Dynamic Prediction

Unlike static models that rely on a single baseline snapshot, dynamic prediction ingests repeated measurements over time. This includes lab values, vital signs, or imaging biomarkers collected at irregular intervals. The model updates its understanding of the patient's trajectory, capturing the rate of change and variability in biomarkers rather than just a single value. This allows the system to detect acceleration in disease progression that a one-time measurement would miss.

A pragmatic approach where predictions are updated at specific landmark times (e.g., every 6 months). At each landmark, the model uses only patients still at risk and their most recent data. This avoids complex joint modeling and naturally handles time-varying covariates without parametric assumptions. It is computationally efficient for large electronic health record datasets and directly addresses the question: 'Given that the patient has survived to this point, what is their updated prognosis?'

A sophisticated statistical framework that simultaneously models the longitudinal biomarker trajectory and the time-to-event outcome. It typically links a linear mixed-effects submodel for the biomarker with a Cox proportional hazards submodel for survival. This corrects for endogenous measurement error—the fact that observed biomarker values are noisy snapshots of a true underlying process. The shared random effects capture the association between the trajectory and the hazard.

Predictions are conditional on survival to the present and project risk over a fixed future horizon (e.g., 5-year risk from now). This sliding window approach provides clinically actionable timeframes. A patient's 5-year risk of cardiovascular event is recalculated at each visit, incorporating their latest cholesterol trends and blood pressure readings. This contrasts with static predictions made at diagnosis that become outdated as the patient's health evolves.

Patients with worsening health are more likely to miss follow-up visits or withdraw from studies. This informative censoring biases static models. Dynamic prediction frameworks, particularly joint models, can account for this by modeling the dependence between the measurement process and the event risk. The model recognizes that a sudden absence of data may itself be a prognostic signal, preventing overly optimistic risk estimates for deteriorating patients.

The ultimate output is a continuously updated, patient-specific survival curve that changes as new data flows in. This can be embedded in clinical dashboards or electronic health record alerts. For example, in oncology, a dynamic model might predict that a patient's risk of progression has crossed a threshold, triggering a recommendation for a treatment change or an earlier scan. This moves prognosis from a one-time statement to an ongoing monitoring tool.

A statistical framework that simultaneously models a longitudinal biomarker trajectory and a time-to-event outcome. Unlike two-stage approaches, joint models correct for measurement error inherent in repeatedly observed biomarkers.

• Links a linear mixed-effects submodel for the biomarker with a Cox or parametric survival submodel
• Uses the current value or rate of change of the biomarker as predictors
• Provides dynamic predictions that update as new lab values arrive
• Essential for prostate cancer monitoring with PSA trajectories

A computationally efficient alternative to joint modeling that resets the analysis clock at specific landmark times. Patients still at risk at the landmark are re-stratified based on their most recent biomarker value.

• Avoids complex joint likelihood estimation
• Requires careful handling of immortal time bias
• Predictions update at discrete intervals rather than continuously
• Commonly used in oncology trials with scheduled imaging assessments

Predictor variables whose values change over the observation period, requiring specialized handling in survival models. Standard Cox regression with time-varying covariates uses the counting process format to split patient histories into intervals.

• Each interval assumes constant covariate values
• Prevents immortal time bias where future survival time incorrectly influences baseline predictors
• Requires data restructuring into (start, stop] format
• Critical for modeling drug dosage changes or lab value fluctuations

A recursive algorithm that estimates the true underlying state of a noisy biomarker signal. In dynamic prediction, Kalman filters smooth repeated measurements to extract the latent disease trajectory before feeding it into survival models.

• Operates in predict-update cycles as new data arrives
• Separates biological signal from measurement noise
• Provides uncertainty estimates for the filtered state
• Used in real-time monitoring systems for ICU patients

A strictly proper scoring rule adapted for time-dependent predictions to evaluate dynamic prognostic models. It measures the mean squared error between predicted survival probabilities and observed outcomes at a specific prediction horizon.

• Assesses both calibration and discrimination
• Requires handling of censored observations via IPCW weighting
• Can be plotted over time to show when predictions degrade
• Gold standard for comparing joint models against landmark approaches

A technique to correct for dependent or informative censoring when evaluating dynamic prediction models. Weights uncensored observations by the inverse of their estimated probability of remaining uncensored.

• Assumes censoring mechanism can be modeled from observed covariates
• Prevents optimistic bias in validation studies
• Essential when sicker patients drop out more frequently
• Applied in calculating weighted Brier scores and AUCs