Open Access Open Badges Methodology article

Exposure time independent summary statistics for assessment of drug dependent cell line growth inhibition

Steffen Falgreen1*, Maria Bach Laursen1, Julie Støve Bødker1, Malene Krag Kjeldsen1, Alexander Schmitz1, Mette Nyegaard2, Hans Erik Johnsen1, Karen Dybkær1 and Martin Bøgsted13

  • * Corresponding author: Steffen Falgreen

Author Affiliations

1 Department of Haematology, Aalborg University Hospital, Aalborg, Denmark

2 Department of Biomedicine, Aarhus University, Aarhus, Denmark

3 Department of Mathematical Sciences, Aalborg University, Aalborg, Denmark

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BMC Bioinformatics 2014, 15:168  doi:10.1186/1471-2105-15-168

Published: 5 June 2014



In vitro generated dose-response curves of human cancer cell lines are widely used to develop new therapeutics. The curves are summarised by simplified statistics that ignore the conventionally used dose-response curves’ dependency on drug exposure time and growth kinetics. This may lead to suboptimal exploitation of data and biased conclusions on the potential of the drug in question. Therefore we set out to improve the dose-response assessments by eliminating the impact of time dependency.


First, a mathematical model for drug induced cell growth inhibition was formulated and used to derive novel dose-response curves and improved summary statistics that are independent of time under the proposed model. Next, a statistical analysis workflow for estimating the improved statistics was suggested consisting of 1) nonlinear regression models for estimation of cell counts and doubling times, 2) isotonic regression for modelling the suggested dose-response curves, and 3) resampling based method for assessing variation of the novel summary statistics. We document that conventionally used summary statistics for dose-response experiments depend on time so that fast growing cell lines compared to slowly growing ones are considered overly sensitive. The adequacy of the mathematical model is tested for doxorubicin and found to fit real data to an acceptable degree. Dose-response data from the NCI60 drug screen were used to illustrate the time dependency and demonstrate an adjustment correcting for it. The applicability of the workflow was illustrated by simulation and application on a doxorubicin growth inhibition screen. The simulations show that under the proposed mathematical model the suggested statistical workflow results in unbiased estimates of the time independent summary statistics. Variance estimates of the novel summary statistics are used to conclude that the doxorubicin screen covers a significant diverse range of responses ensuring it is useful for biological interpretations.


Time independent summary statistics may aid the understanding of drugs’ action mechanism on tumour cells and potentially renew previous drug sensitivity evaluation studies.

Dose response experiments; NCI60; Doxorubicin; Mathematical modelling; Differential equation modelling; Nonlinear regression; Isotonic regression; Bootstrap; Parametric bootstrap