# Predictive Capacity of COVID-19 Test Positivity Rate

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## Abstract

**:**

## 1. Introduction

## 2. Material and Methods

#### 2.1. The Statistical Method Applied

#### 2.2. Estimation of the Model Order and the $\lambda $ Parameter

## 3. Results

#### 3.1. Analysis of the TPR Predictive Capacity

#### 3.2. Forecasting Hospital Overload

## 4. Discussion

- (1)
- The data on the antigen tests administrated are provided;
- (2)
- The time series of new positive cases should include the daily number of new positives tested using only antigen tests;
- (3)
- The TPR should reach a peak before the hospitalized and ICU patients reach theirs.

- Growth rate: positives daily variation;
- Incidence: fraction of COVID-19 positives per 100,000 individuals;
- The reproduction number ${R}_{t}$: number of secondary infections generated from a case at time t.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**The TPR index (orange dotted lines) and hospitalized patients time series of Toscana, Veneto, Piemonte, and Alto Adige.

**Figure 3.**Forecasting hospitalized patients growth in 5 different scenarios for regions: Toscana, Alto Adige, Piemonte, and Veneto (also including a fast lowering example). The orange dotted lines represent the TPR index.

**Figure 4.**Developing point-of-care (instant) screening tests for COVID-19: data collection, sensors technology, TPR calculation, and information flows.

**Table 1.**This table presents the results of the regression models with Seasonal Auto Regressive Moving Average (SARIMA) errors concerning patients admitted in hospitals and intensive care units for Toscana, Veneto, Alto Adige, and Piemonte regions. The columns Days and Beds indicate the TPR predictive capacity in days (with the associated t-value) and the estimated variation of beds in both hospitals and Intensive Care Units (ICUs).

Region | Days | Hospitalized t-Value | Beds | Days | ICU t-Value | Beds |
---|---|---|---|---|---|---|

Toscana | 12 | 2.34 | 54 | 12 | 2.05 | 9 |

Piemonte | 12 | 3.82 | 86 | 12 | 2.03 | 36 |

Veneto | 13 | 2.07 | 82 | 13 | 2.52 | 12 |

Alto Adige | 12 | 1.92 | 30 | 12 | 5.60 | 8 |

**Table 2.**This table presents the detailed results of the experiment presented in Section 3.1, for studying the SARIMA lagged correlation between the TPR time series and those of patients admitted in hospitals and ICUs. The last two columns Days and Beds indicate the TPR predictive capacity in days and the number of additional beds in hospital or ICU after 12 days for each TPR unit.

Toscana | ||||||||||

SARIMA(2, 1, 0)(1, 0, 1) Box Cox trans: $\lambda $ = 1.2 ${\beta}_{t-value}$ = 2.34 | ||||||||||

${\varphi}_{1}$ | ${\varphi}_{2}$ | ${\Phi}_{1}$ | ${\Theta}_{1}$ | $\beta $ | $Days$ | $Beds$ | ||||

Hosp: | 0.45 | 0.18 | 0.91 | −0.69 | 100.61 | 12 | 54 | |||

s.e. | 0.08 | 0.09 | 0.063 | 0.13 | 43.00 | |||||

SARIMA(2, 1, 0)(0, 0, 1) Box Cox trans: $\lambda $ = 1.2 ${\beta}_{t-value}$ = 2.05 | ||||||||||

${\varphi}_{1}$ | ${\varphi}_{2}$ | ${\Theta}_{1}$ | $\beta $ | $Days$ | $Beds$ | |||||

ICU: | 0.12 | 0.29 | 0.15 | 10.18 | 12 | 9 | ||||

s.e. | 0.09 | 0.09 | 0.09 | 4.98 | ||||||

Veneto | ||||||||||

SARIMA(2,1,1)(1,0,1) Box Cox trans: $\lambda $= 1.4 ${\beta}_{t-value}$=2.07 | ||||||||||

${\varphi}_{1}$ | ${\varphi}_{2}$ | ${\theta}_{1}$ | ${\Phi}_{1}$ | ${\Theta}_{1}$ | $\beta $ | $Days$ | $Beds$ | |||

Hosp: | 0.73 | 0.21 | −0.76 | 0.77 | −0.60 | 341.70 | 13 | 82 | ||

s.e. | 0.11 | 0.09 | 0.08 | 0.15 | 0.19 | 164.82 | ||||

SARIMA(0,1,1)(0,1,1) Box Cox trans: $\lambda $ = 1.34 ${\beta}_{t-value}$ = 2.52 | ||||||||||

