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‘Super' or just ‘above average'? Supershedders and the transmission of Escherichia coli O157:H7 among feedlot cattle

Simon E. F. Spencer

Simon E. F. Spencer

Department of Statistics, University of Warwick, Coventry, UK

[email protected]

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Thomas E. Besser

Thomas E. Besser

Department Veterinary Microbiology and Pathology, Washington State University, Pullman, WA 99164, USA

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Rowland N. Cobbold

Rowland N. Cobbold

School of Veterinary Science, University of Queensland, Gatton, Queensland, Australia 4343

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Nigel P. French

Nigel P. French

mEpiLab, Infectious Disease Research Centre, Institute of Veterinary Animal and Biomedical Sciences, Massey University, Palmerston North, New Zealand

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Published:https://doi.org/10.1098/rsif.2015.0446

    Abstract

    Supershedders have been suggested to be major drivers of transmission of Escherichia coli O157:H7 (E. coli O157:H7) among cattle in feedlot environments, despite our relatively limited knowledge of the processes that govern periods of high shedding within an individual animal. In this study, we attempt a data-driven approach, estimating the key characteristics of high shedding behaviour, including effects on transmission to other animals, directly from a study of natural E. coli O157:H7 infection of cattle in a research feedlot, in order to develop an evidence-based definition of supershedding. In contrast to the hypothesized role of supershedders, we found that high shedding individuals only modestly increased the risk of transmission: individuals shedding over 103 cfu g−1 faeces were estimated to pose a risk of transmission only 2.45 times greater than those shedding below that level. The data suggested that shedding above 103 cfu g−1 faeces was the most appropriate definition of supershedding behaviour and under this definition supershedding was surprisingly common, with an estimated prevalence of 31.3% in colonized individuals. We found no evidence that environmental contamination by faeces of shedding cattle contributed to transmission over timescales longer than 3 days and preliminary evidence that higher stocking density increased the risk of transmission.

    1. Introduction

    Shiga toxin-producing Escherichia coli O157:H7 (E. coli O157:H7) continue to present a serious threat to public health in many countries around the world [13]. The pathogen is associated with severe haemorrhagic diarrhoea and serious sequelae which can result in loss of life [4,5]. Cattle are considered the main reservoir host [6,7] since the emergence of E. coli O157:H7 in 1982 [8], considerable efforts have been made to reduce the risk of zoonotic transmission via food and environmental pathways, prompting the development of interventions such as vaccination [9,10]. Infection in cattle has major consequences for international trade in animal products, particularly meat from cattle, and this, combined with the direct public health costs, presents a major burden to the economies of many countries [11].

    Mathematical models have been used to inform the design and impact of interventions [1214], understand transmission dynamics in dairy [15,16] and beef [17,18] production systems, and determine the key processes that drive infection dynamics [16,19]. To date, much of the modelling has been carried out by constructing and simulating from mechanistic models [16] and, fitting these models to experimental infection data [20] or cross-sectional data on prevalence and concentration of E. coli O157:H7 in cattle faeces [19].

    A number of studies have focused on the role and importance of ‘supershedders’ in transmission and the maintenance of infection in cattle [1,19]. Although the precise definition varies, supershedders are usually defined as animals shedding relatively large concentrations of E. coli O157:H7 in their faeces, generally between 103 and 104 cfu g−1, for an extended period [21,22]. They are considered to be responsible for a disproportionate amount of transmission. For example, using data from Scotland [23], high shedders, defined as greater than or equal to 3 × 103 cfu g−1 faeces were estimated to constitute 8% of the cattle but 99% of the bacteria shed. It has been suggested that these high shedders represent those animals that are colonized at the recto-anal junction (RAJ), whereas the subset of low shedders are not colonized, and in some way represent a distinct process, whereby non-colonized animals amplify E. coli O157:H7 elsewhere in the gut lumen and shed more briefly [1]. However, some important questions remain: is there robust evidence for the presence of a distinct, identifiable sub-population of cattle that are colonized and shed at high levels for a prolonged period and, if so, how important are these animals for ongoing transmission and maintenance of this pathogen in groups of animals?

