# The Role of a PMI-Prediction Model in Evaluating Forensic Entomology Experimental Design, the Importance of Covariates, and the Utility of Response Variables for Estimating Time Since Death

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## Abstract

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## 1. Introduction

_{min}) [4,5].

#### Some Specialized Terminology

## 2. Lesson 1: Employ an Unbiased Sampling Technique for Generating Training Data

## 3. Lesson 2: Exceed the Minimum Sample Size for a Categorical Response

## 4. Lesson 3: The Practical Significance of a Covariate, or the Practical Value of a Response, Should Be Evaluated by Predictive Model Performance

## 5. Conclusions

_{min}. We argue that this prediction should be mathematically explicit, should yield a range of values rather than a single value, and that defining this range as a confidence set would conform to mainstream scientific practice.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

IP | Inverse prediction |

PMI | Postmortem interval |

PMI_{min} | Minimum postmortem interval |

SI | Succession interval |

TD | Training data |

MS | Mystery specimen |

## References

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**Figure 1.**Blow fly growth data illustrating how inverse prediction model performance can depend on the design of the training data experiment. The histograms show the complete data set (n = 1405) of larval length as a function of age. The inverse prediction model (red lines defining a growth curve) reflect published sampling methods and were calculated based on subsamples of 10 from each cohort that were (

**A**) randomly selected or (

**B**) the largest individuals. Each green peak shows the coverage proportion for 95% prediction intervals on age from length for each larva in the 60 h cohort. Model A performed relatively well in that 100% of predictions included the true age and the line falls away steeply on each side. Model B performed poorly. From [18].

**Figure 2.**Chrysomya megacephala larval mean width as a function of age at 25.8 °C and fed either pork heart or pork liver. The data are from [25]. Red dotted lines show 95% inverse prediction confidence bands [12]. Although there was a significant effect of food type on size (F = 18.27, df = 8/700, p < 0.0001), when the liver model was used to predict the age of all heart larvae, more than 95% of inverse prediction confidence sets on age included the true age.

**Table 1.**Smallest sample size needed to reject a condition value at the 5% level based on a categorical response, such as when estimating succession interval from insect presence/absence or estimating insect age from life stage. For example, a succession pattern of a single species would have two response categories: present or absent on each training data (TD) experimental corpse at a given time since placement. If the number of TD corpses was 7–17, a time since death is rejected if zero TD corpses match the mystery specimen (MS, a corpse with a known set of insect species but unknown postmortem interval (PMI)). With 17–27 TD corpses, a time since death is rejected if zero or one TD corpse matches the MS, etc. Non-rejected values constitute a 95% confidence set on succession interval [12].

Reject If ≤ No. TD Matching MS | ||||||
---|---|---|---|---|---|---|

No. Response Categories | 0 | 1 | 2 | 3 | 4 | 5 |

2 | 7 | 17 | 28 | 39 | 52 | 64 |

3 | 15 | 34 | 55 | 78 | 102 | 128 |

4 | 22 | 51 | 83 | 117 | 153 | 191 |

8 | 52 | 118 | 192 | 272 | 357 | 444 |

**Table 2.**95% confidence limits about the age of a 56-hour-old Chrysomya megacephala larva using the multivariate method of [16]. Training data larvae were reared on pork heart at 25.8 °C and sampled at ages 17, 36, 40, 56, 60, 85, 90 and 96 h [25]. Age prediction models were based on combinations of the two continuous responses—body length (L) and body width (W)—and the categorical response, instar (I). An asterisk indicates rejection of an age (column values), so the prediction interval is shown by the gap in each row. The narrower the interval, the better the model performance.

MODEL | 17 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 | 65 | 70 | 75 | 80 | 85 | 90 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

L | * | * | * | * | * | * | * | * | * | * | * | |||||

W | * | * | * | * | * | * | * | * | * | * | ||||||

L, W | * | * | * | * | * | * | * | * | * | * | ||||||

I | * | * | * | * | * | * | * | * | * | * | * | * | ||||

L, I | * | * | * | * | * | * | * | * | * | * | * | * | * | |||

W, I | * | * | * | * | * | * | * | * | * | * | * | * | * | * | ||

L, W, I | * | * | * | * | * | * | * | * | * | * | * | * | * | * |

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**MDPI and ACS Style**

Wells, J.; LaMotte, L.
The Role of a PMI-Prediction Model in Evaluating Forensic Entomology Experimental Design, the Importance of Covariates, and the Utility of Response Variables for Estimating Time Since Death. *Insects* **2017**, *8*, 47.
https://doi.org/10.3390/insects8020047

**AMA Style**

Wells J, LaMotte L.
The Role of a PMI-Prediction Model in Evaluating Forensic Entomology Experimental Design, the Importance of Covariates, and the Utility of Response Variables for Estimating Time Since Death. *Insects*. 2017; 8(2):47.
https://doi.org/10.3390/insects8020047

**Chicago/Turabian Style**

Wells, Jeffrey, and Lynn LaMotte.
2017. "The Role of a PMI-Prediction Model in Evaluating Forensic Entomology Experimental Design, the Importance of Covariates, and the Utility of Response Variables for Estimating Time Since Death" *Insects* 8, no. 2: 47.
https://doi.org/10.3390/insects8020047