Dynamic prediction of adverse outcomes in discharged COPD patients using patient-reported outcomes

Abstract

Background

To develop dynamic prediction models based on longitudinal patient-reported outcomes (PROs) and evaluate the time-varying risk of adverse outcomes after hospital discharge in patients with chronic obstructive pulmonary disease (COPD), thereby improving the accuracy of risk prediction.

Methods

Hospitalized COPD patients who met the inclusion and exclusion criteria from five hospitals in Shanxi Province between December 2020 and April 2022 were included. The occurrence of readmission or death within three years after discharge was defined as the adverse outcome. PROs measured repeatedly during follow-up were treated as time-varying predictors. Three dynamic prediction approaches were constructed and compared: the Joint Latent Class Model (JLCM), Shared Random-Effects Model (SREM), and Landmark model. Model performance was evaluated and compared using the time-dependent area under the receiver operating characteristic curve (AUC), Brier score, and calibration curves. In addition, individual-level trajectories of PRO scores and their corresponding dynamic risk predictions were illustrated.

Results

A total of 344 COPD patients were included, among whom 111 patients (32.27%) experienced adverse outcomes during follow-up. Model comparison demonstrated that the SREM model consistently achieved higher AUC values and lower Brier scores across all landmark time points, and its calibration curves were close to the ideal diagonal line, indicating the best predictive performance. In the survival submodel, the association parameter for PRO scores was statistically significant (P < 0.001). Each one-unit increase in PRO score was associated with a 4.3% reduction in the risk of adverse outcomes (HR = 0.957, 95% CI: 0.933–0.980). In addition, educational level, procalcitonin, and C-reactive protein levels were significantly associated with the risk of adverse outcomes. In the longitudinal submodel, dyspnea severity (mMRC grade) was significantly negatively associated with PRO scores.

Conclusions

Longitudinal PRO data effectively capture the dynamic changes in health status among COPD patients and can serve as important time-varying predictors for adverse outcomes. Among the three dynamic prediction approaches evaluated, the SREM model demonstrated the best predictive performance. These findings provide a scientific basis for risk stratification and individualized management strategies in COPD patients after hospital discharge.

Clinical trial registration

The study was registered with the Chinese Clinical Trial Registry (Registration number: ChiCTR2200064900;Date of Registration:2022-10-21).

Background

Worldwide, Chronic Obstructive Pulmonary Disease (COPD) is one of the most prevalent chronic conditions; it is characterized by high rates of rehospitalization and mortality. Estimates indicate that 25.0%–87.0% of COPD patients are readmitted within a year of discharge, and the disease accounts for approximately three million deaths annually, imposing a substantial societal and economic burden [1, 2]. Therefore, the early identification of high-risk patients and the implementation of targeted interventions are of critical importance for improving the long-term prognosis of individuals with COPD.

It is noteworthy that the 30-day readmission rate, as an important healthcare quality indicator widely used internationally, plays a significant role in evaluating short-term prognosis and the effectiveness of post-discharge management [3]. However, this indicator primarily reflects short-term risk and is insufficient to comprehensively capture disease progression and dynamic changes in risk during the mid- to long-term follow-up period [4]. Therefore, from the perspective of a longer follow-up duration, dynamically assessing the risk of adverse outcomes holds greater clinical value for the long-term management of chronic diseases.

At present, research on predicting the risk of readmission in COPD patients has made certain progress. Common approaches include risk prediction models based on administrative or insurance claims data (claim-based models) [5], as well as multidimensional comprehensive prediction tools proposed in recent years (such as the PRECISE model) [6]. These models are mostly constructed based on baseline information, including demographic characteristics, prior hospitalization history, and comorbidities, and can achieve risk stratification to a certain extent. However, such models generally lack characterization of patients’ subjective health status and predominantly adopt static modeling strategies, making it difficult to reflect the dynamic changes in patients’ health status over time. Consequently, their predictive performance and clinical applicability are limited.

In recent years, patient-reported outcomes (PROs) have increasingly been recognized as important indicators for evaluating health status and prognosis in chronic diseases. PROs directly reflect patients’ subjective experiences regarding symptoms, functional status, psychological well-being, and social adaptation. In the field of COPD, commonly used PRO measurement instruments include the St George’s Respiratory Questionnaire (SGRQ), the modified Medical Research Council dyspnea scale (mMRC), as well as generic health-related quality of life measures such as the SF-36 (or SF-12). Numerous studies have demonstrated that PRO measures have significant value in predicting adverse outcomes in COPD, including hospital readmission, acute exacerbations, and mortality [7, 8]. However, most existing studies have constructed static prediction models based on single or baseline PRO measurements, using information from only one time point to assess risk. Such approaches are unable to capture the dynamic changes in patients’ health status during follow-up, which may result in inaccurate risk estimation or reduced predictive performance [9].

With the increasing availability of longitudinal follow-up data, dynamic prediction models have gradually become an important research direction in chronic disease risk assessment. These models integrate longitudinally measured biomarkers or clinical indicators with time-to-event outcomes, enabling the continuous updating of individual risk predictions as new follow-up information becomes available [10]. Consequently, dynamic prediction approaches can improve both the accuracy and clinical applicability of risk prediction. In recent years, dynamic prediction models have been widely applied in fields such as oncology [11], cardiovascular diseases [12], and renal diseases [13]. However, in the COPD field, existing studies have primarily focused on objective indicators such as pulmonary function and inflammatory biomarkers, while relatively little attention has been paid to PRO data, which comprehensively reflect patients’ multidimensional health status. In particular, studies investigating dynamic risk prediction based on longitudinal PRO data remain limited.

