# Prediction of Hospital Readmission from Longitudinal Mobile Data Streams

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## Abstract

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## 1. Introduction

- We develop a new method that incorporates the static medical administration risk assessment value currently used in hospitals as the initial risk probability in an LSTM structure to infer the readmission risk progression trajectory of each patient from their processed behavioral mobile data.
- We develop a new ranking method to evaluate the performance of the generated models. This method particularly contributes to selecting models that more accurately estimate the levels of risk in early days after discharge where patients are at a higher risk of readmission.
- To our knowledge, this is the first approach for prediction of daily readmission risk progression through leveraging mobile data and deep learning frameworks. This framework can contribute to the continuous monitoring of patients outside of hospitals and help clinical professionals to identify patients at risk and act accordingly.

## 2. Background and Related Work

## 3. Deep Learning Framework for Prediction of Daily Readmission Risk

#### 3.1. Calculating Probabilities of Readmission Risk

**L**ength of stay at the hospital,

**A**cuity of the admission,

**C**omorbidities, and

**E**mergency department visits during the previous 6 months, while HOSPITAL relies on low

**H**emoglobin level at discharge, discharge from an

**O**ncology service, low

**S**odium level at discharge,

**P**rocedure during hospital stay,

**I**ndex admission

**T**ype, number of hospital

**A**dmissions during the previous year, and

**L**ength of stay. We use these measures to calculate an initial risk probability at the time of hospital discharge. The initial probability is then used in other functions we develop to measure a daily readmission risk.

#### 3.1.1. Initial Risk of Readmission

#### 3.1.2. Final Risk of Readmission

#### 3.1.3. Daily Risk of Readmission

#### 3.2. Modeling Approach

#### 3.3. Using Actual vs. Predicted Probability of Previous Day

#### 3.4. Measuring Performance

#### 3.4.1. Ranking Metrics

#### 3.4.2. Ranking Process

#### 3.5. Classic Models as Baselines

#### 3.5.1. Multiple Linear Regression (MLR)

#### 3.5.2. Regression Tree (RT)

#### 3.5.3. Support Vector Regression (SVR)

## 4. Evaluation

#### 4.1. Dataset

#### 4.2. Sensor Data Processing

#### 4.2.1. Feature Extraction

#### 4.2.2. Handling Missing Values

- Remove features (columns in the dataset) that miss more than 80% of the values.
- Remove features with variance less than 0.3.
- Impute the missing values in the remaining feature cells following the imputation method of Moving Average Algorithm that first uses the moving average of the previous N values ($N\ge 1$) (if they are nonempty) to replace the missing values for each patient and each feature. The algorithm then replaces the remaining missing cells with a constant value (−1) that is different from the feature values.

#### 4.2.3. Normalization

#### 4.3. Model Parameters and Settings

#### 4.3.1. Input Data Source

#### 4.3.2. Data Range

#### 4.3.3. Initial and Daily Probability Calculation

#### 4.3.4. LSTM Parameters

- The default number of hidden layers is two. However, we build models with one and two layers.
- The early stopping callback will stop the training if the training loss is not decreased after 50 epochs.
- The number of hidden units is adjusted by the number of features. If the adjustment of hidden units is disabled, the number is set to use the total number of features as the count for hidden units.
- Mean absolute error is used as the loss function.
- The activation functions are tanh and sigmoid at hidden layer and output layers, respectively.

#### 4.4. Results

#### 4.4.1. Optimizing the Prediction Trend

**Imputation with previous k days**. We build models with k previous days (k = 0 to 5) and observe that this impacts the performance of the models. This indicates that closeness in the range of feature values and the patient status is related to these values on previous days. The best performance is observed in the model that uses the average value of the previous two days’ values to impute the missing values (Table 4).**Features Filtering**. Removing the features when the first day’s value is missing improves the model’s predictions drastically. This indicates that the first day of data is an important input for the LSTM to initialize the model. Without this input, the feature would act as noise that disturbs the training process (Table 4).**Input Data Sources**. Our analysis demonstrates that models that include all sensor, symptoms, and deviation data are more accurate and provide better performance than models that include only a subset of these sources (Table 5). We also find that the performance of the model with only sensor data is better than the model with only symptoms data. This demonstrates that sensor data may play an important role in predicting readmission probabilities.**Initial and Daily Probability**. Using an average of HOSPITAL and LACE scores as the initial probability score yields a better performance than does using either score alone. We also observe that the predicted trend lines closely follow the actual probabilities when an exponential function is used to calculate the daily risk of readmission. We also observe that restarting the probability for readmitted patients to the initial probability after the second discharge increases the covariance between the actual and predicted values. The model using the exponential function could simulate the trend of readmission risk appropriately in all patients. (Table 6).

