Author: [AUTHOR] Published on 4/10/2026 12:00:00 AMIn clinical oncology drug development, dose selection decisions are guided by the totality of evidence, including biomarkers, efficacy, safety, survival outcomes, and patient-reported outcomes, ideally integrated through quantitative modeling. A recent review highlighted the growing role of integrated models in oncology drug development and their value for dose optimization 1. Among the approaches discussed was the multistate survival model, a relatively new addition to the MIDD toolkit that can jointly describe outcomes such as ORR, PFS, OS, and time to treatment discontinuation due to adverse events. In this blog, we take a closer look at this framework and provide a practical introduction to its structure, parameterization, advantages, and selected applications in oncology development and dose optimization.
What is a Multistate Survival Model?
A multistate survival model extends conventional parametric time-to-event analysis by representing the patient journey as a series of clinically meaningful states connected by transitions. Rather than modeling only a single endpoint, such as death, the framework captures intermediate events, including tumor response, progression, treatment discontinuation, second-line therapy, and death, within one coherent model.
In oncology, examples of states may include:
- Disease progression states: Stable Disease (SD), Response (CR or PR), and Progression (PD),
- Treatment-related States: Treatment discontinuation due to adverse events (AEs) and initiation of second-line treatment,
- Absorbing States: Death or Dropout/Loss to Follow-up.
The following figure illustrates the difference between conventional endpoint-specific analyses and a multistate modeling approach. Standard analyses, such as exposure–response analyses, typically evaluate endpoints including ORR, PFS, and OS separately. In contrast, multistate models integrate these outcomes within a unified framework by explicitly modeling transitions between clinically relevant states over time.
How is a Multistate Survival Model Parameterized?
The multistate models used in these analyses are parameterized by defining clinical states as interconnected compartments, where the amount in each compartment represents the probability that a patient occupies that state. At treatment initiation, all patients are assumed to start in the initial state, typically stable disease, with probability 1. This probability is then redistributed across downstream states over time through a system of ordinary differential equations (the example equations below is consistent with the figure above).
(dP1)⁄dt=- P1∙ (λ12 (t) + λ13 (t) + λ14 (t) + λ15 (t) + λ16 (t))
(dP2)⁄dt=P1 ∙ λ12 (t) - P2 ∙ (λ23 (t) + λ24 (t) + λ25 (t) + λ26 (t))
(dP3)⁄dt=P1 ∙ λ13 (t) +P2∙ λ23 (t) - P3∙ λ36 (t)
(dP4)⁄dt=P1∙ λ14 (t) + P2 ∙ λ24 (t) - P4 ∙ λ46 (t)
(dP5)⁄dt=P1 ∙ λ15 (t) + P2 ∙λ25 (t) - P5 ∙ λ56 (t)
(dP6)⁄dt=P1 ∙ λ16 (t) + P2 ∙λ26 (t) + P3∙λ36 (t) + P4 ∙λ46 (t)+ P5 ∙λ56 (t)
The sum of all state probabilities at any time point must always equal 1.
P1 (t) + P2 (t) + P3 (t) + P4 (t) + P5 (t) + P6 (t) = 1
Transition Hazards: Transition-specific hazards can be described using parametric distributions such as the exponential, Weibull, or log-logistic distributions.
Covariate and Predictor Effects: Covariates and other predictors, such as systemic drug exposure or baseline patient characteristics, can be incorporated into selected transition hazards, typically through an exponential model of the baseline hazard.
Observation Resetting: After each observed state assessment, the probability of the observed state is reset to 1, and the probabilities of the remaining states are reset to 0. This allows the model to project subsequent transitions from the patient’s most recently observed clinical state (i.e., following the Markov process).
Time Dependencies: Depending on the application, the model may also be parameterized as a semi-Markov process, so that transition hazards depend not only on the previously observed state, but also on the time since treatment initiation or the time spent in the current or preceding state.
How are survival endpoints derived from a multistate model?
The following figure presents examples of simulation-based diagnostic plots for multistate model development, including state occupation over time and survival endpoints derived from multistate observations. Examples of how clinically relevant time-to-event endpoints can be derived from the multistate records are outlined below.
Progression-Free Survival (PFS)
- Event Definition: PFS is a composite endpoint defined as the time from time 0 (treatment initiation, diagnosis, or randomization) to transition into either the progression state or the death state, provided that progression is defined according to standard criteria such as RECIST 1.1.
- Censoring Definition: PFS is censored at the time of the last available RECIST-based state observation if a patient transitions to states such as treatment discontinuation due to AEs, or reaches the data cutoff date without a preceding transition into progression or death.
Overall Survival (OS)
- Event Definition: OS is defined as the time from time 0 to transition into the death state from any other state.
- Censoring Definition: OS is right-censored if a patient drops out and is lost to follow-up, or if the patient is still alive at the end of follow-up.
Time to Treatment Discontinuation due to AEs
- Event Definition: This endpoint is defined as the time from time 0 to the transition into the state of treatment discontinuation due to AEs.
- Censoring Definition: If a patient transitions to the progression state or to the state of discontinuation for other reasons, the observation is right-censored at that time. If the patient remains on treatment at the end of the study, the observation is censored at the data cutoff date.
The Advantages of Multistate Modeling
The multistate framework offers several advantages over traditional endpoint-specific analyses.
