SNFsim: A Discrete Event Simulator for Decision Support in Skilled Nursing Facilities
- Department of Computer Science, Canada
- PointClickCare, Canada
- Department of Epidemiology and Biostatistics, Canada
Figures
Skilled nursing intake flow and staffing process.
The red circled numbers denote the temporal ordering of the referral process, starting at the hospital and ending with a patient accepting an offer from a nursing facility. The green circled numbers denote the temporal ordering of a scheduling coordinator making staffing decisions. It is important to note that the intake flow and staffing process occur at different times.
Code snippet demonstrating an example setup for training an RL agentusing SNFsim.
Simplified SNFsim simulation step.
We assume preset configuration values. Algorithm 1 presents an equivalent but more granular presentation of a simulation step.
Patient information typically available to the SNF at the point of referral.
Bivariate relationships between a subset of columns in the generated dataset versus the original dataset.
(a) Age distribution by gender. (b) LoS distribution by age group.
SNF intake flow and joint staffing decision process.
The red circled numbers denote the temporal ordering of a referral, beginning at the hospital and concluding with a patient accepting an offer from a nursing facility. This is abstracted, and is assumed rather than implemented within SNFsim. The blue circled numbers denote the temporal ordering of a referral within SNFsim, beginning with an empirically sampled referral and concluding with the SNF accepting the referral. The green circled numbers represent the temporal ordering of a simplified staffing decision process within SNFsim, beginning with assessment of the care needs of current inpatients and concluding with increasing, decreasing, or not altering current staffing hours.
Random Forest model performance for patient rehospitalization prediction.
ROC curve (AUC = 0.921) shows excellent discrimination between rehospitalized and non-rehospitalized patients. Precision-Recall curve (average precision = 0.592) demonstrates strong performance relative to baseline prevalence of 7.4%. The model substantially outperforms logistic regression (AUC = 0.867) using the same feature set.
Performance comparison of five rollouts between P1 and P2 in the snf_v0 environment.
Performance comparison of five rollouts between P1 and P2 in the snf_v0 environment.
PPO agent training performance under varied weight configurations across 200,000 timesteps.
Objective weights follow the order [reimbursement, nursing costs, rehospitalization, occupancy]. (a) Balanced approach with uniform weights [1.0, 1.0, 1.0, 1.0]. (b) Care optimization with weights [0.4, 0.4, 1.6, 1.6], emphasizing rehospitalization minimization and occupancy management while de-emphasizing financial metrics. (c) Financial optimization with weights [1.6, 1.6, 0.4, 0.4], prioritizing reimbursement maximization and nursing cost minimization over patient care and facility occupancy. The theoretical summed reward range is [-4, 4].
PDPM HIPPS code classification build sample.
Example of the ICD-10-CM hierarchy for a specific cholera diagnosis.
This hierarchy tree demonstrates that a cholera diagnosis falls under chapter 1 (certain infectious and parasitic diseases), section A00- A09 (intestinal infectious diseases), category A00 (cholera), and could ultimately be one of codes A00.0, A00.1, or A00.9 (biovar cholerae, biovar eltor, or unspecified). Beginning from the top layer and descending, there is an increase in group specificity.
Flow of environment for the snf_v0 Gymnasium environment.
Tables
Marginal similarity between original and synthetic data including the metrics mean diff (percentage difference in means), KDE Sim (kernel density overlap), TV dist (total variation distance), JS sim (Jensen-Shannon similarity), and cov (category coverage).
