Learning Continuous Patient Trajectories from Electronic Health Records

Silas Ruhrberg Estévez; Kara Liu; Christopher Chiu; Benjamin Atta Owusu; Umesh Kadam; Russ B. Altman; Mihaela van der Schaar

cs.LGSep 28, 2026

Learning Continuous Patient Trajectories from Electronic Health Records

Authors: Silas Ruhrberg Estévez, Kara Liu, Christopher Chiu, Benjamin Atta Owusu, Umesh Kadam, Russ B. Altman, Mihaela van der Schaar

Organizations: University of Cambridge · Stanford University · University of Exeter

Abstract

Electronic health records provide irregular observations of latent patient states that evolve continuously over time. Recent autoregressive models condition on clinical histories to forecast future events as sequences of discrete observations. Conversely, multi-marginal flow matching provides a continuous-time formulation, but using multiple observations to supervise training paths does not itself give the learned dynamics access to preceding patient history. We introduce EHRFlow, a multi-marginal flow-matching framework that conditions on encoded patient history, thereby allowing future dynamics to depend on the patient's prior clinical trajectory. Our proposed framework accommodates irregular observation times and supports forecasting at arbitrary horizons. Across controlled synthetic benchmarks, EHRFlow improves clinical-code forecasting and latent-state recovery. On real-world clinical datasets comprising more than one million patients, including an independent external validation cohort, EHRFlow improves horizon-averaged top-5 clinical-code accuracy over autoregressive and history-independent flow-matching baselines. Finally, in a controlled counterfactual simulation, conditional guidance approximates the known effect of an antihypertensive intervention without training a task-specific outcome model.

Figures & tables

Figure 1: Schematic of an unobserved, continuously evolving patient state (top) and sparse EHR observations (bottom).

Figure 2: Autoregressive models condition on the observed sequence but predict future events discretely. Conditional flow matching (CFM) models have pairwise latent transitions. Multi-marginal flow matching (MMFM) uses multiple observations to define the training trajectory, and EHRFlow additionally conditions the learned vector field on the preceding patient history.

Figure 3: Patients with similar current states may have different future trajectories depending on how they reached those states.

Figure 4: Training and forecasting with EHRFlow . (1) An encoder and decoder learn visit-level latent representations. (2) A history encoder is pretrained on observations up to the forecast anchor. (3) Both encoders are frozen. Future observations define paths and target velocities for training the history-conditioned field. (4) At inference, the field is integrated from the encoded anchor and decoded into clinical predictions.

	Anthracycline	RA on DMARD	CKD	RRMS	Heart failure	Synthea
Decoder-only	0.510 $\pm$ 0.017	0.821 $\pm$ 0.010	0.614 $\pm$ 0.008	0.600 $\pm$ 0.023	0.405 $\pm$ 0.019	0.432 $\pm$ 0.029
Encoder-decoder	0.507 $\pm$ 0.015	0.860 $\pm$ 0.007	0.668 $\pm$ 0.016	0.593 $\pm$ 0.013	0.403 $\pm$ 0.019	0.278 $\pm$ 0.121
GRU-ODE-Bayes	0.546 $\pm$ 0.022	0.829 $\pm$ 0.042	0.656 $\pm$ 0.022	0.524 $\pm$ 0.026	0.386 $\pm$ 0.064	0.439 $\pm$ 0.052
Neural CDE	0.411 $\pm$ 0.066	0.729 $\pm$ 0.061	0.577 $\pm$ 0.069	0.491 $\pm$ 0.044	0.305 $\pm$ 0.084	0.601 $\pm$ 0.027
CFM (adjacent)	0.574 $\pm$ 0.035	0.971 $\pm$ 0.003	0.812 $\pm$ 0.014	0.781 $\pm$ 0.024	0.602 $\pm$ 0.026	0.790 $\pm$ 0.014
Metric FM	0.597 $\pm$ 0.036	0.963 $\pm$ 0.004	0.789 $\pm$ 0.021	0.759 $\pm$ 0.062	0.627 $\pm$ 0.053	0.766 $\pm$ 0.008

Table 1: Top-5 clinical-code accuracy across synthetic benchmarks, averaged over forecast horizons. Entries show mean

\pm

standard deviation across runs.

