Partial least squares Regression generalized linear models

This function implements an extension of Partial least squares Regression to Cox Models.

DKplsRcox(Xplan, ...)

DKplsRcoxmodel(Xplan, ...)

# S3 method for default
DKplsRcoxmodel(
  Xplan,
  time,
  time2,
  event,
  type,
  origin,
  typeres = "deviance",
  collapse,
  weighted,
  scaleX = TRUE,
  scaleY = TRUE,
  nt = min(2, ncol(Xplan)),
  limQ2set = 0.0975,
  dataPredictY = Xplan,
  pvals.expli = FALSE,
  alpha.pvals.expli = 0.05,
  tol_Xi = 10^(-12),
  weights,
  control,
  sparse = FALSE,
  sparseStop = TRUE,
  plot = FALSE,
  allres = FALSE,
  kernel = "rbfdot",
  hyperkernel,
  verbose = TRUE,
  ...
)

# S3 method for formula
DKplsRcoxmodel(
  Xplan,
  time,
  time2,
  event,
  type,
  origin,
  typeres = "deviance",
  collapse,
  weighted,
  scaleX = TRUE,
  scaleY = NULL,
  dataXplan = NULL,
  nt = min(2, ncol(Xplan)),
  limQ2set = 0.0975,
  dataPredictY = Xplan,
  pvals.expli = FALSE,
  model_frame = FALSE,
  alpha.pvals.expli = 0.05,
  tol_Xi = 10^(-12),
  weights,
  subset,
  control,
  sparse = FALSE,
  sparseStop = TRUE,
  plot = FALSE,
  allres = FALSE,
  kernel = "rbfdot",
  hyperkernel,
  verbose = TRUE,
  model_matrix = FALSE,
  contrasts.arg,
  ...
)

Arguments

Xplan

a formula or a matrix with the eXplanatory variables (training) dataset

...

arguments to pass to plsRmodel.default or to plsRmodel.formula

time

for right censored data, this is the follow up time. For interval data, the first argument is the starting time for the interval.

time2

The status indicator, normally 0=alive, 1=dead. Other choices are TRUE/FALSE (TRUE = death) or 1/2 (2=death). For interval censored data, the status indicator is 0=right censored, 1=event at time, 2=left censored, 3=interval censored. Although unusual, the event indicator can be omitted, in which case all subjects are assumed to have an event.

event

ending time of the interval for interval censored or counting process data only. Intervals are assumed to be open on the left and closed on the right, (start, end]. For counting process data, event indicates whether an event occurred at the end of the interval.

type

character string specifying the type of censoring. Possible values are "right", "left", "counting", "interval", or "interval2". The default is "right" or "counting" depending on whether the time2 argument is absent or present, respectively.

origin

for counting process data, the hazard function origin. This option was intended to be used in conjunction with a model containing time dependent strata in order to align the subjects properly when they cross over from one strata to another, but it has rarely proven useful.

typeres

character string indicating the type of residual desired. Possible values are "martingale", "deviance", "score", "schoenfeld", "dfbeta", "dfbetas", and "scaledsch". Only enough of the string to determine a unique match is required.

collapse

vector indicating which rows to collapse (sum) over. In time-dependent models more than one row data can pertain to a single individual. If there were 4 individuals represented by 3, 1, 2 and 4 rows of data respectively, then collapse=c(1,1,1,2,3,3,4,4,4,4) could be used to obtain per subject rather than per observation residuals.

weighted

if TRUE and the model was fit with case weights, then the weighted residuals are returned.

scaleX

Should the Xplan columns be standardized ?

scaleY

Should the time values be standardized ?

nt

number of components to be extracted

limQ2set

limit value for the Q2

dataPredictY

predictor(s) (testing) dataset

pvals.expli

should individual p-values be reported to tune model selection ?

alpha.pvals.expli

level of significance for predictors when pvals.expli=TRUE

tol_Xi

minimal value for Norm2(Xi) and \(\mathrm{det}(pp' \times pp)\) if there is any missing value in the dataX. It defaults to \(10^{-12}\)

weights

an optional vector of 'prior weights' to be used in the fitting process. Should be NULL or a numeric vector.

control

a list of parameters for controlling the fitting process. For glm.fit this is passed to glm.control.

sparse

should the coefficients of non-significant predictors (<alpha.pvals.expli) be set to 0

sparseStop

should component extraction stop when no significant predictors (<alpha.pvals.expli) are found

plot

Should the survival function be plotted ?)

allres

FALSE to return only the Cox model and TRUE for additionnal results. See details. Defaults to FALSE.

kernel

the kernel function used in training and predicting. This parameter can be set to any function, of class kernel, which computes the inner product in feature space between two vector arguments (see kernels). The kernlab package provides the most popular kernel functions which can be used by setting the kernel parameter to the following strings:

list("rbfdot")

Radial Basis kernel "Gaussian"

list("polydot")

Polynomial kernel

list("vanilladot")

Linear kernel

list("tanhdot")

Hyperbolic tangent kernel

list("laplacedot")

Laplacian kernel

list("besseldot")

Bessel kernel

list("anovadot")

ANOVA RBF kernel

list("splinedot")

Spline kernel

hyperkernel

the list of hyper-parameters (kernel parameters). This is a list which contains the parameters to be used with the kernel function. For valid parameters for existing kernels are :

• sigma, inverse kernel width for the Radial Basis kernel function "rbfdot" and the Laplacian kernel "laplacedot".