| Variable | Mean Diff. | KDE Sim. | TV Dist. | JS Sim. | Cov. |
|---|---|---|---|---|---|
| Continuous: | |||||
| Age | 0.02% | 88.1% | |||
| Length of Stay | 13.8% | 92.4% | |||
| Categorical: | |||||
| ICD-10-CM | 0.194 | 79.1% | 78.7% | ||
| Insurance Type | 0.150 | 83.6% | 100% | ||
| PDPM Code | 0.138 | 83.4% | 98.2% | ||
| Gender | 0.080 | 87.2% | 100% | ||
Multivariate Logistic Regression Results
| Model A | Model B | Model C | Model D | |||||
|---|---|---|---|---|---|---|---|---|
| Feature | Coef. | P | Coef. | P | Coef. | P | Coef. | P |
| LoS | -3.173 | *** | -3.180 | *** | -3.193 | *** | ||
| meanHours | -0.216 | *** | -0.215 | *** | ||||
| reimbursement | +0.188 | *** | -0.344 | * | -0.329 | * | ||
| age | -0.028 | -0.005 | -0.005 | |||||
| NPG | -0.230 | *** | -0.274 | *** | -0.293 | *** | ||
| SLP | +0.077 | +0.100 | +0.083 | |||||
| PT_OT | +0.033 | +0.035 | ||||||
| NTA | _0.448 | ** | _0.428 | ** | ||||
| days_since_start | +0.052 | |||||||
| gender | +0.017 | |||||||
| Additional categorical features in Model D (not included): | ||||||||
| ICD-10-CM Chapter (***), facility, insurance type | ||||||||
| Number of features | 2 | 3 | 8 | 13 | ||||
| AUC-ROC | 0.550 | 0.867 | 0.873 | 0.867 | ||||
| Max VIF | 14.7 | 2.1 | 33.3 | 36.6 | ||||
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Model D contains full feature set used in Random Forest (RF AUC=0.921 vs. Logistic Regression AUC=0.867). ***p < 0.001, **p < 0.01, *p < 0.05. N=7,948; 588 (7.4%) readmissions.
Required SNF Configuration Parameters
| Parameter | Description | Default Value |
|---|---|---|
| total_beds | Number of beds in the facility | 100 |
| occupancy_bounds | Target min/max occupancy range | 75%/90% |
| nursing_hours_target | Target min/max nursing hours per patient | 2.5/3.5 |
| full_time_cna | Total available full-time nursing assistants | 20 |
| prn_cna | Total available pro re nata (as-needed) staff | 10 |
| agency_cna | Total available agency-contracted staff | 15 |
| referral_rate | Mean number of daily referrals | 5 |
| min_cna_hours | Mandated nursing hours per patient day | 2.8 |
| fac_state | State where the SNF is located | New York |
| readmission_threshold | Threshold for readmission prediction | 0.7 |
Summary of training performance across different PPO weight configurations.
| Metric | Balanced | Financial Focus | Care Focus |
|---|---|---|---|
| Weights | [1.0, 1.0, 1.0, 1.0] | [1.6, 1.6, 0.4, 0.4] | [0.4, 0.4, 1.6, 1.6] |
| Average Reward | 1.41 | 0.40 | 2.54 |
| First Quarter Avg | 1.07 | 0.13 | 1.88 |
| Last Quarter Avg | 1.53 | 0.53 | 2.94 |
| Improvement (%) | 42.74% | 312.67% | 56.00% |
| Trend Slope | 0.5982 | 0.5307 | 1.3929 |
Outcomes by policy configuration over 10 different 365-day episodes. Weight vectors indicate a priori selection of importance for [reimbursement, nursing cost, rehospitalization, occupancy] objectives.
| Metric | Balanced | Financial Focus | Care Focus |
|---|---|---|---|
| Weights | [1.0, 1.0, 1.0, 1.0] | [1.6, 1.6, 0.4, 0.4] | [0.4, 0.4, 1.6, 1.6] |
| Occupancy Rate | 55.62% ± 0.24% | 53.89% ± 0.20% | 72.97% ± 0.39% |
| Rehospitalization Rate | 37.3% ± 4.1% | 42.8% ± 3.6% | 13.6% ± 3.4% |
| Referral Acceptance Rate | 80.0% | 100.0% | 60.1% |
| Daily Revenue | $31, 618 ± $131 | $32, 199 ± $136 | 38, 467 ± $141 |
| Daily Cost | $6, 938 ± $1.81 | $6, 922 ± $1.75 | $9, 933 ± $1.44 |
| Daily Profit | $24, 680 | $25,277 | $28,534 |
PDPM payment groups to code value.