	CPRD	AMC-EHR
Decoder-only	0.368 $\pm$ 0.012	0.259 $\pm$ 0.008
Encoder-decoder	0.335 $\pm$ 0.001	0.232 $\pm$ 0.037
GP-CFM	0.554 $\pm$ 0.021	0.275 $\pm$ 0.004
MMFM	0.548 $\pm$ 0.014	0.279 $\pm$ 0.004
EHRFlow (GP-CFM)	0.638 $\pm$ 0.009	0.283 $\pm$ 0.013
EHRFlow (MMFM)	0.621 $\pm$ 0.021	0.302 $\pm$ 0.016

Table 2: Top-5 clinical-code accuracy on real-world CPRD and AMC-EHR datasets, averaged over forecast horizons.

	Average top-5 acc.
	GP-CFM	MMFM
EHRFlow	0.899 $\pm$ 0.001	0.897 $\pm$ 0.002
EHRFlow matched	0.897 $\pm$ 0.002	0.897 $\pm$ 0.002
EHRFlow , zero context	0.868 $\pm$ 0.002	0.869 $\pm$ 0.001
EHRFlow , end-to-end GRU	0.873 $\pm$ 0.004	0.878 $\pm$ 0.003
EHRFlow , fully end-to-end	0.876 $\pm$ 0.008	0.865 $\pm$ 0.004

Table 3: EHRFlow ablations: top-5 clinical-code accuracy averaged across synthetic datasets and forecast horizons.

EHRFlow (GP-CFM)
Design	Observed	Guided	Error
Paired	$-23.20\pm 0.59$	$-19.42\pm 2.33$	$1.06\pm 2.33$
Split-arm	$-22.58\pm 0.59$	$-18.41\pm 1.62$	$2.07\pm 1.62$
EHRFlow (MMFM)
Paired	$-23.20\pm 0.59$	$-18.83\pm 2.27$	$1.65\pm 2.27$
Split-arm	$-22.58\pm 0.59$	$-20.41\pm 1.72$	$0.07\pm 1.72$

Table 4: Recovery of the simulator-defined hypertension effect with CFG.

Appendix figures & tables15 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 5: Left: individual forecast error against flow time. Centre: flow-matching risk against history reliability

\rho

. Right: variance of the generated state at

\rho=0.9

; both flows recover the marginal

1+s^{2}

, only the history-conditioned flow recovers the variance given

H

1+\kappa s^{2}

Figure 6: Smooth vector-field paths through the same knots on synthetic data.

Figure 7: Six knot-interpolating families fitted with the same network architecture (10 seeds). Differences between conditional paths are reduced in the fitted flows, with pairwise endpoint Wasserstein-1 distances of 0.02–0.04.

Figure 8: Clinical-code top-5 accuracy by forecast horizon across the five synthetic datasets and Synthea. Lines show the mean across random seeds; bands indicate

\pm

one standard deviation.

Figure 9: Clinical-code top-1 accuracy by forecast horizon across the five synthetic datasets and Synthea. Lines show the mean across random seeds; bands indicate

\pm

one standard deviation.

Figure 10: Clinical-code macro-AUROC by forecast horizon across the five synthetic datasets and Synthea. Lines show the mean across random seeds; bands indicate

\pm

one standard deviation.

Figure 11: Clinical-code forecasting performance by horizon on CPRD (external Gold cohort) and AMC-EHR. Rows show top-5 accuracy, top-1 accuracy, and macro-AUROC. Lines show the mean across random seeds; shaded bands indicate

\pm

one standard deviation.

	Heart failure	RA on DMARD	CKD	RRMS	Anthracycline
CFM (adjacent)	1.48 $\pm$ 0.05	0.36 $\pm$ 0.04	1.14 $\pm$ 0.01	1.96 $\pm$ 0.06	1.07 $\pm$ 0.06
Metric FM	1.41 $\pm$ 0.08	0.34 $\pm$ 0.03	1.10 $\pm$ 0.06	2.06 $\pm$ 0.04	1.35 $\pm$ 0.23
GP-CFM	1.24 $\pm$ 0.06	0.26 $\pm$ 0.00	0.99 $\pm$ 0.05	2.23 $\pm$ 0.12	1.07 $\pm$ 0.05
MMFM	1.34 $\pm$ 0.02	0.27 $\pm$ 0.01	1.01 $\pm$ 0.06	2.35 $\pm$ 0.11	0.98 $\pm$ 0.01
EHRFlow (GP-CFM)	1.18 $\pm$ 0.12	0.23 $\pm$ 0.00	0.78 $\pm$ 0.03	1.58 $\pm$ 0.06	0.81 $\pm$ 0.01
EHRFlow (MMFM)	1.24 $\pm$ 0.12	0.25 $\pm$ 0.01	0.73 $\pm$ 0.12	1.67 $\pm$ 0.08	0.94 $\pm$ 0.05

