The title of this blog entry refers to a letter published in the journal entitled, CPT: Pharmacometrics & Systems Pharmacology. The letter is open-access so those of you interested can read it online here. In this blog entry we will go through it.
The letter discusses a rather strange modelling practice which is becoming the norm within certain modelling and simulation groups in the pharmaceutical industry. There has been a spate of publications citing that tumour re-growth rate (GR) and time to tumour re-growth (TTG), derived using models to describe imaging time-series data, correlates to survival [1-6]. In those publications the authors show survival curves (Kaplan-Meiers) highlighting a very strong relationship between GR/ TTG and survival. They either split on the median value of GR/TTG or into quartiles and show very impressive differences in survival times between the groups created; see Figure 2 in  for an example (open access).
Do these relationships seem too good to be true? In fact they may well be. In order to derive GR/TTG you need time-series data. The value of these covariates are not known at the beginning of the study, and only become available after a certain amount of time has passed. Therefore this type of covariate is typically referred to as a time-dependent covariate. None of the authors in [1-6] describe GR/TTG as a time-dependent covariate nor treat it as such.
When the correlations to survival were performed in those articles the authors assumed that they knew GR/TTG before any time-series data was collected, which is clearly not true. Therefore survival curves, such as Figure 2 in , are biased as they are based on survival times calculated from study start time to time of death, rather than time from when GR/TTG becomes available to time of death. Therefore, the results in [1-6] should be questioned and GR/TTG should not be used for decision making, as the question around whether tumour growth rate correlates to survival is still rather open.
Could it be the case that the GR/TTG correlation to survival is just an illusion of a flawed modelling practice? This is what we shall answer in a future blog-post.
 W.D. Stein et al., Other Paradigms: Growth Rate Constants and Tumor Burden Determined Using Computed Tomography Data Correlate Strongly With the Overall Survival of Patients With Renal Cell Carcinoma, Cancer J (2009)
 W.D. Stein, J.L. Gulley, J. Schlom, R.A. Madan, W. Dahut, W.D. Figg, Y. Ning, P.M. Arlen, D. Price, S.E. Bates, T. Fojo, Tumor Regression and Growth Rates Determined in Five Intramural NCI Prostate Cancer Trials: The Growth Rate Constant as an Indicator of Therapeutic Efficacy, Clin. Cancer Res. (2011)
 W.D. Stein et al., Tumor Growth Rates Derived from Data for Patients in a Clinical Trial Correlate Strongly with Patient Survival: A Novel Strategy for Evaluation of Clinical Trial Data, The Oncologist. (2008)
 K. Han, L. Claret, Y. Piao, P. Hegde, A. Joshi, J. Powell, J. Jin, R. Bruno, Simulations to Predict Clinical Trial Outcome of Bevacizumab Plus Chemotherapy vs. Chemotherapy Alone in Patients With First-Line Gastric Cancer and Elevated Plasma VEGF-A, CPT Pharmacomet. Syst. Pharmacol. (2016)
 J. van Hasselt et al., Disease Progression/Clinical Outcome Model for Castration-Resistant Prostate Cancer in Patients Treated With Eribulin, CPT Pharmacomet. Syst. Pharmacol. (2015)
 L. Claret 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)