Longitudinal Inpatient Simulation

• Longitudinal inpatient simulation is a modeling approach that represents inpatient care as an evolving process with explicit time dynamics and patient state transitions.
• It encompasses diverse paradigms such as discrete-event simulation, semi-Markov trajectory analysis, and continuous-time multi-state models to reflect real-world patient flow and resource allocation.
• Integrating predictive models with simulation frameworks allows accurate forecasting of key metrics like length of stay, occupancy, and transfer delays in healthcare systems.

Searching arXiv for recent and relevant papers on longitudinal inpatient simulation and closely related patient-flow simulation. Longitudinal inpatient simulation denotes a family of models that represent inpatient care as an evolving trajectory rather than a static episode. Across the literature, it encompasses continuous-time patient flow through emergency departments and inpatient units, ward-level census processes over multi-day stays, patient-level life-course simulations driven by competing hazards, path-dependent microsimulation, and learned world models that forecast future clinical states under specified interventions (Alenany et al., 2020, Ranjan et al., 2015, Wang et al., 21 May 2026). Its defining features are explicit time, changing patient state, finite inpatient resources, and longitudinal outputs such as length of stay, occupancy, boarding, transfer delay, discharge timing, and downstream risk.

1. Scope and conceptual boundaries

In the narrowest formulation, longitudinal inpatient simulation may consist of a short hospital trajectory that links emergency care to inpatient admission. One emergency-department model implements the path “ED arrival $\rightarrow$ triage $\rightarrow$ diagnostics/treatment $\rightarrow$ admit vs discharge $\rightarrow$ (if admit) inpatient unit,” but does not simulate the subsequent inpatient stay or discharge; inpatient access is represented only by “a given probability of free beds” (Alenany et al., 2020). In a broader formulation, a patient flow network includes “Admission & triage,” “Treatment & monitoring,” and “Discharge,” with simulation intended to evaluate bed utilization and resource allocation over the inpatient spell (Chowdhury et al., 30 Jan 2025).

Other papers extend the horizon substantially. A chronic disease policy model simulates “continuous life courses for each patient using discrete event simulation,” with repeated events, competing risks, and trajectories that continue until death (Green et al., 2010). A path-dependent microsimulation advances individuals year by year and explicitly tracks medical spending, health status, family income, insurance, and medical debt over a multi-year period (Propp et al., 5 Feb 2025). A regional psychiatric access model makes the longitudinal character explicit in three senses: “continuous time dynamics,” “patient trajectories across multiple facilities,” and “evolving system state” (Adeyemi et al., 2023).

These formulations suggest that longitudinal inpatient simulation is best understood as a spectrum. At one end are operational ED-to-bed transfer models; at the other are hospital-wide or population-wide longitudinal simulators in which inpatient episodes are embedded within larger trajectories of health, utilization, and policy exposure.

2. Principal modeling paradigms

The dominant operational formalism is discrete-event simulation. Emergency-department flow with early inpatient transfer is modeled in Rockwell Arena V15 as a discrete-event system with arrivals, service completions, transfers, and prediction-triggered routing events (Alenany et al., 2020). Regional psychiatric bed placement is modeled in R with Simmer as a continuous-time event-calendar DES in which ED arrivals, transfer requests, accept/reject decisions, travel, inpatient admission, and discharge are all scheduled events (Adeyemi et al., 2023).

A second major paradigm is semi-Markov trajectory modeling. The Clustering and Scheduling Integrated approach defines a patient trajectory as a stochastic location process over wards with associated lengths of stay, and represents it as

$$\mathbf{y}^{(n)} = \left(\{u_1,\nu_1\},\ldots,\{u_{L^{(n)}},\nu_{L^{(n)}}\},\{\bar{u}\}\right),$$

where ward transitions and holding times are cluster-specific and non-exponential (Ranjan et al., 2015). This representation is especially suited to multi-ward inpatient flow because it allows arbitrary sojourn distributions, revisits, and ward interactions.

