Abattoir post-mortem inspection offers good opportunities for pig health monitoring  and it has been widely used as a data source for epidemiology-based analyses. Most of these studies focus on the identification of risk factors influencing the presence of the major abattoir pathologies: pneumonia, pleurisy and milk spot liver [2–9]. Few reports investigate how the different pathologies are interrelated [1, 10, 11]. Identification of the associations between pathologies may assist in elucidating theories on their biological connection and could greatly contribute to facilitating their control – for example by encouraging veterinarians to establish intervention strategies aimed at reducing the prevalence of not just one, but two or more conditions simultaneously. Knowledge of associations between lesions could also be employed to inform official abattoir inspection systems, in which the presence of one pathology could trigger an inspection for others.
Official routine meat inspections are implemented world-wide with the main objective of ensuring food safety. This system, however, is imperfect and is particularly lacking in sensitivity [12, 13]. Pig health schemes were proposed to provide an integrated system to capture abattoir information based on more detailed post-mortem inspection  which is considered to improve classification characteristics, particularly sensitivity . Good examples of these initiatives in Europe are the British pig health schemes. On a regular basis, swine specialists carry out detailed post-mortem examinations in parallel to the official food-safety routine meat inspections. These schemes monitor the presence of various pathologies detected by means of a detailed inspection of the pluck and the skin of the slaughtered pig. These pathologies are normally associated with a reduction in performance traits or are potential indicators of the presence of welfare problems in the herds [10, 15–17].
Graphical modelling has been increasingly used in veterinary epidemiology to investigate and express the relationships between factors influencing diseased/unproductive status in livestock [18–23]. Frequently, studies utilising graphical models are based on structure discovery approaches, which are data-driven multivariate methodologies resulting in graphical outputs such as networks or path/chain models. Structure discovery has been employed to explore how mastitis and fertility management influence production in dairy herds ; to identify changes in pig behaviour related to early piglets mortality ; to investigate the most likely pathogens involved in clinical mastitis in dairy cows ; and to identify those farm risk factors associated with bovine viral diarrhoea . Besides these examples, other studies employed graphical models informed using existing/expert knowledge to describe risk factors influencing the prevalence of Mycoplasma hyopneumoniae ; and to estimate the risk of leg disorders in finishing pigs . A crucial distinction among the abovementioned papers, is that these two latter studies [21, 22] did not use structure discovery to inform structure of the network, but were rather based on published knowledge and expert opinion. The latter is highly subjective and if, as in this study, extensive data are available, then extracting the co-dependence network structure from observed data provides objective and robust empirical analyses.
Multi-dimensional machine learning methodology (also known as Bayesian graphical modelling) is a variety of graphical modelling structure discovery techniques used to identify the dependency structure that encodes the joint probability distribution between variables [24, 25], allowing for both visualization and estimation of associations. In short, this process consists of a series of model searches to identify the multi-dimensional model that best explains the data, using Bayes factors to compare between models . This approach allows estimation of the associations between variables and distinguishes between direct and indirect dependence  (dependence being equivalent to biological association), contributing to generate hypotheses about the nature of the interrelationships. Multi-dimensional machine learning methodology offers an intuitively appealing and technically elegant way to investigate multiple associations between variables compared to more conventional multivariate statistical approaches (e.g. principal component and factor analyses). This methodology is used extensively in fields such as bioinformatics and genetics [26–28] and only recently has been applied in the veterinary field .
This paper uses a multi-dimensional machine learning methodology to identify whether associations exist between the different pathologies reported by the British pig health schemes. The results of this study could assist veterinarians in the control of these conditions by implementing strategies to control several conditions at once. These results could be also utilised to review current pig abattoir inspection strategies, and inform more targeted risk based inspections. Farmed pigs are normally considered as a grouped unit, where complex interactions take place between the environment, mainly determined by the housing system and the husbandry practices, and the pigs, characterised by their genetics, idiosyncratic behaviour and baseline health status . For these reasons this study focuses on the interrelationship occurring between pathologies at batch level.