Follow-Up Bias in Tumor Dynamic Modeling: A Comparison of Classical and Neural-ODE Approaches

CPT Pharmacometrics Syst Pharmacol 2026 AI 6 Explanations View Original
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Pages 1-2
The Problem with Tumor Growth Models

Why Tumor Dynamic Models Matter. Tumor dynamic models (TGI models) are mathematical frameworks that track how tumor size changes over time in response to treatment. They are essential tools in oncology drug development for evaluating treatment efficacy, informing Go/No-go development decisions, and optimizing drug dosing strategies.

Limitations of RECIST. Traditional tumor response assessment using RECIST (Response Evaluation Criteria in Solid Tumors) categorizes tumor size into response strata but fails to capture the rich longitudinal information in tumor measurements -- including rates of shrinkage, depth of response, and overall trajectory over time. TGI models were developed to overcome this by modeling continuous tumor dynamics.

The Immunotherapy Challenge. Classical TGI models were developed during an era dominated by chemotherapy, where tumors typically shrink and then regrow as resistance develops. Immune checkpoint inhibitors (ICIs) like atezolizumab produce fundamentally different response patterns: delayed responses, prolonged stable disease, and durable responses that sometimes persist even after treatment ends. These patterns challenge the assumptions built into classical models.

The Follow-Up Bias Problem. Early-phase drug development decisions are often required before trial data are fully mature, meaning models must predict future tumor trajectories from incomplete datasets. Classical models with exponential growth terms are particularly prone to biased predictions under these conditions, potentially overestimating tumor burden and leading to overly conservative assessments of treatment efficacy.

TL;DR: Classical tumor growth models developed for chemotherapy may produce systematically biased predictions when applied to immature immunotherapy trial data, which can mislead early drug development decisions.
Pages 2-5
Study Design and Model Comparison

Large-Scale Clinical Dataset. The study analyzed data from 3,106 patients with non-small cell lung cancer (NSCLC) enrolled across four completed phase III atezolizumab trials: IMPower130, IMPower131, IMPower132, and IMPower150. Both atezolizumab-containing arms and control arms (chemotherapy, targeted therapies) were included, covering diverse treatment modalities.

Time Truncation Design. To simulate early decision-making scenarios, the dataset was artificially truncated to simulate what would be available at 25%, 50%, or 75% of total trial duration. Models were then trained on the 'seen' data and evaluated on the 'unseen' future measurements, mimicking interim analysis conditions.

Five Classical Models. Five established pharmacometric TGI models were compared: Stein, Claret, Bonate, Moore, and Wang. All were implemented as nonlinear mixed-effects models in NONMEM software, incorporating random effects on key kinetic parameters such as tumor growth rate (KG) and drug-effect rate.

The TDNODE Framework. The Tumor Dynamic Neural-ODE (TDNODE) is a deep learning alternative using an encoder-decoder architecture. A recurrent neural network encoder summarizes each patient's baseline and on-treatment tumor history into a latent state, which a Neural-ODE decoder then uses to generate a continuous tumor-size trajectory. TDNODE was trained with L2 regularization and a masking scheme preventing access to future data.

Evaluation Metrics. Predictive performance was quantified using relative percent error (RPE), root mean squared error (RMSE), and R-squared (R2). A weighted bootstrap of 500 iterations was performed to assess sensitivity to informative dropout (patients who progress early and have fewer measurements).

TL;DR: Five classical pharmacometric tumor models were compared against the deep learning TDNODE framework using data from 3,106 NSCLC patients, with artificial truncation at 25%, 50%, and 75% of trial follow-up.
Pages 6-8
Prediction Bias in Classical Models

Consistent Overestimation by Classical Models. All five classical TGI models demonstrated moderate to high positive prediction bias, consistently overestimating future tumor size when fitted to truncated datasets. This bias increased as the amount of available data decreased: predictions were worst at 25% follow-up and improved (but remained positive) at 75% follow-up.

Stein Model: Worst Performer. The Stein model, which assumes unconstrained exponential tumor growth, showed the most pronounced errors, with a bootstrapped mean relative percent error (RPE) of 334% at 25% truncation, declining to 79% at 75% truncation. Its assumption of unbounded growth made it particularly unsuitable for immunotherapy trials where prolonged stable disease is common.

Claret Model: Less Biased but Still Problematic. The Claret model, which incorporates a resistance parameter moderating tumor growth over time, showed comparatively lower bias (RPE of 97% at 25% truncation and 33% at 75% truncation). However, its underlying assumption of inevitable tumor regrowth still caused overprediction in cases of sustained immunotherapy response.