| PT/OT | SLP | NURS | NPG | Code Value |
|---|---|---|---|---|
| TA | SA | ES3 | NA | A |
| TB | SB | ES2 | NB | B |
| TC | SC | ES1 | NC | C |
| TD | SD | HDE2 | ND | D |
| TE | SE | HDE1 | NE | E |
| TF | SF | HBC2 | NF | F |
| TG | SG | CBC2 | G | |
| TH | SH | CA2 | H | |
| TI | SI | CBC1 | I | |
| TJ | SJ | CA1 | J | |
| TK | SK | BAB2 | K | |
| TL | SL | BAB1 | L | |
| TM | HBC1 | M | ||
| TN | LDE2 | N | ||
| TO | LDE1 | O | ||
| TP | LBC2 | P | ||
| LBC1 | Q | |||
| CDE2 | R | |||
| CDE1 | S | |||
| PDE2 | T | |||
| PDE1 | U | |||
| PBC2 | V | |||
| PA2 | W | |||
| PBC1 | X | |||
| PA1 | Y |
PT and OT case mix groups and PT and OT CMIs based on clinical category and PT and OT function score.
| Clinical Category | PT & OT Function Score | PT & OT Case Mix Group | PT CMI | OT CMI |
|---|---|---|---|---|
| Major Joint Replacement or Spinal Surgery | 0-5 | TA | 1.53 | 1.49 |
| Major Joint Replacement or Spinal Surgery | 6-9 | TB | 1.69 | 1.63 |
| Major Joint Replacement or Spinal Surgery | 10-23 | TC | 1.88 | 1.68 |
| Major Joint Replacement or Spinal Surgery | 24 | TD | 1.92 | 1.53 |
| Other Orthopedic | 0-5 | TE | 1.42 | 1.41 |
| Other Orthopedic | 6-9 | TF | 1.61 | 1.59 |
| Other Orthopedic | 10-23 | TG | 1.67 | 1.64 |
| Other Orthopedic | 24 | TH | 1.16 | 1.15 |
| Medical Management | 0-5 | TI | 1.13 | 1.17 |
| Medical Management | 6-9 | TJ | 1.42 | 1.44 |
| Medical Management | 10-23 | TK | 1.52 | 1.54 |
| Medical Management | 24 | TL | 1.09 | 1.11 |
| Non-Orthopedic Surgery and Acute Neurologic | 0-5 | TM | 1.27 | 1.30 |
| Non-Orthopedic Surgery and Acute Neurologic | 6-9 | TN | 1.48 | 1.49 |
| Non-Orthopedic Surgery and Acute Neurologic | 10-23 | TO | 1.55 | 1.55 |
| Non-Orthopedic Surgery and Acute Neurologic | 24 | TP | 1.08 | 1.09 |
PDPM assessment type to code value.
| Assessment Type | Code Value |
|---|---|
| Initial Patient Assessment | 0 |
| PPS 5-Day Assessment | 1 |
PT and OT case mix groups and PT and OT CMIs based on clinical category and PT and OT function score.
| Clinical Category | PT & OT Function Score | PT & OT Case Mix Group | PT CMI | OT CMI |
|---|---|---|---|---|
| Major Joint Replacement or Spinal Surgery | 0-5 | TA | 1.53 | 1.49 |
| Major Joint Replacement or Spinal Surgery | 6-9 | TB | 1.69 | 1.63 |
| Major Joint Replacement or Spinal Surgery | 10-23 | TC | 1.88 | 1.68 |
| Major Joint Replacement or Spinal Surgery | 24 | TD | 1.92 | 1.53 |
| Other Orthopedic | 0-5 | TE | 1.42 | 1.41 |
| Other Orthopedic | 6-9 | TF | 1.61 | 1.59 |
| Other Orthopedic | 10-23 | TG | 1.67 | 1.64 |
| Other Orthopedic | 24 | TH | 1.16 | 1.15 |
| Medical Management | 0-5 | TI | 1.13 | 1.17 |
| Medical Management | 6-9 | TJ | 1.42 | 1.44 |
| Medical Management | 10-23 | TK | 1.52 | 1.54 |
| Medical Management | 24 | TL | 1.09 | 1.11 |
| Non-Orthopedic Surgery and Acute Neurologic | 0-5 | TM | 1.27 | 1.30 |
| Non-Orthopedic Surgery and Acute Neurologic | 6-9 | TN | 1.48 | 1.49 |
| Non-Orthopedic Surgery and Acute Neurologic | 10-23 | TO | 1.55 | 1.55 |
| Non-Orthopedic Surgery and Acute Neurologic | 24 | TP | 1.08 | 1.09 |
SLP case mix groups and SLP CMIs based on whether patient has a mechanically altered diet or swallowing disorder and the presence of acute neurological conditions, SLP-related comorbidity, or cognitive impairment.
