Estimation of time to progression and post progression survival using joint modeling of summary level OS and PFS data with an ordinary differential equation model

Nagase, Mario; Doshi, Sameer; Dutta, Sandeep; Lin, Chih-Wei

doi:10.1007/s10928-022-09816-w

Cited by 2 publications

(6 citation statements)

References 17 publications

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“…According to the definition of hazard,

H ()(, t) = - ()(, normald S ()(, t) / normald t) / S ()(, t)

, and only accounting for subjects who are at risk of the events (e.g., excluding subjects in other states having no risk of the events), the survival probabilities for OS, OS censor, PFS, PFS censor, (

S_{OS}, S_{OS_normalC}, S_{PFS}

, and

S_{PFS_normalC}

) and cumulative probability for PD and TR (

F_{TTP}

and

F_{TTR}

) can be derived from hazard functions and expected number of subjects in different states as described by Nagase et al. as follows 8

\begin{matrix} left H_{OS} ()(, t) goodbreak= \frac{H_{1_5} ()(, t) \cdot A_{1} ()(, t) + H_{12_5} ()(, t) \cdot A_{1_2} ()(, t) + H_{13_5} ()(, t) \cdot A_{1_3} ()(, t) + H_{14_5} ()(, t) \cdot A_{1_4} ()(, t) + H_{123_5} ()(, t) \cdot A_{12_3} ()(, t) + H_{124_5} ()(, t) \cdot A_{12_4} ()(, t)}{A_{1} ()(, t) + A_{1_2} ()(, t) + A_{1_3} ()(, t) + A_{1_4} ()(, t) + A_{12_3} ()(, t) + A_{12_4} ()(, t)} \end{matrix}

…”

Section: Methodsmentioning

confidence: 99%

“…Few multistate models with "initial," "progression," and "death" states were proposed to evaluate PFS and OS jointly. [5][6][7][8] These models were able to quantify the interdependence between PFS and OS, to explore confounding effects that might explain the possible discrepancies in OS and PFS, and to distinguish TTP and post-progression survival from PFS and OS. Krishnan et al expanded the multistate model to incorporate drug exposure and tumor growth inhibition models and provide a better understanding of drug efficacy and characterization of different states.…”

Section: Introductionmentioning

confidence: 99%

“…Quantitative multistate models to jointly describe early and late TTE endpoints, such as time‐to‐response (TTR), time to progressive disease (TTP), progression‐free survival (PFS), and OS, would be valuable to better understand the relationships between these endpoints and see how patients respond to treatment through states of disease prognosis. Few multistate models with “initial,” “progression,” and “death” states were proposed to evaluate PFS and OS jointly 5–8 . These models were able to quantify the interdependence between PFS and OS, to explore confounding effects that might explain the possible discrepancies in OS and PFS, and to distinguish TTP and post‐progression survival from PFS and OS.…”

Section: Introductionmentioning

confidence: 99%

“…Few multistate models with “initial,” “progression,” and “death” states were proposed to evaluate PFS and OS jointly. 5 , 6 , 7 , 8 These models were able to quantify the interdependence between PFS and OS, to explore confounding effects that might explain the possible discrepancies in OS and PFS, and to distinguish TTP and post‐progression survival from PFS and OS. Krishnan et al.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A multistate platform model for time‐to‐event endpoints in oncology clinical trials

Lin,

Nagase,

Doshi

et al. 2023

CPT Pharmacom & Syst Pharma

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A multistate platform model was developed to describe time‐to‐event (TTE) endpoints in an oncology trial through the following states: initial, tumor response (TR), progressive disease (PD), overall survival (OS) event (death), censor to the last evaluable tumor assessment (progression free survival [PFS] censor), and censor to study end (OS censor), using an ordinary differential equation framework. Two types of piecewise functions were used to describe the hazards for different events. Piecewise surge functions were used for events that require tumor assessments at the scheduled study visit times (TR, PD, and PFS censor). Piecewise constant functions were used to describe hazards for events that occur evenly throughout the study (OS event and OS censor). The multistate TTE model was applied to describe TTE endpoints from a published Phase 3 study. The piecewise surge functions well described the observed surges of hazards/events for TR, PD, PFS, and OS occurring near scheduled tumor assessments and showed good agreement with all Kaplan Meier (KM) curves. With the flexibility of piecewise hazard functions, the model was able to evaluate covariate effects in a time‐variant fashion to better understand the temporal patterns of disease prognosis through different disease states. This model can be applied to advance the field of oncology trial design and optimization by: (1) enabling robust estimations of baseline hazards and covariate effects for multiple TTE endpoints, (2) providing a platform model for understanding the composition and correlations between different TTE endpoints, and (3) facilitating oncology trial design optimization through clinical trial simulations.

