Evaluating the application of dynamic prediction models in oncological prognostic studies with repeated measurement predictors

Abstract

Recent cancer prognosis research emphasizes longitudinal data’s importance for survival prediction, yet its analysis challenges researchers, often leading to oversimplified dual-timepoint comparisons (e.g., pre- vs. post-treatment). To meet precision oncology needs, this study evaluated dynamic prediction model (DPM) applications by a cross-sectional analysis of published studies. A comprehensive search of PubMed and Web of Science identified 6,549 records, from which 174 DPMs in 165 studies were analyzed. These studies covered 19 cancers and showed a rising trend in DPM usage (trend test, p < 0.001). Notably, 58.6% of studies used only one dynamic predictor. Seven DPM categories were identified: two-stage models (most common at 32.2%), joint models (28.2%), time-dependent covariate models (12.6%), multi-state models (10.3%), landmark Cox models (8.6%), artificial intelligence (4.6%), and others (3.4%). DPM distribution significantly shifted over 5 years (Chi-square test, p < 0.001), trending towards joint models and AI. We described and compared these DPMs across multiple dimensions, including principles, advantages and limitations, and clinical application scenarios. Joint models, integrating longitudinal and survival data, and artificial intelligence, extracting high-dimensional features, offer promising precision prognosis pathways. Future research should prioritize developing DPMs capable of handling high-dimensional data from smaller samples to improve treatment monitoring and prognosis.

Introduction

Clinical prediction models are well-established techniques widely used in clinical research¹. Prognostic prediction models, for instance, are utilized for stratifying high-risk populations, predicting patient survival outcomes, and identifying individuals who would benefit from specific treatments^1,2. In the field of cancer research, there are numerous clinical prognostic prediction models³. This is due to the nature of cancer treatments, where patients require follow-up assessments to evaluate endpoints, with particular focus on treatment response, patient prognosis, and the discovery of important biomarkers^3,4. Furthermore, with the recent advancements in immunotherapy, there is increasing interest in predicting treatment responses from an early treatment phase^5–7. Investigators are now analyzing the relationship between dynamic biomarkers measured at different time points during treatment cycles and follow up the outcomes in clinical trials to better understand the efficacy of immunotherapy⁸.

However, cancer is a dynamic and evolving system, traditional prognostic prediction models often rely on static characteristics for long-term predictions, which may struggle to achieve accurate results^9–12. During the continuous monitoring and treatment process, important covariates such as tumor size, imaging features may change, producing time-varying effects on prognosis, and important intermediate events may have taken place, such as locoregional recurrence (LRR) and distant metastasis (DM), which may alter a patient’s prognosis^7,13. Morin et al leveraged over a decade of cancer electronic health records (EHRs) to build a high-end platform that enables dynamic, individualized prognosis prediction using these high-quality data¹⁴. As real-world follow-up data continuously accumulate, updating a patient’s clinical characteristics and status, their prognosis should be re-evaluated using the latest available information. Of course, we shouldn’t solely rely on the latest data while ignoring the influence of the past. Thus, integrating past and present data to determine the optimal method for future predictions is ideal, aligning better with physicians’ clinical reasoning and actual practice. For example, Fontein et al. developed a prediction model for the 5-year dynamic survival of early-stage breast cancer patients at specific time points after initiating adjuvant endocrine therapy¹⁵. The model incorporated not only patient and tumor characteristics, such as age at diagnosis, estrogen receptor status, and tumor status, but also dynamic factors that influenced prognosis within 3 years after starting endocrine therapy, including treatment adherence and the occurrence of locoregional recurrence or distant metastasis, as well as time-dependent covariates like high-risk nodal stage (N2/3) and HER2-positive status. The model’s feature of allowing continuous revision of the patient’s residual mortality risk can help motivate patients to continue treatment, improve adherence, and ultimately enhance survival. In a study van’t Land et al. focused on the prognostic value of changes in the SIII during treatment with FOLFIRINOX chemotherapy alone, or FOLFIRINOX followed by stereotactic body radiotherapy, in patients with advanced pancreatic cancer¹⁶. They found that it was only necessary to collect the SIII values at three time points during the treatment. Through the model, they could determine that for every one-unit increase in log of SIII, the hazard ratio for death increases by 60.4%.

Dynamic prediction models (DPMs) can link dynamic changes in features obtained during patients’ follow-up to disease prognosis⁹. Currently, DPM is a highly active area in clinical prediction methodology research, providing excellent theoretical support for clinical applications^17,18. A review conducted in 2020, focusing on constructing clinical prediction models using repeated measurement variables, summarized several DPMs from methodological studies, including time-dependent covariate modeling, generalized estimating equations, landmark analysis, two-stage modeling, joint modeling, trajectory classification, and machine learning¹⁷. From a theoretical perspective, DPMs can reduce parameter estimation bias and improve model construction efficiency by combining the dynamic changes in patient features with prognosis in a joint modeling framework, compared to static models that using fixed, baseline input data typically collected at a single point⁹. Studies have compared static versus dynamic approaches in chronic diseases like type 2 diabetes and found that dynamic models continuously improve predictive performance as follow-up data are sequentially incorporated¹⁹. In addition, by constructing DPMs, we can continually update overall survival (OS), say dynamic overall survival (DOS) probability at different prediction timepoints during follow-up¹⁴.

Despite several studies having evaluated DPMs in methodological literatures^17,20–22 and clinical studies^23–27, a comprehensive understanding of the application scenarios and efficiencies of these methods within specific clinical fields in the rapidly evolving oncological contexts remains elusive, particularly with regarding to time-varying predictors (e.g., longitudinal biomarkers) and intermediate clinical events (e.g., metastasis)^3,5. Hence, we focus on oncological prognostic studies that employ DPMs with time-repeated measurement predictors and/or intermediate events. We analyze the types of methods used in those clinical studies and examine the current adaptability of methodological approaches in practical clinical settings. Our key contribution lies in providing actionable insights to optimize selection and application of DPMs for specific clinical scenarios (e.g., immunotherapy response monitoring, dynamic prediction of patient prognosis, postoperative recurrence monitoring), enhance prediction robustness, and ultimately advance precision oncology. By bridging the gap between theoretical methodology and clinical deployment, our study aims to facilitate the more widespread use of dynamic prediction and achieve more robust results in future research endeavors. This is crucial for the effective monitoring of treatment responses and dynamic prediction of patient prognosis.