From a methodological perspective, commonly used dynamic prediction approaches include the Joint Latent Class Model (JLCM) [14], Shared Random-Effects Model (SREM) [15], and Landmark model [11]. The SREM jointly models the longitudinal process and survival outcomes through shared random effects, allowing the association between individual-level longitudinal trajectories and event risk to be quantified [15]. The JLCM identifies latent subgroups within the population, thereby revealing heterogeneous risk patterns associated with different disease progression trajectories [16, 17]. the Landmark model updates prediction information at predefined landmark time points, offering advantages in modeling flexibility and relatively simple computation [18]. Although these three approaches differ in their theoretical assumptions, risk characterization mechanisms, and clinical interpretability, comparative applications of these models for dynamic prediction based on PRO data in COPD patients remain limited.

Therefore, using multicenter longitudinal PRO follow-up data from COPD patients after hospital discharge, this study constructed JLCM, SREM, and Landmark dynamic prediction models to dynamically estimate the risk of adverse outcomes, including readmission or death. The predictive performance of the three models was further compared to evaluate the application value of longitudinal PRO data in prognostic assessment for COPD. The findings are expected to provide a scientific basis for individualized risk management and precision follow-up strategies for patients with COPD after hospital discharge.

Methods

Study population

This multicenter study was conducted between December 2020 and April 2022 across five respiratory departments in Shanxi Province, China: the Second Hospital of Shanxi Medical University, Taiyuan People’s Hospital, Gujiao Central Hospital, Jincheng General Hospital, and Pianguan County People’s Hospital.

The inclusion criteria were as follows: (1) age ≥ 18 years; and (2) diagnosis of COPD according to the Global Initiative for Chronic Obstructive Lung Disease (GOLD) guidelines.

The exclusion criteria included: (1) cognitive or communication impairments (e.g., due to language or intellectual disability) that precluded the comprehension or completion of the study’s questionnaires; and (2) inability to provide informed consent.

During the study period, patients were regularly followed up via telephone. A small proportion of patients (approximately 4.97%) failed to complete part or all of the scheduled telephone follow-ups; therefore, a total of 344 patients who completed follow-up were included in the analysis.

This study was approved by the Ethics Committee of the Second Hospital of Shanxi Medical University Second Hospital (Ethics Approval No. 2022YX123) and was registered in the Chinese Clinical Trial Registry (Registration No. ChiCTR2200064900). Written informed consent was obtained from all participants prior to enrollment. The study was conducted in strict accordance with established ethical principles for medical research.

Study design

Data collection and outcome definition

In this study, the Chronic Obstructive Pulmonary Disease Patient-Reported Outcome Measure (COPD-PROM), independently developed by our research group, was used. Its complete development and validation process has been described in detail in previous studies [19]. The scale comprises 52 items across four domains: physiological, psychological, social, and treatment-related and encompasses 11 dimensions (detailed in Table 1), designed to comprehensively assess patients’ health status in terms of symptom experience, functional capacity, psychological well-being, and treatment-related perceptions.Items are rated using a five-point Likert scale reflecting the patient’s status over the previous two weeks, with scores ranging from 1 to 5. Positively worded items were scored according to the original responses, whereas negatively worded items were reverse-coded using the formula 6 minus the original score. The total score, calculated as the sum of all item scores, ranges from 52 to 260, with higher scores indicating better health-related quality of life (HRQOL).

Table 1.

Overview of PRO Instruments for Patients with COPD

Domain	Dimension	Item
Physiological domain(PHD)	Specific symptoms(SPE)	1a,2a,3a,4a,5a,6a,7a,8a,9a,10a,11a
	General symptoms(GEN)	12a,13a,14a,15a,16a
	Independence(IND)	17a,18a,19a,
Psychological domain(PSD)	Anxiety(ANX)	20a,21a,22a,23a,24a,25a,26a
	Depression(DEP)	27a,28a,29a,30a,31a,32a
Social domain(SOD)	Disease cognition(COG)	33, 34,35,
	Impact on social activities(LMP)	36a,37a,38a,39a,40a,
	Social support(SUP)	41,42,43
Therapeutic domain(THD)	Therapy adherence(TAD)	44,45
	Adverse drug reaction(ADR)	46a,47a
	Therapeutic satisfaction(SAT)	48,49,50,51,52

Note: ‘a’ denotes a reverse scoring entry

The COPD-PROM has undergone rigorous psychometric validation in prior studies. Confirmatory factor analysis demonstrated a goodness-of-fit index of 0.89, indicating strong structural validity. The split-half reliability of the total scale was 0.757, and Cronbach’s α was 0.923, reflecting excellent internal consistency and reliability. Furthermore, clinical sample evaluations indicated that the scale effectively discriminates between COPD patients and healthy individuals, demonstrating robust discriminative validity and practical applicability in clinical settings [20].

At hospital admission, the patient-reported outcome (PRO) scale was administered and baseline information was collected, including demographic characteristics (sex, age, marital status, and educational level), History of comorbid chronic diseases(e.g., hypertension, diabetes, cardiovascular disease, et al.), laboratory test results (including procalcitonin and C-reactive protein), and dyspnea severity as assessed by the modified Medical Research Council (mMRC) scale. Follow-up assessments were conducted according to a predefined schedule: at 3, 6, 9, and 12 months after discharge, followed by subsequent assessments every six months until the end of follow-up or occurrence of a study endpoint. At each follow-up, patient-reported outcomes (PROs) were collected using the COPD-PROM scale, generating longitudinal repeated-measures data to characterize the dynamic changes in patients’ health status over time. Due to missed visits or incomplete follow-up, the number of follow-up assessments varied across individuals, with a mean follow-up count of three per patient.

The endpoint of the composite study was defined as either (1) COPD-related rehospitalization due to acute exacerbations or (2) all-cause mortality occurring within three years of hospital discharge.Outcome assessment procedures were conducted uniformly across all participants regardless of sociodemographic characteristics. Rehospitalization events and mortality information were obtained through hospital records and scheduled follow-up assessments.

