# Bayesian Decision Analysis: An Underutilized Tool in Veterinary Medicine

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## Abstract

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## Simple Summary

## Abstract

## 1. Introduction

## 2. The Principles of Bayesian Decision Analysis

## 3. Materials and Methods

#### 3.1. Case Description

#### 3.2. Case Analysis

#### 3.2.1. Diagnosis Probability Estimates

**Table 2.**Outside clinician-derived composite prior (posterior probabilities from Table 1 become prior probabilities due to a different reference time point) and conditional probabilities for differential diagnoses and diagnostic findings after all pre-surgical diagnostics in an approximately 1-year-old ferret presenting for two days of lethargy and inappetence, and one day history of diarrhea. Posterior probabilities of differential diagnoses at time of euthanasia are shown.

Diagnosis | Prior Probability (%) | Conditional Probability (%) Exploratory Laparotomy | Conditional Probability (%) Lymph Node Cytology | Conditional Probability (%) Clinical Progression | Prior × Conditional Probabilities | Posterior Probability (%) |
---|---|---|---|---|---|---|

Lymphoma | 5 | 23.7 | 35 | 15 | 62,801 | 10 |

GI Foreign Body | 31 | 12 | 6.7 | 11.7 | 28,658 | 4 |

Systemic Coronaviral Infection | 0.1 | 7 | 11.7 | 13.3 | 145 | 0.02 |

Helicobacter Gastritis | 5 | 60 | 6.1 | 19.3 | 36,966 | 6 |

Disseminated Idiopathic Myofasciitis | 6 | 12 | 6.1 | 55 | 26,146 | 4 |

Bacterial Gastroenteritis | 52 | 51.7 | 6.1 | 30.7 | 501,131 | 76 |

Unknown Toxicosis | 1 | 8.7 | 5.3 | 13.3 | 350 | 0.05 |

SUM | 656,197 |

#### 3.2.2. Outcome Utility Estimates

#### 3.2.3. Decision Tree & Treatment Threshold Sensitivity Analysis

## 4. Results

#### 4.1. Diagnosis Probability Estimates

#### 4.2. Outcome Utility Estimates

#### 4.3. Decision Tree & Treatment Threshold

## 5. Discussion

## 6. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

## References

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**Figure 1.**Each of seven differential diagnosis probabilities for a 1-year-old castrated male ferret that presented to a veterinary teaching hospital following two days of lethargy and inappetence, and one day of diarrhea. The cumulative composite posterior probabilities for each differential diagnosis change as each new piece of diagnostic evidence is incorporated into the clinical picture.

**Figure 2.**Decision tree for the clinical case of a ferret with a possible gastrointestinal foreign body (GI FB). The square node represents a decision to be made by the clinician, while the oval nodes, called chance nodes, represent the different outcomes dictated by diagnosis probability. The numbers in the oval nodes represent expected values (∑ (utility × diagnosis probability)) of each choice. For example, the composite probability of a GI FB at time of surgery (0.31) was multiplied by the utility value of the surgery + GI FB outcome (83.3) to equal 25.8; then the probability of not having a GI FB (1 − 0.31 = 0.69) was multiplied by the utility value of the surgery + no GI FB outcome (60) to equal 41.4. When 41.4 and 25.8 were added together and rounded to the nearest whole number, the expected value of surgery was revealed to be 67. This process was repeated for the “no surgery” choice to reveal an expected value of 76. In this case, the “no surgery” choice provides greater value.

**Figure 3.**Template for using Bayes’ theorem to think probabilistically in diagnosis. Differential diagnoses should be exhaustive and mutually exclusive, meaning they should cover the realm of possibilities and that only one is the true primary cause of disease. If necessary, inclusion of an “other” category, consisting of aggregated low probability diagnoses, may be considered. Conditional probabilities may come from literature, expert opinion, or in the case of certain diagnostic assays, data from the manufacturer or lab. Any probability, prior or conditional, of 0 will result in that diagnosis having a posterior probability of 0, so it is important to consider whether a diagnosis or a diagnostic finding is possible, i.e., has a probability > 0, rather than simply unlikely. Posterior probability in this template is expressed as a percentage, rather than on a 0 to 1 scale. An interactive spreadsheet formulation has been included in the supplementary material (Table S4) to allow easier application of this tool.