${\theta}_{1}$ | ${\Theta}_{1}$ | $\beta $ | $Days$ | $Beds$ | ||||||

ICU: | 0.06 | −0.67 | 20.72 | 13 | 12 | |||||

s.e. | 0.09 | 0.09 | 8.22 | |||||||

Alto Adige | ||||||||||

SARIMA(3, 1, 0)(0, 1, 1) Box Cox transf: $\lambda $ = 1.69 ${\beta}_{t-value}$ = 1.92 | ||||||||||

${\varphi}_{1}$ | ${\varphi}_{2}$ | ${\varphi}_{3}$ | ${\Theta}_{1}$ | $\beta $ | $Days$ | $Beds$ | ||||

Hosp: | 0.27 | −0.25 | 0.36 | −1.00 | 182.07 | 12 | 30 | |||

s.e. | 0.08 | 0.08 | 0.09 | 0.07 | 94.66 | |||||

SARIMA(0, 0, 3)(0, 1, 2)) Box Cox transf: $\lambda $ = 1.98 ${\beta}_{t-value}$ = 5.60 | ||||||||||

${\theta}_{1}$ | ${\theta}_{2}$ | ${\theta}_{3}$ | ${\Theta}_{1}$ | ${\Theta}_{2}$ | $\beta $ | $Days$ | $Beds$ | |||

ICU: | 1.06 | 1.04 | 0.63 | −0.58 | −0.30 | 27.12 | 12 | 8 | ||

s.e. | 0.06 | 0.07 | 0.06 | 0.13 | 0.10 | 4.84 | ||||

Piemonte | ||||||||||

SARIMA(10,1,1)(1,1,1) Box Cox: $\lambda $ = 3 ${\beta}_{t-value}$ = 3.82 | ||||||||||

${\varphi}_{3}$ | ${\varphi}_{5}$ | ${\varphi}_{6}$ | ${\varphi}_{10}$ | ${\Theta}_{1}$ | ${\Phi}_{1}$ | ${\theta}_{1}$ | $\beta $ | $Days$ | $Beds$ | |

Hosp: | 0.22 | 0.11 | 0.31 | 0.19 | 0.16 | 0.21 | −1.0 | 211,187.31 | 12 | 86 |

s.e. | 0.08 | 0.07 | 0.08 | 0.07 | 0.09 | 0.09 | 0.05 | 55,285.44 | ||

SARIMA(3,1,0)(0,1,1) Box Cox: $\lambda $=1.2 ${\beta}_{t-value}$=2.03 | ||||||||||

${\varphi}_{1}$ | ${\varphi}_{2}$ | ${\varphi}_{3}$ | ${\theta}_{1}$ | $\beta $ | $Days$ | $Beds$ | ||||

ICU: | 0.38 | 0.36 | 0.17 | −0.83 | 60.33 | 12 | 36 | |||

s.e. | 0.08 | 0.08 | 0.08 | 0.08 | 29.74 |

Region | Situation | Training Set | Obs | Test Set | Obs |
---|---|---|---|---|---|

Toscana | fast growing | 02/09/20–10/31/20 | 60 | 01/11/20–15/11/20 | 15 |

Piemonte | red zone start | 02/09/20–06/11/20 | 66 | 07/11/20–22/11/20 | 15 |

Veneto | slow growing | 02/09/20–09/12/20 | 99 | 13/12/20–28/12/20 | 15 |

Veneto | fast lowering | 02/09/20–29/12/20 | 136 | 15/01/21–30/01/21 | 15 |

Alto Adige | fast growing | 02/09/20–04/11/20 | 64 | 05/11/20–20/11/20 | 15 |

**Table 4.**Pure predictive capacity in days of different COVID-19 indicators with respect to hospitalization.

Metrics | What It Represents | Days |
---|---|---|

TPR | Number of active cases in a region also | 15 |

embodying the unknown portion of asymptomatic | ||

Growth rate | Variation of detected positive cases in a region | 4 |

Incidence | Number of known cases in a region | 4 |

${R}_{t}$ index | Variation of the infections dynamics in a region | 4 |

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**MDPI and ACS Style**

Fenga, L.; Gaspari, M.
Predictive Capacity of COVID-19 Test Positivity Rate. *Sensors* **2021**, *21*, 2435.
https://doi.org/10.3390/s21072435

**AMA Style**

Fenga L, Gaspari M.
Predictive Capacity of COVID-19 Test Positivity Rate. *Sensors*. 2021; 21(7):2435.
https://doi.org/10.3390/s21072435

**Chicago/Turabian Style**

Fenga, Livio, and Mauro Gaspari.
2021. "Predictive Capacity of COVID-19 Test Positivity Rate" *Sensors* 21, no. 7: 2435.
https://doi.org/10.3390/s21072435