Data processing

Among the variables included in this study, no missing data were observed for categorical variables, whereas continuous variables exhibited a certain proportion of missing values, with missing rates ranging from 8.1% to 12.5%. For the patient-reported outcome (PRO) data, information was collected through telephone follow-up conducted by uniformly trained research personnel. Data entry was independently performed by two investigators using EpiData 3.1 software, followed by double-entry verification and consistency checks to minimize data entry errors and ensure data integrity. Under this data management procedure, no missing values were observed in the longitudinal PRO data; For baseline variables with missing data, variables with a missing rate exceeding 30% were excluded in accordance with previous studies. For variables with a missing rate below 30%, missing values were imputed using the missForest algorithm [21]. To visually present the extent of missing data and the changes in variable distributions before and after imputation, this study plotted the distribution of missing proportions and comparative distributions of data before and after imputation. The relevant results are provided in the Supplementary Materials (Supplementary Figure S1 ~ S2). Negatively worded items in the COPD-PROM were reverse-coded prior to score calculation. The total PRO score was computed as the sum of subdomain scores, with higher scores indicating a better health-related quality of life (HRQoL).

Model construction

In this study, the participants were randomly divided into a training set and a testing set at a ratio of 7:3. The joint latent class model (JLCM), shared random effects model (SREM), and landmark model were developed in the training set. Using an internal validation approach with an independent testing set, dynamic AUC and dynamic Brier scores at different time points were calculated in the testing set to comprehensively evaluate the predictive performance of each model and assess their generalizability to new samples.

For the longitudinal sub-model, with PRO scores as the continuous dependent variable, linear mixed-effects models including only a single fixed effect were first constructed for each baseline variable to perform univariable screening of potential predictors. Variables demonstrating statistical significance and clinical relevance were subsequently incorporated into a multivariable linear mixed-effects model, with age and sex adjusted as fixed effects, and random intercepts and random slopes for time included to capture inter-individual variability.For the survival submodel, an initial univariate Cox proportional hazards regression was performed to screen candidate variables. Variables with statistical significance and clinical importance were then entered into a multivariable Cox model using backward stepwise selection for final analysis.

JLCM

The Joint Latent Class Model (JLCM) consists of three components: a latent class model, a longitudinal submodel, and a survival submodel [9]. In the latent class model, it is assumed that the study population comprises G latent classes, and each individual belongs to one and only one class. The probability that individual i belongs to a specific class is represented by the discrete random variable . The probability that individual i belongs to class g can be expressed as follows:

1

Where denotes the covariates influencing latent class membership; represents the intercept for the g-th latent class; and denotes the class-specific parameter vector associated with covariates . The model assumes that each latent class has its own marker trajectory and event risk, which constitutes the core assumption of the JLCM framework.

The longitudinal submodel is specified using a linear mixed-effects model. The j-th repeated measurement for individual i is expressed as:

2

where represents the matrix of fixed-effect covariates shared across latent classes; denotes the corresponding vector of fixed-effect parameters; is the matrix of covariates associated with random effects; represents the individual-specific random-effects vector; and denotes the random error term, assumed to follow a normal distribution.

The survival submodel is formulated using a proportional hazards model, expressed as:

3

where denotes the class-specific baseline hazard function; represents the covariate vector; and is the corresponding parameter vector.

Model parameters are estimated using the maximum likelihood method, and the log-likelihood function is defined as:

4

where denotes the complete parameter vector of the JLCM with G latent classes; represents the probability of belonging to class g; is the probability density function of the longitudinal data for class g, assumed to follow a multivariate normal distribution; denotes the instantaneous hazard function; and represents the corresponding class-specific survival function.

In this study, hyperparameter tuning was performed for the JLCM. Three forms of baseline hazard functions were evaluated: the Weibull function, cubic splines, and the piecewise constant hazard function. Based on the optimal parameter settings, models with different numbers of latent classes (≥ 2)were fitted. Additionally, the baseline hazard functions across latent classes were specified as either class-specific (Specific) or proportional hazards (PH). Specifically, the Specific structure allows both the shape and magnitude of the baseline hazard functions to differ across latent classes, whereas the PH structure assumes identical hazard shapes with proportional scaling factors between classes. The optimal number of latent classes and the best-fitting baseline hazard specification were determined using log-likelihood (logLik), Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), sample-size adjusted BIC (SABIC), and entropy.

SREM

The Shared Random-Effects Model (SREM) consists of a linear mixed-effects model for the longitudinal process and a Cox proportional hazards model for the time-to-event outcome [15]. In this study, the dependent variable was the PRO score, which was repeatedly measured at multiple time points for each participant. The linear mixed-effects model is specified as follows:

5

6

where denotes the PRO score of the i-th patient at time t; represents the design matrix associated with the fixed effects β; β is the vector of fixed-effect parameters; is the design matrix associated with the random effects; denotes the subject-specific random-effects vector for patient i; and represents the residual error term, assumed to follow a normal distribution , capturing measurement error and serial correlation. The random effects follow and are assumed to be independent of the residual errors, that is, .

The Cox proportional hazards model is defined as:

7

where denotes the baseline hazard function; represents the covariate vector for patient i; and is the corresponding vector of regression coefficients, quantifying the effects of covariates on the risk of the event.

The longitudinal measurements and survival outcomes are linked through an association parameter, formulated as:

8

where represents the latent true longitudinal trajectory derived from the linear mixed-effects model; denotes baseline covariates; 𝛾 represents the regression coefficients of the covariates; and 𝛼 is the association parameter in the joint model, quantifying the influence of the longitudinal biomarker on the survival outcome.

Model parameters were estimated within a Bayesian framework using Markov chain Monte Carlo (MCMC) methods.