A third paradigm is continuous-time multi-state simulation based on competing hazards. In the chronic disease model, each current state has multiple outgoing edges with cause-specific hazards, and the next event is determined by

$T = \min_r T_r,\qquad C = \arg\min_r T_r,$

so that patient histories unfold as continuous-time event sequences rather than fixed-cycle updates (Green et al., 2010).

Statistical joint models provide another route. One general family writes the event hazard as

$$\lambda\bigl(t, Z(t)\bigr) = \lambda_{0}(t)\,\exp\{ b^\top Z(t) \},$$

allowing discharge, death, transfer, or other terminal events to depend on time-varying longitudinal covariates, including settings with substantial missingness in intermediate observations (Zheng et al., 2018). Related work on informative visiting processes shows that observation times may depend on severity, making naïve longitudinal analysis biased when the visit process is not ignorable (Gasparini et al., 2018).

Recent work adds learned dynamical models. An action-conditioned world model forecasts future clinical state by

$$\hat{y}_{i,t+k} = f_\theta\!\big(\mathcal{H}_{i,t},\,b_i,\,a_{i,t:t+k-1},\,\tau_{i,t+1:t+k}\big),$$

combining latent state encoding, intervention encoding, recurrent transition dynamics, and closed-loop rollout training (Wang et al., 21 May 2026). For daily inpatient aggression, a global stacked LSTM produces one-step-ahead binary risk via

$$P\bigl(y^p_{n+1} = 1\bigr) = \sigma \left( \mathbf{w}_d \cdot h_{n,Z} + \beta \right),$$

thereby treating inpatient risk as a longitudinal forecasting problem rather than a one-off classification task (Quinn et al., 2023).

3. Representation of trajectories, states, and resources

Longitudinal inpatient simulation depends on how patients, beds, and observations are encoded. In emergency and inpatient flow models, patient entities commonly carry demographic, temporal, and acuity attributes. One ED simulation uses Age, Gender, Arrival day, Arrival hour, Triage level, diagnostic needs, and admission status, together with shift-dependent staffing for physicians, nurses, orderlies, receptionists, and radiology technicians (Alenany et al., 2020). A large inpatient length-of-stay study treats each hospitalization as an episode with demographics, admission type, Emergency Department Indicator, CCS diagnosis and procedure codes, APR DRG code, APR MDC code, APR Severity of Illness Code, APR Risk of Mortality, Total Charges, and Total Costs (Chowdhury et al., 30 Jan 2025).

At the ward-network level, trajectory-based models treat hospital movement itself as the state process. The semi-Markov mixture model assigns each latent patient type a mixture weight, an initial ward distribution, a transition matrix, and a holding-time tensor, so that occupancy probabilities and total length-of-stay distributions can be derived analytically from the fitted trajectory process (Ranjan et al., 2015). In psychiatric access simulation, the resource state is equally explicit: each inpatient unit has a finite bed count, an age-service eligibility set, a mean coordination time, and an acceptance probability, while occupancy, queues, and “free bed” signals are updated continuously through the simulated year (Adeyemi et al., 2023).

Longitudinal patient simulators extend state representation beyond beds and wards. The Inpatient Pathway Decision Support benchmark represents each hospital episode as a staged Triage–Diagnosis–Treatment process built from MIMIC-IV demographics, radiology, medical history, ICD-derived disease categories, and service-derived treatment categories (Chen et al., 17 Mar 2025). A mental-health simulator constructs unified profiles from demographic attributes, standardized clinical symptoms, counseling dialogues, and longitudinal life-event histories, then converts noisy histories into structured, temporally grounded memory cards using a Chain-of-Change agent (Li et al., 24 Mar 2026).

This breadth of representation matters because “inpatient” can mean different objects of simulation: bed occupancy, multi-ward movement, physiological progression, conversational behavior, or all of them at once. The literature suggests that fidelity depends less on any single formalism than on whether the state encoding preserves the relevant longitudinal dependencies.

