Benjamin Ribba (1), Nick Holford (2), France Mentré (3)
(1) Inria Sophia-Antipolis Méditerranée, France, (2) Department of Pharmacology and Clinical Pharmacology, University of Auckland, Auckland, New Zealand, (3) IAME, UMR 1137, INSERM & Université Paris Diderot, Sorbonne Paris Cité, Paris, F-75018, France.
Objectives: Mixed-effect models are increasingly being used to analyze the time-course of tumor size and to identify tumor size metrics as predictors of overall survival in cancer patients. However, analysis of survival by tumor response may be misleading about the effect of treatment on survival [1, 2]. Our objective is to address how the use of empirical Bayes individual parameter estimates (EBE) might influence the Type 1 error of falsely detecting or failing to detect tumor size metrics as predictors of overall survival.
Methods: We simulated tumor size data by using an empirical model reported by Claret et al. [3]. Survival times were simulated independently from tumor size by sampling from an exponential distribution. The influence of using EBE on Type 1 error was explored through 9 different simulation scenarios with mean survival times from 6 to 180 weeks. The simulated tumor size data was used to obtain EBE using a mixed-effect approach (NONMEM, version 7.2). The EBE of individual parameters were used to calculate individual derived metrics: the tumor size ratio at week 6 (TSR6) and the time to tumor growth (TTG).
Results: The type 1 error was increased for TTG for all scenarios, and approached a peak of 43.4% in the scenario with a mean survival time of 48 weeks. The smaller inflation of Type 1 error observed with very short mean survival times of 6 and 12 weeks is linked to a very high shrinkage for TTG reducing the variability of the metrics across patients. The type 1 error of TSR6 was outside the prediction interval in the scenario with a mean survival time of 6 weeks. At longer survival times (36 to 180 weeks) the Type 1 error was at or below the prediction interval. When the “true” simulated individual parameters were used to calculate reference values of TTG (ITTG) and TSR6 (ITSR6), the Type 1 error rates were all within the prediction interval. These results demonstrate that the increased Type 1 error is associated with using EBE individual estimates which have high shrinkage.
Conclusions: The use of the metric TTG is problematic with substantial inflation of Type 1 error, especially, when mean survival time is close to TTG. The use of a metric similar to TSR6 as used by Wang et al. [4] could also be problematic in making appropriate drug development decisions because the Type 1 error rate is too high when the mean survival time is similar to the time of tumor size ratio evaluation and too low when mean survival times are longer.
References:
[1] Buyse, M. and P. Piedbois, On the relationship between response to treatment and survival time. Stat Med, 1996. 15: p. 2797-812.
[2] Anderson, J.R., K.C. Cain, and R.D. Gelber, Analysis of survival by tumor response and other comparisons of time-to-event by outcome variables. J Clin Oncol, 2008. 26(24): p. 3913-5.
[3] Claret, L., et al., 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. 31(17): p. 2110-4. [4] Wang, Y., et al., Elucidation of relationship between tumor size and survival in non-small-cell lung cancer patients can aid early decision making in clinical drug development. Clinical pharmacology and therapeutics, 2009. 86(2): p. 167-74.
Reference: PAGE 23 (2014) Abstr 3199 [www.page-meeting.org/?abstract=3199]
Poster: Drug/Disease modeling - Oncology