penAFT-package | R Documentation |

This package contains numerous functions related to the penalized Gehan estimator. In particular, the main functions are for solution path computation, cross-validation, prediction, and coefficient extraction.

The primary functions are `penAFT`

and `penAFT.cv`

, the latter of which performs cross-validation. In general, both functions fit the penalized Gehan estimator. Given `(\log(y_1), x_1, \delta_1),\dots,(\log(y_n), x_n, \delta_n)`

where `y_i`

is the minimum of the survival time and censoring time, `x_i`

is a `p`

-dimensional predictor, and `\delta_i`

is the indicator of censoring, `penAFT`

fits the solution path for the argument minimizing

`\frac{1}{n^2}\sum_{i=1}^n \sum_{j=1}^n \delta_i \{ \log(y_i) - \log(y_j) - (x_i - x_j)'\beta \}^{-} + \lambda g(\beta)`

where `\{a \}^{-} := \max(-a, 0) `

, `\lambda > 0`

, and `g`

is either the weighted elastic net penalty or weighted sparse group lasso penalty. The weighted elastic net penalty is defined as

`\alpha \| w \circ \beta\|_1 + \frac{(1-\alpha)}{2}\|\beta\|_2^2`

where `w`

is a set of non-negative weights (which can be specified in the `weight.set`

argument). The weighted sparse group-lasso penalty we consider is

`\alpha \| w \circ \beta\|_1 + (1-\alpha)\sum_{l=1}^G v_l\|\beta_{\mathcal{G}_l}\|_2`

where again, `w`

is a set of non-negative weights and `v_l`

are weights applied to each of the `G`

(user-specified) groups.

For a comprehensive description of the algorithm, and more details about rank-based estimation in general, please refer to the referenced manuscript.

Aaron J. Molstad and Piotr M. Suder Maintainer: Aaron J. Molstad <amolstad@ufl.edu>

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