| Condition* | Mechanically Altered Dietor Swallowing Disorder | SLP Case Mix Group | SLP CMI |
|---|---|---|---|
| None | Neither | SA | 0.68 |
| None | Either | SB | 1.82 |
| None | Both | SC | 2.66 |
| Any One | Neither | SD | 1.46 |
| Any One | Either | SE | 2.33 |
| Any One | Both | SF | 2.97 |
| Any Two | Neither | SG | 2.04 |
| Any Two | Either | SH | 2.85 |
| Any Two | Both | SI | 3.51 |
| All Three | Neither | SJ | 2.98 |
| All Three | Either | SK | 3.69 |
| All Three | Both | SL | 4.19 |
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*
Presence of Acute Neurological Condition, SLP-Related Comorbidity, or Cognitive Impairment.
Nursing payment group (CMG) and corresponding CMIs based on RUG-IV Nursing RUG, extensive services status, clinical conditions, depression status, and restorative nursing services.
| RUG-IV Nursing RUG | Extensive Services | Clinical Conditions | Depression | RNS | Function Score | CMG | CMI |
|---|---|---|---|---|---|---|---|
| ES3 | Trach & Ventilator | 0-14 | ES3 | 4.04 | |||
| ES2 | Trach or Ventilator | 0-14 | ES2 | 3.06 | |||
| ES1 | Infection Isolation | 0-14 | ES1 | 2.91 | |||
| HE2/HD2 | SMC | Yes | 0-5 | HDE2 | 2.39 | ||
| HE1/HD1 | SMC | No | 0-5 | HDE1 | 1.99 | ||
| HC2/HB2 | SMC | Yes | 6-14 | HBC2 | 2.23 | ||
| HC1/HB1 | SMC | No | 6-14 | HBC1 | 1.85 | ||
| LE2/LD2 | RMC | Yes | 0-5 | LDE2 | 2.07 | ||
| LE1/LD1 | RMC | No | 0-5 | LDE1 | 1.72 | ||
| LC2/LB2 | RMC | Yes | 6-14 | LBC2 | 1.71 | ||
| LC1/LB1 | RMC | No | 6-14 | LBC1 | 1.43 | ||
| CE2/CD2 | CRC | Yes | 0-5 | CDE2 | 1.86 | ||
| CE1/CD1 | CRC | No | 905 | CDE1 | 1.62 | ||
| CC2/CB2 | CRC | Yes | 6-14 | CBC2 | 1.54 | ||
| CA2 | CRC | Yes | 15-16 | CA2 | 1.08 | ||
| CC1/CB1 | CRC | No | 6-14 | CBC1 | 1.34 | ||
| CA1 | CRC | No | 15-16 | CA1 | 0.94 | ||
| BB2/BA2 | BCS | 2+ | 11-16 | BAB2 | 1.04 | ||
| BB1/BA1 | BCS | 0-1 | 11-16 | BAB1 | 0.99 | ||
| PE2/PD2 | ADL | 2+ | 0-5 | PDE2 | 1.57 | ||
| PE1/PD1 | ADL | 0-1 | 0-5 | PDE1 | 1.47 | ||
| PC2/PB2 | ADL | 2+ | 6-14 | PBC2 | 1.21 | ||
| PA2 | ADL | 2+ | 15-16 | PA2 | 0.7 | ||
| PC1/PB1 | ADL | 0-1 | 6-14 | PBC1 | 1.13 | ||
| PA1 | ADL | 0-1 | 15-16 | PA1 | 0.66 |
Non-Therapy Ancillaries (NTA) CMIs based on NTA case mix groups and NTA score ranges.
