# Parallelized calculation of cross-validated risk score predictions from L1/L2/Elastic Net penalized regression. calculates risk score predictions by a nested cross-validation, using the optL1 and optL2 functions of the penalized R package for regression. In the outer level of cross-validation, samples are split into training and test samples. Model parameters are tuned by cross-validation within training samples only. By setting nprocessors > 1, the outer cross-validation is split between multiple processors. The functions support z-score scaling of training data, and application of these scaling and shifting coefficients to the test data. It also supports repeated tuning of the penalty parameters and selection of the model with greatest cross-validated likelihood. ```r opt.nested.crossval(outerfold=10, nprocessors=1, cl=NULL, ...) ``` ## Arguments - `outerfold`: number of folds in outer cross-validation (the level used for validation) - `nprocessors`: An integer number of processors to use. If specified in opt.nested.crossval, iterations of the outer cross-validation are sent to different processors. If specified in opt.splitval, repeated starts for the penalty tuning are sent to different processors. - `cl`: Optional cluster object created with the makeCluster() function of the parallel package. If this is not set, pensim calls makeCluster(nprocessors, type="SOCK"). Setting this parameter can enable parallelization in more diverse scenarios than multi-core desktops; see the documentation for the parallel package. Note that if cl is user-defined, this function will not automatically run parallel::stopCluster() to shut down the cluster. - ``...``: optFUN (either "opt1D" or "opt2D"), scaling (TRUE to z-score training data then apply the same shift and scale factors to test data, FALSE for no scaling) are passed onto the opt.splitval function. Additional arguments are required, to be passed to the optL1 or optL2 function of the penalized R package. See those help pages, and it may be desirable to test these arguments directly on optL1 or optL2 before using this more CPU-consuming and complex function. ## Details This function calculates cross-validated risk score predictions, tuning a penalized regression model using the optL1 or optL2 functions of the penalized R package, for each iteration of the cross-validation. Tuning is done by cross-validation in the training samples only. Test samples are scaled using the shift and scale factors determined from the training samples. parameter. If nprocessors > 1, it uses the SNOW package for parallelization, dividing the iterations of the outer cross-validation among the specified number of processors. Some arguments MUST be passed (through the ... arguments) but which are documented for the functions in which they are used. These include, from the opt.splitval function: optFUN="opt1D" for Lasso or Ridge regression, or "opt2D" for Elastic Net. See the help pages for opt1D and opt2D for additional arguments associated with these functions. scaling=TRUE to scale each feature (column) of the training sample to z-scores. These same scaling and shifting factors are applied to the test data. If FALSE, no scaling is done. Note that only data in the penalized argument are scaled, not the optional unpenalized argument (see documentation for opt1D, opt2D, or cvl from the penalized package for descriptions of the penalized and unpenalized arguments). Alternatively, the standardize=TRUE argument to the penalized package functions can be used to do scaling internally. nsim=50 this number specifies the number of times to repeat tuning of the penalty parameters on different data foldings for the cross-validation. setpen="L1" or "L2" : if optFUN="opt1D", this sets regression type to LASSO or Ridge, respectively. See ?opt1D. L1range, L2range, dofirst, L1gridsize, L2gridsize: options for Elastic Net regression if optFUN="opt2D". See ?opt2D. ## Returns Returns a vector of cross-validated continuous risk score predictions. ## References Waldron L, Pintilie M, Tsao M-S, Shepherd FA, Huttenhower C*, Jurisica