Industrial hog operation (IHO) workers can be occupationally exposed to

Research indicates that swine production workers are at increased risk for nasal carriage of livestock-associated strains of

Understanding the risk factors of

In this paper, we propose a Markov model as an approach to predict changes in worker nasal carriage of

The data used for this model were obtained from a four-month prospective longitudinal cohort study of

We developed a discrete time Markov chain model to describe how industrial hog operation workers transition between

We represented the initial state of our Markov chain with an initial state vector _{i}, where i is the nasal carriage state (NC=0, HA=1, and LA=2). We modeled time in equal intervals of two weeks to correspond with study visits. A worker can transition directly from any of the three states into any other state or stay in the same state during a given two-week Markov cycle. We assumed that only one single state transition could happen for each worker during each cycle. Accordingly, there are nine possible transitions that can occur in each Markov cycle, including remaining in the same state. The probabilities of each transition occurring are expressed mathematically in the transition probability matrix _{ij}, where the worker transitions from the ith state at time t to the jth state at time t+1. By definition of a Markov process, we assume that a worker’s probability of moving from one state to another state is dependent only on the current state of the worker (i.e., P_{ij} is constant for a given i and j). We used a straightforward process to determine transition probabilities (see

The estimated distribution of worker carriage states after

We assume that if there are no changes in workplace conditions, nasal carriage of

This mathematical property of Markov models allows us to predict what carriage state is expected to dominate this population at steady state if conditions remain the same.

To estimate the proportion of workers in each nasal carriage state throughout the study period, we multiplied the baseline vector (representing the distribution of workers in each nasal carriage state) with the transition probability matrix developed from the data collected during study visits raised to the

We examined the influence of workers’ self-reported mask use on the transition probabilities by developing stratified transition probability matrices for consistent mask use and for occasional mask use. At each study visit, individuals report average mask use within the two-week Markov cycle. We evaluated every single time-step (two week) transition that occurred over the study period. Each transition was matched with the worker’s self-reported mask-use during that two-week interval. We stratified the observed transitions into two groups based on the average reported face mask use of the participant during the two-week Markov cycle in which the transition occurred. We defined “consistent use” as self-reported mask use of 80% or more during the prior two weeks and “occasional use” as self-reported mask use less than 80% in the prior two weeks. These definitions were aligned with definitions used in previous analysis of this data (

To test the validity of our model, and to understand how much data are needed to create a reliable model (in other words, how much data is sufficient to make a reasonable prediction), we created multiple transition probability matrices using varying amounts of data and then compared each model’s output to observed data. In other words, we created eight separate models, with the first model holding back the majority of the study data and subsequent models increasing the amount of study data used to define the transition probabilities. Specifically, the transition probability matrix for Model 1 was developed using transition data from baseline to visit 1. Model 2 was built using transition data from baseline to visit 1 ^{th} power,

In the initial study visit, 58 (57.4%), 25 (24.8%), and 18 (17.8%) of workers were in the NC, HA, and LA nasal carriage states, respectively. Thus, the distribution of workers in each state is represented by the vector

Steady state distributions for each of the three models are shown in

With a study population of 101 workers, 9 study visits, and 8 transitions per worker, there were 808 total transitions in 8 Markov cycles. Due to missing nasal swab or mask use data for some of the participants, 137 transitions were excluded, and 676 transitions were observed and included in our models.

This study modeled changes in nasal carriage of

In the occasional mask use model, it is predicted that livestock associated strains of

Our analysis indicates that the Markov models perform reasonably well (R^{2} > 0.9) in predicting future nasal carriage with as little as 4 weeks’ worth of longitudinal data. Mean squared errors for Models 2 through 8 indicate that these models perform reasonably well (MSE < 0.005) at predicting nasal carriage states after 2 Markov cycles. In this dataset, reasonably accurate predictions were made with data from only three study visits. While more research is needed to establish how much data is needed to create an accurate transition probability matrix for changes in worker health over time, this research supports the fact that even limited amount of longitudinal data could have useful predictive power in research and occupational exposure monitoring. This might inform the way that future longitudinal studies are designed. Mathematical models, in combination with limited sampling data, may be used to understand workplace nasal carriage over time with reasonable accuracy, provided that workplace conditions and worker behaviors remain constant.