    In this study, we present a formal consideration of the relationship between the concentration of E. coli O157:H7 shed in faeces and transmission, using the results from a large-scale study of natural infection in feedlot cattle [22] and fitting Bayesian susceptible–infected–susceptible (SIS) models that consider in detail the relationship between shedding and R0, and the characteristics of the tests used to detect shedding cattle. We derive the relationship between shedding and transmission and provide new insight into the role played by ‘supershedders’ in the maintenance of infection in cattle populations. Finally, we consider an appropriate definition of ‘supershedding’.

    2. Material and methods

    2.1. Experimental data collection

    The data originate from a study of naturally occurring infection in feedlot cattle, described elsewhere [22]. In brief, 20 pens of eight steers were sampled approximately twice weekly over a 13-week grain feeding period. Animals were held in small research pens located on a working commercial feedlot with over 10 000 animals on the premises. The pens were non-adjacent, so that animals could only come into physical contact with their pen-mates. On each sampling date, samples consisted of a recto-anal mucosal swab (RAMS) sample [24] and a sample of freshly passed manure. Each sample was tested by PCR for the presence of E. coli O157:H7 and the shedding level measured by bacteriologic cultures as described [22]. The 12 pens in the north of the facility measured 6 × 17 m (102 m2), whereas the eight south pens measured 6 × 37 m (222 m2).

    2.2. Transmission model

    A discrete time SIS transmission model (figure 1) was used to model the spread of infection through a pen. In this framework, each individual is assumed to belong to one of two states for each day in the study: either susceptible or colonized (infected). Colonized individuals were assumed to shed sufficient quantities of bacteria to infect other individuals in the pen, possibly indirectly via the environment, and so being colonized was assumed to be the same as being infectious. Likewise we did not allow for any potential immunity, and so being uncolonized was assumed to be the same as being susceptible to infection. We denote the colonization status of individual i in pen p on day t by Xp,i,t (for p = 1,…,20, i = 1,…,8, t = 1,…,99), where Xp,i,t = 1 if the individual was colonized and Xp,i,t = 0 otherwise.

    Figure 1.

    Figure 1. Illustration of the transmission model.

    Susceptible individuals were assumed to be at risk from colonization from both unmeasured sources outside of the pen (contaminated feed, wildlife, etc.) and other colonized individuals within the pen. We assumed that the probability a susceptible individual avoids being colonized from sources outside of the pen on any given day was eα: the probability of observing no events in 1 time unit of a Poisson process with rate α. This parametrization therefore allows α to be interpreted as the colonization rate from outside of the pen.

    The main aim of this study was to quantify the relationship between the risk of colonization and shedding. We assume the probability that an individual in pen p which is susceptible on day t avoids colonization on day t + 1 from individual j is given by exp{−βfp,j,t(Xp,j,1:t)}, where the function fp,j,t characterizes the total force of infection from material shed between days 1 and t by individual j in pen p and Xp,i,1:t denotes the vector (Xp,i,1,…,Xp,i,t). Therefore, the probability that an individual susceptible on day t avoids colonization on day t + 1 is given by

    Display Formula

    These assumptions yield a non-Markovian model that has the potential to allow infectious material to accumulate in the environment and cause colonizations later in the study. Note that we do not distinguish between different transmission pathways, so that all within-pen colonizations (direct contact between animals, or indirect transmission via the pen floor, the water trough etc.) are captured by the parameter β. We assumed that the rate of colonization between the study pens was negligible. The north pens and the south pens were of significantly different sizes and so we allowed for different transmission rates in these two environments, denoted by βN and βS, respectively.

    Once colonized, individuals were assumed to remain so for a number of days that followed a negative binomial distribution with shape parameter r and mean duration μ. More precisely, for r > 0, μ > 1 and k = 1,2,…,

    Display Formula
    where 1k is a vector of k ones. This non-standard parametrization ensures that the minimum duration of colonization is 1 day, the mean duration is μ and the variance is μ−1 + (μ−1)2/r. Finally, we assumed that at the start of the study each animal was colonized independently with probability π.

