# Performs resampling for a stratified weighted Cox model by componentwise likelihood based boosting for developing subgroup covariate signatures `resample.CoxBoost` is used to perform resampling for stratified Cox proportional hazards models by componentwise likelihood based boosting with weights for developing subgroup covariate signatures. Specifically, this weighted Cox regression approach is for performing a subgroup analysis, not for the standard subgroup analysis but for a weighted form of it where the observations of the not analyzed subgroup are down-weighted. `resample.CoxBoost` calls `cv.CoxBoost` and `CoxBoost`. ```r resample.CoxBoost( time, status, x, rep = 100, maxstepno = 200, multicore = TRUE, mix.list = c(0.001, 0.01, 0.05, 0.1, 0.25, 0.35, 0.5, 0.7, 0.9, 0.99), stratum, stratnotinfocus = 0, penalty = sum(status) * (1/0.02 - 1), criterion = "hscore", unpen.index = NULL, trace = FALSE ) ``` ## Arguments - `time`: vector of length `n` with the observed times of each individual. - `status`: vector of length `n` with entries `0` for censored observations and `1` for observations having an event. - `x`: `n * p` matrix of mandatory and optional covariates. - `rep`: number of resampling data sets used for the evaluation of model stability. Should be equal to `length(iter)`. - `maxstepno`: maximum number of boosting steps needed for cross-validation in `cv.CoxBoost`. So the optimal step number for fitting the compontentwise boosting has a range between zero and `maxstepno`. - `multicore`: logical value: If `TRUE` then the cross-validation for selecting the number of optimal boosting steps within each resampling data set is been parallelized, if `FALSE` there will be no parallelization. - `mix.list`: vector of different relative weights between zero and one, for specifying weights for the individual observations for the weighted regression approach. For each weight, a stratified Cox regression by componentwise boosting is fitted. - `stratum`: vector specifying different groups of individuals for a stratified Cox regression. In `CoxBoost` fit each group gets its own baseline hazard. - `stratnotinfocus`: value for the group which is not analyzed but should be weighted down in the analysis with the different weights element of `mix.list`. - `penalty`: penalty value for the covariates for the update of an individual element in each boosting step. The mandatory covariates should get a penalty value of zero, which can be realized with `unpen.index`. - `criterion`: indicates the criterion to be used for selection in each boosting step in `CoxBoost`. The default is `"hscore"` for using a heuristic when evaluating a subset of covariates in each boosting step. For the different other options see `CoxBoost`. - `unpen.index`: index for mandatory covariates, which should get no penalty value in the log-partial likelihood function. - `trace`: logical value indicating whether progress in estimation should be indicated by printing the number of the cross-validation fold and the index of the covariate updated in the `cv.CoxBoost` and `CoxBoost` methods. ## Returns `resample.CoxBoost` returns a list of length `rep` list elements with each list element being further a list of the following two objects: - **CV.opt**: number of optimal boosting steps obtained from `cv.CoxBoost` for each weight. - **beta**: beta coefficients obtained from `CoxBoost` as vector for each weight. ## Details The `CoxBoost` function can be used for performing variable selection for time-to-event data based on componentwise likelihood based boosting (Binder and Schumacher, 2009; Binder et al., 2013) for obtaining signatures for high dimensional data, such as gene expression or high throughput methylation measurements. If there is any heterogeneity due to known patient subgroups, it would be interesting for developing subgroup signatures to account for this heterogeneity. To account for heterogeneity in the data a stratified Cox model via `stratum` can be performed, which allows for different baseline hazards in each subgroup. For performing a stratified `CoxBoost` for such heterogeneous subgroups the `stratum` can be set to a subgroup variable, containing also the subgroup for which a subgroup signature should be developed. A standard subgroup analysis may lead to a decreased statistical power. With a weighted approach based on componentwise likelihood-based boosting one can develop subgroup signatures without losing statistical power as it is the case in standard