[R] Interperting results of glmnet and coxph plot, Brier score and Harrel's C-Index - am I doing something wrong ???
Bert Gunter
gunter.berton at gene.com
Sat Sep 28 16:28:40 CEST 2013
This appears to be a statistics, not an R-help question, so should
probably be asked on a statistics list, not here (e.g.
stats.stackexchange.com).
But if I understand your issue correctly, perhaps the heart f the
matter is: why do you think a stable fit must explain a lot of the
variation? Feel free to ignore if I I'm wrong or discuss further on
the statistics list.
Cheers,
Bert
On Sat, Sep 28, 2013 at 2:39 AM, E Joffe <ejoffe at hotmail.com> wrote:
> Hi all,
>
> I am using COX LASSO (glmnet / coxnet) regression to analyze a dataset of
> 394 obs. / 268 vars.
> I use the following procedure:
> 1. Construct a coxnet on the entire dataset (by cv.glmnet)
> 2. Pick the significant features by selecting the non-zero coefficient
> under the best lambda selected by the model
> 3. Build a coxph model with bi-directional stepwise feature selection
> limited to the coxnet selected features.
>
> To validate the model I use both Brier score (library=peperr) and Harrel's
> C-Index (library=Hmisc) with a bootstrap of 50 iterations.
>
>
> MY QUESTION : I am getting fairly good C-Index (0.76) and Brier (0.07)
> values for the models however per the coxnet the %Dev explained by the model
> is at best 0.27 and when I plot the survfit of the coxph the plotted
> confidence interval is very large.
> What am I missing here ?
>
> %DEV=27%
>
>
>
> Brier score - 0.07 ($ipec.coxglmnet -> [1] 7.24)
> C-Index - 0.76 ($cIndex -> [1] 0.763)
>
>
>
> DATA: [Private Health Information - can't publish] 394 obs./268 vars.
>
> CODE (need to define a dataset with 'time' and 'status' variables):
>
> library("survival")
> library ("glmnet")
> library ("c060")
> library ("peperr")
> library ("Hmisc")
>
> #creat Y (survival matrix) for glmnet
> surv_obj <- Surv(dataset$time,dataset$status)
>
>
> ## tranform categorical variables into binary variables with dummy for
> dataset
> predict_matrix <- model.matrix(~ ., data=dataset,
> contrasts.arg = lapply
> (dataset[,sapply(dataset, is.factor)], contrasts))
>
> ## remove the statu/time variables from the predictor matrix (x) for
> glmnet
> predict_matrix <- subset (predict_matrix, select=c(-time,-status))
>
> ## create a glmnet cox object using lasso regularization and cross
> validation
> glmnet.cv <- cv.glmnet (predict_matrix, surv_obj, family="cox")
>
> ## get the glmnet model on the full dataset
> glmnet.obj <- glmnet.cv$glmnet.fit
>
> # find lambda index for the models with least partial likelihood
> deviance (by cv.glmnet)
> optimal.lambda <- glmnet.cv$lambda.min # For a more parsimoneous
> model use lambda.1se
> lambda.index <- which(glmnet.obj$lambda==optimal.lambda)
>
>
> # take beta for optimal lambda
> optimal.beta <- glmnet.obj$beta[,lambda.index]
>
> # find non zero beta coef
> nonzero.coef <- abs(optimal.beta)>0
> selectedBeta <- optimal.beta[nonzero.coef]
>
> # take only covariates for which beta is not zero
> selectedVar <- predict_matrix[,nonzero.coef]
>
> # create a dataframe for trainSet with time, status and selected
> variables in binary representation for evaluation in pec
> reformat_dataSet <- as.data.frame(cbind(surv_obj,selectedVar))
>
> # glmnet.cox only with meaningful features selected by stepwise
> bidirectional AIC feature selection
> glmnet.cox.meaningful <- step(coxph(Surv(time,status) ~
> .,data=reformat_dataSet),direction="both")
>
>
>
>
> ##--------------------------------------------------------------------------
> -----------------------------
> ## MODEL PERFORMANCE
>
> ##--------------------------------------------------------------------------
> -----------------------------
> ##
>
>
> ## Calculate the Brier score - pec does its own bootstrap so this
> function runs on i=51 (i.e., whole trainset)
>
> ## Brier score calculation to cox-glmnet
> peperr.coxglmnet <- peperr(response=surv_obj, x=selectedVarCox,
> fit.fun=fit.coxph, load.all=TRUE,
> indices=resample.indices(n=nrow(surv_obj),
> method="boot", sample.n=50))
>
> # Get error predictions from peperr
> prederr.coxglmnet <- perr(peperr.coxglmnet)
>
> # Integrated prediction error Brier score calculation
> ipec.coxglmnet<-ipec(prederr.coxglmnet,
> eval.times=peperr.coxglmnet$attribute, response=surv_obj)
>
>
> ## C-Index calculation 50 iter bootstrapping
>
> for (i in 1:50){
> print (paste("Iteration:",i))
> train <- sample(1:nrow(dataset), nrow(dataset), replace = TRUE) ##
> random sampling with replacement
> # create a dataframe for trainSet with time, status and selected
> variables in binary representation for evaluation in pec
> reformat_trainSet <- reformat_dataSet [train,]
>
>
> # glmnet.cox only with meaningful features selected by stepwise
> bidirectional AIC feature selection
> glmnet.cox.meaningful.test <- step(coxph(Surv(time,status) ~
> .,data=reformat_dataSet),direction="both")
>
> selectedVarCox <-
> predict_matrix[,attr(glmnet.cox.meaningful.test$terms,"term.labels")]
> reformat_testSet <- as.data.frame(cbind(surv_obj,selectedVarCox))
> reformat_testSet <- reformat_dataSet [-train,]
>
>
> # compute c-index (Harrell's) for cox-glmnet models
> if (is.null(glmnet.cox.meaningful)){
> cIndexCoxglmnet <- c(cIndexCoxglmnet,NULL)
> }else{
> cIndexCoxglmnet <- c(cIndexCoxglmnet,
> 1-rcorr.cens(predict(glmnet.cox.meaningful,
> reformat_testSet),Surv(reformat_testSet$time,reformat_testSet$status))[1])
> }
> }
>
> #Get average C-Index
> cIndex<- mean (unlist(cIndexCoxglmnet),rm.na=TRUE)
>
> #create a list of all the objects generated
>
> assign(name,c(eval(parse(text=name)),glmnet.cv=list(glmnet.cv),glmnet.obj=li
> st(glmnet.obj),
>
> selectedVar=list(colnames(selectedVar)),glmnet.cox=list(glmnet.cox),
>
> glmnet.cox.meaningful=list(glmnet.cox.meaningful),ipec.coxglmnet=list(ipec.c
> oxglmnet),
> cIndex=cIndex))
>
> # save image of the workspace after each iteration
> save.image("final_subgroup_analysissubgroup_analysis.RData")
>
>
>
> ______________________________________________
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> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
--
Bert Gunter
Genentech Nonclinical Biostatistics
Internal Contact Info:
Phone: 467-7374
Website:
http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm
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