Landmark model

The Landmark modeling approach requires preprocessing of the follow-up data. The procedure is as follows: [22] first, 3, 6, 9, and 12 months after discharge were selected as a series of landmark time points. Based on the prediction objective, a dynamic prediction window was defined from each landmark time point to three years after discharge. At each landmark time point, only patients who had not yet experienced the adverse event were included to construct the corresponding landmark dataset. Subsequently, Cox proportional hazards models were fitted separately for each landmark dataset. The model can be expressed as:

9

where denotes the covariate values observed at the landmark time ; represents the corresponding regression coefficients; and is the baseline hazard function.

This approach is equivalent to fitting multiple independent Cox proportional hazards models, which requires estimation of a large number of parameters and may complicate model interpretation. Moreover, as the landmark time increases, the corresponding landmark datasets contain fewer remaining individuals, making the estimation of regression coefficients and baseline hazard functions more sensitive to limited sample sizes. Therefore, this approach is generally not recommended in practice. A more common strategy is to stack the landmark datasets to construct a super dataset. In this framework, a smooth function of the landmark time can be incorporated into the baseline hazard function to account for the updating effect of the landmark time point on the baseline risk:

10

In this study, for the survival sub-models based on the Cox proportional hazards model (including the SREM model and the Landmark model), the proportional hazards (PH) assumption was assessed for all covariates included in the models, and the overall PH assumption of the models was also evaluated. Schoenfeld residual tests indicated that the proportional hazards assumption was not violated (all P > 0.05). In addition, the global test of the model produced a result of GLOBAL = 10.308 (P = 0.17), indicating that the overall model satisfied the proportional hazards assumption. Therefore, the fundamental assumption of the Cox survival sub-models was considered to be met, supporting the validity of the model construction in this study.

A detailed comparison of the core assumptions, modeling mechanisms, interpretability, and clinical application scenarios of the three dynamic prediction models is presented in Supplementary Table S1.

Model evaluation and individual prediction

To evaluate the predictive performance of the three models at different time points, time-dependent area under the receiver operating characteristic curve (AUC) and dynamic Brier score curves were generated in the testing dataset. The AUC reflects the model’s discriminative ability to distinguish between individuals who experience the event and those who do not; higher values indicate better predictive performance [23]. The Brier score measures the discrepancy between predicted probabilities and observed outcomes, with lower values indicating greater predictive accuracy [24]. Additionally, individual prediction was conducted by randomly selecting a participant and plotting the trajectory of PROs alongside estimated survival probabilities at different time points, based on the optimal prediction model.

Statistical Analysis and Software Implementation

Continuous variables are expressed as and compared using two-sample independent t-tests. Categorical variables are presented as counts and percentages and compared using the test, with a significance threshold of α = 0.05. All statistical analyses and dynamic model constructions were performed using R version 4.4.2. Missing data imputation was conducted using the missForest package; JLCM were fitted using the lcmm package; SREM with JMbayes2; and Landmark models with the dynamicLM package.

Results

Baseline characteristics

This study included 344 patients with COPD, with a mean of three follow-up visits per patient. The mean age was 67.73, and 293 were male. The cohort was randomly divided into training and testing sets of 242 and 102, respectively. The groups’ baseline characteristics are summarized in Table 2. A comparison revealed no statistically significant baseline differences between the two sets (P > 0.05), indicating good balance and comparability. During follow-up, 111 patients experienced adverse outcomes.

Table 2.

Baseline Characteristics of the Training and Validation Cohorts

Variable	Total sample (n = 344)	Test set (n = 102)	Train set (n = 242)	P-value
Age (years)	67.73 ± 9.51	67.51 ± 10.06	67.82 ± 9.28	0.784
Sex
Male	293 (85.17%)	83 (81.37%)	210 (86.78%)	0.198
Female	51 (14.83%)	19 (18.63%)	32 (13.22%)
BMI(kg·m− 2)	22.54 ± 3.93	22.97 ± 3.67	22.35 ± 4.03	0.187
Marital Statusa				0.701
Unmarried	11 (3.20%)	3(2.94%)	8 (3.31%)
Married	311 (90.41%)	95 (93.14%)	216 (89.26%)
Divorced	2 (0.58%)	0 (0.00%)	2 (0.83%)
Widowed	20 (5.81%)	4 (3.92%)	16 (6.61%)
Occupationa				0.926
Farmer	144 (41.86%)	40 (39.22%)	104 (42.98%)
Worker	15 (4.36%)	5 (4.90%)	10 (4.13%)
Manager	5 (1.45%)	1 (0.98%)	4 (1.65%)
Business/Service	5 (1.45%)	1 (0.98%)	4 (1.65%)
Other	175 (50.87%)	55 (53.92%)	120 (49.59%)
Education Level				0.913
Primary School	220 (63.95%)	63(61.76%)	157 (64.88%)
Junior High School	64 (18.60%)	21 (20.59%)	43 (17.77%)
High School (including Vocational School)	45 (13.08%)	14 (13.73%)	31 (12.81%)
Bachelor’s Degree or Above	15 (4.36%)	4 (3.92%)	11 (4.55%)
Medical insurance type				0.981
Urban employee basic medical Insurance	150 (43.60%)	45(44.12%)	105 (43.39%)
Urban resident basic medical Insurance	131 (38.08%)	38 (37.25%)	93 (38.43%)
New rural cooperative medical Insurance	41 (11.92%)	13 (12.75%)	28 (11.57%)
Other	22 (6.40%)	6 (5.88%)	16 (6.61%)
smoking history	280 (81.40%)	80 (78.43%)	200 (82.64%)	0.359
Drinking history	149 (43.31%)	40 (39.22%)	109 (45.04%)	0.319
Family history	30 (8.72%)	10(9.80%)	20 (8.26%)	0.644
Past medical history	271 (78.78%)	82(80.39%)	189 (78.10%)	0.635
Procalcitonin (ng/ml), PCT	1.63 ± 3.84	1.39 ± 2.31	1.73 ± 4.33	0.456
C-reactive protein (mg/L)CRP	13.25 ± 10.64	11.54 ± 5.65	13.97 ± 12.01	0.052
mMRC scalea				0.067
Level 0	10 (2.91%)	5 (4.90%)	5 (2.07%)
Level 1	76 (22.09%)	18 (17.65%)	58 (23.97%)
Level 2	81 (23.55%)	30 (29.41%)	51 (21.07%)
Level 3	135 (39.24%)	33 (32.35%)	102 (42.15%)
Level 4	42 (12.21%)	16 (15.69%)	26 (10.74%)
Physiological domain	64.42 ± 12.33	65.42 ± 13.44	64 ± 11.83	0.329
Psychological domain	50.91 ± 8.42	51.59 ± 8.80	50.63 ± 8.26	0.335
Social domain	39.73 ± 5.11	40.22 ± 5.28	39.53 ± 5.04	0.256
Therapeutic domain	39.73 ± 5.25	39.84 ± 5.20	39.68 ± 5.28	0.794
PRO Total Score	194.80 ± 23.52	197.07 ± 25.47	193.84 ± 22.63	0.245