**Table 1.**Outside clinician-derived composite prior and conditional probabilities for differential diagnoses and diagnostic findings, respectively, in an approximately 1-year-old ferret presenting for two days of lethargy and inappetence, and one day history of diarrhea. Pre-surgical posterior probabilities are also shown.

Diagnosis | Prior Probability (%) | Conditional Probability (%) Physical Exam | Conditional Probability (%) Radiography | Conditional Probability (%) Ultrasonography | Conditional Probability (%) CBC | Conditional Probability (%) Chemistry | Prior × Conditional Probabilities | Posterior Probability (%) |
---|---|---|---|---|---|---|---|---|

Lymphoma | 9.3 | 25 | 25 | 11.7 | 35 | 30 | 71,458,333 | 5 |

GI Foreign Body | 46.7 | 20 | 20 | 43.3 | 35 | 15.3 | 434,103,704 | 31 |

Systemic Coronaviral Infection | 5.3 | 8.3 | 18.3 | 5.3 | 23.7 | 18.3 | 1,885,542 | 0.1 |

Helicobacter Gastritis | 10.7 | 8.3 | 28.3 | 23.3 | 30 | 41.7 | 73,456,790 | 5 |

Disseminated Idiopathic Myofasciitis | 7.7 | 43.3 | 21.7 | 13.7 | 46.7 | 20 | 91,816,379 | 6 |

Bacterial Gastroenteritis | 18.3 | 27 | 28.3 | 32 | 46.7 | 35 | 733,040,000 | 52 |

Unknown Toxicosis | 2.7 | 10.3 | 21.7 | 26.7 | 27 | 18.7 | 8,024,178 | 1 |

SUM | 1,413,784,925 |

**Table 3.**Individual and composite (average) estimates of relative utility for different clinical outcomes from the original clinical team. The utility for no surgery + no gastrointestinal foreign body was assumed to be 100 (maximum).

Clinical Outcome | Individual Estimated Utility | Composite Estimated Utility | ||
---|---|---|---|---|

Surgery + Gastrointestinal Foreign Body | 90 | 80 | 80 | 83.3 |

Surgery + No Gastrointestinal Foreign Body | 70 | 60 | 50 | 60 |

No Surgery + Gastrointestinal Foreign Body | 25 | 25 | 20 | 23.3 |

No Surgery + No Gastrointestinal Foreign Body | 100 | |||

Treatment Threshold | 32% chance of GI FB | 42% chance of GI FB | 45% chance of GI FB | 40% chance of GI FB |

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**MDPI and ACS Style**

Cummings, C.O.; Mitchell, M.A.; Perry, S.M.; Fleissner, N.; Mayer, J.; Lennox, A.M.; Johnson-Delaney, C.A.
Bayesian Decision Analysis: An Underutilized Tool in Veterinary Medicine. *Animals* **2022**, *12*, 3414.
https://doi.org/10.3390/ani12233414

**AMA Style**

Cummings CO, Mitchell MA, Perry SM, Fleissner N, Mayer J, Lennox AM, Johnson-Delaney CA.
Bayesian Decision Analysis: An Underutilized Tool in Veterinary Medicine. *Animals*. 2022; 12(23):3414.
https://doi.org/10.3390/ani12233414

**Chicago/Turabian Style**

Cummings, Charles O., Mark A. Mitchell, Sean M. Perry, Nicholas Fleissner, Jörg Mayer, Angela M. Lennox, and Cathy A. Johnson-Delaney.
2022. "Bayesian Decision Analysis: An Underutilized Tool in Veterinary Medicine" *Animals* 12, no. 23: 3414.
https://doi.org/10.3390/ani12233414