- Integration of multiple endpoints: By describing the full patient trajectory, multistate models integrate ORR, time to response, duration of response, PFS, and OS etc. within a single framework. This also captures the dependence between endpoints, such that early response and progression data can improve the prediction of later outcomes, such as OS.
- Respect for composite endpoints: Multistate models explicitly reflect the composite nature of endpoints such as PFS, where the event is defined by transition to progression or death, while also accounting for transitions to treatment discontinuation that may act as competing pathways and lead to censoring.
- Transition-specific exposure effects: Exposure can be evaluated separately on individual transitions. Rather than estimating a single overall effect on a composite PFS hazard, the model can assess whether exposure affects stable disease to response, stable disease to progression, or response to progression differently.
- Bias reduction: By explicitly representing intermediate states and post-baseline events, the framework can help reduce bias arising from treatment changes over time. Examples of this are presented in the next section on applications.
Applications in Clinical Oncology Drug Development
In recent years, the multistate framework has been used to address several complex challenges in oncology drug development. A few illustrative examples are highlighted below.
- Dose Selection In a Phase I expansion cohort evaluating bintrafusp alfa in non-small cell lung cancer (NSCLC), patients were randomized in a 1:1 ratio to 500 mg or 1200 mg. A six-state multistate model was developed to capture the totality of the efficacy endpoint data 2. Although dose did not reach strict statistical significance on any single transition, the combined information remained clinically informative. Simulations predicted an approximately 70% probability of at least a 1-month longer median OS for 1200 mg versus 500 mg, providing a quantitative rationale for selecting the higher dose for future development.
- Accounting for Second-Line Immunotherapy In the IMpower131 study evaluating atezolizumab plus chemotherapy in squamous NSCLC, the trial showed significant PFS improvement but failed to show a statistically significant OS benefit in standard analyses (P=0.16). This was highly confounded because 44% of patients in the control arm crossed over to receive second-line immunotherapy upon progression. A multistate model, including a "second-line therapy" state together with other disease-relevant states, was developed to describe PFS and OS 3. Through simulations that mathematically "turned off" the second-line treatment effect, the authors showed that adding atezolizumab to chemotherapy provided a significant, unconfounded OS benefit (Hazard Ratio = 0.75), thereby uncovering the true efficacy of the primary regimen.
- Early Phase Go/No-Go Decision Making Early-phase single-arm trials usually have limited sample sizes and lack mature survival follow-up, making Go/No-Go decisions for Phase 3 highly risky when relying purely on ORR benchmarks. Using data from the CLEOPATRA and OAK trials, researchers demonstrated that a multistate model can take early response and progression data from the experimental arm, borrow the post-progression survival hazard from historical control data, and accurately predict the eventual Phase 3 OS Hazard Ratio 4. This significantly improves the operating characteristics (reducing false-positive and false-negative rates) for advancing a molecule compared to simple RECIST response rate rules.
- Handling Immortal Time Bias in Toxicity–Survival Analyses Treatment-emergent toxicities are often associated with improved survival in oncology, but such analyses are highly vulnerable to immortal time bias because patients must remain alive and on treatment long enough to experience the toxicity. In a sunitinib case study, a multistate framework was used together with stepwise adjustment to account for toxicity timing, progression-related bias, and baseline confounding. This showed that the apparent protective association between toxicities and survival was markedly attenuated after appropriate bias handling, illustrating how multistate and related time-aware approaches can improve interpretation of toxicity–survival relationships.
Final thoughts
For Project Optimus and related dose-optimization efforts, the key principle is that dose selection should rely on the totality of evidence, not on a single endpoint in isolation. Multistate survival models align naturally with that principle because they integrate multiple clinically relevant outcomes within one quantitative framework.
They are not intended to replace every standard analysis, but they are a valuable addition to the MIDD toolkit when the goal is to integrate response, progression, survival, and treatment-modification trajectories, and to support more informed dose-selection decisions. For pharmacometricians, they offer a flexible framework for linking dose, exposure, intermediate outcomes, and survival. For clinicians and drug developers, they offer something equally important: a more complete and clinically interpretable view of treatment benefit and risk balance than any single endpoint alone.
- Liu, H. et al. Integrated modeling of biomarkers, survival and safety in clinical oncology drug development. Adv. Drug Deliv. Rev. 216, 115476 (2025). doi: 10.1016/j.addr.2024.115476.
- Liu, H. et al. A multistate modeling and simulation framework to learn dose-response of oncology drugs: Application to bintrafusp alfa in non-small cell lung cancer. CPT Pharmacometrics Syst Pharmacol (2023) doi:10.1002/psp4.12976.
- Krishnan, S. M. et al. Multistate pharmacometric model to define the impact of second-line immuno-therapies on the survival outcome of IMpower131 study. Clin. Pharmacol. Ther. (2023) doi:10.1002/cpt.2838.
- Beyer, U., Dejardin, D., Meller, M., Rufibach, K. & Burger, H. U. A multistate model for early decision-making in oncology. Biom. J. 62, 550–567 (2020). doi: 10.1002/bimj.201800250
- Liu, H, et al. Optimizing Sunitinib Dosing in mRCC: Addressing Confounding Bias and Immortal Time Bias in Exposure- and Toxicity-survival Analyses using a Multistate Survival Modeling Framework. PAGE meeting (2025)