| NTA Score Range | NTA Case Mix Group | CMI |
|---|---|---|
| 12+ | NA | 3.25 |
| 9-11 | NB | 2.53 |
| 6-8 | NC | 1.85 |
| 3-5 | ND | 1.34 |
| 1-2 | NE | 0.96 |
| 0 | NF | 0.72 |
Urban rate components.
| Rate Component | PT | OT | SLP | Nursing | NTA | Non-Case-Mix (NCM) |
|---|---|---|---|---|---|---|
| Per Diem Amount | $62.84 | $58.49 | $23.46 | $109.55 | $82.64 | $98.10 |
Rural rate components.
| Rate Component | PT | OT | SLP | Nursing | NTA | Non-Case-Mix (NCM) |
|---|---|---|---|---|---|---|
| Per Diem Amount | $71.63 | $65.79 | $29.56 | $104.66 | $78.96 | $99.91 |
Day in stay adjustment factor.
| Day in Stay | Adjustment Factor |
|---|---|
| 1-20 | 1.00 |
| 21-27 | 0.98 |
| 28-34 | 0.96 |
| 35-41 | 0.94 |
| 42-48 | 0.92 |
| 49-55 | 0.90 |
| 56-62 | 0.88 |
| 63-69 | 0.86 |
| 70-76 | 0.84 |
| 77-83 | 0.82 |
| 84-90 | 0.80 |
| 91-97 | 0.78 |
| 98-150 | 0.76 |
NTA component adjustment factor.
| Day in Stay | Adjustment Factor |
|---|---|
| 1-3 | 3.00 |
| 4-150 | 1.00 |
Estimated Hourly Wages for Full-time, PRN, and Agency CNAs by State based on (Nursa, 2024).
| State | Full-time CNA ($/hr) | PRN CNA ($/hr) | Agency CNA ($/hr) |
|---|---|---|---|
| Alabama | 15.04 | 18.05 | 20.30 |
| Alaska | 22.63 | 27.16 | 30.55 |
| Arizona | 19.69 | 23.63 | 26.58 |
| Arkansas | 15.41 | 18.49 | 20.80 |
| California | 22.63 | 27.16 | 30.55 |
| Colorado | 20.95 | 25.14 | 28.28 |
| Connecticut | 20.70 | 24.84 | 27.95 |
| Delaware | 18.57 | 22.28 | 25.07 |
| Florida | 17.67 | 21.20 | 23.85 |
| Georgia | 16.77 | 20.12 | 22.64 |
| Hawaii | 21.63 | 25.96 | 29.20 |
| Idaho | 17.92 | 21.50 | 24.19 |
| Illinois | 19.87 | 23.84 | 26.82 |
| Indiana | 18.10 | 21.72 | 24.44 |
| Iowa | 18.45 | 22.14 | 24.91 |
| Kansas | 17.32 | 20.78 | 23.38 |
| Kentucky | 17.30 | 20.76 | 23.36 |
| Louisiana | 14.63 | 17.56 | 19.75 |
| Maine | 20.65 | 24.78 | 27.88 |
| Maryland | 19.60 | 23.52 | 26.46 |
| Massachusetts | 21.22 | 25.46 | 28.65 |
| Michigan | 18.71 | 22.45 | 25.26 |
| Minnesota | 19.40 | 23.28 | 26.19 |
| Mississippi | 12.35 | 14.82 | 16.67 |
| Missouri | 15.07 | 18.08 | 20.34 |
| Montana | 16.83 | 20.20 | 22.72 |
| Nebraska | 17.00 | 20.40 | 22.95 |
| Nevada | 19.89 | 23.87 | 26.85 |
| New Hampshire | 20.36 | 24.43 | 27.49 |
| New Jersey | 19.02 | 22.82 | 25.68 |
| New Mexico | 16.20 | 19.44 | 21.87 |
| New York | 19.56 | 23.47 | 26.41 |
| North Carolina | 16.24 | 19.49 | 21.92 |
| North Dakota | 18.33 | 22.00 | 24.75 |
| Ohio | 16.05 | 19.26 | 21.67 |
| Oklahoma | 13.39 | 16.07 | 18.08 |
| Oregon | 18.67 | 22.40 | 25.20 |
| Pennsylvania | 17.23 | 20.68 | 23.26 |