Results

General characteristics

We screened 6549 records through PubMed and Web of Science, published up to 31 Dec 2023, and also reviewed the citations of relevant screened records. Our final analysis included 174 DPMs from 165 articles (Fig. 1). A detailed list of these articles was in Supplementary Table S3. The studies spanned 1991 to 2023, with an increasing annual publication trend (Fig. 2A) (trend test p < 0.001). They covered various diseases, with breast cancer, prostate cancer, and lung cancer as the top three most studied (Fig. 2B). Table 1 outlined the studies’ general characteristics. Most of the data sources were hospital-based (61.8%), single-centered (55.5%), and retrospective (87.3%), but there were 32.4% using data from clinical trials. The median number of patients analyzed at baseline was 472 (IQR: 199, 1591), ranging from 13 to 175,000. Prognostic outcomes mainly included overall survival (74.1%), other time-to-event endpoints (35.6%, e.g., recurrence-free survival, disease-free survival, progression-free survival, and cause-specific death), and binary endpoints (6.3%, e.g., treatment response, disease recurrence, and death). The studies included patients most treated with surgical resection (16.7%), chemotherapy (10.9%), and immunotherapy (9.8%) as a single treatment, while 28.2% included patients with more than one treatment.

Fig. 1.

Flowchart of the study.

Fig. 2. Application of dynamic prediction approaches in the included oncological prognostic studies.

A Number of models presented by year. B Number of models orders by types of cancers. C The distribution of the seven categories of dynamic prediction approaches. D The change of distribution of these dynamic prediction approaches between pre-2019 and 2019–2023 using percentage bar charts.

Table 1.

General characteristics of the prognostic oncological studies with repeated measurement predictors and/or intermediate events

Characteristics	Levels	Total (N = 174)
Data source	Hospital	108 (62.1)
	Clinical triala	56 (32.2)
	Register database	10 (5.7)
Prospective study	Yes	22 (12.6)
	No	152 (87.4)
Multicenter	Yes	77 (44.3)
	No	97 (55.7)
Treatmentb	Surgical resection	29 (16.7)
	Chemotherapy	19 (10.9)
	Immunotherapy	17 (9.8)
	Radiotherapy	14 (8.0)
	Endocrine therapy	13 (7.5)
	Targeted therapy	8 (4.6)
	Other same type of treatment	25 (14.4)
	Different treatments	49 (28.2)
Number of patients analyzed at baseline	Median (Interquartile range)	472 (199,1591)
	Range [min, max]	[13,175000]
	[1–100)	10 (5.7)
	[100–500)	79 (45.4)
	[500–1000)	29 (16.7)
	≥1000	56 (32.2)
Types of primary outcome (multiple choices)
Overall survival	Yes	129 (74.1)
Other time-to-event outcome	Yes	62 (35.6)
Binary outcome (e.g., response, recurrence, death)	Yes	11 (6.3)
Characteristics of dynamic predictors
Number of dynamic predictors	Median (Interquartile range)	1 (1,2)
	1	102 (58.6)
	2	33 (19.0)
	3	18 (10.3)
	>3	21 (12.1)
Multiple dynamic predictors in a single model	Yes	56 (32.2)
	No	118 (67.8)
Types of dynamic predictors
Continuous variables	Yes	111 (63.8)
Categorical variables	Yes	74 (42.5)
Top five most analyzed dynamic predictors
Intermediate eventc	Yes	42 (24.1)
Tumor size-based metric	Yes	30 (17.2)
Prostate-specific antigen	Yes	18 (10.3)
Score obtained from scaled	Yes	15 (8.6)
Circulating free DNA	Yes	13 (7.5)
Reporting of dynamic predictors
Reporting of the number of time pointse	Yes	128 (73.6)
	No	46 (26.4)
Reporting of the sample size at each time point	Yes	74 (42.5)
	No	100 (57.5)
Reporting of time interval for repeated measurement	Yes	130 (74.7)
	No	44 (25.3)
Reporting of follow up time for prognostic outcome	Yes	132 (75.9)
	No	42 (24.1)
Reporting of missing data	Yes	36 (20.7)
	No	138 (79.3)
Reporting of handling of missing data	Yes	26 (14.9)
	No	148 (85.1)

^aData from finished clinical trials were reused to construct dynamic prediction models. ^bTreatment here refers to non-static variables.

^cIn the included studies, intermediate events mainly included local recurrence, distant metastasis, response, tumor burden change, cured, and others (hypothyroidism, clonal evolution, discharge alive, admission after hospital discharge).

^dScore obtained from scale refers to the score derived from a specific measurement tool or questionnaire, such as a quality-of-life score, depression score, or fatigue score. ^eThe metric was considered reported if a study provided either the median or the maximum number of repeated-measured time points in its results.

Characteristics of dynamic predictors

The median number of DPs was 1 (IQR: 1,2), with most studies (58.6%) assessing a single DP, 19.0% evaluating two, and 10.3% having three (Table 1). Five studies (2.9%) utilized high-dimensional predictors like CT/MRI images or multimodal data across multiple time points. One third of studies (32.2%) handled multiple longitudinal predictors in a single model, with both continuous (63.8%) and categorical (42.5%) variables. The top five most used DPs included intermediate event (24.1%), tumor size-based metric (17.2%), prostate-specific antigen (10.3%), score obtained from scale (8.6%), and circulating free DNA (7.5%). Local-regional recurrence and distant metastasis were the two most commonly used intermediate events. We found new DPs like scores estimated from machine learning models and circulating free DNA have emerged post-2012 and post-2019, respectively (Supplementary Table S3). The reporting challenges of repeated measurements included the number of time points, varying sample size at each time point, and handling missing data. While 73.6% of studies reported time points, only 42.5% detailed sample sizes at each time point, and 20.7% addressed missing data, with just 14.9% describing methods for dealing with it.

Clinical scenarios and the necessity of using dynamic prediction models

Table 2 indicated that DPMs have been applied across various diseases, including 19 cancer types and pan-cancer, with representative cases provided for each cancer. Supplementary Table S4 showed the differences of DPs, prognostic outcomes, and study purposes among different diseases. In these studies, breast cancer commonly evaluated intermediate events (16/29), prostate cancer focused on prostate-specific antigen (18/22), and lung cancer examined circulating free DNA (6/21) and tumor size metrics (6/21). Statistically significant differences were found in the types of variables used (both continuous and categorical, p = 0.048 and p < 0.001) among the different diseases.