Note: ‘a’ indicates that Fisher’s exact test was used for analysis

Variable selection

The final set of fixed effects included in the longitudinal submodel comprised sex, age, type of health insurance, educational attainment, and modified Medical Research Council (mMRC) dyspnea grade. The survival submodel incorporated educational attainment, C-reactive protein (CRP), and baseline scores for both the physical and psychological domains. The regression coefficients and their 95% confidence intervals for all candidate variables during the variable selection process are provided in the Supplementary Materials (Supplementary Table S2 ~ S3).

Optimal hyperparameter selection for the JLCM

The fitting results of different JLCM models are shown in Table 3. A stepwise modeling strategy was adopted in this study. First, under the assumption of no latent classes (ng = 1), different baseline hazard function forms (Models 1 ~ 5) were compared to identify the optimal baseline hazard structure. On this basis, models with varying numbers of latent classes and hazard function specifications (Models 6 ~ 11) were further compared to determine the optimal latent class model.

Table 3.

Comparison of Model Fit among Different JLCM Specifications

Model	Number of latent classes	Baseline Hazard Function Type	Class-Specific Baseline Hazard Specification	loglik	AIC	BIC	SABIC	entropy	Proportion of individuals per Class (%)
1	1	Weibull		-3816.897	7693.794	7798.462	7703.368	1.000	100.000
2	1	Piecewise		-3807.538	7679.075	7790.721	7689.287	1.000	100.000
3	1	Splines		-3830.405	7730.810	7852.923	7741.979	1.000	100.000
4	1	3-equi-piecewise		-3816.982	7685.965	7776.677	7694.262	1.000	100.000
5	1	3-quant-piecewise		-3817.330	7686.660	7777.372	7694.957	1.000	100.000
6	2	3-equi-piecewise	PH	-3811.078	7684.155	7792.313	7694.048	0.577	29.752, 70.248
7	2	3-equi-piecewise	Specific	-3810.268	7684.535	7796.181	7694.747	0.595	29.339, 70.661
8	3	3-equi-piecewise	PH	-3804.421	7680.843	7806.444	7692.331	0.691	2.066, 40.496, 57.438
9	3	3-equi-piecewise	Specific	-3806.267	7688.533	7821.113	7700.660	0.677	39.669, 58.678, 1.653
10	4	3-equi-piecewise	PH	-3804.377	7690.755	7833.801	7703.838	0.556	16.529, 54.959, 2.480, 26.033
11	4	3-equi-piecewise	Specific	-3805.772	7699.543	7853.056	7713.584	0.612	21.488, 30.991, 47.107, 0.413

Note: loglik Log-likelihood value, AIC Akaike Information Criterion, BIC Bayesian Information Criterion, SABIC Sample-Size Adjusted Bayesian Information Criterion

During the baseline hazard function selection stage (Models 1 ~ 5), Models 1 ~ 3 compared the fitting performance of three baseline hazard functions under no latent classes, among which the Piecewise form showed a better fit, with the lowest AIC and BIC values. Based on this, Models 4 and 5 further fitted three equally spaced nodes (3-equi-piecewise) and three quantile-based nodes (3-quant-piecewise), respectively. The results indicated that the 3-equi-piecewise model achieved the best fit, with the smallest AIC and BIC values, and was therefore selected as the optimal baseline hazard function form.

After determining the baseline hazard function (Models 6–11), JLCM models with 2 to 4 latent classes were further fitted based on the 3-equi-piecewise specification, with both PH and Specific hazard function forms specified for the latent classes. The results showed that the model with two latent classes and a PH hazard function provided the best fit, with the lowest AIC value. At this point, the proportions of the two latent classes were 29.752% and 70.248%, respectively.

Model evaluation

Figure 1 illustrates the temporal trends of AUC values for the three dynamic prediction models when the landmark time points were set at 3, 6, 9, and 12 months. Overall, the SREM model consistently achieved the highest AUC values across all landmark time points, with most AUC values ranging from 0.75 to 0.90, indicating good discriminative ability for predicting adverse outcomes after discharge in patients with COPD. The Landmark model showed slightly lower AUC values (approximately 0.70–0.80), whereas the JLCM model demonstrated relatively lower AUC values (approximately 0.66–0.78). From a clinical perspective, an AUC greater than 0.70 is generally considered to indicate acceptable discrimination, while an AUC greater than 0.80 suggests good predictive performance. In the present study, the SREM model reached or approached 0.80 at most prediction time points, suggesting substantial potential for identifying COPD patients at high risk of readmission or death after discharge. In contrast, although the overall AUC values of the JLCM model were slightly lower, their temporal fluctuations were relatively small, indicating greater stability. This characteristic may be advantageous in long-term dynamic risk assessment during clinical follow-up.

Fig. 1.