Our models also support the conclusions of prior studies that indicate that occupational mask use among this cohort may have a protective effect for nasal colonization of

One purpose of our study is to illustrate the use of Markov modeling in industrial hygiene applications. To our knowledge, this is the first application of a Markov chain to model industrial hog operation worker nasal carriage of

Due to resource limitations and worker privacy concerns, quality repeated measures data on worker nasal carriage may be impractical to obtain. Therefore, there are many advantages to using models to predict what future carriage distributions look like using a limited number of data points. This study estimated the occupational risk of

We developed a Markov model to predict nasal carriage of

Robust longitudinal data for occupational cohorts are typically scarce. If movement of workers between various infection states can be accurately predicted, researchers may be able to determine the long-term impact of interventions using fewer data points. Given that models that were developed using one third of the data points produced similar results to models that used all data, researchers may be able to design more cost-effective sampling strategies in the future. Markov models have practical applications for occupational settings and should be considered as a tool for predicting changes in worker health states and evaluating the effectiveness of workplace controls.

The authors would like to thank the workers and community members who participated in the study from which this data were obtained. The authors also thank the community-based organization members who made essential contributions to this research and without whom, this study would not be possible.

Funding for this study was provided by National Institute for Occupational Safety and Health (NIOSH) grant K01OH010193; Johns Hopkins NIOSH Education and Research Center grant T42OH008428; a directed research award from the Johns Hopkins Center for a Livable Future; award 018HEA2013 from the Sherrilyn and Ken Fisher Center for Environmental Infectious Diseases Discovery Program at the Johns Hopkins University, School of Medicine, Department of Medicine, Division of Infectious Diseases; and National Science Foundation (NSF) grant 1316318 as part of the joint NSF-National Institutes of Health (NIH)-U.S. Department of Agriculture Ecology and Evolution of Infectious Diseases program. C.D.H. and G.R. were supported by NIOSH grant K01OH010193, E.W. “Al” Thrasher Award 10287, NIEHS grant R01ES026973, and NSF grant 1316318. M.F.D. was supported by the NIH Office of the Director (K01OD019918). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

The findings and conclusions in this report are those of the authors and do not necessarily represent the official position of the National Institute for Occupational Safety and Health, Centers for Disease Control and Prevention.

Study Design. 101 industrial hog operation workers were enrolled in the original study. Study visits occurred two weeks apart. The figure above represents one individual as she or he transitions between different nasal carriage states over the course of the study. Transitions between these states over the two-week time intervals are represented by an arrow. NC = no nasal carriage of

State transition diagram. Arrows indicate possible transitions that can occur over one Markov cycle. Arrows leading from a circle back to itself indicates that a worker may stay in the same state over a Markov cycle. NC = no nasal carriage of S. aureus; HA = nasal carriage of human-associated

Steady state distributions for the complete model (i.e. unstratified model using data from all observed transitions) and the models stratified by mask use. Percentages are shown with 95% confidence intervals in parenthesis. Consistent mask use is defined as self-reported mask use ≥ 80% of the time and occasional mask use is defined as self-reported mask use <80%.

Predicted versus observed values for Model 1 and Model 8.

Mean square error for Models 1–8 for predicting the proportion of individuals in each nasal carriage state at the final study visit. The mean squared error is computed by calculating the difference between each pair of predicted and observed values and averaging the squared differences.

General structure of transition probability matrices and initial state vectors for Markov models used in this study. The probability of moving between two states in one Markov cycle is represented by P_{ij}, where the worker transitions from the ith state at time t to the jth state at time t+1.

Transition Probability Matrix | ||||
---|---|---|---|---|

State at time t+1 | ||||

No nasal carriage of | Nasal carriage of human-associated | Nasal carriage of livestock-associated | ||

State at time t | NC | P_{00} | P_{01} | P_{02} |

HA | P_{10} | P_{11} | P_{12} | |

LA | P_{20} | P_{21} | P_{22} | |

Initial State Vector | ||||

State at time t = 0 | N_{0} | N_{1} | N_{2} |

Transition probability matrices developed using (a) all transitions observed during the study period, (b) transitions observed when workers self-reported mask use in prior two weeks, either consistent (≥ 80% reported mask use) or occasional (<80% reported mask use), and (c) the subset of transitions where workers reported complete mask use (100% reported mask use) or no mask use (0% reported mask use). For 45 observed transitions, data on mask use in the prior two weeks are missing. Gray shaded cells represent transitions to the same state (i.e. the line of identity).