Table 2.

Clinical scenarios and necessity of using dynamic prediction approaches with representative cases

Variables	N (%)	Representative cases
Disease area
Breast cancer	29 (16.7)	16/29 analyzed the impact of intervening events (e.g., recurrence) on prognosis; 11/29 constructed dynamic prognostic models, among which one employed longitudinal NLP to process unstructured medical reports as multi-nomics data.
Prostate cancer	22 (12.6)	18/22 explored the impact of dynamic PSA on prognosis in various types of prostate cancer; 14/22 constructed dynamic prognostic models; no study considered intervening events.
Lung cancer	21 (12.1)	6/21 analyzed the impact of post-treatment cfDNA monitoring (e.g., negative and positive) on prognosis; 6/21 explored the effect of changing tumor size on prognosis using different methods.
Pan-cancer	17 (9.8)	6/17 explored the impact of changing tumor size on prognosis using various methods; 4/17 utilized scale scores as dynamic predictive values; 10/17 constructed dynamic prognostic models.
Colorectal cancer	15 (8.6)	One combined longitudinal MRI images to establish a multitask DL model to predict treatment response; One used longitudinal CT images to predict the ability of early treatment response with DL; other longitudinal indicators were comparatively diverse.
Liver cancer	12 (6.9)	One used time-series clinical variables to dynamically prognosticating patients’ survival paths.
Blood cancer	11 (6.3)	One analyzed the correlation between dynamic MRD and PFS.
Bone and soft tissue cancer	8 (4.6)	5/8 utilized landmark Cox models to assess the correlation between intervening events (e.g., LRR, DM) and OS.
Head and neck cancer	8 (4.6)	One constructed a prognostic model based on longitudinal cfEBV DNA load post-treatment, employing joint model to make risk stratification, determining follow-up schedules, and selecting candidates for adjuvant therapy.
Pancreatic cancer	5 (2.9)	One assessed whether longitudinal monitoring of SIII had prognostic value for OS.
Melanoma	4 (2.3)	One analyzed the dynamic changes of circulating soluble PD-1 and PD-L1 and their association with OS.
Ovarian cancer	4 (2.3)	All used joint model finding longitudinal variable CA125 was associated with prognosis in patients with different types of ovarian cancer.
Urothelial cancer	4 (2.3)	All focused on the correlation between longitudinal changes in tumor size and prognosis.
Brain cancer	3 (1.7)	2/3 included tumor volume measurement as a longitudinal variable, discovering its value and temporal patterns in predicting prognosis.
Gastric cancer	3 (1.7)	2/3 modeled recurrence as an intervening event in multi-state model, which could help identify effective factors affecting death.
Childhood cancer	2 (1.1)	One used a 10-year childhood cancer survivors’ cohort to identify three trajectory groups to represent temporal diagnostic pattern and compared the late mortality among these groups.
Esophageal cancer	2 (1.1)	One analyzed longitudinal health-related quality of life and time-to-event endpoint using joint models assuming different (e.g., linear or spline-based) trajectories.
Renal cancer	2 (1.1)	One developed a dynamic prognostic model for kidney renal clear cell carcinoma patients by combining clinical and genetic scores generated by prediction models.
Pleural mesothelioma	1 (0.6)	The study treated linear thickness, disease volume, and normalized lung volume as time-dependent variables and evaluated their associations with overall survival.
Thyroid cancer	1 (0.6)	The study developed a model to estimate the effects of long-term dosing with motesanib and survival, incorporating tumor size at different time points. No dynamic study was found after 2010.
Study purposes (Multiple choices)
To evaluate association and/or prognostic value	122 (70.1)	The earliest study purpose. In 1991, one used an intermediate event (i.e., ipsilateral breast tumor recurrence) as a time-dependent covariate to determine whether it was an important predictor of DDFS in patients with breast cancer after lumpectomy.
To construct prognostic prediction model	80 (46.0)	Various dynamic prediction approaches could be utilized. As early as 2005, one constructed a joint model to incorporate post-treatment follow-up PSA and clinical recurrence and to make individualized prediction.
To study disease transition	17 (9.8)	16/17 used multi-state model and 1/17 used joint model. As early as 1999, one investigated transitions of breast cancer disease, including the first tumor, LRR, DM, or death using a multi-state model, which allowed to study the effect of covariates for each transition, considering patients’ history.
To select significant factors	13 (7.5)	One evaluated the prognostic impact of the initial status and trajectories of longitudinal muscle and BMI values as a prognostic factor on OS in patients with CRC using both Cox model with summary statistics and two-stage Cox model.
To determine surrogate endpoints or biomarkers	13 (7.5)	One assessed time to nadir and depth of nadir as surrogates for OS in metastatic CRC using joint models.
To provide personalized treatment strategies	6 (3.4)	One developed a model for predicting the risk of Gleason upgrading in patients with prostate cancer on active surveillance and using the predicted risks to create risk-based personalized biopsy schedules as an alternative to one-size-fits-all schedules.
Necessity of using dynamic prediction approaches
A1-Making better prediction	77 (44.2)	All AI studies incorporating dynamic predictors were to make better prediction. One developed an AI framework integrating longitudinal electronic health records with real-world data to enable continuous pan-cancer prognostication.
A2-Investigating correlation	73 (42.0)	Various methods could be used to investigate the relationship between dynamic predictors and prognosis. Recently, one evaluated predictive value of the dynamic ctDNA during chemoradiotherapy with clinical outcomes for locally advanced NSCLC patients.
A3-Including intervening events	16 (9.2)	One employed a semi-Markov multi-state model for the simultaneous analysis of various endpoints (i.e., LRR, DM) describing the course of breast cancer.
A4-Identifying risk factors	8 (4.6)	One assessed the trajectories of CEA, CA19-9, and CA125 within 3 years after surgery, and evaluated the impact of these three tumor markers jointly on CRC outcomes in terms of preoperative levels and longitudinal trajectories.

