The TEND (Tomorrow’s Expected Number of Discharges) Model Accurately Predicted the Number of Patients Who Were Discharged from the Hospital the Next Day
BACKGROUND: Knowing the number of discharges that will occur is important for administrators when hospital occupancy is close to or exceeds 100%. This information will facilitate decision making such as whether to bring in extra staff, cancel planned surgery, or implement measures to increase the number of discharges. We derived and internally validated the TEND (Tomorrow’s Expected Number of Discharges) model to predict the number of discharges from hospital in the next day.
METHODS: We identified all patients greater than 1 year of age admitted to a multisite academic hospital between 2013 and 2015. In derivation patients we applied survival-tree methods to patient-day covariates (patient age, sex, comorbidities, location, admission urgency, service, campus, and weekday) and identified risk strata having unique discharge patterns. Discharge probability in each risk strata for the previous 6 months was summed to calculate each day’s expected number of discharges.
RESULTS: Our study included 192,859 admissions. The daily number of discharges varied extensively (median 139; interquartile range [IQR] 95-160; range 39-214). We identified 142 discharge risk strata. In the validation patients, the expected number of daily discharges strongly predicted the observed number of discharges (adjusted R2 = 89.2%; P < 0.0001). The relative difference between observed and expected number of discharges was small (median 1.4%; IQR −5.5% to 7.1%).
CONCLUSION: The TEND model accurately predicted the daily number of discharges using information typically available within hospital data warehouses. Further study is necessary to determine if this information improves hospital bed management.
© 2018 Society of Hospital Medicine
METHODS
Study Setting and Databases Used for Analysis
The study took place at The Ottawa Hospital, a 1000-bed teaching hospital with 3 campuses that is the primary referral center in our region. The study was approved by our local research ethics board.
The Patient Registry Database records the date and time of admission for each patient (defined as the moment that a patient’s admission request is registered in the patient registration) and discharge (defined as the time when the patient’s discharge from hospital was entered into the patient registration) for hospital encounters. Emergency department encounters were also identified in the Patient Registry Database along with admission service, patient age and sex, and patient location throughout the admission. The Laboratory Database records all laboratory studies and results on all patients at the hospital.
Study Cohort
We used the Patient Registry Database to identify all people aged 1 year or more who were admitted to the hospital between January 1, 2013, and December 31, 2015. This time frame was selected to (i) ensure that data were complete; and (ii) complete calendar years of data were available for both derivation (patient-days in 2013-2014) and validation (2015) cohorts. Patients who were observed in the emergency room without admission to hospital were not included.
Study Outcome
The study outcome was the number of patients discharged from the hospital each day. For the analysis, the reference point for each day was 1 second past midnight; therefore, values for time-dependent covariates up to and including midnight were used to predict the number of discharges in the next 24 hours.
Study Covariates
Baseline (ie, time-independent) covariates included patient age and sex, admission service, hospital campus, whether or not the patient was admitted from the emergency department (all determined from the Patient Registry Database), and the Laboratory-based Acute Physiological Score (LAPS). The latter, which was calculated with the Laboratory Database using results for 14 tests (arterial pH, PaCO2, PaO2, anion gap, hematocrit, total white blood cell count, serum albumin, total bilirubin, creatinine, urea nitrogen, glucose, sodium, bicarbonate, and troponin I) measured in the 24-hour time frame preceding hospitalization, was derived by Escobar and colleagues7 to measure severity of illness and was subsequently validated in our hospital.8 The independent association of each laboratory perturbation with risk of death in hospital is reflected by the number of points assigned to each lab value with the total LAPS being the sum of these values. Time-dependent covariates included weekday in hospital and whether or not patients were in the intensive care unit.
Analysis
We used 3 stages to create a model to predict the daily expected number of discharges: we identified discharge risk strata containing patients having similar discharge patterns using data from patients in the derivation cohort (first stage); then, we generated the preliminary probability of discharge by determining the daily discharge probability in each discharge risk strata (second stage); finally, we modified the probability from the second stage based on the weekday and admission service and summed these probabilities to create the expected number of discharges on a particular date (third stage).
The first stage identified discharge risk strata based on the covariates listed above. This was determined by using a survival tree approach9 with proportional hazard regression models to generate the “splits.” These models were offered all covariates listed in the Study Covariates section. Admission service was clustered within 4 departments (obstetrics/gynecology, psychiatry, surgery, and medicine) and day of week was “binarized” into weekday/weekend-holiday (because the use of categorical variables with large numbers of groups can “stunt” regression trees due to small numbers of patients—and, therefore, statistical power—in each subgroup). The proportional hazards model identified the covariate having the strongest association with time to discharge (based on the Wald X2 value divided by the degrees of freedom). This variable was then used to split the cohort into subgroups (with continuous covariates being categorized into quartiles). The proportional hazards model was then repeated in each subgroup (with the previous splitting variable[s] excluded from the model). This process continued until no variable was associated with time to discharge with a P value less than .0001. This survival-tree was then used to cluster all patients into distinct discharge risk strata.
In the second stage, we generated the preliminary probability of discharge for a specific date. This was calculated by assigning all patients in hospital to their discharge risk strata (Appendix). We then measured the probability of discharge on each hospitalization day in all discharge risk strata using data from the previous 180 days (we only used the prior 180 days of data to account for temporal changes in hospital discharge patterns). For example, consider a 75-year-old patient on her third hospital day under obstetrics/gynecology on December 19, 2015 (a Saturday). This patient would be assigned to risk stratum #133 (Appendix A). We then measured the probability of discharge of all patients in this discharge risk stratum hospitalized in the previous 6 months (ie, between June 22, 2015, and December 18, 2015) on each hospital day. For risk stratum #133, the probability of discharge on hospital day 3 was 0.1111; therefore, our sample patient’s preliminary expected discharge probability was 0.1111.
To attain stable daily discharge probability estimates, a minimum of 50 patients per discharge risk stratum-hospitalization day combination was required. If there were less than 50 patients for a particular hospitalization day in a particular discharge risk stratum, we grouped hospitalization days in that risk stratum together until the minimum of 50 patients was collected.
The third (and final) stage accounted for the lack of granularity when we created the discharge risk strata in the first stage. As we mentioned above, admission service was clustered into 4 departments and the day of week was clustered into weekend/weekday. However, important variations in discharge probabilities could still exist within departments and between particular days of the week.10 Therefore, we created a correction factor to adjust the preliminary expected number of discharges based on the admission division and day of week. This correction factor used data from the 180 days prior to the analysis date within which the expected daily number of discharges was calculated (using the methods above). The correction factor was the relative difference between the observed and expected number of discharges within each division-day of week grouping.
For example, to calculate the correction factor for our sample patient presented above (75-year-old patient on hospital day 3 under gynecology on Saturday, December 19, 2015), we measured the observed number of discharges from gynecology on Saturdays between June 22, 2015, and December 18, 2015, (n = 206) and the expected number of discharges (n = 195.255) resulting in a correction factor of (observed-expected)/expected = (195.255-206)/195.206 = 0.05503. Therefore, the final expected discharge probability for our sample patient was 0.1111+0.1111*0.05503=0.1172. The expected number of discharges on a particular date was the preliminary expected number of discharges on that date (generated in the second stage) multiplied by the correction factor for the corresponding division-day or week group.