    2.3. Modelling the recto-anal mucosal swab and faecal tests

    Very little is known about the internal processes that govern RAJ colonization and the resulting shedding behaviour. Many existing studies have been cross-sectional and are therefore uninformative regarding the duration and intensity of shedding during a typical colonization episode. In this study, we circumvented the need to model such processes internal to the animal by splitting the observed data (the RAMS counts and faecal counts) into two parts. First, we used exponential smoothing to bridge the gaps between the tests and to combine the RAMS counts with the faecal counts. Where there were only negative tests we inserted the detection limit of the tests so that the output can be interpreted as the estimated shedding level over time conditional on the animal being colonized. Second, in an entirely separate inferential step, we fitted the SIS transmission model described in §2.2 to the binary outcomes of the RAMS and faecal tests (i.e. simply whether or not E. coli O157:H7 was detected).

    Since each putative E. coli O157:H7 isolate was confirmed by multiple phenotypic and genetic markers [22], we assumed that both the RAMS and the faecal tests had 100% specificity. We estimated both test sensitivities separately, with parameters θR for the RAMS test and θF for the faecal test. Note that these sensitivities represent the sensitivity of the whole sample acquisition and testing procedure and not simply the laboratory benchmark sensitivity, which could reasonably be assumed to be the same for both tests. We also assumed that the tests were conditionally independent given the colonization status of the animal. Under these assumptions if either the RAMS or the faecal test were positive then the animal must have been colonized. If neither of the tests were positive, the animal may still have been colonized, but neither of the tests was sufficiently sensitive to detect it.

    2.4. Estimating shedding levels

    Exponential smoothing was used to estimate the shedding level on each day for each animal, conditional on the animal being colonized. First, we examined only the cases where both the RAMS and the faecal samples were positive. The mean for RAMS was 4.589 log10 cfu g−1 and the mean for the faecal samples was 3.306, 1.283 lower. This difference is likely to be from the dilution of the bacteria from the RAJ colonization site by faeces. Therefore, for the purposes of combining these two counts into an overall shedding level we subtract 1.283 from each of the RAMS counts to bring them onto the same scale as the faecal counts.

    The shedding level of individual i in pen p on day t was given by

    Display Formula
    where Ti,p is the index set for all of the RAMS and faecal tests for individual i in pen p; ok is the kth observation and wk(t) is the weight of observation k.

    When only one of the two tests was positive then the negative test was given a weight of zero. When neither test was positive, then since we wish to interpret the count as the shedding level given that the animal is positive, we included a single observation with the detection limit of the RAMS sample, which equated to 0.64 log10 cfu g−1 faeces. The weight function wk(t) was calculated using

    Display Formula
    where tk is the day sample ok was taken. The weights were normalized to sum to 1. Finally, λ was chosen to be log(2) so that the influence of each observation halved with each additional day moved away from it.

    2.5. Relating shedding to colonization

    The principal aim of this study was to characterize the relationship between episodes of high shedding and the risk of colonization. We assumed that individuals that shed above a certain quantity contribute a relative increase in risk.

    Display Formula

    The threshold τ can be either chosen to match a prespecified definition of a supershedder or derived directly from the data. We considered the following predefined values for τ : 2, 2.717, 3, 3.333, 3.477 and 4 log10 cfu g−1 for the faecal test (table 2).

    2.6. Extended model: environmental accumulation and decay

    We extended the model in 2.5 so that infectious material shed earlier in the study can accumulate in the environment and retain some risk of infection. It was assumed that the risk reduced by a fixed proportion δ each day, resulting in a geometric decay in risk.