NLP natural language processing, PSA prostate-specific antigen, cfDNA cell-free DNA, ctDNA circulating tumor DNA, cfEBV DNA circulating cell-free Epstein-Barr virus DNA, MRD minimum residual disease, PFS progression-free survival, OS overall survival, LRR local regional recurrence, DM distant metastasis, DDFS distant-disease-free survival, SLD sum of the longest diameters, NLR neutrophil-to-lymphocyte ratio, NSCLC Non-Small Cell Lung Cancer, BMI body mass index, AI artificial intelligence, CEA Carcinoembryonic antigen, CA19-9 carbohydrate antigen 19-9, CA125 carbohydrate antigen 125, CRC colorectal cancer.

These studies served six research purposes, with the primary goal being to assess the correlation of DPs and prognosis (70.1%), followed by developing prognostic models with longitudinal variables (46.0%) (Table 2). Some studies had multiple objectives. The use of dynamic prediction was necessary for various reasons: 44.2% of studies used DPs to build models for more accurate prognosis, such as predicting dynamic 5-year survival rates with accumulated data. Next, 42.0% established correlations between longitudinal indicators and prognosis, using easily measurable clinical factors like prostate-specific antigen, alpha-fetoprotein, or hemoglobin, and found significant prognostic associations. A smaller percentage, 9.2%, analyzed the prognostic impact of intermediate events, such as changes in 5-year survival before and after occurrence of local recurrence. Lastly, 4.6% aimed to identify longitudinal risk factors from DPs. The variations in the number (p < 0.001) and types (both p < 0.001) of repeated measurement predictors investigated, other time-to-event outcomes (p = 0.021), study purposes (p < 0.001), source of method (p < 0.001) were noted across the different necessities for DPMs (Supplementary Table S5).

Types of dynamic prediction models

We identified and detailed seven categories of DPMs from the included studies in Table 3, presented in the order of their initial emergence: TDCM (12.7%), TSM (32.0%), MSM (10.4%), JM (28.3%), LCM (8.7%), AI (4.6%), and others (3.5%). TSM was the most widely used DPM and followed by JM. TSM used an estimated longitudinal parameter as a covariate in a survival outcome model. We identified multiple methods to process longitudinal data in TSM, including aggregate data (27/56, 48.2%), mixed-effect model (12/56, 21.4%), trajectory clustering (11/56, 19.6%), and others (6/56, 10.7%). Furthermore, given the large number of JM used in the included studies, we collected the specifications of these models for longitudinal sub-models and survival sub-models, as well as the shared structure between the two sub-models and its distribution used, which was detailly presented in Supplementary Table S6.

Table 3.

The description of dynamic prediction approaches in use and the current application in the selected oncological prognostic studies with repeated measurement predictor and/or intervening event

