dot-lpbounds: Use linear programming to solve the bounds of TK or T0

In SunPathLab/Butte: BoUnds of Time Till Expansion, inferring the SCNA arrival time in the somatic evolution toward the most recent common ancestor of tumor sample(s).

Use linear programming to solve the bounds of TK or T0

Description

This function estimate the bounds of TK, which is the last time interval in the tumor cell envolution history. Based on different possible history given a copy number ratio, the function makes use of linear programming to minimize and maximize TK. The objective function of the optimization if f(x) = ta, which can be written as [0 0 0 0 0 ... 0 1]T*[t1 t2 t3 ... ta]. The first part of constraints are given by (A-qs')t = 0, where s' refers to the transpose vector calculated by rowSum(A). The second part of constraints is the convexity of time vector t. Each element of t refers to a relative fraction of time. We then combine these two constraints into a single linear system formation. he first constraint directly follows from At/c = q, wherer c is a normalizing constant given by the product s'*t.

Usage

.lpbounds(q, possible_histories, scost = 100, p0 = FALSE)

Arguments

q	q estimated from data
possible_histories	matrices of possible SCNA-SSNV histories, see also function "cnmutHistory"
scost	the cost for slack variables (default 100)
p0	logical, if TRUE, the upper bounds for T0 will be estimated (instead of TK)

Details

Then the feasibility of the solution region of the linear programming problem will only be influenced by q, which is optimized previously from data. The uncertainty of q can make the solution space infeasible. So we add some slack variables to elasticize the linear programming problem. For details, please check: http://web.mit.edu/lpsolve/doc/Infeasible.htm This elasticizing method will find the approximate bounds of TK close to the constraints. "scost" is the argument adjusting the penalty of the additional slack variables.

Value

the lower and upper bounds of the time duration for the last stage

SunPathLab/Butte documentation built on Sept. 19, 2023, 9:42 a.m.