abc.md

Approximate Bayesian computation (ABC)

1. Input
2. Ouput
3. Implementation

The goal is to infer the proliferative advantage experienced by the cells w/ any ecDNA copies (fitness coefficient) experienced by the cells with ecDNA from the data, using a Bayesian framework (/path/to/ecdna abc).

Input

The user specifies the quantities available for the sample of interest to perform ABC using the binary ./target/release/preprocess.

The quantities given as input can be any combination of the following:

1. the ecDNA distribution, csv file or json file: if csv file, then each entry represent the copy number of each cell. If json file, then the file represents an histogram with keys as the ecDNA copies and entries the number of cells in sample for each copy number
2. the mean of the ecDNA distribution: a single entry csv file with the sample's mean of the ecdna distribution
3. the entropy of the ecDNA distribution: a single entry csv file with the sample's entropy of the ecdna distribution
4. the frequency of the cells w/ ecDNA: a single entry csv file with the sample's frequency of cells w/ any ecDNA copy

Adding information about the data (i.e. providing the program with several input quantities) will give a more precise inference of the fitness coefficient.

ecDNA distribution file example: csv file 1,0,10,1,20,0,2 or similarly json file {"0": 2, "1": 2, "10": 1, "20":1}

Output

abc.tar.gz which is a archived folder, where a csv file for each run is stored. This file has the following structure, where each entry is the result of the abc run for one sample:

Field	Type	Description
parental_idx	int	The idx of the subsampled run, if not present there was no subsampling
idx	int	Index of the run
timepoint	int	The int specifying the timepoint associated to the entry
seed	int	Seed used to generate the run
ecdna	float	One of the metric for ABC: the Kolmogorov-Smirnov distance between the ecDNA distributions
mean	float	One of the metric for ABC: the relative difference between the ecDNA distribution means
entropy	float	One of the metric for ABC: the relative difference between the ecDNA distribution entropies
f1	float	Selection coefficient of the cells w/ ecDNA
f2	float	Selection coefficient of the cells w/o ecDNA
d1	float	Death coefficient of the cells w/ ecDNA
d2	float	Death coefficient of the cells w/o ecDNA
cells	NbIndividuals	Number of cells in the sample when the abc rejection algorithm was ran
tumour_cells	NbIndividuals	Number of cells in the tumour population when the abc rejection algorithm was ran
init_mean	float	Mean of the ecDNA distribution used to initialize the system
init_cells	NbIndividuals	Number of cells used to initialize the system
init_copies	int	Copies of ecDNA used to initialize the system

Implementation

All simulations are first saved, then filtered out while plotting

To infer the most probable fitness coefficient from the data, we compare the data provided by the user to stochastic realizations of a birth-death process with exponential growth. ABC compares the runs from the simulation (for which the fitness coefficient is known) against the real data to recover the posterior distribution of the fitness coefficient (proliferative advantage of the cells w/ any ecDNA copies).

Instead of keeping only the appropriate runs, i.e. those similar to the patient's data, during the simulations implemented in rust, we save all the runs at first and then filter out those that have an associated distance bigger than a certain threshold during the plotting phase (python code). Doing so we can tune the threshold after the expensive simulations, i.e. without the need of rerunning all ABC simulations.

Simulations run in parallel and can be easily merged

Since runs in ABC are independent, we can run the same experiment twice and then merge the runs from the two experiments, if they were ran using the same parameters and input. Since runs in ABC are independent, we can run them in parallel with rust (rayon iter API).