Root Cause: Structural Assumptions vs. IO Biology. The analysis identified a fundamental mismatch: approximately 60% of atezolizumab-treated patients showed sustained responses or stable disease by SLD measurements, yet all classical models assume eventual tumor regrowth. When fitted to early data without evidence of regrowth, models estimated high growth parameters (KG), leading to overestimated future tumor size.

TL;DR: Classical tumor growth models consistently overestimated future tumor size, with the Stein model reaching 334% RPE at 25% follow-up, driven by a structural assumption of inevitable tumor regrowth that conflicts with immunotherapy response patterns.
Pages 5, 6, 8
TDNODE's Superior Performance

TDNODE Substantially Outperforms Classical Models. Across all truncation scenarios, TDNODE achieved dramatically lower prediction errors. At 25% follow-up, TDNODE's RPE was 61% versus the classical models' range of 97% to 462%. At 75% follow-up, TDNODE's RPE was 19% versus 33% to 79% for classical models.

Better R-Squared Values. TDNODE achieved R-squared values of 0.81 at 25% truncation and 0.90 at 75% truncation, indicating strong alignment between predicted and observed tumor sizes. Classical models ranged from 0.04 to 0.34 at 25% truncation, reflecting poor predictive accuracy with limited data.

Data-Driven Flexibility. Unlike classical models with fixed mathematical structures, TDNODE learns tumor dynamics directly from patient data without imposing assumptions about growth kinetics. When trained on limited data, it can still produce flexible trajectories guided by observed patterns rather than defaulting to pre-programmed growth assumptions.

Complete Response Difficulty. All models -- including TDNODE -- struggled to accurately predict complete response (CR) trajectories, where tumors disappear entirely. This represents an important limitation and area for future development, as CR patients have dramatically different dynamics from partial responders.

TL;DR: TDNODE achieved 61% RPE at 25% follow-up and 19% at 75% follow-up, far outperforming all five classical models and demonstrating that data-driven deep learning can substantially reduce follow-up bias.
Pages 6, 7, 8, 10
Implications for Drug Development

Risk of Conservative Efficacy Interpretation. When classical models overestimate future tumor burden, drug development teams may falsely conclude that a treatment is less effective than it actually is. In early-phase Go/No-go decisions, this could lead to discontinuing promising therapies prematurely -- a costly error for both drug development programs and patients.

Parameter Estimation Failure with Immature Data. Even when a classical TGI model adequately describes the observed (seen) data, the inferred growth rate parameters may be biased due to limited follow-up. These biased parameters then drive all future predictions, making systematic errors unavoidable even without explicit extrapolation.

Relative vs. Absolute Metrics. Many successful historical TGI applications have relied on comparing relative metrics between randomized groups (e.g., hazard ratios between treatment arms), which are more robust to shared follow-up limitations. Absolute SLD forecasting in single-arm or early-readout settings is much more vulnerable to follow-up bias and requires more flexible modeling approaches.

Interpretability Trade-off. While TDNODE demonstrates superior predictive performance, its deep learning architecture limits mechanistic interpretability. The authors acknowledge this trade-off and suggest future work combining explainable AI techniques with hybrid mechanistic-deep learning models to retain both predictive power and biological interpretability.

TL;DR: Follow-up bias in classical tumor models could lead to premature abandonment of effective drugs in early-phase trials, while TDNODE's data-driven approach avoids this bias but sacrifices mechanistic interpretability.
Page 10
Future of Tumor Dynamic Modeling

Critical Need for Bias Assessment. The study demonstrates that tumor dynamic models should be evaluated under time-truncated conditions before being applied for clinical decision support. Understanding how prediction bias changes with follow-up duration is an important component of model validation that has been underreported in the literature.

Alternative Approaches for IO Trials. For immuno-oncology trials where durable responses are common, classical models designed for chemotherapy kinetics are fundamentally misaligned with underlying biology. Alternative approaches -- either more flexible parametric models allowing for prolonged tumor control, or data-driven deep learning frameworks like TDNODE -- should be considered.

Regulatory Context. The US FDA's Project Optimus initiative has created new opportunities for tumor dynamic modeling in early-phase regulatory decision-making. This work directly informs which modeling approaches are appropriate for different clinical contexts, with important implications for dose optimization and regulatory submissions.

Study Limitations. Results are limited to NSCLC and atezolizumab treatment programs. Generalizability to other tumor types, drug modalities, or earlier-phase single-arm trials remains to be established. Integration of tumor dynamics with overall survival modeling and joint models handling informative dropout are identified as important future directions.

TL;DR: Classical tumor growth models should not be applied to immature immunotherapy trial data without bias assessment, and deep learning approaches like TDNODE offer a promising alternative for early-phase NSCLC drug development decisions.
Citation: Open Access, 2026. Available at: PMC13042841.