Using Lagged Outpatient Visits to Improve Forecasts of Patient Arrivals at an Inpatient Hospital Open Access

Vece, Gabriel R. (2017)

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Using Lagged Outpatient Visits to Improve Forecasts of

Patient Arrivals at an Inpatient Hospital By: Gabriel R. Vece

Introduction: Recent increases in healthcare expenditures have incentivized hospitals to reduce labor costs without adversely affecting patient outcomes, requiring administrators to forecast when and where patients will arrive for care. Many forecasting approaches involve subjective judgement and, among those that employ statistical methods, finding sources of data that can help predict trends in arrivals presents a significant difficulty. Meanwhile, the "gatekeeper" structure of many large healthcare systems is such that patients are incentivized to visit outpatient clinics, specialists, or primary care providers before coming to hospital, which may imply that surges in hospital visits could be preceded by similar surges in outpatient visits. The goal of this paper will be to investigate the improvement, if any, gained by the inclusion of lagged outpatient visits in a model for forecasting daily inpatient arrivals, modeling the outpatient visits as distributed-lag predictors in a Poisson regression model.

Methods: Several canonical time-series models were fit to the data to establish the performance some common forecasting models. Afterwards, series of outpatient visits to neurologists and to neurosurgeons were modelled as distributed-polynomials using the Aikake Information Criteria (AIC) to select the optimal values of several key parameters, such as lag length and polynomial degree. The polynomials were included in a Poisson regression for forecasting inpatient arrivals, with the model performance assessed by its root mean square error (RMSE) and mean absolute error (MAE) compared to the canonical time series model and a Poisson model excluding the distributed-lag terms.

Results: Although the Poisson model including the distributed-lag terms failed to outperform the naïve or univariate time-series models at making short-term (7-day) forecasts, it achieved better performance with a longer forecast window (30 days). However, this improvement was also seen in the Poisson model excluding the lagged covariates, suggesting that the outpatient series contributed little, if any, added predictive power. Furthermore, a sensitivity analysis showed that the improvements did not hold when the models were fitted at various seasonal subsets of the dataset.

Conclusion: Although the data used in this study constitute only the patterns observed at a particular hospital system at a particular point in time, the results suggest that the outpatient series were unable to significantly improve the model's forecasts. In practice, forecasters may benefit from the use of other multivariate modeling approaches or from more thorough searches for useful predictors.

Table of Contents

Table of Contents

1. Introduction 1

1.1 Problem Statement 2

1.2. Purpose Statement 3

1.2. Purpose Statement 3

2. Background/Literature Review 4

2.1. Staffing Models 4

2.2. Distributed Lag Models 8

3. Methodology 10

3.1. Dataset 10

3.2. Statistical Approach 12

4. Results 15

4.1. Exploratory Data Analysis 15

4.2. Univariate Models 17

4.3. Multivariate Model 19

5. Discussion 24

5.1. Implications 24

5.2. Recommendations 28

References 30

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