    Display Formula

    2.7. Model fitting

    The models described in §2.5 and 2.6 were fitted in a Bayesian framework using Markov chain Monte Carlo (MCMC). In all cases prior distributions were chosen to be relatively uninformative. Parameters representing probabilities (θR, θF and π) were given beta(1,1) priors and updated using Gibbs steps. Parameters on finite domains, such as δ and τ, were given uniform priors. The remaining parameters (table 1) with domains on [0,∞) were given gamma(1,1) priors and updated in blocks using multivariate normal Metropolis–Hastings proposals. Appropriate proposal covariance matrices were estimated from pilot runs. The hidden colonization status Xp,i,t was updated using an adaptation of the method of O'Neill and Roberts [25], described in the electronic supplementary material.

    Table 1.Interpretation and posterior medians of the model parameters, for the model in which the supershedding threshold τ is inferred from the data (see §2.5). Values in parenthesis indicate 95% credible intervals.

    parameter posterior median interpretation
    α 0.009 (0.006, 0.012) external colonization rate (days−1)
    βN 0.011 (0.006, 0.016) within-pen colonization rate, north (days−1)
    βS 0.004 (0.002, 0.009) within-pen colonization rate, south (days−1)
    τ 3.199 (2.319, 5.170) supershedding threshold (log10 cfu g−1 faeces)
    ρ 1.910 (0.111, 4.093) supershedding relative risk
    μ 9.578 (8.170, 11.04) mean colonization duration (days)
    r 1.524 (0.910, 2.518) shape parameter of colonization period
    π 0.098 (0.056, 0.154) probability colonized initially
    θR 0.776 (0.733, 0.817) sensitivity of RAMS
    θF 0.464 (0.423, 0.507) sensitivity of faecal test

    3. Results

    3.1. Raw data

    Escherichia coli O157:H7 was isolated in all 20 study pens, with an average prevalence of 13.5% in north pens and 11.2% in south pens. The RAMS tests (473 positives) were found to be more sensitive than the faecal samples (283 positives). Figure 2a,c shows the time courses of positive tests for pens 7 and 8, which contain four of the five supershedders as defined in Cobbold et al. [22]. Plots for the remaining pens are given in the electronic supplementary material. Figure 2b,d shows the level of shedding for the two individuals highlighted in figure 2a,c. To ensure comparability between RAMS and faecal levels, the RAMS levels have been adjusted to the same scale as the faecal tests in order to account for the dilution of the bacteria with faeces.

    Figure 2.

    Figure 2. Escherichia coli O157:H7 positive tests against time (a,c) for pens 7 and 8 with measured shedding levels and exponentially smoothed shedding levels (b,d) for two animals. The letters ‘SS’ indicate that the animal was termed a supershedder under the definition of [22]. Complete plots given in the electronic supplementary material. (Online version in colour.)

    Using their definition of a supershedder (an individual with mean shedding level greater than 4 log10 cfu per positive RAMS and at least four consecutive positive RAMS), Cobbold et al. [22] identified five supershedding animals contained in three pens. In this study, we reconsidered the concept of identifying individual animals as supershedders and instead focus on supershedding behaviour, which we define to be periods of time in which shedding exceeds a certain threshold. We considered both a list of predefined thresholds for supershedding (table 2) and a threshold estimated from the data.

    Table 2.Posterior median relative risk for selected supershedding thresholds converted to log10 cfu g−1 faeces. Values in parenthesis indicate 95% credible intervals.

    supershedding definition supershedding threshold (log10 cfu g−1 faeces) posterior median relative risk
    102 cfu g−1 faeces 2 1.209 (0.527, 2.653)
    104 cfu g−1 RAMS 2.717 1.843 (0.852, 4.034)
    103 cfu g−1 faeces [26] 3 2.449 (1.232, 4.618)
    104 cfu swab−1 RAMS [22] 3.333 1.930 (0.766, 3.742)
    3 × 103 cfu g−1 faeces [12] 3.477 2.221 (0.793, 4.654)
    104 cfu g−1 faeces [2729] 4 1.622 (0.142, 4.286)

    3.2. Smoothed shedding levels

    The first stage of our analysis was to estimate the shedding level of each animal for each day in the study, given that it was colonized, via exponential smoothing. The smoothed shedding levels for two animals are given in figure 2. When both the RAMS and faecal tests were negative, we assumed that the animal was shedding at the detection limit of the RAMS given that it was colonized. Plots of the smoothed shedding levels for every animal are given in the electronic supplementary material.

