ElemStatLearn (version 2015.6.26.2)

prostate: 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.

Examples

# NOT RUN {
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]
#
if( require(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:
#
if(require(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$coef)
colnames(prostate.lasso.coef) <- seq( 0,1,by=0.1 )
matplot( seq(0,1,by=0.1), t(prostate.lasso.coef[-1,]), type="b", 
        xlab="shrinkage factor", ylab="coefficients", 
        xlim=c(0, 1.2), col="blue", pch=17 )
}
#
# lasso with lars:
if (require(lars)) {
#
prostate.lasso.lars <- lars( as.matrix(train[,1:8]), train[,9], 
         type="lasso", trace=TRUE )
cv.lars( as.matrix(train[,1:8]), train[,9], 
         type="lasso", trace=TRUE, K=10 )
}
#
# CV (cross-validation) using package boot:
#
library(boot)
prostate.glm <- glm( lpsa ~ ., data=train )
# repeat this some times to make clear that cross-validation is
# a random procedure
#
cv.glm( train, prostate.glm, K=10 )$delta                              
#
# This is a two-component vector, raw cross-validated estimate and
#   adjusted cross-validated estimate.
summary( prostate.glm )
#
# }