Philip D. O'Neill

Bayesian inference for partially observed stochastic epidemics

The analysis of infectious disease data is usually complicated by the fact that real life epidemics are only partially observed. In particular, data concerning the process of infection are seldom available. Consequently, standard statistical techniques can become too complicated to implement effectively. In this paper Markov chain Monte Carlo methods are used to make inferences about the missing data as well as the unknown parameters of interest in a Bayesian framework. The methods are applied to real life data from disease outbreaks.

A tutorial introduction to Bayesian inference for stochastic epidemic models using Markov chain Monte Carlo methods

Recent Bayesian methods for the analysis of infectious disease outbreak data using stochastic epidemic models are reviewed. These methods rely on Markov chain Monte Carlo methods. Both temporal and non-temporal data are considered. The methods are illustrated with a number of examples featuring different models and datasets.

Analyses of infectious disease data from household outbreaks by Markov chain Monte Carlo methods

The analysis of infectious disease data presents challenges arising from the dependence in the data and the fact that only part of the transmission process is observable. These difficulties are usually overcome by making simplifying assumptions. The paper explores the use of Markov chain Monte Carlo (MCMC) methods for the analysis of infectious disease data, with the hope that they will permit analyses to be made under more realistic assumptions. Two important kinds of data sets are considered, containing temporal and non-temporal information, from outbreaks of measles and influenza. Stochastic epidemic models are used to describe the processes that generate the data. MCMC methods are then employed to perform inference in a Bayesian context for the model parameters. The MCMC methods used include standard algorithms, such as the Metropolis-Hastings algorithm and the Gibbs sampler, as well as a new method that involves likelihood approximation. It is found that standard algorithms perform well in some situations but can exhibit serious convergence difficulties in others. The inferences that we obtain are in broad agreement with estimates obtained by other methods where they are available. However, we can also provide inferences for parameters which have not been reported in previous analyses.

Bayesian Inference for Stochastic Epidemics in Populations with Random Social Structure

A single-population Markovian stochastic epidemic model is defined so that the underlying social structure of the population is described by a Bernoulli random graph. The parameters of the model govern the rate of infection,the length of the infectious period,and the probability of social contact with another individual in the population. Markov chain Monte Carlo methods are developed to facilitate Bayesian inference for the parameters of both the epidemic model and underlying unknown social structure. The methods are applied in various examples of both illustrative and real-life data,with two different kinds of data structure considered.

Assessing the role of undetected colonization and isolation precautions in reducing Methicillin-Resistant Staphylococcus aureus transmission in intensive care units

BackgroundScreening and isolation are central components of hospital methicillin-resistant Staphylococcus aureus (MRSA) control policies. Their prevention of patient-to-patient spread depends on minimizing undetected and unisolated MRSA-positive patient days. Estimating these MRSA-positive patient days and the reduction in transmission due to isolation presents a major methodological challenge, but is essential for assessing both the value of existing control policies and the potential benefit of new rapid MRSA detection technologies. Recent methodological developments have made it possible to estimate these quantities using routine surveillance data.MethodsColonization data from admission and weekly nares cultures were collected from eight single-bed adult intensive care units (ICUs) over 17 months. Detected MRSA-positive patients were isolated using single rooms and barrier precautions. Data were analyzed using stochastic transmission models and model fitting was performed within a Bayesian framework using a Markov chain Monte Carlo algorithm, imputing unobserved MRSA carriage events.ResultsModels estimated the mean percent of colonized-patient-days attributed to undetected carriers as 14.1% (95% CI (11.7, 16.5)) averaged across ICUs. The percent of colonized-patient-days attributed to patients awaiting results averaged 7.8% (6.2, 9.2). Overall, the ratio of estimated transmission rates from unisolated MRSA-positive patients and those under barrier precautions was 1.34 (0.45, 3.97), but varied widely across ICUs.ConclusionsScreening consistently detected >80% of colonized-patient-days. Estimates of the effectiveness of barrier precautions showed considerable uncertainty, but in all units except burns/general surgery and one cardiac surgery ICU, the best estimates were consistent with reductions in transmission associated with barrier precautions.