    3.3. Natural history parameters

    The primary focus for this study was in developing an appropriate model to relate the risk of colonization to the shedding level. Nonetheless fitting an explicit transmission model allowed us to estimate several biologically interesting parameters relating to the natural history of E. coli O157:H7 colonization and the study procedures. These parameters appear in all of the models and since their inferred values were broadly unaltered by the choice of supershedding threshold (τ), we summarize the results here from the model described in 2.5, in which the value of τ was inferred from the data. Posterior summaries and parameter interpretations are given in table 1.

    We estimated the posterior median colonization period to be 9.6 days, with a posterior median shape parameter of 1.5. We also estimated that 9.8% of the animals were colonized at the start of the study. The posterior median test sensitivity of the RAMS was estimated to be 78% and the faecal test 47%.

    We inferred the posterior probability of colonization for every animal in every day of the study. Animal 6 in pen 8 is given as a typical example in figure 3a, with the RAMS and faecal tests superimposed at 1 if positive and at 0 if negative. Full details of these posterior distributions are given in the supplement.

    Figure 3.

    Figure 3. (a) Posterior colonization probability with positive and negative tests marked at 1 and 0, respectively. (b) Posterior expected reproduction function against shedding level with 95% credible intervals as dotted lines. (c) Posterior and prior distributions of the supershedding threshold τ. (d) Posterior and prior distributions for the relative risk ρ posed by individuals shedding above the supershedding threshold τ. (Online version in colour.)

    3.4. Colonization parameters

    The posterior median rate of external transmission was 0.009 which implies each pen receives one external infectious contact on average every 14.5 days. In the north pens, the posterior median of the within-pen colonization rate was 0.011, which implies that a single colonized individual within the pen exerts approximately the same infectious pressure as all of the external sources of infection. In the south pens the within-pen colonization rate was roughly half that of the north pens, recalling that the south pens were approximately twice the area of the north pens. The posterior median of the ratio βN/βS was 2.41 (95% CI 1.31–5.70).

    Figure 3c shows the posterior distribution of the supershedding threshold τ. Recall that individuals shedding at levels above τ pose a relative risk ρ times that of individuals shedding below τ. The posterior distribution of ρ is given in figure 3d. The joint posterior distribution of ρ and τ (given in the electronic supplementary material) reveals that when τ > 4 the shape of the posterior follows the shape of the prior distribution and so the data were only weakly informative about the risk posed by individuals shedding above this level.

    Clearly, the supershedding threshold τ and the relative risk ρ are highly dependent parameters, and so to better illustrate their relationship we have calculated the posterior expected reproduction function (figure 3b). The reproduction function is an extension of the basic reproduction number R0 stratified as a function of the level of shedding. We define the reproduction function to be the expected number of secondary colonizations that would result from a single colonized individual shedding at a fixed level throughout their colonization period, in an otherwise uncolonized pen. This quantity encapsulates all of the epidemic parameters except for the external transmission rate, and has the property that where the reproduction function is greater than one the level of transmission within the pen is sufficient to result in a sustained outbreak without any external contributions.

    3.5. Fixed supershedding threshold

    We wished to explore further the effect that different definitions of supershedding would have on the risk posed by supershedders. We refitted the model with supershedding threshold fixed at a range of predefined values.

    When τ was chosen to be 103 cfu g−1 faeces, we found that the posterior median relative risk was 2.449 for supershedding cattle. Results for other choices of τ are given in table 2. The 95% credible interval for the relative risk did not include 1 under this definition of supershedding, showing significant evidence of an increase in risk. The remaining definitions did not show significant evidence for an increase.

