multiview.cox.path {multiview}

Fit a Cox regression model with elastic net regularization for a path of lambda values

Description

Fit a Cox regression model via penalized maximum likelihood for a path of lambda values. Can deal with (start, stop] data and strata, as well as sparse design matrices.

Usage

multiview.cox.path(
  x_list,
  x,
  y,
  rho = 0,
  weights = NULL,
  lambda = NULL,
  offset = NULL,
  alpha = 1,
  nlambda = 100,
  lambda.min.ratio = ifelse(nobs < nvars, 0.01, 1e-04),
  standardize = TRUE,
  intercept = TRUE,
  thresh = 1e-07,
  exclude = integer(0),
  penalty.factor = rep(1, nvars),
  lower.limits = -Inf,
  upper.limits = Inf,
  maxit = 1e+05,
  trace.it = 0,
  nvars,
  nobs,
  xm,
  xs,
  control,
  vp,
  vnames,
  is.offset
)

Arguments

x_list

a list of x matrices with same number of rows nobs

x

the cbinded matrices in x_list

y

the quantitative response with length equal to nobs, the (same) number of rows in each x matrix

rho

the weight on the agreement penalty, default 0. rho=0 is a form of early fusion, and rho=1 is a form of late fusion. We recommend trying a few values of rho including 0, 0.1, 0.25, 0.5, and 1 first; sometimes rho larger than 1 can also be helpful.

weights

observation weights. Can be total counts if responses are proportion matrices. Default is 1 for each observation

lambda

A user supplied lambda sequence, default NULL. Typical usage is to have the program compute its own lambda sequence. This sequence, in general, is different from that used in the glmnet::glmnet() call (named lambda) Supplying a value of lambda overrides this. WARNING: use with care. Avoid supplying a single value for lambda (for predictions after CV use stats::predict() instead. Supply instead a decreasing sequence of lambda values as multiview relies on its warms starts for speed, and its often faster to fit a whole path than compute a single fit.

offset

A vector of length nobs that is included in the linear predictor (a nobs x nc matrix for the "multinomial" family). Useful for the "poisson" family (e.g. log of exposure time), or for refining a model by starting at a current fit. Default is NULL. If supplied, then values must also be supplied to the predict function.

alpha

The elasticnet mixing parameter, with 0\le\alpha\le 1. The penalty is defined as

(1-\alpha)/2||\beta||_2^2+\alpha||\beta||_1.

alpha=1 is the lasso penalty, and alpha=0 the ridge penalty.

nlambda

The number of lambda values - default is 100.

lambda.min.ratio

Smallest value for lambda, as a fraction of lambda.max, the (data derived) entry value (i.e. the smallest value for which all coefficients are zero). The default depends on the sample size nobs relative to the number of variables nvars. If nobs > nvars, the default is 0.0001, close to zero. If nobs < nvars, the default is 0.01. A very small value of lambda.min.ratio will lead to a saturated fit in the nobs < nvars case. This is undefined for "binomial" and "multinomial" models, and glmnet will exit gracefully when the percentage deviance explained is almost 1.

standardize

Logical flag for x variable standardization, prior to fitting the model sequence. The coefficients are always returned on the original scale. Default is standardize=TRUE. If variables are in the same units already, you might not wish to standardize. See details below for y standardization with family="gaussian".

intercept

Should intercept(s) be fitted (default TRUE)

thresh

Convergence threshold for coordinate descent. Each inner coordinate-descent loop continues until the maximum change in the objective after any coefficient update is less than thresh times the null deviance. Defaults value is 1E-7.

exclude

Indices of variables to be excluded from the model. Default is none. Equivalent to an infinite penalty factor for the variables excluded (next item). Users can supply instead an exclude function that generates the list of indices. This function is most generally defined as ⁠function(x_list, y, ...)⁠, and is called inside multiview to generate the indices for excluded variables. The ... argument is required, the others are optional. This is useful for filtering wide data, and works correctly with cv.multiview. See the vignette 'Introduction' for examples.

