[R] Interperting results of glmnet and coxph plot, Brier score and Harrel's C-Index - am I doing something wrong ???

[Bert Gunter]

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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> and provide commented, minimal, self-contained, reproducible code.
>



-- 

Bert Gunter
Genentech Nonclinical Biostatistics

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