    3.6. Extended model: environmental accumulation and decay

    Finally, we consider an extended model described in 2.6 in which faecal material accumulates in the environment once it has been shed, before decaying away. This allows individuals to become colonized from animals that were shedding earlier in the study but are not shedding contemporaneously. Figure 4 displays the posterior distribution for the half-life of risk attributed to faecal material shed into the environment. The posterior median half-life for the risk of colonization was 0.45 days (95% CI: 0.15–1.68). The majority of the posterior distribution lies shorter than 2 days, which is less than the shortest interval between tests. Therefore, there is no evidence from these data that faecal material shed into the environment posed a risk of colonization to other animals in the pen for substantial amounts of time after it had been shed. Posterior distributions for the remaining parameters (given in the electronic supplementary material) are remarkably similar to the ones for the model without environmental accumulation.

    Figure 4.

    Figure 4. Posterior and prior distributions for the half-life of the risk from faecal material shed into the environment. (Online version in colour.)

    4. Discussion

    The three key findings from this study are that (i) supershedding individuals appear to pose approximately double the risk of transmission resulting in colonization, compared with low shedding individuals; (ii) a data-driven estimate for the definition of a supershedding threshold was 3 log10 cfu g−1 faeces; and (iii) there was no evidence of environmental transmission occurring over timescales longer than 2 days.

    Finding (i) contrasts sharply with the prevailing view expressed in the literature on supershedders of E. coli O157:H7, that as high shedding animals are expelling several orders of magnitude more bacteria, then their risk of transmission must be raised by a similar amount [19]. Our finding appeared to be robust to whether the threshold for supershedding was estimated from the data (figure 3d) or whether it was predetermined (table 2). Even low-dose exposures have been shown to lead to colonizations in challenge studies [30,31], and this might explain why the risk of colonization was not strongly related to the number of bacteria shed. It has been suggested that interventions targeting high shedding individuals would be disproportionally effective [19,22] but our results suggest that such interventions would not reduce within-herd transmission by as much as anticipated.

    Our results do suggest a potential intervention to reduce transmission within pens. The south pens were 2.18 times the area of the north pens, and the transmission rate 2.41 times lower in the south pens. This might suggest reducing animal density as a means to reduce within-pen transmission in the feedlot environment. It was notable that in the south pens the reproduction functions were generally below one, implying that infection from outside the pen was necessary for the infection to persist in the pen. The animal densities in these study pens approximate those of high-density (north pens) and low-density (south pens) commercial feedlot pens, so the range of stocking density here is directly relevant to those in use in the industry [32]. Furthermore, the use of increased stocking density during summer months as a management tool to reduce feedlot dust emissions [33,34] roughly correlates with the higher average E. coli O157:H7 faecal prevalence in feedlot cattle during that period [35]. Our study was not designed to investigate pen area as a risk factor for transmission, however, our data are supported by a previous study in which it was observed that cattle density within feedlot pens correlated with the prevalence of faecal E. coli O157:H7 shedding [36]. On the other hand, Renter et al. [37] did not detect an effect of confinement on the prevalence of faecal shedding of E. coli O157:H7 by cattle when comparing feedlot and pastured cattle, after controlling for the younger age of the feedlot cattle. It may be that there are different drivers of transmission in pasture environments, such as infection from wild animals and increased contact between cattle around water sources.

    Cobbold et al. [22] defined a supershedder to be an individual with a mean RAMS greater than 4 log10 cfu swab−1 with at least four consecutive RAMS tests. Although this definition characterizes individuals that are colonized at the RAJ with high levels of bacteria and for a sustained period, there are two important drawbacks with this as a general definition of supershedding. First, it is difficult to generalize to cross-sectional studies or longitudinal studies with a different sampling frequency because of the requirement for four consecutive positive tests. Second, because the average RAMS level is taken over all positive tests in the study it will regress towards the mean shedding level as greater numbers of positives appear. Consequently, this definition actually favours individuals with fewer positives. There is clear evidence of this effect in figure 2, where three of the four supershedders identified by Cobbold et al. (labelled on the left-hand side with ‘SS’) have close to the minimum number of positive RAMS tests—just four consecutive ones. The remaining supershedder identified in the study also had four positive RAMS tests (not shown).