Time-dependent AUCs of the three dynamic prediction models at different follow-up time points. Note: AUC: Area under the curve; JLCM: Joint Latent Class Model; SREM: Shared Random Effects Model; A Dynamic prediction results based on PRO data up to 3 months of follow-up; B Dynamic prediction results based on PRO data up to 6 months of follow-up; C Dynamic prediction results based on PRO data up to 9 months of follow-up; D Dynamic prediction results based on PRO data up to 12 months of follow-up

Figure 2 presents the trends of Brier scores for the three models across different landmark time points (3, 6, 9, and 12 months) as the prediction horizon increased. Overall, the SREM model exhibited lower Brier scores at most prediction time points, indicating smaller prediction errors and higher accuracy. In contrast, the Brier scores of the Landmark model gradually increased with longer prediction horizons, suggesting reduced stability for long-term predictions. Meanwhile, the Brier scores of the JLCM model showed a gradual decreasing trend, indicating that its predictive performance improved as additional follow-up information accumulated over time.

Fig. 2.

Time-dependent Brier scores of the three dynamic prediction models at different follow-up time points. Note: AUC: Area under the curve; JLCM: Joint Latent Class Model; SREM: Shared Random Effects Model; A Dynamic prediction results based on PRO data up to 3 months of follow-up; B Dynamic prediction results based on PRO data up to 6 months of follow-up; C Dynamic prediction results based on PRO data up to 9 months of follow-up; D Dynamic prediction results based on PRO data up to 12 months of follow-up

From a clinical application perspective, lower Brier scores indicate more accurate estimation of the probability of adverse outcomes at the individual level. The present findings suggest that the SREM model provides superior risk estimation for short- and medium-term predictions, whereas the JLCM model demonstrates relatively better stability for long-term follow-up predictions. This implies that different models may offer advantages in different clinical contexts: the SREM model may be more suitable for short-term risk identification and early intervention, while the JLCM model may be more appropriate for long-term dynamic risk monitoring.

In addition, the predictive performance of the models was evaluated across multiple landmark time points (3, 6, 9, and 12 months) and various prediction horizons, allowing the stability of model predictions to be assessed under different combinations of landmark times and prediction windows. This approach provides additional evidence supporting the robustness of the model results.

Interpretation of the optimal model

Based on the results of the time-dependent AUC curves and dynamic Brier score curves, the SREM model demonstrated superior predictive performance across different landmark time points and prediction horizons. This finding indicates that the model has a stronger discriminative ability to distinguish between patients who will and will not experience adverse outcomes in the future, while maintaining relatively low prediction error. These results suggest that joint modeling of longitudinal PRO data and survival outcomes allows more comprehensive utilization of follow-up information, thereby improving the accuracy of dynamic prediction of adverse outcomes in patients with COPD.

Figure 3 presents the relationship between the predicted probabilities and the observed probabilities generated by the SREM model at different landmark time points (3, 6, 9, and 12 months). As shown in the figure, most of the prediction curves are close to the 45° diagonal line, indicating good agreement between the predicted probabilities and the actual observed event probabilities. This result demonstrates that the model exhibits good calibration performance, suggesting that the SREM model maintains high predictive accuracy and stability across different follow-up time points. These findings further support the applicability of the SREM model for dynamic prediction of adverse outcomes in patients with COPD.

Fig. 3.

Calibration curves of the SREM model at different follow-up time points. Note: A Dynamic prediction results based on PRO data up to 3 months of follow-up; B Dynamic prediction results based on PRO data up to 6 months of follow-up; C Dynamic prediction results based on PRO data up to 9 months of follow-up; D Dynamic prediction results based on PRO data up to 12 months of follow-up

Table 4 presents the estimation results from the SREM model.In the longitudinal submodel, the mMRC dyspnea grade significantly influenced the trajectory of the PRO scores. Compared with grade 0, higher grades were associated with substantial reductions in PRO scores: grade 1 decreased by 15.064 points (P = 0.027), grade 2 by 15.568 points (P = 0.024), grade 3 by 25.796 points (P < 0.001), and grade 4 by 39.393 points (P < 0.001), suggesting that increased dyspnea severity is strongly correlated with poorer HRQoL, suggesting that dyspnea is an important determinant of quality of life in patients with COPD. Baseline characteristics such as age, sex, education level, and health insurance type were not statistically significant predictors of PRO trajectories (P > 0.05). The individual trajectories of PRO over time and their longitudinal trajectories across different outcome groups are presented in the Supplementary Materials (Supplementary Figure S3–4).

Table 4.

Parameter Estimates of the SREM Model

	b/HR	95%CI	P
Longitudinal submodel
Intercept	224.243	202.967 ~ 245.465	< 0.001
Age (years)	-0.006	-0.254 ~ 0.244	0.962
Sex(reference: female)	-1.106	-7.869 ~ 5.633	0.744
Education level(reference: primary school)
Junior High School	0.118	-5.857 ~ 6.14	0.976
High School (including Vocational School)	-0.374	-7.359 ~ 6.478	0.914
Bachelor’s Degree or Above	6.81	-4.341 ~ 17.881	0.227
Medical insurance type(reference: Urban employee basic medical Insurance)
Urban resident basic medical Insurance	-3.978	-9.248 ~ 1.43	0.149
New rural cooperative Medical insurance	-3.481	-10.989 ~ 4.148	0.362
Other	-1.971	-11.543 ~ 7.657	0.686
MMRC scale(reference: Level 0)
Level 1	-15.064	-29.31~-1.922	0.027
Level 2	-15.568	-30.179~-1.995	0.024
Level 3	-25.796	-40.391~-12.669	< 0.001
Level 4	-39.393	-54.843~-25.203	< 0.001
Survival submodel
Education level(reference: Primary School)
Junior high school	1.219	0.526 ~ 2.649	0.625
High school (including Vocational school)	0.273	0.068 ~ 0.850	0.021
Bachelor’s degree or above	0.811	0.124 ~ 3.377	0.867
CRP	1.034	1.015 ~ 1.050	0.001
Physiological domain	1.002	0.971 ~ 1.035	0.938
Psychological domain	0.972	0.938 ~ 1.009	0.141
Association parameter	0.957	0.933 ~ 0.980	< 0.001

