pec2: Clone of pec::pec function
In adibender/ldatools: Utility functions for life-time data analysis

Slightly modified such that start/stop formulas are accepted and processed.

pec2(
  object,
  formula,
  data,
  traindata,
  times,
  cause,
  start,
  maxtime,
  exact = TRUE,
  exactness = 100,
  fillChar = NA,
  cens.model = "cox",
  ipcw.refit = FALSE,
  ipcw.args = NULL,
  splitMethod = "none",
  B,
  M,
  reference = TRUE,
  model.args = NULL,
  model.parms = NULL,
  keep.index = FALSE,
  keep.matrix = FALSE,
  keep.models = FALSE,
  keep.residuals = FALSE,
  keep.pvalues = FALSE,
  noinf.permute = FALSE,
  multiSplitTest = FALSE,
  testIBS,
  testTimes,
  confInt = FALSE,
  confLevel = 0.95,
  verbose = TRUE,
  savePath = NULL,
  slaveseed = NULL,
  na.action = na.fail,
  ...
)

`object`	A named list of prediction models, where allowed entries are (1) R-objects for which a predictSurvProb method exists (see details), (2) a `call` that evaluates to such an R-object (see examples), (3) a matrix with predicted probabilities having as many rows as `data` and as many columns as `times`. For cross-validation all objects in this list must include their `call`.
`formula`	A survival formula as obtained either with `prodlim::Hist` or `survival::Surv`. The left hand side is used to find the status response variable in `data`. For right censored data, the right hand side of the formula is used to specify conditional censoring models. For example, set `Surv(time,status)~x1+x2` and `cens.model="cox"`. Then the weights are based on a Cox regression model for the censoring times with predictors x1 and x2. Note that the usual coding is assumed: `status=0` for censored times and that each variable name that appears in `formula` must be the column name in `data`. If there are no covariates, i.e. `formula=Surv(time,status)~1` the `cens.model` is coerced to `"marginal"` and the Kaplan-Meier estimator for the censoring times is used to calculate the weights. If `formula` is `missing`, try to extract a formula from the first element in object.
`data`	A data frame in which to validate the prediction models and to fit the censoring model. If `data` is missing, try to extract a data set from the first element in object.
`traindata`	A data frame in which the models are trained. This argument is used only in the absence of crossvalidation, in which case it is passed to the predictHandler function predictSurvProb
`times`	A vector of time points. At each time point the prediction error curves are estimated. If `exact==TRUE` the `times` are merged with all the unique values of the response variable. If `times` is missing and `exact==TRUE` all the unique values of the response variable are used. If missing and `exact==FALSE` use a equidistant grid of values between `start` and `maxtime`. The distance is determined by `exactness`.
`cause`	For competing risks, the event of interest. Defaults to the first state of the response, which is obtained by evaluating the left hand side of `formula` in `data`.
`start`	Minimal time for estimating the prediction error curves. If missing and `formula` defines a `Surv` or `Hist` object then `start` defaults to `0`, otherwise to the smallest observed value of the response variable. `start` is ignored if `times` are given.
`maxtime`	Maximal time for estimating the prediction error curves. If missing the largest value of the response variable is used.
`exact`	Logical. If `TRUE` estimate the prediction error curves at all the unique values of the response variable. If `times` are given and `exact=TRUE` then the `times` are merged with the unique values of the response variable.
`exactness`	An integer that determines how many equidistant gridpoints are used between `start` and `maxtime`. The default is 100.
`fillChar`	Symbol used to fill-in places where the values of the prediction error curves are not available. The default is `NA`.
`cens.model`	Method for estimating inverse probability of censoring weigths: `cox`: A semi-parametric Cox proportional hazard model is fitted to the censoring times `marginal`: The Kaplan-Meier estimator for the censoring times `nonpar`: Nonparametric extension of the Kaplan-Meier for the censoring times using symmetric nearest neighborhoods – available for arbitrary many strata variables on the right hand side of argument `formula` but at most one continuous variable. See the documentation of the functions `prodlim` and `neighborhood` from the prodlim package. `aalen`: The nonparametric Aalen additive model fitted to the censoring times. Requires the `timereg` package.