Reproduction numbers and thresholds in stochastic epidemic models I. Homogeneous populations

We compare threshold results for the deterministic and stochastic versions of the homogeneous SI model with recruitment, death due to the disease, a background death rate, and transmission rate beta cXY/N. If an infective is introduced into a population of susceptibles, the basic reproduction number, R0, plays a fundamental role for both, though the threshold results differ somewhat. For the deterministic model, no epidemic can occur if R0 less than or equal to 1 and an epidemic occurs if R0 greater than 1. For the stochastic model we find that on average, no epidemic will occur if R0 less than or equal to 1. If R0 greater than 1, there is a finite probability, but less than 1, that an epidemic will develop and eventuate in an endemic quasi-equilibrium. However, there is also a finite probability of extinction of the infection, and the probability of extinction decreases as R0 increases above 1.

Introduction and snapshot review: Relating infectious disease transmission models to data

Disease transmission models are becoming increasingly important both to public health policy makers and to scientists across many disciplines. We review some of the key aspects of how and why such models are related to data from infectious disease outbreaks, and identify a number of future challenges in the field.

Estimation of measles vaccine efficacy and critical vaccination coverage in a highly vaccinated population

Measles is a highly infectious disease that has been targeted for elimination from four WHO regions. Whether and under which conditions this goal is feasible is, however, uncertain since outbreaks have been documented in populations with high vaccination coverage (more than 90%). Here, we use the example of a large outbreak in a German public school to show how estimates of key epidemiological parameters such as the basic reproduction number (R0), vaccine efficacy (VES) and critical vaccination coverage (pc) can be obtained from partially observed outbreaks in highly vaccinated populations. Our analyses rely on Bayesian methods of inference based on the final size distribution of outbreak size, and use data which are easily collected. For the German public school the analyses indicate that the basic reproduction number of measles is higher than previously thought (, 95% credible interval: 23.6–40.4), that the vaccine is highly effective in preventing infection (, 95% credible interval: 0.993–0.999), and that a vaccination coverage in excess of 95 per cent may be necessary to achieve herd immunity (, 95% credible interval: 0.961–0.978). We discuss the implications for measles elimination from highly vaccinated populations.

A modification of the general stochastic epidemic motivated by AIDS modelling

This paper considers a model for the spread of an epidemic in a closed, homogeneously mixing population in which new infections occur at rate fxy/(x + y), where x and y are the numbers of susceptible and infectious individuals, respectively, and 0 is an infection parameter. This contrasts with the standard general epidemic in which new infections occur at rate fxy. Both the deterministic and stochastic versions of the modified epidemic are analysed. The deterministic model is completely soluble. The time-dependent solution of the stochastic model is derived and the total size distribution is considered. Threshold theorems, analogous to those of Whittle (1955) and Williams (1971) for the general stochastic epidemic, are proved for the stochastic model. Comparisons are made between the modified and general epidemics. The effect of introducing variability in susceptibility into the modified epidemic is studied. EPIDEMICS; SIZE OF EPIDEMIC; DETERMINISTIC AND STOCHASTIC MODELS; TIMEDEPENDENT SOLUTION; THRESHOLD THEOREMS; EMBEDDED RANDOM WALKS; VARIABILITY IN SUSCEPTIBILITY AMS 1991 SUBJECT CLASSIFICATION: PRIMARY 92D30 SECONDARY 60J27

Computation of final outcome probabilities for the generalised stochastic epidemic

This paper is concerned with methods for the numerical calculation of the final outcome distribution for a well-known stochastic epidemic model in a closed population. The model is of the SIR (Susceptible→Infected→ Removed) type, and the infectious period can have any specified distribution. The final outcome distribution is specified by the solution of a triangular system of linear equations, but the form of the distribution leads to inherent numerical problems in the solution. Here we employ multiple precision arithmetic to surmount these problems. As applications of our methodology, we assess the accuracy of two approximations that are frequently used in practice, namely an approximation for the probability of an epidemic occurring, and a Gaussian approximation to the final number infected in the event of an outbreak. We also present an example of Bayesian inference for the epidemic threshold parameter.