Bold values indicate statistically significant differences (P < 0.05)

MMRC Modified Medical Research Council, CRP C-reactive protein

In the survival submodel, the association parameter for PRO scores was statistically significant (P < 0.001), indicating that for each unit increase in the PRO score, the risk of adverse outcomes decreased by 4.3% (HR = 0.957, 95% CI: 0.933–0.980). This finding further supports that incorporating patient-reported outcome measures into dynamic prediction models can improve the accuracy of risk assessment for adverse outcomes in COPD patients. Additionally, each one-unit increase in baseline PCT was associated with a 28.3% reduction in risk (HR = 0.717, 95% CI: 0.564–0.890), whereas each unit increase in baseline CRP corresponded to a 3.4% increase in risk (HR = 1.034, 95% CI: 1.015–1.050). Educational attainment also had a partial influence on risk: patients with a high school education had significantly reduced risk compared to those with primary education (HR = 0.273, 95% CI: 0.068–0.850), whereas no statistically significant differences were observed for those with junior high or undergraduate education.

Individualized prediction

Based on the SREM, we conducted an individualized dynamic risk prediction for a randomly selected COPD patient. This patient is an 80-year-old male with primary school education; he is covered by the Urban Employee Basic Medical Insurance scheme. At the baseline, his CRP level was 12.995 mg/L, and his mMRC dyspnea grade was 1. His baseline PRO score was 196. He has been followed for 12 months without experiencing any adverse events. Using longitudinal data from the previous five follow-up visits, we projected his survival probability over the subsequent two years.The specific situation is shown in Fig. 4.Overall, the PRO scores of the patient showed a slight upward trend during follow-up, while the predicted survival probability showed a slight decline over time, although it remained above 80% throughout the observation period. These findings suggest that the patient had a relatively high probability of survival over the subsequent two years, with HRQOL remaining relatively stable and a low short-term risk of adverse outcomes. This result demonstrates that dynamic prediction based on joint modeling can utilize longitudinal follow-up information to provide individualized risk assessment, thereby offering valuable guidance for clinical follow-up management and early intervention strategies.

Fig. 4.

Individualized dynamic prediction of adverse outcomes based on the SREM model

Discussion

In this study, three dynamic prediction models—Joint Latent Class Model (JLCM), Shared Random-Effects Model (SREM), and Landmark model—were constructed to estimate the time-varying risk of adverse outcomes after discharge in patients with COPD, and their predictive performance was systematically compared. In addition, the study explored the influence of longitudinal follow-up data derived from the COPD-PRO scale and baseline characteristics on the risk of adverse outcomes. The results indicated that the SREM model demonstrated the best predictive performance, and that longitudinal changes in PRO scores, educational level, procalcitonin (PCT), and C-reactive protein (CRP) were significantly associated with adverse outcomes. Compared with conventional prediction models based solely on baseline information, the present study integrated longitudinal PRO follow-up data, enabling dynamic updating of individual risk estimates. This approach facilitates earlier identification of high-risk patients and provides a useful reference for post-discharge follow-up management and individualized intervention strategies in COPD patients.

Comparative performance of the dynamic prediction models

Although the JLCM incorporates latent class submodels in its design, allowing the capture of heterogeneity across patient subgroups, the SREM outperformed the JLCM in the systematic model evaluation. This result may be attributed to several factors. First, it may be related to the study’s limited sample size. Roustaei et al. demonstrated that the SREM tends to outperform the JLCM under small-sample conditions, which is consistent with our findings [25]. Second, the relatively short follow-up period may have influenced the results. Stone et al. pointed out that the JLCM’s long-term predictive accuracy is limited when longitudinal data spans are short, and that the model is highly sensitive to slight changes during specification, which can affect the determination of latent class numbers and consequently reduce predictive performance—again, consistent with our observations [26]. Third, the difference may be related to model adaptability. In this study, the SREM used Bayesian estimation for parameter inference, whereas the JLCM applied maximum likelihood estimation; [27] prior research suggests that Bayesian methods offer superior flexibility and adaptability compared to maximum likelihood approaches [28, 29].

In addition, the present study found that the JLCM model exhibited greater stability than the Landmark model, which is consistent with findings from previous studies [30]. However, Li et al. reported that the relative performance of different dynamic prediction approaches largely depends on the data structure and study design, and no single method consistently outperforms others in terms of predictive accuracy [10]. Therefore, in practical research settings, the selection of an appropriate dynamic prediction method should be guided by the characteristics of the available data and the specific research objectives.

Determinants of adverse outcomes following discharge

In the longitudinal submodel of the SREM, a negative association between mMRC grade and PRO scores was observed, which is consistent with previous studies [30]. This finding suggests that the modified Medical Research Council (mMRC) dyspnea scale can serve as an important indicator of symptom severity and disease burden in patients with COPD. In the survival submodel, elevated C-reactive protein (CRP) levels were identified as a risk factor for adverse outcomes. A study by Jens et al. reported that higher CRP levels were associated with an increased frequency of adverse outcomes in COPD patients (HR = 1.86, 95% CI: 1.29–2.67), which is consistent with the findings of the present study [31]. Other studies have also demonstrated that higher baseline CRP levels are significantly associated with increased late mortality in patients with COPD. As an important biomarker reflecting systemic inflammatory responses, CRP plays a key role in the clinical diagnosis, assessment of disease severity, and monitoring of treatment response in COPD, and is also widely regarded as a valuable indicator for prognostic risk assessment. Elevated CRP levels generally indicate enhanced systemic inflammation, which may promote airway inflammatory responses and lung tissue damage, thereby accelerating disease progression and increasing the risk of adverse outcomes [32]. Previous studies have shown that lower educational attainment significantly increases the risk of hospitalization among COPD patients and is positively associated with disease severity and all-cause mortality (HR = 0.992, 95% CI: 0.989–0.995). Additionally, PRO scores were inversely associated with the risk of adverse COPD outcomes. Previous research has demonstrated that when patients report better health status, the subsequent risk of adverse events is significantly reduced,²⁸ again in line with our results. These findings underscore the importance of multifaceted interventions—encompassing physiological, psychological, therapeutic, and social dimensions—to improve prognosis in patients with COPD.