I*: Optimized application of penalized regression methods to diverse genomic data. Bioinformatics 2011, 27:3399-3406. (*equal contribution) ## Author(s) Levi Waldron et al. ## Note Depends on the R packages: penalized, parallel ## See Also opt.splitval ## Examples ```r data(beer.exprs) data(beer.survival) ##select just 100 genes to speed computation: set.seed(1) beer.exprs.sample <- beer.exprs[sample(1:nrow(beer.exprs), 100), ] gene.quant <- apply(beer.exprs.sample, 1, quantile, probs = 0.75) dat.filt <- beer.exprs.sample[gene.quant > log2(100), ] gene.iqr <- apply(dat.filt, 1, IQR) dat.filt <- as.matrix(dat.filt[gene.iqr > 0.5, ]) dat.filt <- t(dat.filt) dat.filt <- data.frame(dat.filt) library(survival) surv.obj <- Surv(beer.survival$os, beer.survival$status) ## First, test the regression arguments using functions from ## the penalized package. I use maxlambda1=5 here to ensure at least ## one non-zero coefficient. testfit <- penalized::optL1( response = surv.obj, maxlambda1 = 3, penalized = dat.filt, fold = 2, positive = FALSE, standardize = TRUE, trace = TRUE ) ## Now pass these arguments to opt.nested.splitval() for cross-validated ## calculation and assessment of risk scores, with the additional ## arguments: ## outerfold and nprocessors (?opt.nested.crossval) ## optFUN and scaling (?opt.splitval) ## setpen and nsim (?opt1D) ## Ideally nsim would be 50, and outerfold and fold would be 10, but the ## values below speed computation 200x compared to these recommended ## values. Note that here we are using the standardize=TRUE argument of ## optL1 rather than the scaling=TRUE argument of opt.splitval. These ## two approaches to scaling are roughly equivalent, but the scaling ## approaches are not the same (scaling=TRUE does z-score, ## standardize=TRUE scales to unit central L2 norm), and results will ## not be identical. Also, using standardize=TRUE scales variables but ## provides coeffients for the original scale, whereas using ## scaling=TRUE scales variables in the training set then applies the ## same scales to the test set. set.seed(1) ## In this example I use two processors: preds <- pensim::opt.nested.crossval( outerfold = 2, nprocessors = 1, #opt.nested.crossval arguments optFUN = "opt1D", scaling = FALSE, #opt.splitval arguments setpen = "L1", nsim = 1, #opt1D arguments response = surv.obj, #rest are penalized::optl1 arguments penalized = dat.filt, fold = 2, maxlambda1 = 5, positive = FALSE, standardize = TRUE, trace = FALSE ) ## We probably also want the coefficients from the model fit on all the ## data, for future use: beer.coefs <- pensim::opt1D( setpen = "L1", nsim = 1, maxlambda1 = 5, response = surv.obj, penalized = dat.filt, fold = 2, positive = FALSE, standardize = TRUE, trace = FALSE ) ## We can also include unpenalized covariates, if desired. ## Note that when keeping only one variable for a penalized or ## unpenalized covariate, indexing a dataframe like [1] instead of doing ## [,1] preserves the variable name. With [,1] the variable name gets ## converted to "". beer.coefs <- pensim::opt1D( setpen = "L1", nsim = 1, maxlambda1 = 5, response = surv.obj, penalized = dat.filt[-1], # This is equivalent to dat.filt[, -1] unpenalized = dat.filt[1], fold = 2, positive = FALSE, standardize = TRUE, trace = FALSE ) ## (note the non-zero first coefficient this time, due to it being unpenalized). ## Summarization and plotting. preds.dichot <- preds > median(preds) coxfit.continuous <- coxph(surv.obj ~ preds) coxfit.dichot <- coxph(surv.obj ~ preds.dichot) summary(coxfit.continuous) summary(coxfit.dichot) nobs <- length(preds) cutoff <- 12 if (requireNamespace("survivalROC", quietly = TRUE)) { preds.roc <- survivalROC::survivalROC( Stime = beer.survival$os, status = beer.survival$status, marker = preds, predict.time = cutoff, span = 0.25 * nobs ^ (-0.20) ) plot( preds.roc$FP, preds.roc$TP, type = "l", xlim = c(0, 1), ylim = c(0, 1), lty = 2, xlab = paste("FP", "\n", "AUC = ", round(preds.roc$AUC, 3)), ylab = "TP", main = "LASSO predictions\n ROC curve at 12 months" ) abline(0, 1) } ```

opt.nested.crossval function