4. Prediction–simulation coupling

A central development in the field is the direct insertion of predictive models into simulation logic. In an ED model, a decision tree trained on synthetic ED records is translated into VBA inside Arena so that, directly after triage, predicted admissions can be transferred early to inpatient units if beds are available. The test accuracy of the early-prediction tree is 0.75, and the best combined operational scenario, “Scenario B + ML,” reduces LOS from 98.68 to 89.41 minutes and DTDT from 19.04 to 17.48 minutes, corresponding to 9.39% and 8.18% reductions (Alenany et al., 2020).

A large-scale inpatient LoS framework is explicitly positioned as hybrid: machine learning, process mining, and simulation are treated as complementary components. Using 2.3 million inpatient discharge records from New York State, the study predicts LoS bins at or near admission; among the compared models, LightGBM attains Accuracy 0.78, Precision 0.89, Recall 0.84, F1 0.83, Kappa 0.61, and MCC 0.63 (Chowdhury et al., 30 Jan 2025). The intended simulation role is clear: predicted LoS becomes a patient-specific service-time input for bed and resource models.

Neural sequence models push the coupling further. For inpatient aggression, the RNN-BOF model is trained on daily windows of aggression, psychometric scores, and static covariates and reaches AUC-PRG 0.9761 with a 10-day window, outperforming benchmark psychometric instruments and earlier machine-learning approaches on the same longitudinal task (Quinn et al., 2023). At a longer horizon, the ChronoMedicalWorld Model uses an action-conditioned latent world-model architecture and a six-term objective combining next-observation supervision, next-latent prediction, SIGReg latent regularisation, and three physiology-aware shape priors. In a chronic kidney disease case study, it achieves a dynamic-50% history rollout test MAE of 7.384 and RMSE of 10.256, compared with 7.964 and 11.069 for a tuned GPT-5.5 baseline (Wang et al., 21 May 2026).

These examples indicate two distinct but compatible roles for prediction inside longitudinal inpatient simulation. One is operational triggering: classify likely admissions, estimate likely LoS, or prioritize bed requests. The other is dynamical emulation: learn the longitudinal state transition itself and roll it forward under observed or hypothetical actions.

5. Operational applications and empirical findings

The most direct inpatient applications concern access, census, and scheduling. In a regional psychiatric DES covering numerous EDs and 41 inpatient units, baseline mean treatment delay is 1.56 hours for adults and 2.83 hours for vulnerable patients, while overall mean occupancy across units is 70.9%. The first intervention—prioritizing facilities most likely to accept—reduces mean coordination time for vulnerable transferred patients by 0.151 hours but slightly increases mean treatment delay. Concurrent referral policies reduce coordination time, with statistically significant gains once at least two concurrent referrals are sent per round (Adeyemi et al., 2023). The substantive finding is not a single best policy, but a trade-off: shorter coordination may come at the cost of longer travel.

At the hospital-wide ward-network level, the CSI framework shows that better longitudinal trajectory estimation materially changes scheduling outcomes. In a real hospital with 55 wards and about 11,000 inpatients, average transfers are 4.1 per patient. When the same optimization model is driven by different census estimators, CSI-based semi-Markov clustering yields a 97% increase in elective admissions and a 22% increase in utilization, whereas traditional estimation approaches yield markedly smaller gains, including 30% and 8% for k-means-based estimation (Ranjan et al., 2015). The paper’s explicit claim is that the limiting factor in Hospital Admission Scheduling and Control is often the census model rather than the optimization itself.

Longitudinal policy analysis has also been extended beyond bed operations. A path-dependent microsimulation for health, income, and employment is used to evaluate a financing proposal in which eligible individuals borrow from the federal government to cover health costs. In its case study, the policy covers about 46 million people and, over 15 years, total health expenditures fall by \$33B compared with status quo, while average out-of-pocket costs fall by \$1,343 per year for covered individuals (Propp et al., 5 Feb 2025). Although not a bed-management model, it demonstrates how inpatient-relevant expenditures and utilization can be embedded in a broader longitudinal policy environment.