| Rhode Island | 19.39 | 23.27 | 26.18 |
| South Carolina | 15.47 | 18.56 | 20.88 |
| South Dakota | 14.90 | 17.88 | 20.12 |
| Tennessee | 15.56 | 18.67 | 21.01 |
| Texas | 16.94 | 20.33 | 22.87 |
| Utah | 16.12 | 19.34 | 21.76 |
| Vermont | 18.60 | 22.32 | 25.11 |
| Virginia | 17.10 | 20.52 | 23.09 |
| Washington | 20.80 | 24.96 | 28.08 |
| West Virginia | 14.22 | 17.06 | 19.20 |
| Wisconsin | 17.58 | 21.10 | 23.73 |
| Wyoming | 17.38 | 20.86 | 23.46 |
ICD-10-CM Chapters and corresponding categories.
| Chapter | Title | Categories |
|---|---|---|
| 1 | Certain Infectious and Parasitic Diseases | A00-B99 |
| 2 | Neoplasms | C00-D49 |
| 3 | Diseases of the Blood and Blood-Forming Organs | D50-D89 |
| 4 | Endocrine, Nutritional, and Metabolic Diseases | E00-E89 |
| 5 | Mental, Behavioral, and Neurodevelopmental Disorders | F01-F99 |
| 6 | Diseases of the Nervous System | G00-G99 |
| 7 | Diseases of the Eye and Adnexa | H00-H59 |
| 8 | Diseases of the Ear and Mastoid Process | H60-H95 |
| 9 | Diseases of the Circulatory System | I00-I99 |
| 10 | Diseases of the Respiratory System | J00-J99 |
| 11 | Diseases of the Digestive System | K00-K95 |
| 12 | Diseases of the Skin and Subcutaneous Tissue | L00-L99 |
| 13 | Diseases of the Musculoskeletal System and Connective Tissue | M00-M99 |
| 14 | Diseases of the Genitourinary System | N00-N99 |
| 15 | Pregnancy, Childbirth, and the Puerperium | O00-O9A |
| 16 | Certain Conditions Originating in the Perinatal Period | P00-P96 |
| 17 | Congenital Malformations, Deformations, and Chromosomal Abnormalities | Q00-Q99 |
| 18 | Symptoms, Signs, and Abnormal Clinical and Laboratory Findings | R00-R99 |
| 19 | Injury, Poisoning, and Certain Other Consequences of External Causes | S00-T88 |
| 20 | External Causes of Morbidity | V00-Y99 |
| 21 | Factors Influencing Health Status and Contact with Health Services | Z00-Z99 |
| 22 | Codes for Special Purposes | U00-U85, U89 |
PPO Hyperparameters
| Hyperparameter | Value |
|---|---|
| Learning rate (α) | 3 × 10-4 |
| Batch size | 64 |
| Steps per update | 2048 |
| Epochs per batch | 10 |
| Clipping parameter (ε) | 0.2 |
| Max gradient norm | 0.5 |
| Discount factor (γ) | 0.99 |
| GAE λ | 0.95 |
| Entropy coefficient | 0.01 |
| Total timesteps | 200,000 |
| Policy architecture | MultiInputPolicy |
Data and code availability
The raw data sets analyzed during this study are not publicly available as they are proprietary. However, synthetic data generated in this paper is included in the base repository. The base SNFsim code is available at https://github.com/Scorks/SNFsim.