A Patient World Model for Early Forecasting of Digital Health Campaign Outcomes: Capabilities and Limits

Yunlong Wang

cs.LGSep 20, 2026

A Patient World Model for Early Forecasting of Digital Health Campaign Outcomes: Capabilities and Limits

Authors: Yunlong Wang

Organizations: Advanced Analytics, IQVIA Wayne, PA, USA

Abstract

Digital direct-to-consumer (DTC) health campaigns are usually measured after the fact. In-flight forecasting commonly relies on a separate classifier for every cutoff and horizon. We treat this task as a dynamic-system problem and build a compact patient world model. The architecture maintains a latent state per patient, learns exposure-conditioned state dynamics jointly with a weekly conversion hazard, and rolls forward into future conversion curves. We evaluate it on a US campaign dataset with 147{,}173 patients and 5.2 million at-risk person-weeks. In a retrospective evaluation conditioned on recorded future exposures, the model forecasts the remaining new-to-brand prescription volume through week 52 with a relative error of 2.9% from a week-4 cutoff and 0.8--2.6% from cutoffs at weeks 8--26. The strongest non-recurrent baseline, a pooled-hazard gradient boosting model given the same survival rollout and information, has relative errors of 13.6--33.1%. Per-horizon classifiers perform substantially worse. A Fisher-information analysis motivates dense next-exposure supervision when conversions are rare. Removing this auxiliary objective increases prescription-volume error by approximately $2$ -- $14\times$ , while providing no consistent disadvantage on the more common specialist-visit outcome. We also evaluate scenario simulation. Switching all future exposure off raises predicted conversion from 0.31 to 0.89, a pattern consistent with selection effects in observational exposure data. This result highlights the limits of interpreting exposure-conditioned rollouts causally.

Figures & tables

Panel of Figure 1 — Figure 1: The proposed architecture, unrolled. It is defined by three components and one inference pattern: a swappable sequence-state module $f_{\theta}$ (instantiated as a GRU in this work), a hazard head $g_{\mathcal{R}}$ , a transition head $g_{\mathcal{T}}$ for dense next-action supervision, and the recursive survival rollout that multiplies weekly hazards into a coherent cumulative-incidence forecast. The transition head takes $({\mathbf{z}}_{i,r},{\mathbf{a}}_{i,r})$ , shown by the curved input. During training both heads apply at every at-risk week. The figure shows $g_{\mathcal{T}}$ once on the observed prefix and $g_{\mathcal{R}}$ from the cutoff onward, where forecasting happens. After the cutoff (dashed cells), the same module runs on recorded or hypothetical exposures ${\mathbf{a}}^{\prime}$ .

Model	$\tau{=}4$	$\tau{=}8$	$\tau{=}13$	$\tau{=}26$	$\tau{=}39$	Coherent
	NBRx volume rel. error (%) at cutoff $\tau$
Per- $(\tau,H)$ GBM	2582.0	3054.8	3754.7	8491.6	18389.9	19–24%
Per- $(\tau,H)$ GBM + future	2581.8	3054.1	3754.0	8491.9	18389.9	11–31%
Naive extrapolation	64.4	82.6	97.4	166.1	146.7	100%
Pooled-hazard GBM	13.6	17.3	19.2	33.1	44.3	100%
GRU forecaster ( $\lambda{=}0$ )	5.2	7.4	8.2	11.1	5.6	100%

Table 1: The headline task: forecast the campaign’s final NBRx volume from an early cutoff

\tau

(rx outcome, test split, known future exposures). Relative error (%) of the forecast final converter count. “Coherent” is the fraction of monotone per-patient curves (range across cutoffs). Test risk sets hold 21,963 down to 16,940 patients. Observed future converters

n_{+}

= 711, 601, 489, 206, 76. At

\tau{=}39

the

1\sigma

sampling floor is

1/\sqrt{76}\approx 11.5\%

, so that column cannot rank the coherent models (see text). All numbers as-run.

Figure 2: The headline result (rx outcome, test split). (a) Relative error of the forecast final NBRx volume versus the cutoff $\tau$ (log scale). The shaded band is the $\pm 1\sigma$ sampling floor implied by Proposition 2 ( $\approx 1/\sqrt{n_{+}}$ ). No method, however good, can be expected to beat it. The world model sits inside the floor at every cutoff up to week 26. The fair coherent baseline sits 4–5 $\sigma$ above it, and the per-horizon practice two to four orders of magnitude above it. Read horizontally, a small $\tau$ means a long rollout ( $\tau=4$ rolls 48 weeks), and the world model’s error does not grow with rollout length, as Proposition 1 requires. (b) Predicted NBRx cumulative-incidence trajectories from cutoff $\tau=8$ against the observed curve, estimated by Kaplan–Meier (KM), the standard estimator of cumulative incidence under right-censoring. The world model tracks the observed curve across all 44 remaining weeks. The whole curve is calibrated, not just the endpoint. The per-cell curve leaves the frame.

	Dose scale $\alpha$
Simulator ( $\tau$ )	0	0.25	0.5	1	1.5	2	4
World model ( $\tau{=}4$ )	0.893	0.312	0.310	0.310	0.311	0.311	0.316
Pooled-hazard GBM ( $\tau{=}4$ )	0.632	0.315	0.314	0.313	0.318	0.325	0.364
World model ( $\tau{=}8$ )	0.708	0.267	0.265	0.265	0.266	0.267	0.270
Pooled-hazard GBM ( $\tau{=}8$ )	0.504	0.273	0.272	0.271	0.275	0.279	0.307

Table 2: Scenario simulation (T3): simulated dose-response on the dx outcome. Each cell is the mean predicted cumulative conversion of the test risk set when all future exposure is scaled by

\alpha

( do

(\alpha\cdot{\mathbf{a}})

), for the world-model simulator and the perturbed pooled-hazard GBM. The

\alpha=0

column is a selection artifact, not an effect (see text). The

\alpha=4

column is outside the observed dose support.

Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

Model	AUROC (enr.)	AUROC (IPW)	AUPRC (enr.)	Cal. slope	ECE
Base rate	0.500	0.500	0.009	—	—
Logistic regression	0.855	0.838	0.051	1.005	0.0011
LightGBM (flat)	0.872	0.855	0.059	0.648	0.0006
MLP	0.873	0.856	0.065	0.929	0.0009
GRU world model (proposed)	0.880	0.864	0.067	0.957	0.0002

Appendix

Table 3: One-step hazard prediction (T1), dx outcome, full test split (22,086 patients, 768,431 at-risk person-weeks, 6,856 positives). AUROC is reported on the enriched cohort and IPW-corrected to natural prevalence. AUPRC is on the enriched cohort.

Model	$\tau{=}4$	$\tau{=}8$	$\tau{=}13$	$\tau{=}26$	$\tau{=}39$	Coherent
	Volume rel. error (%) at cutoff $\tau$
Per- $(\tau,H)$ GBM	209.3	256.0	326.7	645.1	1572.8	54–70%
Per- $(\tau,H)$ GBM + future	209.2	255.8	326.6	644.9	1572.9	27–72%
Naive extrapolation	97.3	96.8	101.9	120.3	140.5	100%
Pooled-hazard GBM	8.7	9.2	8.8	6.0	6.2	100%
GRU forecaster ( $\lambda{=}0$ )	6.6	5.4	3.4	5.7	15.5	100%

Appendix

Table 4: Campaign-level trajectory forecasting (T2), dx outcome, test split, full cohort. Volume relative error (%) at the campaign end and coherence. Test risk sets: 20,396 down to 12,805.

n_{+}

= 5,874 down to 631.

	AUROC (IPW)					Trajectory ICI
Model	4	8	13	26	39	4	8	13	26	39
Per- $(\tau,H)$ GBM	.718	.675	.695	.664	.544	.139	.160	.201	.326	.533
Naive extrapolation	.500	.500	.500	.500	.500	.149	.126	.114	.083	.050
Pooled-hazard GBM	.912	.908	.903	.896	.891	.012	.012	.010	.005	.004
GRU forecaster ( $\lambda{=}0$ )	.935	.930	.924	.917	.904	.010	.008	.006	.002	.004
GRU world model (proposed)	.935	.930	.925	.917	.909	.012	.011	.008	.002	.004

Appendix

Table 5: Patient-level discrimination and trajectory calibration on dx (T2), full cohort. AUROC is IPW-corrected. ICI is the mean absolute gap between predicted and KM-observed cumulative-incidence curves.

Figure 3: Trajectory forecasting on dx (test split). (a) Final-volume relative error versus cutoff (log scale). (b) Mean predicted cumulative-incidence trajectories from $\tau=8$ against the Kaplan–Meier curve. The coherent models sit in the same single-digit band. The per-cell practice explodes with the horizon.

Regime	Model	$\tau{=}4$	$\tau{=}8$	$\tau{=}13$	$\tau{=}26$	$\tau{=}39$
dx, full cohort	Pooled-hazard GBM	8.7	9.2	8.8	6.0	6.2
( $n_{+}$ : 5874–631)	GRU forecaster	6.6	5.4	3.4	5.7	15.5
	GRU world model	7.5	6.5	4.8	4.5	15.3
dx, dynamics-rich	Pooled-hazard GBM	15.0	15.2	19.5	21.5	36.1
( $n_{+}$ : 599–91)	GRU forecaster	2.3	0.7	0.3	7.8	16.9
	GRU world model	4.0	1.6	3.2	6.8	17.6

Appendix

Table 6: The regime map (volume rel. error, %): the three coherent models on the full dx cohort, the dynamics-rich dx subgroup (

\geq 5

total active weeks), and the full rx cohort. Small-

n_{+}

cells are noisy.

Figure 4: The regime map (Table 6 , drawn): final-volume relative error of the three coherent models, log scale. (a) Full sparse dx cohort: the aggregate ceiling of P2. (b) Dynamics-rich patients and (c) the rare rx outcome: the regime dependence of P3.

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Digital medicine now captures data that traces individual health trajectories and reveals population health dynamics through electronic health records, claims, remote monitoring, wearable devices, mobile devices, social sensing data, medical images, etc. But much of its modeling still centers on task-specific, outcome-specific, and prediction-specific estimation. The next frontier is not simply better prediction, but action in an evolving health world shaped by multiple decision-makers, heterogeneous populations, resource constraints, and feedback in care delivery. This is why digital medicine now needs world models: not only to estimate what will happen, but to represent how actions change what can happen next -- whom to prioritize, how to allocate scarce resources, how to adapt care across subgroups, and how interventions reshape future health trajectories and population dynamics. We call such a model population health world model (PHWM): a more foundational representation of an evolving health world in which health states, individual trajectories, population health dynamics, interventions, constraints, and feedback are intrinsically coupled. Building a PHWM endows three unmet structural gaps in current digital medicine: dynamic health-state modeling, population-level intervention intelligence, and validation, equity, and governance for action-oriented use. We argue that addressing these gaps requires three minimal capabilities: representation learning under action-dependent observation, multi-scale intervention intelligence, and validation with explicit decision boundaries, while highlighting the importance of social, contextual, and public-health sensing data for action-oriented digital medicine.

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