A further expansion is inpatient pathway decision support. The IPDS benchmark contains 51,274 inpatient cases, nine triage departments, 17 major disease categories, and 16 standardized treatment options. On diagnosis, the Multi-Agent Inpatient Pathways framework improves accuracy by 25.10% over HuatuoGPT2-13B, and in a 100-case clinical compliance study it outperforms three board-certified clinicians by 10%–12% with ICC(2,k) of 0.81 against ground truth (Chen et al., 17 Mar 2025). This is not bed simulation, but it operationalizes longitudinal inpatient care as a structured sequence of admission, diagnosis, and treatment decisions.

6. Statistical challenges, limitations, and likely directions

A recurrent methodological problem is that longitudinal healthcare data are often observed through an informative process. In electronic health records, observation times may be correlated with underlying disease severity, so standard mixed models that assume independence between visit timing and outcome can be biased. Monte Carlo comparisons show that a correctly specified joint model of the visiting process and longitudinal outcome performs best when visiting is informative, whereas adjustment for total number of visits can perform poorly (Gasparini et al., 2018). This has direct implications for inpatient simulation, because data used to calibrate daily or event-driven trajectories may already encode severity-dependent observation intensity.

Missingness poses a second challenge. A simulation-based estimator for general joint models is designed for settings where some longitudinal covariates are “systematically missed for some of the covariate dimensions,” and proves consistency and asymptotic normality while remaining compatible with parallel computing and stochastic descending algorithms (Zheng et al., 2018). For inpatient modeling, this is relevant whenever certain covariates are observed only at admission or discharge, or only when clinically indicated.

Operational simplifications are equally consequential. The ED admission-detour model explicitly stops short of a full hospital-wide longitudinal model: inpatient bed availability is a probability, not a dynamic occupancy process; there is no inpatient LOS, no discharge event, no ICU-versus-ward differentiation, and no feedback from inpatient congestion to ED boarding (Alenany et al., 2020). The hybrid LoS framework likewise proposes simulation as part of the architecture but “does not describe a fully implemented simulation engine in detail,” and the records are “episodes” rather than multi-row time-stamped trajectories per patient (Chowdhury et al., 30 Jan 2025). The psychiatric access model fixes bed capacity and does not model rehospitalization or repeated visits (Adeyemi et al., 2023).

Recent patient simulators identify another limitation: snapshot prompting. A mental-health simulation framework argues that snapshot-style prompts yield “homogeneous behaviors and incoherent disease progression in multi-turn interactions,” and proposes data-grounded profiles plus temporally structured memory instead (Li et al., 24 Mar 2026). A medical world-model paper makes a parallel claim that general-purpose LLMs “drift under repeated interventions,” motivating closed-loop rollout training and physiology-aware shape priors (Wang et al., 21 May 2026). These results suggest that future inpatient simulation will likely require explicit temporal memory, action conditioning, and training protocols aligned with deployment-time multi-step rollout.

The literature itself proposes several next steps. Suggested extensions include explicit bed pools for ICU, PICU, CCU, and general wards; inpatient LOS distributions by unit; dynamic bed occupancy with ED boarding when capacity is full; process mining combined with simulation and prediction; state-transition or semi-Markov models with richer within-stay dynamics; time-varying covariates; reinforcement learning for dynamic control; and validation against historical occupancy, throughput, and waiting-time curves (Alenany et al., 2020, Chowdhury et al., 30 Jan 2025, Green et al., 2010, Wang et al., 21 May 2026). A plausible implication is that “longitudinal inpatient simulation” is moving toward composite architectures in which operations research, statistical longitudinal modeling, and learned patient-state dynamics are treated as interoperable rather than competing paradigms.