prostate {ElemStatLearn} | R Documentation

## Prostate Cancer Data

### Description

Data to examine the correlation between the level of prostate-specific antigen and a number of clinical measures in men who were about to receive a radical prostatectomy.

### Usage

    data(prostate)

### Format

A data frame with 97 observations on the following 10 variables.

lcavol
  log cancer volume
lweight
  log prostate weight
age
  in years
lbph
  log of the amount of benign prostatic hyperplasia
svi
  seminal vesicle invasion
lcp
  log of capsular penetration
gleason
  a numeric vector
pgg45
  percent of Gleason score 4 or 5
lpsa
  response
train
  a logical vector

### Details

The last column indicates which 67 observations were used as the "training set" and which 30 as the test set, as described on page 48 in the book.

### Source

### References

### Examples

    if(interactive())par(ask=TRUE)
    str( prostate )
    cor( prostate[,1:8] )
    pairs( prostate[,1:9], col="violet" )
    train <- subset( prostate, train==TRUE )[,1:9]
    test  <- subset( prostate, train=FALSE )[,1:9]
    #
    library(leaps)
    # The book (page 56) uses only train subset, so we the same:
    prostate.leaps <- regsubsets( lpsa ~ . , data=train, nbest=70, #all!
                         really.big=TRUE )
    prostate.leaps.sum <- summary( prostate.leaps )
    prostate.models <- prostate.leaps.sum$which
    prostate.models.size <- as.numeric(attr(prostate.models, "dimnames")[[1]])
    hist( prostate.models.size )
    prostate.models.rss <- prostate.leaps.sum$rss
    prostate.models.best.rss <-
         tapply( prostate.models.rss, prostate.models.size, min )
    prostate.models.best.rss
    # Let us add results for the only intercept model
    prostate.dummy <- lm( lpsa ~ 1, data=train )
    prostate.models.best.rss <- c(
             sum(resid(prostate.dummy)^2),
              prostate.models.best.rss)
    # Making a plot:
    plot( 0:8, prostate.models.best.rss, ylim=c(0, 100),
          type="b", xlab="subset size", ylab="Residual Sum Square",
          col="red2" )
    points( prostate.models.size, prostate.models.rss, pch=17, col="brown", cex=0.7 )
    # For a better plot, should remove the best for each size from last call!
    # Now with ridge regression:
    # Ridge regression in R is multiply implemented, at least:
    # MASS: lm.ridge
    # mda : gen.ridge
    #( survival: ridge)
    # Design: pentrace
    # mgcv: pcls (very general)
    # simple.ridge (in this package)
    #
    library(mda)
    #
    prostate.ridge.list <- lapply(list(lambda=seq(0,8,by=0.4)), function(lambda)
        gen.ridge(train[,1:8], y=train[,9,drop=FALSE],   lambda=lambda))
    # Problems with this usage.
    # simpler usage:
    #
    prostate.ridge <- gen.ridge(train[,1:8], y=train[,9,drop=FALSE], lambda=1)
    #
    # Since there is some problems with the mda functions, we use our own:
    #
    prostate.ridge <- simple.ridge( train[,1:8], train[,9], df=1:8 )
    #
    # coefficient traces:
    #
    matplot( prostate.ridge$df, t(prostate.ridge$beta), type="b",
            col="blue", pch=17, ylab="coefficients" )
    # Calculations for the lasso:
    #
    library(lasso2)
    prostate.lasso <- l1ce( lpsa ~ ., data=train, trace=TRUE, sweep.out=~1,
                         bound=seq(0,1,by=0.1) )
    prostate.lasso.coef <- sapply(prostate.lasso, function(x) x$coef)
    colnames(prostate.lasso.coef) <- seq( 0,1,by=0.1 )
    matplot( seq(0,1,by=0.1), t(prostate.lasso.coef[-1,]), type="b",
            xlab="shrinkage factor", ylab="coefficients",
            xlim=c(0, 1.2), col="blue", pch=17 )
    #
    # lasso with lars:
    library(lars)
    #
    prostate.lasso.lars <- lars( as.matrix(train[,1:8]), train[,9],
             type="lasso", trace=TRUE )
    cv.lars( as.matrix(train[,1:8]), train[,9],
             type="lasso", trace=TRUE, K=10 )
    #
    # CV (cross-validation) using package boot:
    #
    library(boot)
    prostate.glm <- glm( lpsa ~ ., data=train )
    # repeat this some times to make clear that cross-validation is
    # a random procedure
    #
    cv.glm( train, prostate.glm, K=10 )$delta
    #
    # This is a two-component vector, raw cross-validated estimate and
    #   adjusted cross-validated estimate.
    summary( prostate.glm )
    #

[Package ElemStatLearn version 0.1-4 Index]