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.