R: Fits the entire L1 regularization path for Cox proportional...

coxpath {glmpath}

R Documentation

Fits the entire L1 regularization path for Cox proportional hazards model

Description

This algorithm uses predictor-corrector method to compute the entire regularization path for Cox proportional hazards model with L1 penalty.

Usage

  coxpath(data, nopenalty.subset = NULL, method = c("breslow", "efron"),
          lambda2 = 1e-5, max.steps = 10 * min(n, m), max.norm = 100 * m,
          min.lambda = (if (m >= n) 1e-3 else 0), max.vars = Inf,
          max.arclength = Inf, frac.arclength = 1, add.newvars = 1,
          bshoot.threshold = 0.1, relax.lambda = 1e-7,
          approx.Gram = FALSE, standardize = TRUE,
          eps = .Machine$double.eps, trace = FALSE)

Arguments

`data`	a list consisting of `x:` a matrix of features, `time:` the survival time, and `status:` censor status with 1 if died and 0 if censored.
`nopenalty.subset`	a set of indices for the predictors that are not subject to the L1 penalty
`method`	approximation method for tied survival times. Approximations derived by Breslow (1974) and Efron (1977) are available. Default is `breslow.`
`lambda2`	regularization parameter for the L2 norm of the coefficients. Default is `1e-5.`
`max.steps`	an optional bound for the number of steps to be taken. Default is `10 * min{nrow(x), ncol(x)}.`
`max.norm`	an optional bound for the L1 norm of the coefficients. Default is `100 * ncol(x).`
`min.lambda`	an optional (lower) bound for the size of `\lambda`. When `ncol(x)` is relatively large, the coefficient estimates are prone to numerical precision errors at extremely small `\lambda`. In such cases, early stopping is recommended. Default is `0` for `ncol(x) < nrow(x)` cases and `1e-3` otherwise.
`max.vars`	an optional bound for the number of active variables. Default is `Inf.`
`max.arclength`	an optional bound for arc length (L1 norm) of a step. If `max.arclength` is extremely small, an exact nonlinear path is produced. Default is `Inf.`
`frac.arclength`	Under the default setting, the next step size is computed so that the active set changes right at the next value of lambda. When `frac.arclength` is assigned some fraction between 0 and 1, the step size is decreased by the factor of `frac.arclength` in arc length. If `frac.arclength=0.2,` the step length is adjusted so that the active set would change after five smaller steps. Either `max.arclength` or `frac.arclength` can be used to force the path to be more accurate. Default is `1.`
`add.newvars`	`add.newvars` candidate variables (that are currently not in the active set) are used in the corrector step as potential active variables. Default is `1.`
`bshoot.threshold`	If the absolute value of a coefficient is larger than `bshoot.threshold` at the first corrector step it becomes nonzero (therefore when `\lambda` is considered to have been decreased too far), `\lambda` is increased again. i.e. A backward distance in `\lambda` that makes the coefficient zero is computed. Default is `0.1.`
`relax.lambda`	A variable joins the active set if `\|l'(\beta)\| > \lambda`*(1-`relax.lambda`). Default is `1e-7.` If no variable joins the active set even after many (>20) steps, the user should increase `relax.lambda` to `1e-6` or `1e-5,` but not more than that. This adjustment is sometimes needed because of the numerical precision/error propagation problems. In general, the paths are less accurate with relaxed lambda.
`approx.Gram`	If `TRUE,` an approximated Gram matrix is used in predictor steps; each step takes less number of computations, but the total number of steps usually increases. This might be useful when the number of features is large.
`standardize`	If `TRUE,` predictors are standardized to have a unit variance.
`eps`	an effective zero
`trace`	If `TRUE,` the algorithm prints out its progress.

Details

This algorithm implements the predictor-corrector method to determine the entire path of the coefficient estimates as the amount of regularization varies; it computes a series of solution sets, each time estimating the coefficients with less regularization, based on the previous estimate. The coefficients are estimated with no error at the knots, and the values are connected, thereby making the paths piecewise linear.

Value

A coxpath object is returned.

`lambda`	vector of `\lambda` values for which the exact coefficients are computed
`lambda2`	`\lambda_2` used
`step.length`	vector of step lengths in `\lambda`
`corr`	matrix of `l'(\beta)` values (derivatives of the log-partial-likelihood)
`new.df`	vector of degrees of freedom (to be used in the plot function)
`df`	vector of degrees of freedom at each step
`loglik`	vector of log-partial-likelihood computed at each step
`aic`	vector of AIC values
`bic`	vector of BIC values
`b.predictor`	matrix of coefficient estimates from the predictor steps
`b.corrector`	matrix of coefficient estimates from the corrector steps
`new.A`	vector of boolean values indicating the steps at which the active set changed (to be used in the plot/predict functions)
`actions`	actions taken at each step
`meanx`	means of the columns of x
`sdx`	standard deviations of the columns of x
`xnames`	column names of x
`method`	method used
`nopenalty.subset`	nopenalty.subset used
`standardize`	`TRUE` if the predictors were standardized before fitting

Author(s)

Mee Young Park and Trevor Hastie

References

Mee Young Park and Trevor Hastie (2007) L1 regularization path algorithm for generalized linear models. J. R. Statist. Soc. B, 69, 659-677.

Examples

data(lung.data)
attach(lung.data)
fit.a <- coxpath(lung.data)
fit.b <- coxpath(lung.data, method="efron")
detach(lung.data)

[Package glmpath version 0.98 Index]