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“…According to the definition of hazard,

H ()(, t) = - ()(, normald S ()(, t) / normald t) / S ()(, t)

S_{OS}, S_{OS_normalC}, S_{PFS}

, and

S_{PFS_normalC}

) and cumulative probability for PD and TR (

F_{TTP}

and

F_{TTR}

) can be derived from hazard functions and expected number of subjects in different states as described by Nagase et al. as follows 8

\begin{matrix} left H_{OS} ()(, t) goodbreak= \frac{H_{1_5} ()(, t) \cdot A_{1} ()(, t) + H_{12_5} ()(, t) \cdot A_{1_2} ()(, t) + H_{13_5} ()(, t) \cdot A_{1_3} ()(, t) + H_{14_5} ()(, t) \cdot A_{1_4} ()(, t) + H_{123_5} ()(, t) \cdot A_{12_3} ()(, t) + H_{124_5} ()(, t) \cdot A_{12_4} ()(, t)}{A_{1} ()(, t) + A_{1_2} ()(, t) + A_{1_3} ()(, t) + A_{1_4} ()(, t) + A_{12_3} ()(, t) + A_{12_4} ()(, t)} \end{matrix}

…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A multistate platform model for time‐to‐event endpoints in oncology clinical trials

Lin,

Nagase,

Doshi

et al. 2023

CPT Pharmacom & Syst Pharma

Self Cite

View full text Add to dashboard Cite

show abstract

“…x a, for example, phase II study, used to guide the design of the next phases of the drug development process. Nagase et al 46 recently published an article detailing an analogous method for describing and predicting PFS based on a parametric multistate ordinary differential equation model. Instead of modeling the tumor dynamics directly, they model the number of patients remaining, with disease progression, dead, and censored, with the corresponding hazard rates as transition rates from one state to They highlight that, for example, a mixed effect TGI model could be incorporated their approach to describe individual data.…”

Section: Progression-free Survivalmentioning

confidence: 99%

Model‐based prediction of progression‐free survival for combination therapies in oncology

Baaz

Cardilin

Jirstrand

2023

CPT Pharmacom & Syst Pharma

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Progression‐free survival (PFS) is an important clinical metric for comparing and evaluating similar treatments for the same disease within oncology. After the completion of a clinical trial, a descriptive analysis of the patients' PFS is often performed post hoc using the Kaplan–Meier estimator. However, to perform predictions, more sophisticated quantitative methods are needed. Tumor growth inhibition models are commonly used to describe and predict the dynamics of preclinical and clinical tumor size data. Moreover, frameworks also exist for describing the probability of different types of events, such as tumor metastasis or patient dropout. Combining these two types of models into a so‐called joint model enables model‐based prediction of PFS. In this paper, we have constructed a joint model from clinical data comparing the efficacy of FOLFOX against FOLFOX + panitumumab in patients with metastatic colorectal cancer. The nonlinear mixed effects framework was used to quantify interindividual variability (IIV). The model describes tumor size and PFS data well, and showed good predictive capabilities using truncated as well as external data. A machine‐learning guided analysis was performed to reduce unexplained IIV by incorporating patient covariates. The model‐based approach illustrated in this paper could be useful to help design clinical trials or to determine new promising drug candidates for combination therapy trials.

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Estimation of time to progression and post progression survival using joint modeling of summary level OS and PFS data with an ordinary differential equation model

Cited by 2 publications

References 17 publications

A multistate platform model for time‐to‐event endpoints in oncology clinical trials

A multistate platform model for time‐to‐event endpoints in oncology clinical trials

Model‐based prediction of progression‐free survival for combination therapies in oncology

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