#### 4.4.2. Comparison with Classic Models

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

LSTM | Long Short-Term Memory |

SMS | Short Message Service |

GPS | Global Positioning System |

MSE | Mean Squared Error |

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**Figure 2.**Mean of four symptoms (Pain, Fatigue, Nausea, and Diarrhea) for single patients. (

**a**) Nonreadmitted patient. (

**b**) Readmitted patient (Readmission day = 16, Second discharge day = 21).

**Figure 3.**Daily risk probabilities generated by different functions. (

**a**) Nonreadmitted patient. (

**b**) Readmitted patient (Readmission day = 16, Second discharge day = 21).

**Figure 6.**(

**a**) Actual probability, i.e., the probability derived from LACE and HOSPITAL scores, as a feature. (

**b**) Predicted probability, i.e., the LSTM’s previous output, as a feature.

**Figure 7.**Results for all patients based on default settings. (

**a**) Previous actual probability as a feature with date. (

**b**) Previous actual probability as a feature without date. (

**c**) Previous predicted probability as a feature with date. (

**d**) Previous predicted probability as a feature without date.

**Figure 8.**Best model after setting optimization. (

**a**) Nonreadmitted patient. (

**b**) Readmitted patient (Readmission day = 16, Second discharge day = 21).

Metrics | MSE | Covariance |
---|---|---|

Overall (First 20 days & All 60 days) | Smallest to Largest | Largest to Smallest |

Readmitted (First 20 days & All 60 days) | Smallest to Largest | Largest to Smallest |

Non-readmitted (First 20 days & All 60 days) | Smallest to Largest | Largest to Smallest |

Features | Description |
---|---|

Activitity | Number of activities, count of activity changes |

Call | Number/Duration of incoming/outgoing calls |

Heart Rate | Min/max/mean/total of heart rates, min/max/mean/totoal of absolute/positive/negative changes |

Light | Min/max/mean/median/standard deviation of illuminance(lux) |

Location | Variance/entropy of location, number of visits/time spend at different clusters |

Message | Number of incoming/outgoing messages |

Screen | Min/max/mean/total length of interaction periods, |

Sleep | Min/max/mean length of asleep/awake/efficiency/restless periods |

Step | Min/max/mean/total length of active/sedentary periods, total number of steps |

**Table 3.**Results of models with default settings (NR: Nonreadmitted patients; R: Readmitted patients).

Model | MSE | Covariance | Point | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

First 20 Days | All 60 Days | First 20 Days | All 60 Days | ||||||||||

All | NR | R | All | NR | R | All | NR | R | All | NR | R | ||

Actual_prob_without_date | 0.01 | 0.00 | 0.04 | 0.01 | 0.00 | 0.02 | 0.02 | 0.00 | 0.02 | 0.03 | 0.02 | 0.04 | 12.00 |

Actual_prob_with_date | 0.02 | 0.01 | 0.06 | 0.01 | 0.00 | 0.04 | 0.01 | 0.00 | 0.02 | 0.02 | 0.01 | 0.03 | 7.67 |

Predicted_prob_with_date | 0.03 | 0.01 | 0.08 | 0.02 | 0.01 | 0.05 | 0.00 | 0.00 | 0.00 | 0.02 | 0.01 | 0.02 | 3.33 |

Predicted_prob_without_date | 0.04 | 0.02 | 0.10 | 0.05 | 0.04 | 0.08 | 0.00 | 0.00 | 0.01 | 0.01 | 0.01 | 0.02 | 1.00 |

**Table 4.**Results of models with different settings of data processing (NR: Nonreadmitted patients; R: Readmitted patients).

