A Bayesian micro-simulation to evaluate the cost-effectiveness of interventions for mastitis control during the dry period in UK dairy herds.

Importance of the dry period with respect to mastitis control is now well established although the precise interventions that reduce the risk of acquiring intramammary infections during this time are not clearly understood. There are very few intervention studies that have measured the clinical efficacy of specific mastitis interventions within a cost-effectiveness framework so there remains a large degree of uncertainty about the impact of a specific intervention and its costeffectiveness. The aim of this study was to use a Bayesian framework to investigate the cost-effectiveness of mastitis controls during the dry period. Data were assimilated from 77 UK dairy farms that participated in a British national mastitis control programme during 2009-2012 in which the majority of intramammary infections were acquired during the dry period. The data consisted of clinical mastitis (CM) and somatic cell count (SCC) records, herd management practices and details of interventions that were implemented by the farmer as part of the control plan. The outcomes used to measure the effectiveness of the interventions were i) changes in the incidence rate of clinical mastitis during the first 30days after calving and ii) the rate at which cows gained new infections during the dry period (measured by SCC changes across the dry period from <200,000cells/ml to >200,000cells/ml). A Bayesian one-step microsimulation model was constructed such that posterior predictions from the model incorporated uncertainty in all parameters. The incremental net benefit was calculated across 10,000 Markov chain Monte Carlo iterations, to estimate the cost-benefit (and associated uncertainty) of each mastitis intervention. Interventions identified as being cost-effective in most circumstances included selecting dry-cow therapy at the cow level, dry-cow rations formulated by a qualified nutritionist, use of individual calving pens, first milking cows within 24h of calving and spreading bedding evenly in dry-cow yards. The results of this study highlighted the efficacy of specific mastitis interventions in UK conditions which, when incorporated into a costeffectiveness framework, can be used to optimize decision making in mastitis control. This intervention study provides an example of how an intuitive and clinically useful Bayesian approach can be used to form the basis of an on-farm decision support tool.

Modelling the effect of antimicrobial treatment on carriage of hospital pathogens with application to MRSA.

Numerous studies have sought to assess the effectiveness of control measures aimed at reducing the spread of pathogens such as Methicillin-resistant Staphylococcus aureus (MRSA) in hospital settings. Far less is known about possible short-term effects of antibiotics and other antimicrobial treatments on pathogen carriage in patients. This paper is concerned with developing and applying methods for the analysis of detailed data on hospital patients which include information on patient treatments and screening tests for the pathogen in question. The carriage status (colonized, or not) of each patient is modelled as a Markov chain, and models for both perfect and imperfect test sensitivity are developed. Goodness-of-fit procedures based on simulation are also proposed. The methods are illustrated using both simulated data and data on MRSA.

Piecewise Approximate Bayesian Computation: fast inference for discretely observed Markov models using a factorised posterior distribution.

Many modern statistical applications involve inference for complicated stochastic models for which the likelihood function is difficult or even impossible to calculate, and hence conventional likelihood-based inferential techniques cannot be used. In such settings, Bayesian inference can be performed using Approximate Bayesian Computation (ABC). However, in spite of many recent developments to ABC methodology, in many applications the computational cost of ABC necessitates the choice of summary statistics and tolerances that can potentially severely bias the estimate of the posterior. We propose a new "piecewise" ABC approach suitable for discretely observed Markov models that involves writing the posterior density of the parameters as a product of factors, each a function of only a subset of the data, and then using ABC within each factor. The approach has the advantage of side-stepping the need to choose a summary statistic and it enables a stringent tolerance to be set, making the posterior "less approximate". We investigate two methods for estimating the posterior density based on ABC samples for each of the factors: the first is to use a Gaussian approximation for each factor, and the second is to use a kernel density estimate. Both methods have their merits. The Gaussian approximation is simple, fast, and probably adequate for many applications. On the other hand, using instead a kernel density estimate has the benefit of consistently estimating the true piecewise ABC posterior as the number of ABC samples tends to infinity. We illustrate the piecewise ABC approach with four examples; in each case, the approach offers fast and accurate inference.

Effect of systemic antibiotics and topical chlorhexidine on meticillin-resistant Staphylococcus aureus carriage in intensive care unit patients.

Antibiotics and antiseptics have the potential to influence carriage and transmission of meticillin-resistant Staphylococcus aureus (MRSA), although effects are likely to be complex, particularly in a setting where multiple agents are used. Here admission and weekly MRSA screens and daily antibiotic and antiseptic prescribing data from 544 MRSA carriers on an intensive care unit (ICU) are used to determine the effect of these agents on short-term within-host MRSA carriage dynamics. Longitudinal data were analysed using Markov models allowing patients to move between two states: MRSA positive (detectable MRSA carriage) and MRSA negative (no detectable carriage). The effect of concurrent systemic antibiotic and topical chlorhexidine (CHX) on movement between these states was assessed. CHX targeted to MRSA screen carriage sites increased transition from culture positive to negative and there was also weaker evidence that it decreased subsequent transition from negative back to positive. In contrast, there was only weak and inconsistent evidence that any antibiotic influenced transition in either direction. For example, whereas univariate analysis found quinolones to be strongly associated with both increased risk of losing and then reacquiring MRSA carriage over time intervals of one day, no effect was seen with weekly models. Similar studies are required to determine the generalisability of these findings.

A novel approach to real-time risk prediction for emerging infectious diseases: a case study in Avian Influenza H5N1.

Mathematical simulation modelling of epidemic processes has recently become a popular tool in guiding policy decisions for potential disease outbreaks. Such models all rely on various parameters in order to specify quantities such as transmission and detection rates. However, the values of these parameters are peculiar to an individual outbreak, and estimating them in advance of an epidemic has been the major difficulty in the predictive credibility of such approaches. The obstruction to classical approaches in estimating model parameters has been that of missing data: (i) an infected individual is only detected after the onset of clinical signs, we never observe the time of infection directly; (ii) if we wish to make inference on an epidemic while it is in progress (in order to predict how it might unfold in the future), we must take into account the fact that there may be individuals who are infected but not yet detected. In this paper we apply a reversible-jump Markov chain Monte Carlo algorithm to a combined spatial and contact network model constructed in a Bayesian context to provide a real-time risk prediction during an epidemic. Using the example of a potential Avian H5N1 epidemic in the UK poultry industry, we demonstrate how such a technique can be used to give real-time predictions of quantities such as the probability of individual poultry holdings becoming infected, the risk that individual holdings pose to the population if they become infected, and the number and whereabouts of infected, but not yet detected, holdings. Since the methodology generalises easily to many epidemic situations, we anticipate its use as a real-time decision-support tool for targetting disease control to critical transmission processes, and for monitoring the efficacy of current control policy.