This package contains numerous functions related to a penalized rank-based estimator of the semiparametric AFT, the so-called penalized Gehan estimator. In particular, the main functions are for solution path computation, cross-validation, prediction, and coefficient extraction.
Aaron J. Molstad and Piotr M. Suder Maintainer: Aaron J. Molstad <amolstad@ufl.edu>
The primary functions are penAFT and penAFT.cv, the latter of which performs cross-validation. In general, both functions fit the penalized Gehan estimator---the minimizer of a rank-based loss function. 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.