Model | MSE | Covariance | Point | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

First 20 Days | All 60 Days | First 20 Days | All 60 Days | |||||||||||

All | NR | R | All | NR | R | All | NR | R | All | NR | R | |||

Imputation with Previous k Days | 2 | 0.03 | 0.01 | 0.06 | 0.02 | 0.01 | 0.04 | 0.00 | 0.00 | 0.00 | 0.02 | 0.02 | 0.03 | 8.80 |

5 | 0.03 | 0.01 | 0.09 | 0.02 | 0.00 | 0.05 | 0.00 | 0.00 | 0.00 | 0.02 | 0.02 | 0.02 | 7.20 | |

1 | 0.15 | 0.16 | 0.12 | 0.09 | 0.09 | 0.07 | 0.00 | 0.00 | 0.00 | 0.03 | 0.03 | 0.04 | 5.60 | |

3 | 0.09 | 0.08 | 0.09 | 0.07 | 0.07 | 0.07 | 0.00 | 0.00 | 0.00 | 0.02 | 0.02 | 0.03 | 5.60 | |

4 | 0.15 | 0.16 | 0.12 | 0.09 | 0.09 | 0.07 | 0.00 | 0.00 | 0.00 | 0.03 | 0.03 | 0.04 | 5.60 | |

0 | 0.16 | 0.17 | 0.13 | 0.10 | 0.11 | 0.08 | 0.00 | 0.00 | -0.01 | 0.03 | 0.03 | 0.04 | 3.20 | |

Features Filtering | Yes | 0.03 | 0.01 | 0.06 | 0.02 | 0.01 | 0.04 | 0.00 | 0.00 | 0.00 | 0.02 | 0.02 | 0.03 | 11.00 |

No | 0.13 | 0.14 | 0.09 | 0.10 | 0.12 | 0.08 | 0.00 | 0.00 | 0.00 | 0.02 | 0.02 | 0.03 | 1.00 |

**Table 5.**Results of models with different settings of input data sources (Sen: Sensor Features; Dev: Deviation Features; Sym: Symptoms Features; NR: Nonreadmitted patients; R: Readmitted patients).

Model | MSE | Covariance | Point | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

First 20 Days | All 60 Days | First 20 Days | All 60 Days | |||||||||||

All | NR | R | All | NR | R | All | NR | R | All | NR | R | |||

Input Data Sources | All | 0.03 | 0.01 | 0.06 | 0.02 | 0.01 | 0.04 | 0.00 | 0.00 | 0.00 | 0.02 | 0.02 | 0.03 | 10.00 |

Sym + Dev | 0.04 | 0.03 | 0.06 | 0.05 | 0.05 | 0.04 | 0.01 | 0.01 | 0.00 | 0.02 | 0.01 | 0.03 | 6.60 | |

Sen + Dev | 0.03 | 0.02 | 0.07 | 0.03 | 0.02 | 0.07 | 0.00 | 0.00 | 0.00 | 0.02 | 0.02 | 0.02 | 6.60 | |

Sen only | 0.12 | 0.12 | 0.12 | 0.08 | 0.08 | 0.09 | 0.00 | 0.00 | 0.00 | 0.03 | 0.02 | 0.04 | 4.60 | |

Sym only | 0.06 | 0.04 | 0.10 | 0.04 | 0.03 | 0.07 | 0.00 | 0.00 | 0.00 | 0.02 | 0.01 | 0.02 | 4.20 | |

Sen+Sym | 0.06 | 0.02 | 0.15 | 0.03 | 0.01 | 0.09 | 0.00 | 0.00 | 0.00 | 0.01 | 0.01 | 0.02 | 4.00 |

**Table 6.**Results of models with different settings of generating probability (WL: Weighted Linear Function; Exp: Exponential Function; Lin:Linear Function; Log:Logarithmic Function; ini: Initial Probability; NR: Nonreadmitted patients; R: Readmitted patients).

