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ctdna computes the expected tumor detection size at a given sampling frequency.

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ctDNA: Circulating tumor DNA

Python package ( to compute the shedding of a biomarker from cancer cells into the bloodstream and its analysis in liquid biopsies (small blood samples). The package can be run from the command line or various methods can be important for customized calculations. Multiple examples are provided below and can be executed within a browser from Cite: Avanzini et al, A mathematical model of ctDNA shedding predicts tumor detection size, Science Advances 6:eabc4308 (2020), in press. For further technical details see the preprint Avanzini et al., bioRxiv (2020): Source code is available at


Installation and Setup


ctdna can be run in the following modes:

  1. dynamics: simulates the evolutionary dynamics of a tumor and its biomarkers over time
  2. distribution: simulates the biomarker distribution at a given tumor size or tumor age
  3. detection: simulates the detection size of a growing tumor for repeated testing at a desired annual false positive rate or a specified p-value threshold
  4. roc: computes the ROC (receiver operating characteristic)

See <PACKAGE_DIRECTORY>/ for default parameter values.


  • Use the interactive binder notebook at to immediately try the package. Examples show how to calculate the probability to detect a specific actionable mutation in tumors with diameters of 1, 1.2, 1.5, and 2 cm with a specificity of 99% example.ipynb
  • Simulate tumor growth and ctDNA shedding dynamics of 10 cancers: ctdna dynamics -b 0.14 -d 0.13 -M 1e10 -n 10
  • Simulate ctDNA at a given tumor size for 100 subjects: ctdna distribution -b 0.14 -d 0.13 -n 100 -M 1e8 --q_d=1.4e-4
  • Simulate monthly relapse testing for previously simulated tumor growth and shedding dynamics: ctdna detection monthly -b 0.14 -d 0.13 -M 1e10 --panel_size 20 --n_muts 20 --annual_fpr 0.05 --seq_eff 0.5 --imaging_det_size 1e9
  • Simulate annual screening with CancerSEEK for previously simulated tumor growth and shedding dynamics: ctdna detection annually -b 0.14 -d 0.136 -M 1e11 --panel_size 2000 --n_muts 1 --annual_fpr 0.01 --seq_eff 0.5 --diagnosis_size 2.25e10
  • Simulate annual screening with CAPPSeq for previously simulated tumor growth and shedding dynamics: ctdna detection annually -b 0.14 -d 0.136 -M 1e11 --panel_size 300000 --n_muts 10 --pval_th 1.5e-7 --seq_eff 0.5 --diagnosis_size 2.25e10


  • -b <> or --birth_rate <>: birth rate of cancer cells

  • -d <> or --death_rate <>: death rate of cancer cells

  • --q_d <>: ctDNA shedding probability per cell death

  • --q_b <>: ctDNA shedding probability per cell birth

  • --lambda1 <>: ctDNA shedding probability per cell per day

  • --t12_mins <>: cfDNA half-life time in minutes

  • --tube_size <>: size of blood sample tube (liters; default 0.015 l)

  • --panel_size <>: sequencing panel size

  • --seq_err <>: sequencing error rate per base-pair (default: 1e-5)

  • --seq_eff <>: sequencing efficiency, ie. fraction of the sampled molecules that are actually successfully sequenced (default: 0.5)

  • --n_muts <>: number of clonal mutations in the cancer that are covered by the sequencing panel

  • -M <> or --det_size <>: tumor detection size where biomarker level is evaluated or size where dynamics simulations are stopped

  • -T <> or --sim_time <>: simulations end when cancer reaches the given time

  • --exact_th <>: approximate growth of tumor after this given threshold is reached

  • -o <> or --output_dir <>: output directory for files (default is defined in <CTDNA_DIRECTORY>/ctdna/

  • --biomarker_wt_freq_ml <> Optional argument to fix the wildtype haploid genome equivalents (hGE) per plasma ml to the given number instead of sampling the plasma DNA concentration from a Gamma distribution with parameters specified in <CTDNA_DIRECTORY>/ctdna/

Detection mode

  • --annual_fpr <>: Specifies desired annual false positive rate (1 - specificity) if test is repeated at the given frequency over a year
  • --pval_th <>: Instead of the desired annual false positive rate --annual_fpr, one can directly provide a p-value threshold that calls somatic point mutations in ctDNA

Authors: Stefano Avanzini & Johannes Reiter, Stanford University,

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