Appendix

Table 5: Median and s.d. of latent-state recovery on the synthetic benchmarks across seeds.

Interior off-grid horizons (270, 545, 912 d)
	Heart failure	RA on DMARD	CKD	RRMS	Anthracycline	Synthea
GRU-ODE-Bayes	0.352 $\pm$ 0.091	0.813 $\pm$ 0.043	0.611 $\pm$ 0.025	0.495 $\pm$ 0.013	0.518 $\pm$ 0.020	0.302 $\pm$ 0.031
Neural CDE	0.267 $\pm$ 0.119	0.664 $\pm$ 0.066	0.492 $\pm$ 0.100	0.438 $\pm$ 0.055	0.386 $\pm$ 0.098	0.562 $\pm$ 0.032
CFM (adjacent)	0.573 $\pm$ 0.030	0.967 $\pm$ 0.003	0.797 $\pm$ 0.012	0.769 $\pm$ 0.029	0.557 $\pm$ 0.040	0.705 $\pm$ 0.012
Metric FM	0.599 $\pm$ 0.063	0.957 $\pm$ 0.006	0.769 $\pm$ 0.024	0.743 $\pm$ 0.079	0.583 $\pm$ 0.042	0.664 $\pm$ 0.018
GP-CFM	0.738 $\pm$ 0.006	0.974 $\pm$ 0.001	0.906 $\pm$ 0.004	0.887 $\pm$ 0.005	0.767 $\pm$ 0.003	0.813 $\pm$ 0.006

Appendix

Table 6: Top-5 clinical-code accuracy at the off-grid horizons, averaged over the horizons of each block (mean

\pm

std over seeds).

Figure 12: Clinical-code top-5 accuracy at trained and off-grid forecast horizons across the synthetic benchmarks. Off-grid evaluation tests interpolation between training horizons and extrapolation outside the training range. Results are averaged across seeds and shown with

\pm

1 s.d.

Heart failure
	EHRFlow (GP-CFM)			EHRFlow (MMFM)
	Direct	Nested	Overlap	Direct	Nested	Overlap
90 d in 180 d	0.872 $\pm$ 0.007	0.876 $\pm$ 0.008	0.952 $\pm$ 0.012	0.867 $\pm$ 0.012	0.870 $\pm$ 0.014	0.940 $\pm$ 0.015
90 d in 365 d	0.872 $\pm$ 0.007	0.874 $\pm$ 0.008	0.929 $\pm$ 0.017	0.867 $\pm$ 0.012	0.869 $\pm$ 0.009	0.913 $\pm$ 0.015
180 d in 365 d	0.811 $\pm$ 0.004	0.817 $\pm$ 0.005	0.936 $\pm$ 0.006	0.807 $\pm$ 0.020	0.813 $\pm$ 0.018	0.928 $\pm$ 0.018
180 d in 730 d	0.811 $\pm$ 0.004	0.820 $\pm$ 0.006	0.909 $\pm$ 0.015	0.807 $\pm$ 0.020	0.819 $\pm$ 0.006	0.896 $\pm$ 0.028

Appendix

Table 7: Trajectory self-consistency per synthetic dataset and nested pair (

h

read off a rollout to

H

). Direct: top-5 code accuracy of a rollout to day

h

; Nested: the same day read off the rollout to

H

; Overlap: shared fraction of the two top-5 sets. Mean

\pm

s.d. over seeds.