penalty.factor

Separate penalty factors can be applied to each coefficient. This is a number that multiplies lambda to allow differential shrinkage. Can be 0 for some variables, which implies no shrinkage, and that variable is always included in the model. Default is 1 for all variables (and implicitly infinity for variables listed in exclude). Note: the penalty factors are internally rescaled to sum to nvars, and the lambda sequence will reflect this change.

lower.limits

Vector of lower limits for each coefficient; default -Inf. Each of these must be non-positive. Can be presented as a single value (which will then be replicated), else a vector of length nvars

upper.limits

Vector of upper limits for each coefficient; default Inf. See lower.limits

maxit

Maximum number of passes over the data for all lambda values; default is 10^5.

trace.it

If trace.it=1, then a progress bar is displayed; useful for big models that take a long time to fit.

nvars

the number of variables (total)

nobs

the number of observations

xm

the column means vector (could be zeros if standardize = FALSE)

xs

the column std dev vector (could be 1s if standardize = FALSE)

control

the multiview control object

vp

the variable penalities (processed)

vnames

the variable names

is.offset

a flag indicating if offset is supplied or not

Details

Sometimes the sequence is truncated before nlambda values of lambda have been used. This happens when cox.path detects that the decrease in deviance is marginal (i.e. we are near a saturated fit).

Value

An object of class "coxnet" and "glmnet".

a0

Intercept value, NULL for "cox" family.

beta

A nvars x length(lambda) matrix of coefficients, stored in sparse matrix format.

df

The number of nonzero coefficients for each value of lambda.

dim

Dimension of coefficient matrix.

lambda

The actual sequence of lambda values used. When alpha=0, the largest lambda reported does not quite give the zero coefficients reported (lambda=inf would in principle). Instead, the largest lambda for alpha=0.001 is used, and the sequence of lambda values is derived from this.

dev.ratio

The fraction of (null) deviance explained. The deviance calculations incorporate weights if present in the model. The deviance is defined to be 2*(loglike_sat - loglike), where loglike_sat is the log-likelihood for the saturated model (a model with a free parameter per observation). Hence dev.ratio=1-dev/nulldev.

nulldev

Null deviance (per observation). This is defined to be 2*(loglike_sat -loglike(Null)). The null model refers to the 0 model.

npasses

Total passes over the data summed over all lambda values.

jerr

Error flag, for warnings and errors (largely for internal debugging).

offset

A logical variable indicating whether an offset was included in the model.

call

The call that produced this object.

nobs

Number of observations.

Examples

set.seed(2)
nobs <- 100; nvars <- 15
xvec <- rnorm(nobs * nvars)
xvec[sample.int(nobs * nvars, size = 0.4 * nobs * nvars)] <- 0
x <- matrix(xvec, nrow = nobs)
beta <- rnorm(nvars / 3)
fx <- x[, seq(nvars / 3)] %*% beta / 3
ty <- rexp(nobs, exp(fx))
tcens <- rbinom(n = nobs, prob = 0.3, size = 1)
jsurv <- survival::Surv(ty, tcens)
fit1 <- glmnet:::cox.path(x, jsurv)

# works with sparse x matrix
x_sparse <- Matrix::Matrix(x, sparse = TRUE)
fit2 <- glmnet:::cox.path(x_sparse, jsurv)

# example with (start, stop] data
set.seed(2)
start_time <- runif(100, min = 0, max = 5)
stop_time <- start_time + runif(100, min = 0.1, max = 3)
status <- rbinom(n = nobs, prob = 0.3, size = 1)
jsurv_ss <- survival::Surv(start_time, stop_time, status)
fit3 <- glmnet:::cox.path(x, jsurv_ss)

# example with strata
jsurv_ss2 <- glmnet::stratifySurv(jsurv_ss, rep(1:2, each = 50))
fit4 <- glmnet:::cox.path(x, jsurv_ss2)