A simulation study to assess the impact of time to growth estimation shrinkage on overall survival association
Claret L, Bruno R.
Parsight a Certara company, Marseilles (France)
Objectives: Model based estimate of time to growth (TTG) of tumor sum of longest diameters (SLD) has been developed to predict overall survival (OS) in metastatic cancer patients in several diseases (1, 2). TTG is superior to earlier metrics such as tumor size ratio at landmarked time point (e.g. end of cycle 2). Recent correspondences and discussions have raised questions about this modeling approach (3-6). The tumor growth inhibition (TGI) observations are limited by the disease progression defined by an SLD increase of 20% for the minimum and/or death (RECIST). The objective of this simulation work is to evaluate the model parameter shrinkage on TTG estimate and the subsequent association with OS with limited number of observations.
Methods: TTG and OS of 500 patients were simulated based on previously published models (1). Several assumptions on the strength of the association (none to full) and on the time difference between TTG and OS were simulated to evaluate the impact on TTG and the TTG-OS association. TTG and the TTG-OS association were estimated by a two stage approach: 1) simplified TGI nonlinear mixed effect model (NONMEM, FOCE) to estimate TTG; 2) a cox proportional hazard semi-parametric model (coxph in R) to estimate the TTG-OS association. For each of 1000 replications the bias and the shrinkage of TTG and the TTG-OS association were evaluated. Alternative tumor size observation schedules were also evaluated in order to improve TTG estimate.
Results: The TTG shrinkage was about 40% (24%-60%) in the original scenario assuming median TTG of 24 weeks and median OS of 83 weeks. It could be reduced down to 35% if the patient follow up is up to 100% increase of the minimum recorded size instead of 20%. On the other hand shrinkage increased up to 50% when the OS survival time was divided by 2. In all scenarios assuming no TTG-OS association, the type I (p<1%) errors were below 3% with a maximum risk when the median survival (83 weeks) was divided by 2 (41.5 weeks). The type II errors (p<1%) were below 3% in scenarios assuming association.
Conclusions: Despite a relatively large shrinkage of TTG due to a limited number of observations the TTG-OS association does not seem to be impacted. This shrinkage depends on the time difference between TTG and OS and the observation schedule. TGI models are developed from the SLD as defined by RECIST (7), it would be worth to optimize tumor size observation schedule to extract more information on the TGI dynamic.
References:
[1] Claret L, Gupta M, Han K, Joshi A, Sarapa N, He J, Powell B, Bruno R. Evaluation of tumor-size response metrics to predict overall survival in Western and Chinese patients with first-line metastatic colorectal cancer. J Clin Oncol. 2013 Jun 10;31(17):2110-4.
[2] Claret L, Bruno R, Lu JF, Sun YN, Hsu CP. Exploratory Modeling and Simulation to Support Development of Motesanib in Asian Patients With Non-Small Cell Lung Cancer Based on MONET1 Study Results. Clin Pharmacol Ther. 2014 Jan 17.
[3] An MW, Mandrekar SJ, Sargent DJ. Application of tumor measurement-based metrics in the real world. J Clin Oncol. 2013 Dec 1;31(34):4374.
[4] Mansmann UR, Laubender RP. Methodologic diligence is needed to define and validate tumor-size response metrics to predict overall survival in first-line metastatic colorectal cancer. J Clin Oncol. 2013 Dec 1;31(34):4373-4.
[5] Claret L, Bruno R. Reply to U.R. Mansmann et al and M.-W. An et al. J Clin Oncol. 2013 Dec 1;31(34):4374-5.
[6] Ribba B, Mentre F, Holfold N, personal communication
[7] Therasse P, Arbuck SG, Eisenhauer EA, Wanders J, Kaplan RS, Rubinstein L, Verweij J, Van Glabbeke M, van Oosterom AT, Christian MC, Gwyther SG. New guidelines to evaluate the response to treatment in solid tumors. European Organization for Research and Treatment of Cancer, National Cancer Institute of the United States, National Cancer Institute of Canada. J Natl Cancer Inst. 2000 Feb 2;92(3):205-16.
