Model predictions based on a fitted ncvsurv object

Similar to other predict methods, this function returns predictions from a fitted ncvsurv object.

Usage

# S3 method for class 'ncvsurv'
predict(
  object,
  X,
  type = c("link", "response", "survival", "hazard", "median", "coefficients", "vars",
    "nvars"),
  lambda,
  which = 1:length(object$lambda),
  ...
)

Arguments

object

Fitted "ncvsurv" model object.

X

Matrix of values at which predictions are to be made. Not used for type="coefficients" or for some of the type settings in predict.

type

Type of prediction:

link returns the linear predictors
response gives the risk (i.e., exp(link))
survival returns the estimated survival function
median estimates median survival times The other options are all identical to their ncvreg() counterparts:
coefficients returns the coefficients
vars returns a list containing the indices and names of the nonzero variables at each value of lambda
nvars returns the number of nonzero coefficients at each value of lambda.

lambda

Values of the regularization parameter lambda at which predictions are requested. For values of lambda not in the sequence of fitted models, linear interpolation is used.

which

Indices of the penalty parameter lambda at which predictions are required. By default, all indices are returned. If lambda is specified, this will override which.

...

Not used.

Value

The return value depends on type. Unless otherwise noted, predictions are returned as a matrix with one row per observation in X (or per observation in the original dataset if X is not provided) and one column per value of lambda. If lambda has length 1, the result is simplified to a vector with one element per observation.

type = "link": A numeric matrix of linear predictors.
type = "response": A numeric matrix of estimated risks.
type = "survival": A list of estimated survival functions (if type = "survival", lambda must be a scalar).
type = "median": A numeric matrix of estimated median survival times.
type = "coefficients": A numeric matrix of estimated coefficients. One row per column of X and one column per value of lambda.
type = "vars": A list with an element for each lambda. Each element is a named vector of integers corresponding to the indices with nonzero coefficients.
type = "nvars": A numeric vector with an element for each value of lambda indicating the number of nonzero coefficients.

Details

Estimation of baseline survival function conditional on the estimated values of beta is carried out according to the method described in Chapter 4.3 of Kalbfleish and Prentice. In particular, it agrees exactly the results returned by survfit.coxph(..., type='kalbfleisch-prentice') in the survival package.

References

Breheny P and Huang J. (2011) Coordinate descent algorithms for nonconvex penalized regression, with applications to biological feature selection. Annals of Applied Statistics, 5: 232-253. doi:10.1214/10-AOAS388
Kalbfleish JD and Prentice RL (2002). The Statistical Analysis of Failure Time Data, 2nd edition. Wiley.

Examples

data(Lung)
X <- Lung$X
y <- Lung$y

fit <- ncvsurv(X, y)
coef(fit, lambda = 0.05)
#>          trt        karno     diagtime          age        prior     squamous 
#>  0.271657331 -0.031750420  0.000000000 -0.004227748  0.000000000 -0.852920353 
#>        small        adeno        large 
#>  0.000000000  0.261188132 -0.466335148 
head(predict(fit, X, type = "link", lambda = 0.05))
#>         1         2         3         4         5         6 
#> -2.778003 -3.074368 -2.646943 -2.752636 -3.078596 -1.423431 
head(predict(fit, X, type = "response", lambda = 0.05))
#>          1          2          3          4          5          6 
#> 0.06216253 0.04621881 0.07086755 0.06375954 0.04602382 0.24088609 

# Survival function
S <- predict(fit, X[1, ], type = "survival", lambda = 0.05)[[1]]
S(100)
#> [1] 0.9421869
S <- predict(fit, X, type = "survival", lambda = 0.05)
plot(S, xlim = c(0, 200))


# Medians
predict(fit, X[1, ], type = "median", lambda = 0.05)
#> [1] 999
M <- predict(fit, X, type = "median")
M[1:10, 1:10]
#>       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
#>  [1,]   80  103  122  151  177  231  278  340  384   411
#>  [2,]   80  110  133  162  231  283  357  392  467   587
#>  [3,]   80  103  122  151  177  231  278  340  384   411
#>  [4,]   80  103  122  151  177  231  278  340  384   411
#>  [5,]   80  110  133  162  231  283  357  392  467   587
#>  [6,]   80   87   92   95  100  105  111  111  117   126
#>  [7,]   80   95  105  117  132  144  156  177  201   242
#>  [8,]   80  111  144  201  278  378  392  553  587   991
#>  [9,]   80   99  112  133  153  177  216  250  283   357
#> [10,]   80  110  133  162  231  283  357  392  467   587

# Nonzero coefficients
predict(fit, type = "vars", lambda = c(0.1, 0.01))
#> $`0.1000`
#>      trt    karno squamous    adeno    large 
#>        1        2        6        8        9 
#> 
#> $`0.0100`
#>      trt    karno      age    prior squamous    adeno    large 
#>        1        2        4        5        6        8        9 
#> 
predict(fit, type = "nvars", lambda = c(0.1, 0.01))
#> 0.1000 0.0100 
#>      5      7