Cox Proportional Hazard Model
> # Demonstration of Cox Proportional Hazard model
> library( survival ) # Library of survival analysis functions
> # Get Afifi's text book lung cancer data
> Lung <- read.table("http://users.humboldt.edu/rizzardi/Data.dir/Surv.txt",
+ header=F, na.strings=".")
>
> names(Lung) <+
c("ID","STAGET","Stagen","Hist","Treat","Perfbl","Poinf","Smokfu","Smokbl","Days","Dea
th")
>
> # Death: 0 = Alive(censored), 1=Dead
> # STAGET: Tumor size: 0=small, 1=large
> # Hist: Histology: 1=squamous cells, 2=other types of cells
> # Treat: 0=control (saline), 1=BCG
> attach( Lung )
>
> Lsurv <- with( Lung, Surv(Days,Death)) # makes survival analysis data
#################################
> coxfitSTAGET <- coxph( Lsurv ~ STAGET ) # 1=large tumor, 0=small
> coxfitSTAGET
Call:
coxph(formula = Lsurv ~ STAGET)
coef exp(coef) se(coef)
z
p
STAGET 0.496
1.64
0.141 3.52 0.00043
Likelihood ratio test=12.5 on 1 df, p=0.000413 n= 401
>
##############################################
> coxfitTreat <- coxph( Lsurv ~ Treat ) # 0=saline, 1=BCG
> coxfitTreat
Call:
coxph(formula = Lsurv ~ Treat)
coef exp(coef) se(coef)
z
p
Treat 0.0755
1.08
0.140 0.538 0.59
Likelihood ratio test=0.29 on 1 df, p=0.59 n= 401
> #########################################################
> coxfitBOTH <- coxph( Lsurv ~ Treat + STAGET )
> coxfitBOTH
Call:
coxph(formula = Lsurv ~ Treat + STAGET)
coef exp(coef) se(coef)
z
p
Treat 0.0832
1.09
0.140 0.593 0.55000
STAGET 0.4973
1.64
0.141 3.527 0.00042
Likelihood ratio test=12.8 on 2 df, p=0.00164 n= 401
> #############################################################################
> fakeage <- runif(401,min=40,max=70)
> coxfitJunk <- coxph( Lsurv ~ STAGET + fakeage )
> coxfitJunk
Call:
coxph(formula = Lsurv ~ STAGET + fakeage)
coef exp(coef) se(coef)
z
p
STAGET
0.49715
1.644 0.14102 3.525 0.00042
fakeage -0.00292
0.997 0.00813 -0.359 0.72000
Likelihood ratio test=12.6
>
>
on 2 df, p=0.00184
n= 401
1
> hazard <- basehaz( coxfitSTAGET )
> names(hazard)
[1] "hazard" "time"
> plot(hazard$time, hazard$hazard, type="l",xlab="days",ylab="baseline hazard")
> title(main="baseline hazard for Cox Proportional model (STAGET)")
>
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0.0
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baseline hazard
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baseline hazard for Cox Proportional model (STAGET)
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>
> coxfitTRTstrataSTG <- coxph( Lsurv ~ Treat + strata(STAGET) )
> coxfitTRTstrataSTG
Call:
coxph(formula = Lsurv ~ Treat + strata(STAGET))
coef exp(coef) se(coef)
z
p
Treat 0.0827
1.09
0.140 0.59 0.56
Likelihood ratio test=0.35 on 1 df, p=0.555 n= 401
> hazard2 <- basehaz( coxfitTRTstrataSTG )
> names( hazard2 )
[1] "hazard" "time"
"strata"
>
> windows()
> plot( hazard2$time, hazard2$hazard, type="n", xlab="days",ylab="baseline hazard")
> points( hazard2$time[hazard2$strata=="STAGET=0"],
+
hazard2$hazard[hazard2$strata=="STAGET=0"], type="l" )
> points( hazard2$time[hazard2$strata!="STAGET=0"],
+
hazard2$hazard[hazard2$strata!="STAGET=0"], type="l", lty=2 )
> legend( 250,1, legend=c("Staget=0","Staget=1"),lty=c(1,2))
> title(main="baseline hazard for Cox Proportional model")
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baseline hazard for Cox Proportional model
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baseline hazard
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# Demonstration of Cox Proportional Hazard model
library( survival ) # Library of survival analysis functions
# Get Afifi's text book lung cancer data
Lung <- read.table("http://users.humboldt.edu/rizzardi/Data.dir/Surv.txt",
header=F, na.strings=".")
names(Lung) <c("ID","STAGET","Stagen","Hist","Treat","Perfbl","Poinf","Smokfu","Smokbl","Days","Death")
#
#
#
#
Death: 0 = Alive(censored), 1=Dead
STAGET: Tumor size: 0=small, 1=large
Hist: Histology: 1=squamous cells, 2=other types of cells
Treat: 0=control (saline), 1=BCG
attach( Lung )
Lsurv <- with( Lung, Surv(Days,Death))
# makes survival analysis data
coxfitSTAGET <- coxph( Lsurv ~ STAGET ) # 1=large tumor, 0=small
coxfitSTAGET
coxfitTreat <- coxph( Lsurv ~ Treat ) # 0=saline, 1=BCG
coxfitTreat
coxfitBOTH <- coxph( Lsurv ~ Treat + STAGET )
coxfitBOTH
fakeage <- runif(401,min=40,max=70)
coxfitJunk <- coxph( Lsurv ~ STAGET + fakeage )
coxfitJunk
hazard <- basehaz( coxfitSTAGET )
names(hazard)
plot(hazard$time, hazard$hazard, type="l",xlab="days",ylab="baseline hazard")
title(main="baseline hazard for Cox Proportional model (STAGET)")
coxfitTRTstrataSTG <- coxph( Lsurv ~ Treat + strata(STAGET) )
hazard2 <- basehaz( coxfitTRTstrataSTG )
names( hazard2 )
windows()
plot( hazard2$time, hazard2$hazard, type="n", xlab="days",ylab="baseline hazard")
points( hazard2$time[hazard2$strata=="STAGET=0"],
hazard2$hazard[hazard2$strata=="STAGET=0"], type="l" )
points( hazard2$time[hazard2$strata!="STAGET=0"],
hazard2$hazard[hazard2$strata!="STAGET=0"], type="l", lty=2 )
legend( 250,1, legend=c("Staget=0","Staget=1"),lty=c(1,2))
title(main="baseline hazard for Cox Proportional model")
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