subgroup analysis. This approach focuses on building a risk prediction signature for a specific stratum by down-weighting the observations (Simon, 2002) from the other strata using a range of weights. The not analyzed subgroup has to be indicated in `stratnotinfocus`, the observations of this subgroup, which is not in focus but should be retained in the analysis, are weighted down by different relative weights. Binder et al. (2012) propose such a weighting approach for high dimensional data but not for time-to-event endpoints. `resample.CoxBoost` performs a weighted regression approach for time-to-event data while using resampling over `rep` resampling data sets, specifically for evaluating the results. The different weights can be entered by `mix.list` which should be from a range between zero and one. For examining the variable selection stability for specific covariates as a function of the weights the beta coefficients are an output value of `resample.CoxBoost`, so that resampling inclusion frequencies (Sauerbrei et. al, 2011) can be calculated and visualized via the functions `stabtrajec` and `weightfreqmap`. For mandatory variables (Binder and Schumacher, 2008), which are only included for adjusting the model no penalty should be added, these can be indicated by the indices in `unpen.index`. ## Examples ```r # Generate survival data with five informative covariates for one subgroup n <- 400; p <- 1000 set.seed(129) group<-rbinom(n,1,0.5) x <- matrix(rnorm(n*p,0,1),n,p) beta.vec1 <- c(c(1,1,1,1,1),rep(0,p-5)) beta.vec0 <- c(c(0,0,0,0,0),rep(0,p-5)) linpred<-ifelse(group==1,x %*% beta.vec1,x %*% beta.vec0) set.seed(1234) real.time<- (-(log(runif(n)))/(1/20*exp(linpred))) cens.time <- rexp(n,rate=1/20) obs.status <- ifelse(real.time <= cens.time,1,0) obs.time <- ifelse(real.time <= cens.time,real.time,cens.time) # Fit a stratified weighted Cox proportional hazards model # by \code{resample.CoxBoost} mix.list=c(0.001, 0.01, 0.05, 0.1, 0.25, 0.35, 0.5, 0.7, 0.9, 0.99) RIF <- resample.CoxBoost( time=obs.time,status=obs.status,x=x, # use more repetitions (eg `rep = 100`) for more stable results rep=5, maxstepno=200,multicore=FALSE, mix.list=mix.list, stratum=group,stratnotinfocus=0,penalty=sum(obs.status)*(1/0.02-1), criterion="hscore",unpen.index=NULL) # RIF is a list with number of resampling data sets list objects, each list # object has further two list objects, the beta coefficients for all # weights and the selected number of boosting steps. # For each list object i \code{RIF[[i]]$beta} contains the beta # coefficients with length mix.list*p for p covariates and with # \code{RIF[[i]]$CV.opt} # For getting an insight in the RIF Distribution of different weights # use the following code: RIF1<-c() for (i in 1: length(RIF)){RIF1<-c(RIF1,RIF[[i]][[1]])} freqmat <-matrix(apply(matrix(unlist(RIF1), ncol=length(RIF))!=0,1,mean), ncol=length(mix.list)) # freqmat is a matrix with p rows and \code{length(mix.list)} columns # which contains resampling inclusion frequencies for the different # covariates and different weights. # two plotting functions are available for the resulting object: stabtrajec(RIF) weightfreqmap(RIF) ``` ## References Binder, H., Benner, A., Bullinger, L., Schumacher, M. (2013). Tailoring sparse multivariable regression techniques for prognostic single-nucleotide polymorphism signatures. Statistics in medicine 32(10), 1778-1791 Binder, H., Müller, T., Schwender, H., Golka, K., Steffens, M., G., H.J., Ickstadt, K., and Schumacher, M (2012). Cluster-Localized Sparse Logistic Regression for SNP Data. Statistical applications in genetics and molecular biology, 11(4), 1-31 Binder, H. and Schumacher, M. (2009). Incorporating pathway information into boosting estimation of high-dimensional risk prediction models. BMC Bioinformatics. 10:18. Binder, H. and Schumacher, M. (2008). Allowing for mandatory covariates in boosting estimation of sparse high-dimensional survival models. BMC Bioinformatics. 9:14. Sauerbrei, W., Boulesteix, A.-L., Binder, H. (2011). Stability investigations of multivariable regression models derived from low- and high-dimensional data. Journal of biopharmaceutical statistics 21(6), 1206-31 Simon, R. (2002). Bayesian subset analysis: application to studying treatment-by-gender interactions. Statistics in medicine 21(19), 2909-16 ## See Also `stabtrajec`, `weightfreqmap`. ## Author(s) Written by Veronika Weyer weyer@uni-mainz.de and Harald Binder binderh@uni-mainz.de .

resample.CoxBoost function