Model | MSE | Covariance | Point | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

First 20 Days | All 60 Days | First 20 Days | All 60 Days | |||||||||||

All | NR | R | All | NR | R | All | NR | R | All | NR | R | |||

Initial Probability | Average | 0.03 | 0.01 | 0.06 | 0.02 | 0.01 | 0.04 | 0.00 | 0.00 | 0.00 | 0.02 | 0.02 | 0.03 | 9.00 |

LACE | 0.03 | 0.01 | 0.08 | 0.02 | 0.00 | 0.05 | 0.00 | 0.00 | 0.00 | 0.02 | 0.02 | 0.03 | 8.50 | |

HOSPITAL | 0.16 | 0.17 | 0.14 | 0.10 | 0.11 | 0.08 | -0.01 | 0.00 | 0.00 | 0.02 | 0.01 | 0.03 | 0.50 | |

Daily Probability | Exp (ini) | 0.12 | 0.11 | 0.12 | 0.06 | 0.05 | 0.09 | 0.01 | 0.00 | 0.01 | 0.04 | 0.03 | 0.06 | 8.14 |

WL(1) | 0.11 | 0.14 | 0.05 | 0.08 | 0.10 | 0.05 | 0.00 | 0.00 | 0.00 | 0.04 | 0.03 | 0.05 | 7.86 | |

WL(ini) | 0.03 | 0.01 | 0.06 | 0.02 | 0.01 | 0.04 | 0.00 | 0.00 | 0.00 | 0.02 | 0.02 | 0.03 | 7.71 | |

Lin(1) | 0.18 | 0.24 | 0.04 | 0.14 | 0.18 | 0.04 | 0.01 | 0.00 | 0.00 | 0.05 | 0.03 | 0.08 | 7.29 | |

Exp(1) | 0.07 | 0.00 | 0.23 | 0.05 | 0.00 | 0.16 | 0.00 | 0.00 | 0.00 | 0.02 | 0.02 | 0.04 | 6.86 | |

Log(ini) | 0.14 | 0.16 | 0.10 | 0.13 | 0.12 | 0.13 | 0.01 | 0.00 | 0.01 | 0.02 | 0.01 | 0.03 | 4.57 | |

Lin(ini) | 0.20 | 0.24 | 0.12 | 0.21 | 0.23 | 0.17 | 0.00 | 0.00 | 0.00 | 0.03 | 0.03 | 0.05 | 3.14 | |

Log(1) | 0.12 | 0.03 | 0.35 | 0.10 | 0.02 | 0.29 | 0.00 | 0.00 | 0.00 | 0.01 | 0.01 | 0.01 | 2.43 |

Model | MSE | Covariance | Point | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

First 20 Days | All 60 Days | First 20 Days | All 60 Days | ||||||||||

All | NR | R | All | NR | R | All | NR | R | All | NR | R | ||

LSTM | 0.12 | 0.11 | 0.12 | 0.06 | 0.05 | 0.09 | 0.01 | 0.00 | 0.01 | 0.04 | 0.03 | 0.06 | 9.33 |

MLR | 0.13 | 0.16 | 0.06 | 0.13 | 0.14 | 0.08 | 0.00 | 0.00 | 0.00 | 0.02 | 0.02 | 0.04 | 5.67 |

RT | 0.16 | 0.19 | 0.10 | 0.15 | 0.16 | 0.12 | 0.00 | 0.00 | 0.00 | 0.03 | 0.02 | 0.04 | 4.67 |

SVR | 0.12 | 0.14 | 0.06 | 0.13 | 0.15 | 0.09 | 0.00 | 0.00 | 0.00 | 0.02 | 0.02 | 0.03 | 4.33 |

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**MDPI and ACS Style**

Qian, C.; Leelaprachakul, P.; Landers, M.; Low, C.; Dey, A.K.; Doryab, A. Prediction of Hospital Readmission from Longitudinal Mobile Data Streams. *Sensors* **2021**, *21*, 7510.
https://doi.org/10.3390/s21227510

**AMA Style**

Qian C, Leelaprachakul P, Landers M, Low C, Dey AK, Doryab A. Prediction of Hospital Readmission from Longitudinal Mobile Data Streams. *Sensors*. 2021; 21(22):7510.
https://doi.org/10.3390/s21227510

**Chicago/Turabian Style**

Qian, Chen, Patraporn Leelaprachakul, Matthew Landers, Carissa Low, Anind K. Dey, and Afsaneh Doryab. 2021. "Prediction of Hospital Readmission from Longitudinal Mobile Data Streams" *Sensors* 21, no. 22: 7510.
https://doi.org/10.3390/s21227510