Model, N(%)	Description	Input and outcome*	Advantages (+) and limitations (−)	Software	Current application
Time-dependent covariate model (TDCM), 22 (12.6%)	The series value of DP is treated as a time-dependent variable in Cox model by using the time points for sequential pairs of the DP, to analyze how the effects of DP change over time with TTE.	Input: the varying values in each time interval Outcome: TTE, where time refers to time interval and event within each time interval	+simple to estimate the correlation of DP with prognosis 1 +easy to interpret the effect size of hazard ratio +able to make risk estimation updated during follow-up for new individuals, using most recent covariate values -ignores measurement error 2-assumes a step function between the repeated measurements -ignores correlations between and within individuals -requires complete DP at event times -not appropriate for endogenous predictors	Widely available (e.g., SAS, R, Stata)	20/22 analyzed the association between DP and TTE. TDCM was the earliest adopted dynamic approach, analyzing the impact of ipsilateral breast tumor recurrence as a time-dependent covariate on DFS among breast cancer patients. 4 other studies also analyzed the influence of intervening event on TTE using TDCM. 8/22 analyzed the impact of DP such as PSA, PLT, and ALB on prognosis. 9/22 established DPM to assess the risk prediction of patients’ prognosis.
Two-stage model (TSM), 56 (32.2%)	TSM uses an estimated longitudinal parameter as a covariate in a survival outcome model.	---	+easy to conduct than joint modeling -considers the modeling processes for repeated measurements and outcome prediction separately, which leads to biased and inefficient estimates 3	---	Three main types of methods for processing DP were used in the longitudinal modeling stage, and in the outcome modeling stage survival model was used.
· Aggregate data, 27/56	DP is aggregated into a single value (i.e., summary statistics) and put into Cox model or parametric survival model.	Input: Summary statistics (e.g., mean, median, variability, maximum, minimum, trend, slope, autocorrelation, number of measurements) Outcome: TTE	+easy to process DP as summary statistics +convenient for small sample size -ignores measurement error -cannot make dynamic prediction -may not fully capture the rich information contained in DP such as variability and timing of exposure -may mishandle non-ignorable missing data mechanisms in the data, leading to biased results	Widely available (e.g., SPSS, R, SAS, Stata)	Recent studies still use this method, though it’s not great at tracking changes. Some with ctDNA measurement at several time points aggregated these measurements into a binary variable (i.e., negative or positive), and then analyzed its impact on prognosis.
· Mixed-effect model, 12/56	DP is modeled and the estimates from mixed model represent the longitudinal patterns.	Input: Estimates of DP from mixed-effect model Outcome: TTE or binary outcome	+flexible to estimate DP trend 4 +can analyze multiple DPs in a single model -errors from model specification, parameter estimation 5	NONMEM, SAS (Proc MIXED), R (lcmm package)	6/12 used non-linear mixed-effect models to analyze tumor size changes over time and established their correlation with prognosis. Others employed mixed models to establish DP change trajectories for prognostic prediction, with two studies explicitly using LCGMM.
· Trajectory clustering, 11/56	It estimates the clustering of DP, then uses the categories of trajectories as the input for survival analysis.	Input: Patterns or groups of individual trajectories over time identified from trajectory clustering model. Outcome: TTE	+does not increase data dimensionality 5,6 -difficult to interpret time-dependent covariates, and not fully modeled the progression patterns -has a risk of overfitting the model to the data	SAS (Proc TRAJ), R (traj package)	Through GBTM, patients were classified into several groups (median 3, range from 2 to 5 in the 11 studies) depending on the patterns of interested DP, and then analyzed its association with prognosis.
· Others, 6/56	DP is modeled by other methods, and the estimates is used as input in survival model.	Input: Estimates of DP change over time from other types of models Outcome: TTE	+flexible to model the DP trend +extracts individual-specific longitudinal features -not dynamic in the longitudinal model incorporating repeated measurements	R (fdapace, MFPCA package)	The models used for DP change over time included MFPCA, sequential pattern mining, scoring model, linear regression per individual, and biexponential model.
Multistate Model (MSM), 18 (10.3%)	MSM consists of at least three states and the corresponding transitions between these states, allowing intervening events (e.g., LRR, DM) to be incorporated into predictions.	Input: Risk factors corresponding to each state. Outcome: TTE corresponding to each state	+provides a better description of the disease process 7,8 +allows for intermediate events in disease progression modeling +able to more accurately and flexibly assess prognostic factors for each transition state -describes a simplified version of the disease process, does not represent a “biological” description -requires more complex modeling, larger sample size, and longer follow-up as the number of states increases	R (msm, mstate package), Stata (multistate command)	18/18 studies used MSM for the analysis of intervening events, and 15/18 for better identifying risk factors of each state. Each study depicted its own disease progression process, which showed different transitions between states. 12/18 considered four states, 4/18 considered three, and 2/18 included five states.
Joint Model (JM), 49 (28.2%)	JM analyzes DP and TTE simultaneously in a single model, through shared random effect combined. It can infer the dependence and association between the DP and TTE to better assess the effect of a treatment.	Input: treatment and covariates Outcome: longitudinal value of DP at each time point, TTE	+allows for a precise estimation of longitudinal and survival parameters 9–11 +permits for simultaneous assessment of the impact of factors of interest on DP and TTE +provides personalized prediction +useful for heterogeneous populations -permits inclusion of multiple DPs in a single model, but increases computational complexity -exists risk of model misclassification	R (JM, JMbayes, JMbayes2, frailtypack packages), STATA (stjm, stjmcsurv command), SAS (JMFit macro), Stan	8/49 studies analyzed multiple DPs (range: 2-5) in a single model. Linear mixed-effects model for DP (32/49) and Cox proportional hazards survival model for TTE (28/49) were the most commonly used sub-models in JM, and these two sub-modeled were most linked by shared random effect (31/49). But the distribution of the random effect was lack of reported (14/49). 6/49 used frailty joint model to analyze intervening events. (Supplementary Table S6)
Landmark Cox model (LCM), 15 (8.6%)	The method takes “snapshots” of study population at specific landmarks and creates datasets for those at risk. It uses Cox model to estimate survival probabilities at each landmark, generating multiple predictions that are then combined into a “super landmark model” for dynamic prediction.	Input: the last observed value of DP at each landmark time points. Outcome: TTE at each landmark time point	+easily implemented in practice 12,13 +permits a large number of DPs in a single model without increasing computing task +can use past or current information from new individuals to make predictions about their future +has flexible variations and extensions -no general guidance on the choice of landmark times -ignores measurement error of DP -implies strong assumptions about the path of DP -decreases statistical power with the landmark time points advances, therefore requires large dataset with long-term follow-up -ignores the events prior to the landmark timepoint	R (dynamicLM, Landmarking packages)	The initial study focused on how prognosis changes after early deaths were excluded and considered the influence of subsequent events (i.e., LRR, DM) during follow-up on prognosis. Another early “landmark” study used the proportional baselines landmark supermodel to obtain dynamic individualized predictions of the 5-year DOS probability by including important factors after treatment. The subsequent 10 studies followed this analytical pattern. 9/13 studies considered intervening events in their models.
Artificial Intelligence (AI), 8 (4.6%)	AI process both structured and unstructured multimodal data. Prognostic analysis with longitudinal data can be achieved using DL capable of processing time series data.	Input: repeated collected CT/MRI/US images, text, multi-omics data, high-dimensional clinical data, or other traditional DPs. Outcome: TTE or binary outcome	+able to analyze high-dimensional and multimodal DPs 14,15+extracts information from nonstructured data +capable of providing dynamic predictions -demands higher quality and quantity of data -often treats TTE as binary outcome, ignores censoring -opaque, with their internal structures and model parameters being difficult to interpret -prone to overfitting, requires more validation	Python (sklearn package) R	8/8 utilized longitudinal data to establish better predictive models, all of which were validated. Among them, 3 used original CT/MR images as input, 1 multimodal data, 1 ctDNA measurements, and 3 traditional clinical factors. The sample sizes varied widely (range: 107–175,000). The algorithms included CNNs with RNNs, SNNs, Dynamic-DeepHit, and NLP.
Others, 6 (3.4%)	Methods for processing longitudinal and prognosis data, respectively, are different from above approaches.	Input: different cycles of treatments, repeated-measured clinical data, etc. Outcome: TTE or binary outcome	+flexible to process both DPs and prognosis -requires more validation of methods and model performance	R STATA	3/6 used GEE to analysis the longitudinal and prognosis. The other 3 used TSA with real-world big data and conventional logistic model, survival paths mapping analysis with conventional Cox model, and naïve Bayes approach.

Citations in this table could be found in Supplementary Information.

DP dynamic predictor, TTE time-to-event outcome, PSA prostate-specific antigen, PLT platelet count, Alb albumin, DPM dynamic prediction model, LRR local regional recurrence, DM distant metastasis, LCGMM latent class growth mixed model, GBTM group-based trajectory model, MFPCA multivariate functional principal component analysis, DOS dynamic overall survival, AI artificial intelligence, DL deep learning, CNN convolutional neural network, RNN recurrent neural networks, NLP natural language processing, SNN Siamese neural networks, GEE generalized estimation equation, TSA time-series analysis.

^aInput and output represent dynamic predictors and prognostic outcome, respectively.

Table 3 outlined the features of all models, including required inputs and outputs, advantages and disadvantages, software availability, and current application of oncological research. Figure 2C illustrated the distribution of number of studies using these methods. We also found that the distribution of these DPMs was significantly changed in the last 5 years (i.e., 2019–2023) compared to pre-2019 (p < 0.001); there was an increasing use of JM and AI (Fig. 2D). A cross-table of cancer type and DPM methods was presented in Supplementary Table S7.

