############## Log-rank tests ############

#### Example I: Motor Data (Part II)
library(survival)
library(MASS)
data(motors)
attach(motors)

# The figure of the Kaplan-Meier estimators (with 95% confidence 
# intervals) shows that there may be difference in survival 
# experiences for temperature = 170 and 190, so we only focus 
# on these two cases. 
motors2 <- motors[motors$temp==170 | motors$temp==190,]
# log-rank test
survdiff(Surv(time, cens)~temp, data=motors2)
Call:
survdiff(formula = Surv(time, cens) ~ temp, data = motors2)

          N Observed Expected (O-E)^2/E (O-E)^2/V
temp=170 10        7     9.74     0.769      6.38
temp=190 10        5     2.26     3.307      6.38

 Chisq= 6.4  on 1 degrees of freedom, p= 0.0115 

# So there is a significant difference between two survival 
# experiences for temperature = 170 and 190 at 5% level but not 
# at 1% level (p-value = 0.0115). 


#### Example II: VA data (Part II)
data(VA)
attach(VA)
# The figure of the Kaplan-Meier estimators (with 95% confidence 
# intervals) shows that there may be no difference in survival 
# experiences for the two treatments because the two confidence 
# bands overlap substantially, but let's perform a formal test 
# to confirm this. 
survdiff(Surv(stime, status)~treat)
Call:
survdiff(formula = Surv(stime, status) ~ treat)

         N Observed Expected (O-E)^2/E (O-E)^2/V
treat=1 69       64     64.5   0.00388   0.00823
treat=2 68       64     63.5   0.00394   0.00823

 Chisq= 0  on 1 degrees of freedom, p= 0.928 

# So there is no significant difference between two survival 
# experiences for the two treatments (p-value = 0.928), as expected.