MMFM path
	Anthracycline	RA on DMARD	CKD	RRMS	Heart failure	Synthea
EHRFlow	0.865 $\pm$ 0.007	0.985 $\pm$ 0.002	0.940 $\pm$ 0.004	0.942 $\pm$ 0.004	0.775 $\pm$ 0.009	0.875 $\pm$ 0.003
EHRFlow param. matched	0.858 $\pm$ 0.004	0.986 $\pm$ 0.001	0.938 $\pm$ 0.005	0.940 $\pm$ 0.006	0.784 $\pm$ 0.010	0.877 $\pm$ 0.004
EHRFlow , zero context	0.783 $\pm$ 0.005	0.979 $\pm$ 0.002	0.910 $\pm$ 0.004	0.898 $\pm$ 0.003	0.766 $\pm$ 0.011	0.876 $\pm$ 0.002
EHRFlow , end-to-end GRU	0.807 $\pm$ 0.014	0.982 $\pm$ 0.002	0.926 $\pm$ 0.007	0.919 $\pm$ 0.005	0.757 $\pm$ 0.010	0.874 $\pm$ 0.003
EHRFlow , fully end-to-end	0.767 $\pm$ 0.021	0.981 $\pm$ 0.002	0.919 $\pm$ 0.006	0.911 $\pm$ 0.011	0.748 $\pm$ 0.009	0.861 $\pm$ 0.008

Appendix

Table 8: History-conditioning ablations per dataset: top-5 clinical-code accuracy averaged over horizons (mean

\pm

std over seeds).

Figure 13: Top-5 clinical-code accuracy, averaged across forecast horizons, is shown for each dataset as the number of day-states

K

available to the history encoder varies. Lines show the mean across random seeds; shaded bands indicate

\pm

one standard deviation.

Dataset	Patients	Events	Codes	Predictive information
Heart failure	20,000	5,311,935	20	Current state only
RA on DMARD	20,000	5,013,692	18	Time since treatment initiation
CKD	20,000	5,234,333	20	Historical progression rate
RRMS	20,000	5,264,932	20	Time since previous relapse
Anthracycline	20,000	5,587,408	22	Cumulative treatment exposure
Synthea	23,072	20,586,237	1,893	Rule-based longitudinal disease history

Appendix

Table 9: Synthetic datasets and the source of history dependence. Event and code counts are those of the processed data the models are trained on.

Wall-clock (h)	Anthracycline	RA on DMARD	CKD	RRMS	Heart failure	Synthea
Decoder-only	56.94 $\pm$ 26.02	47.02 $\pm$ 20.78	51.38 $\pm$ 26.94	52.84 $\pm$ 24.04	50.75 $\pm$ 22.82	23.36 $\pm$ 11.54
Encoder-decoder	11.41 $\pm$ 4.18	12.81 $\pm$ 4.68	13.82 $\pm$ 4.66	10.02 $\pm$ 4.52	15.24 $\pm$ 5.64	14.34 $\pm$ 4.52
GRU-ODE-Bayes	15.95 $\pm$ 2.70	9.78 $\pm$ 1.12	12.40 $\pm$ 1.53	12.86 $\pm$ 2.06	13.00 $\pm$ 1.76	13.78 $\pm$ 1.81
Neural CDE	4.32 $\pm$ 0.92	3.70 $\pm$ 0.39	4.37 $\pm$ 0.51	4.37 $\pm$ 0.48	4.39 $\pm$ 0.43	12.72 $\pm$ 3.78
CFM (adjacent)	1.15 $\pm$ 0.28	0.27 $\pm$ 0.00	0.29 $\pm$ 0.01	0.52 $\pm$ 0.05	0.30 $\pm$ 0.01	1.57 $\pm$ 1.92
Metric FM	1.31 $\pm$ 0.20	0.87 $\pm$ 0.19	1.13 $\pm$ 0.05	0.57 $\pm$ 0.09	1.11 $\pm$ 0.15	0.63 $\pm$ 0.02

Appendix

Table 10: Wall-clock time in hours for each of the synthetic datasets (mean

\pm

std over seeds).

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-7.28\%

MAE,

-7.35\%

RMSE), with the gain dominated by the dialogue portion of patient--health-coach communication. The framework is not CKD-specific: its architecture, loss design, and training protocol apply to any chronic condition that can be cast as periodic clinical state interleaved with structured and conversational interventions.

Abstract

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