Estimation of Solid Tumor Doubling Times from Progression-Free Survival Plots Using a Novel Statistical Approach


Tumor doubling time can significantly affect the outcome of anticancer therapy, but it is very challenging to determine. Here, we present a statistical approach that extracts doubling times from progression-free survival (PFS) plots, which inherently contains information regarding the growth of solid tumors. Twelve cancers were investigated and multiple PFS plots were evaluated for each type. The PFS plot showing fastest tumor growth was deemed to best represent the inherent growth kinetics of the solid tumor, and selected for further analysis. The exponential tumor growth rates were extracted from each PFS plot, along with associated variabilities, which ultimately allowed for the estimation of solid tumor doubling times. The mean simulated doubling times for pancreatic cancer, melanoma, hepatocellular carcinoma (HCC), renal cell carcinoma, triple negative breast cancer, non-small cell lung cancer, hormone receptor positive (HR+) breast cancer, human epidermal growth factor receptor-2 positive (HER-2+) breast cancer, gastric cancer, glioblastoma multiforme, colorectal cancer, and prostate cancer were 5.06, 3.78, 3.06, 2.67, 2.38, 2.40, 4.31, 4.12, and 3.84 months, respectively. For all cancers, clinically reported doubling times were within the estimated ranges. For all cancers, except HCC, the growth rates were best characterized by a log-normal distribution. For HCC, the gamma distribution best described the data. The statistical approach presented here provides a qualified method for extracting tumor growth rates and doubling times from PFS plots. It also allows estimation of the distributional characteristics for tumor growth rates and doubling times in a given patient population.

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This work was supported by NIH grant GM114179 and AI138195 to D.K.S., and the Centre for Protein Therapeutics at University at Buffalo.

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Correspondence to Dhaval K. Shah.

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RB has served as an expert witness through Belmore Neidrauer LLP funded by Janssen Pharmaceutical. All other authors declare they have no competing interests.

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Keith Dolcy is the co-first author.



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Kay, K., Dolcy, K., Bies, R. et al. Estimation of Solid Tumor Doubling Times from Progression-Free Survival Plots Using a Novel Statistical Approach. AAPS J 21, 27 (2019).

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  • PK/PD modeling and simulation
  • preclinical-to-clinical translation
  • progression-free survival
  • solid tumor doubling time
  • tumor growth rate