In addition, we conducted a quantitative analysis comparing the seven DPMs categories across several factors, including baseline sample size, DP types, and the reasons for using dynamic predictions (Fig. 3 and Supplementary Table S8). Significant differences were observed among these models in terms of the source of methods, number of DPs, and consideration of multiple DPs in a single model, the types of DPs, study purposes (all p < 0.05). The necessity for dynamic prediction also varied significantly among these approaches (p < 0.001). Notably, compared to other DPMs, JM has been used to analyze the six study purposes evaluated and to consider the four necessities of using dynamic prediction (all frequencies > 0).

Fig. 3. Quantitative analysis of characteristics among different dynamic prediction models.

A Number of sample size at baseline. B Percentage of reporting of source of methods. C Percentage of using multiple dynamic predictors in a single model. D Percentage of Number of predictors (categorized into four groups, including 1, 2, 3, >3. E Percentage of necessity of using dynamic prediction. F Percentage of considering baseline and longitudinal predictors. B1-B5 represent B1-Focus on longitudinal predictors analysis, B2-Both baseline and multiple longitudinal results are present, with a preference for interested longitudinal predictors, B3-Both baseline and longitudinal results are present, with a preference for longitudinal predictors, B4-Both baseline and longitudinal results are present, no preference, B5-Focus on baseline data, longitudinal predictors as additive analysis, respectively. G Percentage of results with static data analysis. H Percentage of comparison of static and dynamic results. I Study purposes. P values were calculated by Kruskal–Wallis test for number of sample size at baseline and Chi-square test for other variables, and were corrected by Bonferroni method.

Dynamic versus static analysis

A total of 29 studies (17.0%) compared results from both static and dynamic model simultaneously, with 96.6% (28/29) indicating that dynamic models outperformed static ones, and 3.4% (1/29) finding similar performance between the two. A half of the AI studies (50.0%, 4/8) made such comparisons (Fig. 3 and Supplementary Table S8).

Construction of clinical prediction model using dynamic prediction models

Nearly half of the included studies (46.0%, 80/174) constructed clinical prediction models, with joint models being the most common approach (32.5%, 26/80) (Supplementary Table S9). The time-dependent C-index (57.5%) and Brier score (28.7%) were the primary metrics for model performance evaluation. However, 33.8% of the models lacked any evaluation of model performance, and 38.8% were not validated. Internal validation was performed by 32.5% using cross-validation, 17.5% with randomly selected data, and 11.2% with both internal and external validation. Only 7.5% (6/80) reported according to the TRIPOD guidelines²⁸ for predictive models.

Discussion

Our study pioneered a comprehensive examination of DPMs in oncological prognostic research involving repeated measurement predictors and/or intermediate events. While previous work has explored the methodological landscape of dynamic prediction^17,20–22, our data revealed the current status of the application of DPMs in contemporary oncological studies through quantitative analysis. We proved that a rising trend of demand in oncological research involving DPs to assess patient prognosis. DPMs not only expanded the capabilities of static methods in incorporating repeated measured predictors but also uniquely account for the effects of intermediate events on prognosis, thereby substantially boosting the efficacy of data utilization. Meanwhile, the diversity of DPMs has been expanding, with JM becoming more commonly employed and the introduction of innovative techniques such as AI in the last 5 years³. We summarized seven categories of DPMs, including TSM, JM, TDCM, MSM, LCM, AI, and others. Through evaluation in multiple methodological dimensions and clinical applications, we found that though widely used in the current studies, not all methods fully leveraged longitudinal data to achieve the purpose of dynamic prediction. Two-stage models that separately model longitudinal and survival data remain the most commonly used approach. But JM offered a more flexible framework for dynamic analysis across a spectrum of purposes, while MSM provided a convenient mechanism for dissecting the impact of intermediate events in the included studies. Furthermore, despite advancements in dynamic prediction methodologies, their clinical application was still predominantly confined to large datasets featuring a limited number of longitudinal predictors, the development and application of DPMs for high-dimensional data with small sample size, and the model validation and quality of study reporting should be improved in the future.

Researchers have often pondered whether the variables in dynamic prediction differ from those in static models. We found that dynamic analysis has significantly expanded the range of applicable variables beyond what static analysis allows. The benefits of dynamic prediction methods, especially when they incorporate longitudinal predictors, were twofold. Any data that was continuously monitored and exhibits variability was eligible for dynamic modeling. For example, while static models had established a link between baseline carcinoembryonic antigen (CEA), carbohydrate antigen 19-9 (CA19-9), and carbohydrate antigen 125 (CA125) and prognosis of colorectal cancer, dynamic models furthered this by correlating their joint longitudinal values with prognosis in multivariable analysis²⁹. In addition, the use of dynamic prediction has been gaining momentum, notably in emerging fields like immunotherapy, exemplified by the dynamic analysis of circulating free DNA^30,31. During our literature screening, we observed that increasing studies utilized data from DNA, RNA, or single-cell sequencing at several time points to analyze the dynamic changes and even their impact of treatments^32–34. However, due to limited sample size and techniques, many did not employ analysis in a single model by considering the longitudinal measurement error and dynamic prediction.

Furthermore, dynamic models have uniquely accommodated predictors not accounted for in static analysis, such as intermediate events. One study used an intermediate event (i.e., ipsilateral breast tumor recurrence) as a time-dependent covariate to determine whether it was an important predictor of distant-disease-free survival in patients with breast cancer after lumpectomy³⁵. Recurrence was used as a time-dependent DP for survival outcome, whereas many previous static models have treated it as an outcome (e.g., recurrence-free survival) and cannot include it as a baseline predictor for OS. Take OS as a primary endpoint; events like recurrence, metastasis, and treatment responses, which would influence OS, were not observable at baseline but can be integrated into dynamic model as DPs, substantially boosting its predictive power³⁶. If we combine these related intermediate events with OS into a composite endpoint, rather than using them as individual intermediate events, we will not be able to determine the relationship between these events and OS, nor will we be able to identify the true predictors that affect OS. Therefore, DPMs have significant advantages in analyzing intermediate events. In which MSM provides an appropriated framework to process intermediate events and could be used to analyze transitions between disease states. The method depicts transitions between at least three states through a transition diagram, and is possible to analyze risk factors for each state using a single model³⁶. Notably, JM has also been used to study disease transition for data with intermediate events using frailty effect as shared structure between two sub-models³⁷. The current study did not delve into dynamic events that occurred during patient follow-up, such as treatment interventions and transplants. While these studies also employed dynamic modeling techniques, their primary goal was to mitigate immortal time bias of the events^38,39.

