Dynamic Prediction for Hospital Readmission in Patients with Chronic Heart Failure

TL;DR

This study addresses predicting hospital readmission or death in chronic heart failure by dynamically updating risk using longitudinal NT-proBNP trajectories. It implements a Bayesian joint approach that links the latent trajectory $m_i(t)$ of $NT\text{-}proBNP$ to the hazard $h_i(t)$ with a Weibull baseline, using a $180$-day prediction window and 5-fold cross-validation to assess performance. Compared against a static last-value baseline, the dynamic joint approach shows superior discrimination and calibration, especially when NT-proBNP measurements are frequent and predictions extend to $180$–$360$ days, demonstrating the method's value for adaptive, patient-specific HF management. These findings support integrating full biomarker trajectories into decision-support tools to provide timely, personalized risk assessments in real-world clinical settings.

Abstract

Hospital readmission among patients with chronic heart failure (HF) is a major clinical and economic burden. Dynamic prediction models that leverage longitudinal biomarkers may improve risk stratification over traditional static models. This study aims to develop and validate a joint model using longitudinal N-terminal pro-B-type natriuretic peptide (NT-proBNP) measurements to predict the risk of rehospitalization or death in HF patients. We analyzed real-world data from the TriNetX database, including patients with an incident HF diagnosis between 2016 and 2022. The final selected cohort included 1,804 patients. A Bayesian joint modeling framework was developed to link patient-specific NT-proBNP trajectories to the risk of a composite endpoint (HF rehospitalization or all-cause mortality) within a 180-day window following hospital discharge. The model's performance was evaluated using 5-fold cross-validation and assessed with the Integrated Brier Score and Integrated Calibration Index. The joint model demonstrated a strong predictive advantage over a benchmark static model, particularly when making updated predictions at later time points (180-360 days). A joint model trained on patients with more frequent NT-proBNP measurements achieved the highest accuracy. The main joint model showed excellent calibration, suggesting its risk estimates are reliable. Our findings suggest that modeling the full trajectory of NT-proBNP with a joint modeling framework enables more accurate and dynamic risk assessment compared to static, single-timepoint methods. This approach supports the development of adaptive clinical decision-support tools for personalized HF management.

Figures (5)

• Figure 1: Exploratory data analysis of the study cohort. (A) Distribution of the time-to-event (top) for patients who experienced the composite endpoint (n=1,457) and distribution of censoring time (bottom) for patients who did not experience the event (n=347). (B) Kaplan-Meier curve for the composite endpoint (HF rehospitalization or all-cause mortality). The solid line represents the estimated probability of remaining event-free over the follow-up period, with the shaded area indicating the 95% confidence interval. (C) Histogram of log-transformed NT-proBNP measurements (n=9,594) collected from any patient in the study cohort. The transformation was used to produce a more symmetric distribution for statistical modeling. (D) Distribution of the collection times for all NT-proBNP measurements relative to the landmark time $t_0.$ The majority of measurements were recorded early in the follow-up period. (E) Distribution of the number of NT-proBNP measurements per patient. A significant proportion of patients (33%) have three recorded values, which is the minimum required by our inclusion criteria. (F) Individual longitudinal trajectories of log-transformed NT-proBNP levels over time for a random subset of 35 patients. Each colored line represents a single patient, illustrating the substantial inter-patient heterogeneity in biomarker patterns over time.
• Figure 2: Fitted individual NT-proBNP trajectories from the longitudinal submodel for a random subset of 30 patients. Points are the observed log(NT-proBNP) values, and the solid lines are the corresponding fitted trajectories from the model.
• Figure 3: Forest plot of hazard ratios for baseline predictors in the survival (Weibull) submodel. The plot displays the estimated hazard ratios (dots) and their corresponding 95% confidence intervals (horizontal bars) for the composite endpoint of heart failure rehospitalization or all-cause mortality. Each hazard ratio (HR) is derived from the Weibull model coefficients ($\beta$) and scale parameter ($\sigma$) using the transformation $\text{HR} = \exp(-\beta / \sigma)$. An HR $> 1$ indicates an increased risk of the event. Statistically significant associations, based on 95% confidence level, are highlighted in blue.
• Figure 4: Individualized dynamic survival predictions for two representative patients. In both panels the left-most red curve displays the initial predicted survival probability for the 0-180 day window, while right-most red curve shows the updated prediction for the 180-360 day window, incorporating new biomarker data. The red shaded area is its relative 95% credible interval. The blue dots represent the observed log-transformed NT-proBNP values. (A) Patient with a decreasing NT-proBNP trend, leading to an improved survival probability estimate at 180 days. (B) Patient with an increasing NT-proBNP trend, resulting in a worsened prognosis.
• Figure 5: Calibration of the main joint model’s risk predictions for the 0–180 day period post-discharge. (A) Smoothed calibration curve based on a natural spline fit of the cloglog-transformed predicted probabilities within a Cox model. The shaded area represents the 95% confidence interval. (B) Binned calibration plot. Patients are grouped into 5 risk strata to compare average predicted versus observed event rates within each bin.