survivalsvm: survivalsvm
In survivalsvm: Survival Support Vector Analysis

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Performs support vectors analysis for data sets with survival outcome. Three approaches are available in the package: The regression approach takes censoring into account when formulating the inequality constraints of the support vector problem. In the ranking approach, the inequality constraints set the objective to maximize the concordance index for comparable pairs of observations. The hybrid approach combines the regression and ranking constraints in the same model.

survivalsvm(formula = NULL, data = NULL, subset = NULL,
  type = "regression", diff.meth = NULL, gamma.mu = NULL,
  opt.meth = "quadprog", kernel = "lin_kernel", kernel.pars = NULL,
  time.variable.name = NULL, status.variable.name = NULL, sgf.sv = 5,
  sigf = 7, maxiter = 20, margin = 0.05, bound = 10, eig.tol = 1e-06,
  conv.tol = 1e-07, posd.tol = 1e-08)

`formula`	[`formula(1)`] Object of class `formula`. See `formula` for more details.
`data`	[`data.frame(1)`] Object of class `data.frame` containing data points that will be used to fit the model.
`subset`	[`vector(1)`] An index vector specifying the cases to be used in the training sample.
`type`	[`character(1)`] String indicating which type of survival support vectors model is desired. This must be one of the following strings: 'regression', 'vanbelle1', 'vanbelle2' or 'hybrid'.
`diff.meth`	[`character(1)`] String indicating which of `'makediff1'`, `'makediff2'` or `'makediff3'` is used in case of 'vanbelle1', 'vanbelle2' and 'hybrid'.
`gamma.mu`	[`numeric(1)\|vector(1)`] Parameters of regularization. Note that a vector with two parameters is required in case of `hybrid` approach. Just one value is required in case of `regression`, `vanbelle1` or `vanbelle2`.
`opt.meth`	[`character(1)`] Program used to solve the quadratic optimization problem. Either "`quadprog`" or "`ipop`".
`kernel`	[`Kernel(1)`] Kernel used to fit the model: linear kern ('lin_kernel'), additive kernel ('add_kernel'), radial basis kernels ('rbf_kernel') and the polynomial kernel ('poly_kernel').
`kernel.pars`	[`vector(1)`] Parameters of kernel, when required.
`time.variable.name`	[`character`] Name of the survival time variable in `data`, when given in argument.
`status.variable.name`	[`character(1)`] Name of the status variable in `data`.
`sgf.sv`	[`character(1)`] Number of decimal digits in the solution of the quadratic optimization problem.
`sigf`	[`numeric(1)`] Used by `ipop`. See `ipop` for details.
`maxiter`	[`integer(1)`] Used by `ipop`. See `ipop` for details.
`margin`	[`numeric(1)`] Used by `ipop`. See `ipop` for details.
`bound`	[`numeric(1)`] Used by `ipop`. See `ipop` for details.
`eig.tol`	[`numeric(1)`] Used by `nearPD` for adjusting positive definiteness. See `nearPD` for detail.
`conv.tol`	[`numeric(1)`] Used by `nearPD` for adjusting positive definiteness. See `nearPD` for detail.
`posd.tol`	[`numeric(1)`] Used by `nearPD` for adjusting positive definiteness. See `nearPD` for detail.

The following denotations are used for the models implemented:

'regression' referring to the regression approach, named SVCR in Van Belle et al. (2011b),
'vanbelle1' according to the first version of survival surpport vector machines based on ranking constraints, named RANKSVMC by Van Belle et al. (2011b),
'vanbelle2' according to the second version of survival surpport vector machines based on ranking constraints like presented in model1 by Van Belle et al. (2011b) and
'hybrid' combines simultaneously the regression and ranking constraints in the same model. Hybrid model is labeled model2 by Van Belle et al. (2011b).

The argument 'type' of the function survivalsvm is used to set the type of model to be fitted. For the models vanbelle1, vanbelle2 and hybrid, differences between comparable pairs of observations are required. Each observation is compared with its nearest neighbor according to the survival time, and the three possible comparison approaches makediff1, makediff2 and makediff3 are offered to compute the differences between comparable neighbors.

The current version of survivalsvm uses the solvers ipop and quadprog to solve the dual optimization problems deduced from the suport vector formulations of the models presented above. Notice that for using quadprog the kernel matrix needs to be symmetric and positive definite. Therefore when the conditions are not met, the kernel matrix needs be slightly perturbed to obtain the nearest positive definite kernel matrix. The alternative to quadprog is ipop, that can also handle a non-negative definite kernel matrix, however more time may be required to solve the quadratic optimization dual problem. The argument opt.meth is used to select the solver.

The survivalsvm command can be called giving a formula, in which the survival time and the status are grouped into a two colunm matrix using the command Surv from the package survival. An alternative is to pass the data frame of training data points as an argument using data, to mention the name of the survival time variable and the name of the status variable as illustrated in the third example below.

survivalsvm Object of class survivalsvm, with elements:

`call`	command calling this program,
`typeofsurvivalsvm`	type of survival support vector machines approach,
`model.fit`	the fitted survival model,
`var.names`	names of variables used.

This implementation is in part inspired by the Matlab toolbox Survlab (A Survival Analysis Toolbox).

Cesaire J. K. Fouodo

Van Belle, V., Pelcmans, K., Van Huffel S. and Suykens J. A.K. (2011a). Improved performance on high-dimensional survival data by application of Survival-SVM. Bioinformatics (Oxford, England) 27, 87-94.
Van Belle, V., Pelcmans, K., Van Huffel S. and Suykens J. A.K. (2011b). Support vector methods for survival analysis: a comparaison between ranking and regression approaches. Artificial Intelligence in medecine 53, 107-118.

predict.survivalsvm

survivalsvm(Surv(time, status) ~ ., veteran, gamma.mu = 0.1)

survsvm.reg <- survivalsvm(formula = Surv(diagtime, status) ~ ., data = veteran,
                           type = "regression", gamma.mu = 0.1,
                           opt.meth = "ipop", kernel = "add_kernel")
                            
survsvm.vb2 <- survivalsvm(data = veteran, time.variable.name = "diagtime",
                           status.variable.name = "status", 
                           type = "vanbelle2", gamma.mu = 0.1,
                           opt.meth = "quadprog", diff.meth = "makediff3", 
                           kernel = "lin_kernel",
                           sgf.sv = 5, sigf = 7, maxiter = 20, 
                           margin = 0.05, bound = 10)

Loading required package: survival

survivalsvm result

Call:

 survivalsvm(Surv(time, status) ~ ., veteran, gamma.mu = 0.1) 

Survival svm approach              : regression 
Type of Kernel                     : lin_kernel 
Optimization solver used           : quadprog 
Number of support vectors retained : 17