Ensembling Variable Selectors by Stability Selection for the Cox Model

Algorithm 1

The stability selection algorithm for the Cox model.

Input

: an response vector containing survival times for observations.

: an vector containing censoring indicators for observations.

: design matrix.

: regularization parameter set, i.e., .

: ensemble size.

: a pre-set threshold.

Output: an index set for selected variables.

Main process of stability selection

(1) For

(a) Randomly draw a subset of size

without replacement from . Here,

stands for the largest integer less than or equal

to .

(b) For each , run lasso on , and

record the set for selected variables as .

End For

(2) Estimate the probability of each variable being selected as

,   

where , and is an indicator function,

when its condition is satisfied and otherwise.

(3) Select variables which satisfy , i.e. .