• degree, scale, offset for the Polynomial kernel "polydot".

• scale, offset for the Hyperbolic tangent kernel function "tanhdot".

• sigma, order, degree for the Bessel kernel "besseldot".

• sigma, degree for the ANOVA kernel "anovadot".

In the case of a Radial Basis kernel function (Gaussian) or Laplacian kernel, if hyperkernel is missing, the heuristics in sigest are used to calculate a good sigma value from the data.

verbose

Should some details be displayed ?

dataXplan

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in dataXplan, the variables are taken from environment(Xplan), typically the environment from which coxDKplsDR is called.

model_frame

If TRUE, the model frame is returned.

subset

an optional vector specifying a subset of observations to be used in the fitting process.

model_matrix

If TRUE, the model matrix is returned.

contrasts.arg

a list, whose entries are values (numeric matrices, functions or character strings naming functions) to be used as replacement values for the contrasts replacement function and whose names are the names of columns of data containing factors.

method

the method to be used in fitting the model. The default method "glm.fit" uses iteratively reweighted least squares (IWLS). User-supplied fitting functions can be supplied either as a function or a character string naming a function, with a function which takes the same arguments as glm.fit.

Value

Depends on the model that was used to fit the model.

Details

A typical predictor has the form response ~ terms where response is the (numeric) response vector and terms is a series of terms which specifies a linear predictor for response. A terms specification of the form first + second indicates all the terms in first together with all the terms in second with any duplicates removed.

A specification of the form first:second indicates the the set of terms obtained by taking the interactions of all terms in first with all terms in second. The specification first*second indicates the cross of first and second. This is the same as first + second + first:second.

The terms in the formula will be re-ordered so that main effects come first, followed by the interactions, all second-order, all third-order and so on: to avoid this pass a terms object as the formula.

Non-NULL weights can be used to indicate that different observations have different dispersions (with the values in weights being inversely proportional to the dispersions); or equivalently, when the elements of weights are positive integers w_i, that each response y_i is the mean of w_i unit-weight observations.

References

plsRcox, Cox-Models in a high dimensional setting in R, Frederic Bertrand, Philippe Bastien, Nicolas Meyer and Myriam Maumy-Bertrand (2014). Proceedings of User2014!, Los Angeles, page 152.

Deviance residuals-based sparse PLS and sparse kernel PLS regression for censored data, Philippe Bastien, Frederic Bertrand, Nicolas Meyer and Myriam Maumy-Bertrand (2015), Bioinformatics, 31(3):397-404, doi:10.1093/bioinformatics/btu660.

See also

plsR and plsRglm

Author

Frédéric Bertrand
frederic.bertrand@utt.fr
http://www-irma.u-strasbg.fr/~fbertran/

Examples

data(micro.censure)
data(Xmicro.censure_compl_imp)

X_train_micro <- apply((as.matrix(Xmicro.censure_compl_imp)),FUN="as.numeric",MARGIN=2)[1:80,]
X_train_micro_df <- data.frame(X_train_micro)
Y_train_micro <- micro.censure$survyear[1:80]
C_train_micro <- micro.censure$DC[1:80]

# \donttest{
DKplsRcox(X_train_micro,time=Y_train_micro,event=C_train_micro,nt=5)
#> Kernel :  rbfdot 
#> Estimated_sigma  0.012866 
#> Error in model.matrix(mt0, mf0, contrasts.arg = contrasts.arg): argument "contrasts.arg" is missing, with no default
DKplsRcox(~X_train_micro,time=Y_train_micro,event=C_train_micro,nt=5)
#> Error in model.matrix(mt0, mf0, , contrasts.arg = contrasts.arg): argument "contrasts.arg" is missing, with no default
# }

# \donttest{
DKplsRcox(Xplan=X_train_micro,time=Y_train_micro,event=C_train_micro,nt=5,sparse=TRUE, 
alpha.pvals.expli=.15)
#> Kernel :  rbfdot 
#> Estimated_sigma  0.01211527 
#> Error in model.matrix(mt0, mf0, contrasts.arg = contrasts.arg): argument "contrasts.arg" is missing, with no default
DKplsRcox(Xplan=~X_train_micro,time=Y_train_micro,event=C_train_micro,nt=5,sparse=TRUE,
alpha.pvals.expli=.15)
#> Error in model.matrix(mt0, mf0, , contrasts.arg = contrasts.arg): argument "contrasts.arg" is missing, with no default
# }