Strengths and limitations

From a clinical application perspective, the dynamic prediction model developed in this study integrates longitudinal PRO data with survival information, enabling continuous updating of individual risk probabilities during follow-up, thereby allowing clinicians to dynamically re-stratify patients at different time points. Compared with traditional prediction models based on administrative data or baseline information (such as claim-based models and the PRECISE model), the dynamic prediction approach adopted in this study incorporates longitudinal PRO data and survival information. This approach facilitates timely identification of changes in risk, allowing for shortened follow-up intervals, intensified monitoring, and earlier implementation of interventions such as pulmonary rehabilitation, health education, and medication optimization for high-risk patients, while follow-up intensity may be appropriately reduced for low-risk patients, thereby optimizing healthcare resource allocation and improving the efficiency of chronic disease management. In addition, PRO data are derived from patient self-reports and can directly reflect symptom perception, psychological status, and quality of life. These data can be continuously collected via telephone follow-up or digital platforms, demonstrating good feasibility and potential for wider application. The results indicate that PRO scores, inflammatory markers (such as CRP), and educational level are closely associated with the risk of adverse outcomes, suggesting that both subjective and objective indicators should be integrated for multidimensional assessment in clinical practice. Incorporating PROs into a dynamic prediction framework not only contributes to a more comprehensive characterization of disease impact on patients, but also promotes physician–patient communication and participation in treatment decision-making, thereby improving patient adherence and long-term prognosis. However, limitations exist. First, In this study, hospital readmission and all-cause mortality were combined as a composite adverse outcome to reflect the overall risk of clinically significant events after discharge in patients with COPD. Under the “time to first adverse event” framework, these events were treated as a single endpoint; therefore, traditional competing risk issues mainly arise when readmission and death are analyzed as separate outcomes. Future studies with larger samples may further examine these outcomes separately using competing risk or multi-state models. Second, Some potential confounding factors were not included in the analysis. This study did not incorporate certain indicators closely related to adverse outcomes in COPD, such as key biomarkers including FEV1 and NT-proBNP. Although history of chronic diseases was included to reflect overall comorbidity status, specific comorbid conditions (such as heart failure and chronic kidney disease) were not further categorized, and medication information during follow-up was not systematically collected. These factors may influence adverse outcomes, and their absence may, to some extent, affect the precision of model estimation. Future studies could further integrate multidimensional clinical indicators and medication data to improve the interpretability and predictive performance of the models. Third, internal validation was performed using a testing dataset, and model performance was evaluated using time-dependent AUC and Brier scores, which demonstrated good predictive performance of the three models across different time points. However, due to the lack of independent external validation datasets, the generalizability of the models requires further verification in future studies. In addition, the present study primarily evaluated model performance from a statistical perspective. Future research could further incorporate Decision Curve Analysis (DCA) and clinically relevant risk thresholds to assess the practical value of these models in clinical decision-making.

Conclusion

In summary, this study constructed and compared three dynamic prediction models—JLCM, SREM, and Landmark models—to assess the time-varying risk of adverse outcomes after discharge in patients with COPD. The results demonstrated that, under the conditions of the present dataset, the SREM model showed superior predictive performance. By integrating longitudinal PRO follow-up data with survival outcome information, this model enables dynamic prediction of adverse outcome risk in COPD patients. The findings suggest that routinely incorporating patient-reported outcomes into long-term post-discharge follow-up and applying dynamic prediction models to update risk assessments in real time can facilitate earlier identification of high-risk individuals, optimize stratified management strategies, and enable the implementation of precise interventions, ultimately providing scientific evidence and methodological support for improving long-term prognosis in patients with COPD.

Abbreviations

AUC

Area under the receiver operating characteristic curve

COPD

Chronic obstructive pulmonary disease

COPD-PROM

Chronic obstructive pulmonary disease patient-reported outcome Measure

CRP

C-reactive protein

FEV₁

Forced expiratory volume in one second

GOLD

Global Initiative for Chronic Obstructive Lung Disease

HRQoL

Health-related quality of life

JLCM

Joint Latent Class Model

mMRC

Modified Medical Research Council

NT-proBNP

N-terminal pro-brain natriuretic peptide

PROs

Patient-reported outcomes

SREM

Shared Random Effects Model

Authors’ contributions

Yanbo Zhang and Hui Zhao conceived and designed the study. Jie Jin, Hangzhi He, Xiaojuan Hu, Shuping Xie, Xiangli Lu were responsible for data collection, organization, analysis, and interpretation. Jie Jin drafted the initial manuscript. All authors participated in the review and revision of the manuscript and read and approved the final version.

Funding

This research was supported by the National Natural Science Foundation of China (Grant No. 82173631);Higher education ten billion project of shanxi provincial department of education(BY-ZB-2024007).

Data availability

The datasets used and analysed during the current study are available from the corresponding author on reasonable request.

Declarations

Ethics approval and consent to participate

The study was approved by the Ethics Committee of the Second Hospital of Shanxi Medical University (No. 2022YX123). Written informed consent was obtained from all participants.

Consent for publication

All authors have approved the manuscript for publication.

Competing interests

The authors declare no competing interests.