A long short-term memory model for forecasting the surgical case volumes at a hospital

Figures & data

Figure 1. Modeling framework.

Figure 2. Data associated with the primary providers and services provided. Distribution of the (i) primary providers based on years of service; (ii) unique services per provider; (iii) number of surgical procedures by service during May 2014 to September 2021 (data of 2020 is excluded).

Figure 3. Heat map of ten procedures that were not scheduled after December 2018.

Figure 4. Distribution of the volume of surgical cases based on (i) day of the week, (ii) week of year, (iii) month of the year, and (iv) total number per year.

Figure 5. (i) Distribution of the volume of surgical cases during a regular day, Federal holidays, and weekend. (ii - iv) The volume of surgical cases several business days prior and proceeding three major holidays.

Figure 6. (i) Snapshot and (ii) timeline show the relationship between the number of primary providers and the number of times procedure XJS was scheduled per week.

Figure 7. (i) Anomaly scores per observation of procedure XJS. (ii) Distribution of the anomaly score. (iii) A time series of the procedure with the corresponding anomalies.

Figure 8. Distribution of surgical procedures based on the total number of observations during the period of study. (i) Procedures with more than 800 observations; and (ii) Procedures with less than 800 observations.

Table 1. Performance evaluation.

	LSTM	Facebook Prophet	GBM
R^2	0.875	0.547	0.635
RMSE	1.526	3.548	2.432
MAE	0.882	1.657	1.231

Figure 9. Predictions for procedure XJS.

Figure 10. Distribution of the residuals for procedure XJS.

Table 2. Summary of model performance.

	Procedure XJS		Largest cluster: C1
Testing length	6 wk	15 wk	6 wk	15 wk
R^2	0.858	0.341	0.630	0.314
RMSE	1.526	3.091	0.622	0.816
MAE	0.882	1.846	0.429	0.575

Figure 11. Predictions of the largest cluster of procedures, C1.

Figure 12. Results of model deployment and monitoring for procedure XJS.

Table A1. Description of columns in the dataset.

Column Name	Description
date	date of the surgery
proc_id	procedure identification number (i.e., 4 digit numbers)
SID	synthetic procedure identification number (i.e., 3 randomly assigned characters)
proc_descr	procedure description
prov_name	name of the primary healthcare provider

Table A2. Description of features used in the forecasting model.

Feature Name	Type	Description
count^(a)	integer	the number of times a procedure is performed according to the aggregation level (i.e., daily or weekly)
day_of_year, week_of_year	integer	Day of the year and week of the year, respectively
year_XX	binary	Repeated for each year XX. 1 if the date belongs to year XX and 0 when not
sin_YY, cos_YY^(b)	float	Repeated for each YY, where YY comprises of day of the week, month, and quarter. Sine and cosine transformation of feature YY
is_holiday	binary	1 if the date is a Federal holiday and 0 otherwise
is_weekend	binary	1 if the date is either Saturday or Sunday and 0 otherwise
is_anomaly	binary	1 if the date is identified as abnormal and 0 otherwise
num_prov	integer	number of primary providers observed for each month
temp_max, temp_min, prcp, snow_depth	float	Maximum and minimum temperatures, precipitation, snow depth during the entire day, respectively

(a) indicates the target variable.

(b) indicates the encoded cyclical features.