This study focuses on research where the primary outcome is the prognosis of cancer patients. Among the included studies, OS was identified as the most prevalent primary outcome in dynamic modeling, which is consistent with previous study²⁷. In addition to OS, a variety of other primary outcomes were also used, such as recurrence-free survival, disease progression, and treatment response. Notably, different tumors employ distinct metrics to evaluate these outcomes. In solid tumors, imaging is commonly used to assess treatment response, and pathological examination is also employed for evaluation. For example, modified Response Evaluation Criteria in Solid Tumors (mRECIST) is frequently applied to evaluate response to therapies in hepatocellular carcinoma⁴⁰, while in some recent clinical trials, pathological assessment has also been used to determine treatment response⁴¹. Differences in these evaluation methods may lead to discrepancies in the timing of outcome ascertainment, thereby influencing the collection of longitudinal and outcome data as well as the development of DPMs. In the field of dynamic prediction, we can think about the relationship between the prognostic outcomes we choose and time. When the outcomes require a longer time to be observed, such as long-term survival, the corresponding longitudinal variables can also be measured more times during follow-up, which is more conducive to the construction of dynamic models. However, our study did not explicitly summary the follow-up time intervals of the longitudinal data and outcome because the differences among various cancers are substantial, ranging from several weeks to several years. Moreover, there are cases where the follow-up time is not reported or is reported ambiguously.

The present study offered a pragmatic examination of DPMs, tailored to various application scenarios and aimed at enhancing clinical researchers’ grasp of the context and implementation mechanics. While methodological research drives innovation in dynamic prediction, this study prioritized applied research to evaluate how DPMs perform with real-world, center-specific longitudinal and time-to-event data in oncology. Table 3 meticulously detailed the applicable scenarios, most significant advantages and disadvantages, and software for implementation of all extracted models. Researchers are advised to choose the appropriate method based on the purpose of the study and pay attention to the limitations of these methods. TSM was found to be the most frequently used method due to its convenience, and it continued to be widely used recently. However, it should be noted that regardless of the method used to analyze longitudinal part, the method considered the modeling processes for repeated measurements and outcome prediction separately, which leads to biased and inefficient estimates^9,17. In recent years, JM has become the most recommended longitudinal method and received much attention in clinical studies^9,10,18. Although the Landmark Cox model has often been used as a dynamic data analysis method and compared with JM^10,42,43, many studies employing the landmark method were excluded during our screening process. As mentioned above, the method is an analysis framework for many other reasons for use without fulfilling the eligibility of the target studies. We observed that many of the included studies adopted JM, aligning with the optimism of other researchers. The sample size required for JM was moderate, and the software for analysis was also available. However, due to the methodological limitations, more than four-fifths of the JM studies analyzed only one longitudinal variable. Bayesian methods have been used for the analysis of multivariable DPs in JM⁴⁴. One study utilized Bayesian methods analyzed five DPs (i.e., neutrophil to lymphocyte ratio, platelet to lymphocyte ratio, lymphocyte to monocyte ratio, hemoglobin, and prostate-specific antigen) in a single model^45,46. However, current application and methodology needs to extend to high-dimensional longitudinal and time-to-event data analysis⁴⁷.

Our study has identified emerging trends in methodology and purpose in application. For instance, innovations such as AI were gaining ground. AI offers a promising avenue for analyzing high-dimensional and also unstructured data, with the application of deep learning algorithms for dynamic prediction indicating a future trend⁴⁸. The rise of convolutional neural networks (CNN), recurrent neural networks (RNN), and other time series-based deep learning networks, fueled by the successful application of AI in clinical data, has reinvigorated DPMs⁴⁹. For instance, in 2019, one study has proved that transfer learning of CNN with RNN models can fuse imaging data acquired at 1-, 3-, and 6-months follow-up time points to enhance the accuracy of clinical-outcome forecasts⁵⁰. In addition, long short-term memory (LSTM) network and the more concise gated recurrent unit (GRU) network based on RNNs has also been used to better capture dependencies in time-series data and effectively address the problems of vanishing and exploding gradients⁵¹. Furthermore, natural language processing has been employed to dynamically update prognostic estimates as an individual’s disease trajectory evolves¹⁴. Recently, the Transformer deep learning network based on the self-attention mechanism has achieved revolutionary breakthroughs in the field of natural language processing⁵². It extracts and utilizes information with each sequence input and preserves the sequence order through positional encoding. Compared to RNN, it has stronger generalization capabilities and completes computational tasks more quickly through parallel computing. This provides more powerful technical support for time-series and 3D image feature extraction⁵³. However, although technological innovations have provided strong support for DPMs, the field still faces numerous challenges, such as inconsistent data across cancer registries⁵⁴ and interpretability challenges in clinical deployment^55,56. To further advance the development and application of DPMs, it is essential to bolster data support and expand the practical implementation of these technologies, thereby accumulating valuable experience.

Our study also found that the quality of study reporting should be improved in the future, which is consistent with a recently published study²⁷. That study mainly evaluated the reporting and methodological quality of 34 DPM studies on cancer prognosis, finding that while the landmark and joint models show potential, most studies had suboptimal reporting and methodological quality. While our research goes a step further beyond summarizing the methodological characteristics to understand the scenarios and efficiencies of the application of these methods in specific clinical fields. This gap impedes clinical translation, as practitioners lack evidence-based guidance on selecting and implementing DPMs for dynamic risk stratification. However, both our study and the aforementioned study have identified deficiencies in study reporting. The inadequacy in reporting research methods is also an important aspect that undermines the credibility of the models, which needs to be taken seriously by researchers. In future studies, we should clearly report the data used in DPMs, especially the measurement time points of longitudinal data and the sample sizes corresponding to each time point.

Our study has some limitations as follows. Firstly, cancer surveillance studies fell outside the scope of our research, as our primary focus was on cancer prognosis. Second, the heterogeneity observed across various studies prevented us from conducting a meta-analysis. Third, despite our comprehensive search efforts, which included both public databases and literature citations, some studies lack of describing typical dynamic prediction vocabulary may have eluded our search, a limitation imposed by the inherent difficulty of the search process.

