL to give extra insights into its behaviour and also its differences with ABC II. Furthermore, we examine in more detail the assumptions required to use each pBII method. The results, insights and comparisons developed in this paper are illustrated on simple examples and two other substantive applications. The first of the substantive examples involves performing inference for complex quantile distributions based on simulated data while the second is for estimating the parameters of a trivariate stochastic process describing the evolution of macroparasites within a host based on real data. We create a novel framework called Bayesian indirect likelihood (BIL) which encompasses pBII as well as general ABC methods so that the connections between the methods can be established.

A Sequential Monte Carlo Algorithm to Incorporate Model Uncertainty in Bayesian Sequential Design

This article presents a sequential Monte Carlo (SMC) algorithm that can be used for any one-at-a-time Bayesian sequential design problem in the presence of model uncertainty where discrete data are encountered. Our focus is on adaptive design for model discrimination but the methodology is applicable if one has a different design objective such as parameter estimation or prediction. An SMC algorithm is run in parallel for each model and the algorithm relies on a convenient estimator of the evidence of each model that is essentially a function of importance sampling weights. Methods that rely on quadrature for this task suffer from the curse of dimensionality. Approximating posterior model probabilities in this way allows us to use model discrimination utility functions derived from information theory that were previously difficult to compute except for conjugate models. A major benefit of the algorithm is that it requires very little problem-specific tuning. We demonstrate the methodology on three applications, including discriminating between models for decline in motor neuron numbers in patients suffering from motor neuron disease. Computer code to run one of the examples is provided as online supplementary materials.

Bayesian Statistical MUNE Method

We have developed a new method of motor unit number estimation (MUNE) for assessing diseases such as amyotrophic lateral sclerosis (ALS). We used data from the whole stimulus–response curve and then performed a Bayesian statistical analysis. The Bayesian method uses mathematical equations that express the basic elements of motor unit activation after electrical stimulation and allows for the sources of variability and uncertainty in this formulation. The Bayesian MUNE method was used to determine the most probable number of motor units in 8 normal subjects, 49 ALS subjects, and 3 subjects with progressive lower motor neuron (LMN) weakness. In normals the number of motor units was calculated to be 75–85 in hand and 40–58 in foot muscles. In ALS subjects the number of motor units per muscle was less than in normal subjects. In 17 ALS subjects and 3 subjects with LMN weakness the median, ulnar, or peroneal nerve was studied on repeated occasions over an average of 189 days (range 63–1,071) and the number of motor units progressively declined, with a half‐life ranging from 62–834 days. The results of our MUNE technique were reproducible on replicate studies. A Bayesian statistical MUNE method is a new approach that can be used to study ALS patients serially for assessment and treatment trials. Muscle Nerve, 2007

Approximate Bayesian Computation for astronomical model analysis: a case study in galaxy demographics and morphological transformation at high redshift

Free to read Approximate Bayesian Computation’ (ABC) represents a powerful methodology for the analysis of complex stochastic systems for which the likelihood of the observed data under an arbitrary set of input parameters may be entirely intractable – the latter condition rendering useless the standard machinery of tractable likelihood-based, Bayesian statistical inference [e.g. conventional Markov chain Monte Carlo (MCMC) simulation]. In this paper, we demonstrate the potential of ABC for astronomical model analysis by application to a case study in the morphological transformation of high-redshift galaxies. To this end, we develop, first, a stochastic model for the competing processes of merging and secular evolution in the early Universe, and secondly, through an ABC-based comparison against the observed demographics of massive (Mgal > 1011 M⊙) galaxies (at 1.5 < z < 3) in the Cosmic Assembly Near-IR Deep Extragalatic Legacy Survey (CANDELS)/Extended Groth Strip (EGS) data set we derive posterior probability densities for the key parameters of this model. The ‘Sequential Monte Carlo’ implementation of ABC exhibited herein, featuring both a self-generating target sequence and self-refining MCMC kernel, is amongst the most efficient of contemporary approaches to this important statistical algorithm. We highlight as well through our chosen case study the value of careful summary statistic selection, and demonstrate two modern strategies for assessment and optimization in this regard. Ultimately, our ABC analysis of the high-redshift morphological mix returns tight constraints on the evolving merger rate in the early Universe and favours major merging (with disc survival or rapid reformation) over secular evolution as the mechanism most responsible for building up the first generation of bulges in early-type discs.