`ipcw.refit`	If `TRUE` the inverse probability of censoring weigths are estimated separately in each training set during cross-validation.
`ipcw.args`	List of arguments passed to function specified by argument `cens.model`.
`splitMethod`	SplitMethod for estimating the prediction error curves. `none/noPlan`: Assess the models in the same data where they are fitted. `boot`: DEPRECIATED. `cvK`: K-fold cross-validation, i.e. `cv10` for 10-fold cross-validation. After splitting the data in K subsets, the prediction models (ie those specified in `object`) are evaluated on the data omitting the Kth subset (training step). The prediction error is estimated with the Kth subset (validation step). The random splitting is repeated `B` times and the estimated prediction error curves are obtained by averaging. `BootCv`: Bootstrap cross validation. The prediction models are trained on `B` bootstrap samples, that are either drawn with replacement of the same size as the original data or without replacement from `data` of the size `M`. The models are assessed in the observations that are NOT in the bootstrap sample. `Boot632`: Linear combination of AppErr and BootCvErr using the constant weight .632. `Boot632plus`: Linear combination of AppErr and BootCv using weights dependent on how the models perform in permuted data. `loocv`: Leave one out cross-validation. `NoInf`: Assess the models in permuted data.
`B`	Number of bootstrap samples. The default depends on argument `splitMethod`. When `splitMethod` in c("BootCv","Boot632","Boot632plus") the default is 100. For `splitMethod="cvK"` `B` is the number of cross-validation cycles, and – default is 1. For `splitMethod="none"` `B` is the number of bootstrap simulations e.g. to obtain bootstrap confidence limits – default is 0.
`M`	The size of the bootstrap samples for resampling without replacement. Ignored for resampling with replacement.
`reference`	Logical. If `TRUE` add the marginal Kaplan-Meier prediction model as a reference to the list of models.
`model.args`	List of extra arguments that can be passed to the `predictSurvProb` methods. The list must have an entry for each entry in `object`.
`model.parms`	Experimental. List of with exactly one entry for each entry in `object`. Each entry names parts of the value of the fitted models that should be extracted and added to the value.
`keep.index`	Logical. If `FALSE` remove the bootstrap or cross-validation index from the output list which otherwise is included in the splitMethod part of the output list.
`keep.matrix`	Logical. If `TRUE` add all `B` prediction error curves from bootstrapping or cross-validation to the output.
`keep.models`	Logical. If `TRUE` keep the models in object. Since fitted models can be large objects the default is `FALSE`.
`keep.residuals`	Logical. If `TRUE` keep the patient individual residuals at `testTimes`.
`keep.pvalues`	For `multiSplitTest`. If `TRUE` keep the pvalues from the single splits.
`noinf.permute`	If `TRUE` the noinformation error is approximated using permutation.
`multiSplitTest`	If `TRUE` the test proposed by van de Wiel et al. (2009) is applied. Requires subsampling bootstrap cross-validation, i.e. that `splitMethod` equals `bootcv` and that `M` is specified.
`testIBS`	A range of time points for testing differences between models in the integrated Brier scores.
`testTimes`	A vector of time points for testing differences between models in the time-point specific Brier scores.
`confInt`	Experimental.
`confLevel`	Experimental.
`verbose`	if `TRUE` report details of the progress, e.g. count the steps in cross-validation.
`savePath`	Place in your file system (i.e., a directory on your computer) where training models fitted during cross-validation are saved. If `missing` training models are not saved.
`slaveseed`	Vector of seeds, as long as `B`, to be given to the slaves in parallel computing.
`na.action`	Passed immediately to model.frame. Defaults to na.fail. If set otherwise most prediction models will not work.
`...`	Not used.