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, δ_1),…,(\log(y_n), x_n, δ_n)* where *y_i* is the minimum of the survival time and censoring time, *x_i* is a *p*-dimensional predictor, and *δ_i* is the indicator of censoring, `penAFT`

fits the solution path for the argument minimizing

*\frac{1}{n^2}∑_{i=1}^n ∑_{j=1}^n δ_i \{ \log(y_i) - \log(y_j) - (x_i - x_j)'β \}^{-} + λ g(β)*

where *\{a \}^{-} := \max(-a, 0) *, *λ > 0*, and *g* is either the weighted elastic net penalty or weighted sparse group lasso penalty. The weighted elastic net penalty is defined as

*α \| w \circ β\|_1 + \frac{(1-α)}{2}\|β\|_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

*α \| w \circ β\|_1 + (1-α)∑_{l=1}^G v_l\|β_{\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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