(a) Transition Probability Matrix for All Observed Transitions (676 transitions) | |||
---|---|---|---|

State at time t+1 | |||

State at time t | NC | HA | LA |

NC | 0.802 | 0.084 | 0.114 |

HA | 0.208 | 0.658 | 0.134 |

LA | 0.178 | 0.130 | 0.692 |

(b) Transition Probability Matrix Stratified by Mask Use | |||
---|---|---|---|

Consistent Mask Use (319 transitions) | State at time t+1 | ||

State at time t | NC | HA | LA |

NC | 0.783 | 0.128 | 0.089 |

HA | 0.266 | 0.627 | 0.107 |

LA | 0.344 | 0.172 | 0.484 |

Occasional Mask Use (312 transition) | State at time t+1 | ||
---|---|---|---|

State at time t | NC | HA | LA |

NC | 0.689 | 0.108 | 0.203 |

HA | 0.242 | 0.516 | 0.242 |

LA | 0.225 | 0.108 | 0.667 |

(c) Transition Probability Matrix for Models Stratified by Mask Use | |||
---|---|---|---|

100% Mask Use (310 transitions) | State at time t+1 | ||

State at time t | NC | HA | LA |

NC | 0.776 | 0.132 | 0.092 |

HA | 0.266 | 0.627 | 0.107 |

LA | 0.328 | 0.180 | 0.492 |

0% Mask Use (74 transitions) | State at time t+1 | ||
---|---|---|---|

State at time t | NC | HA | LA |

NC | 0.7 | 0.075 | 0.225 |

HA | 0.111 | 0.445 | 0.444 |

LA | 0.36 | 0.16 | 0.48 |

Transition probability matrices and predicted final study visit prediction for Models 1 through 8 of the data sufficiency analysis. Each model was created using varying amounts of data, with the first model holding back the majority of the study data and subsequent models increasing the amount of study data used to define the transition probabilities. The transition probability matrix for Model 1 was developed using transition data from baseline to visit 1. Model 2 was built using transition data from baseline to visit 1 and transition data from visit 1 to visit 2. Model 3 uses transition data from baseline to visit 1, from visit 1 to visit 2, and from visit 2 to visit 3, and so on. Each model is used to predict the distribution of nasal carriage status among the cohort at the final study visit (follow up visit 8). The initial distribution of workers in each state, ^{th} power to produce the final study visit prediction. Transition probability matrices are given in the format displayed in

The correlation coefficient reported here refers to the correlation between the model’s predictions for follow up visits 1 through 8 compared to what was observed among the cohort. The final study visit prediction refers to the models’ output when predicting the distribution of nasal carriage statuses of the cohort at follow up visit 8, given as NC (95% CI); HA (95% CI); LA (95% CI). NC = no nasal carriage of S. aureus; HA = nasal carriage of human-associated

Model | Number of Transitions Used to form Matrix | Transition Probability Matrix | Correlation Coefficient (R^{2}) | Visit 8 Prediction (95% C.I.) NC HA LA |
---|---|---|---|---|

Model 1 | 100 | 0.789 0.123 0.088 | 0.0059 | 0.252 (0.147, 0.357) |

Model 2 | 198 | 0.837 0.096 0.067 | 0.933 | 0.545 (0.430, 0.660) |

Model 3 | 295 | 0.801 0.081 0.118 | 0.9075 | 0.486 (0.364, 0.608) |

Model 4 | 385 | 0.781 0.083 0.136 | 0.9233 | 0.470 (0.343, 0.597) |

Model 5 | 463 | 0.793 0.073 0.134 | 0.9058 | 0.478 (0.356, 0.600) |

Model 6 | 547 | 0.790 0.086 0.124 | 0.926 | 0.474 (0.357, 0.591) |

Model 7 | 613 | 0.797 0.083 0.120 | 0.9268 | 0.491 (0.362, 0.620) |

Model 8 | 676 | 0.801 0.084 0.115 | 0.929 | 0.493 (0.376, 0.610) |

Observed Data | -- | -- | 1 | 0.508 |