netcox_cv {netcox}

cross-validation for netcox

Description

Conduct cross-validation (cv) for netcox.

Usage

netcox_cv(
  x,
  ID,
  time,
  time2,
  event,
  lambda,
  group,
  group_variable,
  penalty_weights,
  par_init,
  nfolds = 10,
  stepsize_init = 1,
  stepsize_shrink = 0.8,
  tol = 1e-05,
  maxit = 1000L,
  verbose = FALSE
)

Arguments

x

Predictor matrix with dimension nm * p, where n is the number of subjects, m is the maximum observation time, and p is the number of predictors. See Details.

ID

The ID of each subjects, each subject has one ID (many rows in x share one ID).

time

Represents the start of each time interval.

time2

Represents the stop of each time interval.

event

Indicator of event. event = 1 when event occurs and event = 0 otherwise.

lambda

Sequence of regularization coefficients \lambda's.

group

G * G matrix describing the relationship between the groups of variables, where G represents the number of groups. Denote the i-th group of variables by g_i. The (i,j) entry is 1 if and only if i\neq j and g_i is a child group (subset) of g_j, and is 0 otherwise. See Examples and Details.

group_variable

p * G matrix describing the relationship between the groups and the variables. The (i,j) entry is 1 if and only if variable i is in group g_j, but not in any child group of g_j, and is 0 otherwise. See Examples and Details.

penalty_weights

Optional, vector of length G specifying the group-specific penalty weights. If not specified, the default value is \mathbf{1}_G. Modify with caution.

par_init

Optional, vector of initial values of the optimization algorithm. Default initial value is zero for all p variables.

nfolds

Optional, the folds of cross-validation. Default is 10.

stepsize_init

Initial value of the stepsize of the optimization algorithm. Default is 1.

stepsize_shrink

Factor in (0,1) by which the stepsize shrinks in the backtracking linesearch. Default is 0.8.

tol

Convergence criterion. Algorithm stops when the l_2 norm of the difference between two consecutive updates is smaller than tol.

maxit

Maximum number of iterations allowed.

verbose

Logical, whether progress is printed.

Details

For each lambda, 10 folds cross-validation (by default) is performed. The cv error is defined as follows. Suppose we perform K-fold cross-validation, denote \hat{\beta}^{-k} by the estimate obtained from the rest of K-1 folds (training set). The error of the k-th fold (test set) is defined as 2(P-Q) divided by R, where P is the log partial likelihood evaluated at \hat{\beta}^{-k} using the entire dataset, Q is the log partial likelihood evaluated at \hat{\beta}^{-k} using the training set, and R is the number of events in the test set. We do not use the negative log partial likelihood evaluated at \hat{\beta}^{-k} using the test set because the former definition can efficiently use the risk set, and thus it is more stable when the number of events in each test set is small (think of leave-one-out). The cv error is used in parameter tuning. To account for balance in outcomes among the randomly formed test set, we divide the deviance 2(P-Q) by R. To get the estimated coefficients that has the minimum cv error, use netcox()$Estimates[netcox()$Lambdas==netcox_cv()$lambda.min]. To apply the 1-se rule, use netcox()$Estimates[netcox()$Lambdas==netcox_cv()$lambda.1se].

Value

A list.

lambdas

A vector of lambda used for each cross-validation.

cvm

The cv error averaged across all folds for each lambda.

cvsd

The standard error of the cv error for each lambda.

cvup

The cv error plus its standard error for each lambda.

cvlo

The cv error minus its standard error for each lambda.

nzero

The number of non-zero coefficients at each lambda.

netcox.fit

A netcox fit for the full data at all lambdas.

lambda.min

The lambda such that the cvm reach its minimum.

lambda.1se

The maximum of lambda such that the cvm is less than the minimum the cvup (the minmum of cvm plus its standard error).

See Also

netcox, plot_netcox_cv.

Examples

grp <- matrix(c(0, 0, 0, 0, 0,
                0, 0, 0, 0, 0,
                1, 1, 0, 0, 0,
                0, 0, 0, 0, 0,
                0, 1, 0, 1, 0),
              ncol = 5, byrow = TRUE)
grp.var <- matrix(c(1, 0, 0, 0, 0, #A1
                    1, 0, 0, 0, 0, #A2
                    0, 0, 0, 1, 0, #C1
                    0, 0, 0, 1, 0, #C2
                    0, 1, 0, 0, 0, #B
                    0, 0, 1, 0, 0, #A1B
                    0, 0, 1, 0, 0, #A2B
                    0, 0, 0, 0, 1, #C1B
                    0, 0, 0, 0, 1  #C2B
                   ), ncol = 5, byrow = TRUE)
eta_g <- rep(1, 5)
x <- as.matrix(sim[, c("A1","A2","C1","C2","B",
                       "A1B","A2B","C1B","C2B")])
lam.seq <- 10^seq(0, -2, by = -0.2)

cv <- netcox_cv(x = x,
                ID = sim$Id,
                time = sim$Start,
                time2 = sim$Stop,
                event = sim$Event,
                lambda = lam.seq,
                group = grp,
                group_variable = grp.var,
                penalty_weights = eta_g,
                nfolds = 5,
                tol = 1e-4,
                maxit = 1e3,
                verbose = FALSE)