    These considerations motivate the need for a more generalizable definition of supershedding behaviour. There remains little evidence from longitudinal studies on how long supershedding behaviour persists in individual animals. It is certainly not well established that individuals identified to be shedding at high levels will again shed at high levels after a period free from colonization. Cattle infected by E. coli O157:H7 respond with specific mucosal and systemic immune responses, and these responses may contribute to clearance of infection [38,39]. However, cattle have been shown to be susceptible to recolonization shortly after clearance in both observational and experimental studies, albeit often accompanied by faecal shedding reduced in level and duration [40,41]. Therefore, the process through which individual animals clear colonization remains undefined. One hypothesis might be that supershedding is the indirect result of interactions between different components of the RAJ microbiome which permits temporary or persistent dominance by E. coli O157:H7. Likewise, the process of decolonization may be the result of changes in the competing bacterial flora at the RAJ, perhaps acting in concert with RAJ mucosal immune responses.

    These considerations lead us to suggest moving away from the idea that individual animals can be categorized as supershedders, but instead that supershedding behaviour is a transient property that can appear and disappear over time. We propose that supershedding behaviour be defined by achieving a single shedding level above a certain threshold. Ideally, the shedding level would be measured using the RAMS test as we found it to be more sensitive than the faecal test and it is presumably more specific to RAJ colonization. However, since faecal sampling is more widespread and far easier to undertake, we have described our results in terms of this test. All that remains is to decide on an appropriate threshold.

    A variety of different thresholds for supershedding of E. coli O157:H7 in cattle have been used in the literature, including 104 cfu RAMS−1 [22], 104 cfu g−1 faeces [2729], 103 cfu g−1 faeces [26] and 3 × 103 cfu g−1 faeces [12]. In this study, we have converted these into cfu per gram of faeces, based on an average swab weight of 0.242 g and a faecal dilution factor of 5.21% (10−1.283) when comparing RAMS and faecal tests. These conversions are summarized in table 2. By fitting a model in which the supershedding threshold τ could be estimated from the data, this study has been the first to provide a data-driven definition of supershedding. The posterior median supershedding threshold was 3.2 log10 cfu g−1 faeces, however, the posterior mode was closer to three. This suggests that 103 cfu g−1 faeces might be the most appropriate threshold for supershedding. This definition also produced the highest relative risk posed by supershedders (table 2). However, note that there is considerable uncertainty in the posterior distribution of the supershedding threshold (figure 3c), and so this finding will be worth re-evaluating as more evidence becomes available.

    The raw prevalence, based on samples in which at least one of the two tests was positive, was 12.6%. The posterior expected prevalence, which takes into account colonized animals that failed to test positive was 14.6%. Using 103 cfu g−1 faeces as the threshold for supershedding behaviour, we find a prevalence of supershedding behaviour of 4.6% and hence the prevalence of supershedding behaviour during colonization was 31.3%. The abundance of supershedding behaviour adds further weight to the idea that supershedding may not be particularly exceptional or influential to transmission and is therefore somewhat misnamed.

    In §3.6, an extended model was fitted which had the ability to capture the accumulation and removal of bacteria in the environment as the study progressed. In particular, the risk of infection from faeces continued beyond the day on which it was shed. This model estimated that the half-life for the risk of colonization from faeces (figure 4) was 0.45 days. This is much smaller than existing survival estimates in experimental settings, such as survival in soils [42,43] and on farmyard material surfaces [44]. We found no significant risk of colonization beyond 2 or 3 days after shedding, which coincides with the shortest time interval between tests in our study. Consequently, there was not the temporal resolution in our dataset to determine whether the risk of infection was spread across a few days or concentrated around the time that shedding occurs. However, the data appear to contain no evidence of longer-term risk of transmission. For reasons of parsimony it therefore appears most sensible to use a Markovian transmission model, in which the risk of transmission occurs only on the day of shedding, because such models require fewer parameters.