DPMs represent a transformative shift in oncology prognostic research, enabling real-time integration of evolving accumulated data and intermediate events to refine survival risk assessment. Through a comprehensive evaluation in multiple methodological dimensions and clinical applications, we found the traditional DPMs, such as two-stage model, persist, innovations like joint models and AI-driven frameworks demonstrate a wide adaptability for longitudinal-survival interdependencies. However, clinical adoption remains constrained by reliance on large datasets and underdeveloped methodologies for high-dimensional, small-sample scenarios. Future research should focus on developing DPMs that can handle high-dimensional data from smaller samples to improve clinical applicability and advance precision oncology.

Methods

Study design

This study was an evaluation of observational oncological research using DPMs in peer-reviewed clinical research journals. We did a systematic review of eligible studies and, more importantly, extracted data on dynamic prediction methods and clinical scenarios from them to perform quantitative analysis. Full specifications of these data were systematically defined below. Dynamic prediction could cover a broad range of aims and methods⁴⁸, in particular, our study focused on the evaluation of DPMs and their application scenarios in oncological prognostic research with at least three time-point repeated measurement predictors and/or intermediate events. We performed this study in accordance to the guidelines of the Preferred Reporting of Items for Systematic Reviews and Meta-Analyses (PRISMA)⁵⁷. Supplementary Table S1 showed a completed PRISMA checklist of the study.

Eligibility criteria and search strategy

Studies mentioning DPMs used for cancer patient’s prognostic analysis of an individual using repeated-measured data were included. The search sources included two parts, and the search strategies referred to previous studies^17,24. First, we searched the PubMed and Web of Science datasets for published articles up to 31 Dec 2023 within the title, abstract, and keywords of the article (search strategies available in the Supplementary Table S2). Second, we searched the relevant literatures involved in published articles or reviews of DPMs. The exclusion criteria included (1) systematic reviews/conferences/editorials/perspectives/comments/abstract only; (2) methodological research; (3) prediction modeling studies without repeated measurements (<3 time points) and intermediate events; (4) cancer diagnosis or surveillance studies; (5) non-cancer studies; and (6) other not relevant studies. In addition, studies with dynamic variable that was an intervention (i.e., transplantation, surgery, drug treatment) were also excluded. QZ and ZHC independently screened the identified articles following the literature search to minimize selection bias. Any disagreements were resolved by discussion till all investigators reached a consensus.

Data extraction

General information of included studies

The following items were extracted from each relevant article: first author, year of publication, journal, disease area, data source, number of enrolled participants, primary outcome of interest, performance of model development and/or validation, and software for modeling. Static analysis using baseline data in each study was also collected.

Characteristics of dynamic predictors

Dynamic predictors (DPs), also named longitudinal predictors including repeated measurement predictors and/or intermediate events, were very important parts in the included studies. Thus, we investigated the usage and reporting of these variables in the literatures, including types of predictors, number, repeated measure time points, sample size at each time point, duration of longitudinal data measurement, and missing data processing. Intermediate events referred to new occurrences or incidents that happened during the course of a study before the primary endpoint, such as disease progression, recurrence, distant metastasis^13,36.

Clinical scenarios and necessity of using DPMs

To understand the current state of utilizing DPs in oncological prognostic studies and clinical questions they have addressed, we assessed the clinical application scenarios and the study purposes, and then summarized and categorized the methods corresponding to each clinical scenario. We collected the purposes of each study and made summarization into several types of aims. The necessity of using DPMs was also generated from the purposes.

Types of DPMs

The types of approaches were summarized according to the methods used in each included study. We referred and adapted to published methodological studies to summarize these types of DPMs^17,20–22. They could be classified into seven types, including joint model (JM), landmark Cox model (LCM), two-stage model (TSM), time-dependent covariate model (TDCM), multi-state model (MSM), artificial intelligence (AI), and others. The AI category referred to the use of deep learning algorithms for longitudinal and survival data analysis. While in cases where machine learning was used in the first stage to generate score from longitudinal data, which were then modeled with prognosis, these models were classified as TSMs. The machine learning algorithms used in these cases did not include deep learning. The differences between these methods were compared. All data extraction was performed by QZ and ZHC using an Excel spreadsheet (Excel for Windows 2016; Microsoft, Redmond, WA, USA). We did not synthesize the effect size of each study because of the different purposes.

Statistical analysis

Continuous variables were described as mean ± standard deviation (SD) or median (interquartile range, IQR), as appropriate, and categorical variables as numbers and percentages. Comparisons between two groups were made using t-test or Mann–Whitney U test for continuous variables and Chi-square test or Fisher’s exact test for categorical variables. Comparisons among more than two groups were made using ANOVA or Kruskal–Wallis test for continuous variables and Chi-square test or Fisher’s exact test for categorical variables. Although some articles used two DPMs, our analysis was based on the number of DPMs rather than the number of articles because our primary focus was on the application of methodologies. This approach is appropriate because only nine articles used two methods each, and the characteristics of the methods are independent, so the conclusions of this study were not affected by clustering effects. The primary analysis of this article was descriptive, but it also included some statistical comparisons based on certain classifications. However, it should be noted that the statistical power of these comparisons may be insufficient, and the type I error may be increased. So, all P values were corrected by Bonferroni method. Trend test to confirm the number of articles changing over time was performed using linear regression. P less than 0.05 was considered statistically significant. All statistical analyses and plots were performed using the R version 4.3.1 software (Bell Laboratories, Murray Hill, NJ; https://cran.r-project.org/bin/windows/base/). The R codes used for statistical analysis in the study were available in Supplementary Information.

Author contributions

Qian Zhou: conceptualization; data curation; formal analysis; funding acquisition; investigation; methodology; project administration; resources; software; supervision; roles/writing— original draft.Zhi-hang Chen: conceptualization; data curation; formal analysis; methodology; writing—review and editing.Sui Peng: data curation; formal analysis; methodology; software; writing—review and editing. Qian Zhou and Zhi-hang Chen were co-first authors.

Data availability

The data that support the findings of this study are available from the corresponding author (QZ) upon reasonable request. The R codes used for statistical analysis in the study were available in Supplementary Information.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41698-025-01162-7.