    If we link together the findings that the risk of transmission is not strongly linked to the level of shedding, but it is related to pen area, then this could support the hypothesis that ingestion of faecal material from the pen floor is the prevailing risk factor for within-pen transmission. In particular the density of recent faecal pats on the pen floor (irrespective of the concentration of bacteria within the faeces) may be worth further investigation as a driver of transmission within the feedlot environment.

    The two diagnostic tests produced very different posterior median sensitivity estimates: 0.78 (95% CI 0.73–0.82) for the RAMS and 0.46 (95% CI 0.42–0.51) for the faecal test. Note that these sensitivities encompass the whole sampling procedure (sample capture, transportation and laboratory work); and not just the laboratory benchmark sensitivity, which could reasonably be assumed to be the same for both tests. The faecal test sensitivity is likely to be lower because of the dilution of the bacteria with faeces, which coincides with most of the existing literature [24,45,46], but not all [4749]. It is unsurprising that there is some variation between studies as the sensitivity is likely to depend strongly on the exact sampling protocol and study design.

    An obvious weakness with the models discussed in this paper is the assumption that the sensitivity of the RAMS and faecal tests does not depend on the shedding level of the animal. A priori we would expect that high shedding individuals would be easier to detect than individuals shedding at levels close to the detection limit of the tests and this should be addressed in future modelling work. A further weakness is that the model does not account for any uncertainty in the shedding levels, which were estimated via exponential smoothing in a separate inferential step. Ideally the shedding level would be estimated concurrently with the colonization status, but to do so would require the model to describe the way that shedding levels evolve through time within an individual animal. At present, there is not enough available data or understanding of the biological processes involved to parametrize such a model.

    4.1. External validity

    The data used in this study come from research pens of eight cattle which, because of their small size, may not entirely reflect the dynamics of transmission within the much larger pens used in commercial feedlots, although pen densities are likely to be comparable. However, the research pens were located outside on a fully operational commercial feedlot and, except for the sampling procedures, the treatment was the same as for the full-scale commercial setting. The costs of performing such intensive sampling on commercial scale pens would be prohibitive and so having sufficient data to reconstruct the transmission dynamics must necessarily come at a cost to external validity. A recent review [50] highlighted only one longitudinal study with larger pen sizes [27] with an average pen size of 31.9, however, the sampling frequency was once per month, which would make reconstructing the transmission process between tests extremely challenging from these data. Our observations regarding the effects of supershedder thresholds and animal density on transmission rates are plausible but should be applied tentatively to other cattle production systems or to other host–agent systems for which supershedders are proposed to play a role.

    To our knowledge this study has been the first to employ a data-driven approach to characterize supershedding behaviour. Although our findings were based on data from only one study on a much smaller scale than a commercial feedlot, our modelling approach could readily be applied to more comprehensive longitudinal datasets as they emerge. In contrast to previous efforts to model the effects of supershedders, we report here little support for dramatically higher effects of these animals in driving transmission. In addition, our data give little indication that individual cattle persistently exhibit supershedder behaviour but rather, are consistent with periodic or episodic supershedding among many or most colonized cattle.

    Authors' contributions

    S.E.F.S. designed the model, carried out the statistical analyses and drafted the manuscript; R.N.C. provided the data; T.E.B., R.N.C. and N.P.F. provided input on contextual interpretation and practical impacts of findings and drafted the manuscript. All authors gave final approval for publication.

    Competing interests

    We declare we have no competing interests.

    Funding

    This work was funded by The Beef Checkoff, with support from National Institutes of Health Public Health Service grants U54-AI-57141, P20-RR16454 and P20-RR15587 and from the US Department of Agriculture National Institute of Food and Agriculture grant no. 2010-04487.

    Footnotes

    Published by the Royal Society. All rights reserved.

    References