#Commands to practical exercise 4
# The commands below assume that:?
#?? (i)? the melanoma data set has been stored in the dataframe "melanoma"
#?? (ii) the survival library has been attached
#?? (iii) "sex" and "ulcer" have both been defined as factors
#???????? (this is no really needed for binary categorical variables,'
#????????? but it is good practice to do so)
# (cf. the R commands to practical exercise 3)
# a)
# First we fit univariate Cox regressions for the two binary covariates:
cox.mel<- coxph(Surv(lifetime,status==1)~sex, data=melanoma)
summary(cox.mel)
cox.mel<- coxph(Surv(lifetime,status==1)~ulcer, data=melanoma)
summary(cox.mel)
# For the numeric covariates, we need to decide whether they should
# enter the Cox regression as coded on the data file, or whether they
# should be transformed or converted to categorical covariates (if a
# useful transformation is hard to find).
# We do not address this question in a systematic manner here, but note
# that the Nelson-Aalen plots from practical exercise 3 indicate that
# tumor thickness should be log-transformed (for ease of interpretation
# using base 2 logs), while age can be entered as coded.
# Then we fit univariate Cox regressions for log2-thickness and age
cox.mel<- coxph(Surv(lifetime,status==1)~ log(thickn,2), data=melanoma)
summary(cox.mel)
cox.mel<- coxph(Surv(lifetime,status==1)~ age, data=melanoma)
summary(cox.mel)
#b)
# First fit a multivariate Cox regression with all four covariates:
cox.mel<- coxph(Surv(lifetime,status==1)~ sex+ulcer+log(thickn,2)+age, data=melanoma)
summary(cox.mel)
# Omit gender (which has largest P value)
cox.mel<- coxph(Surv(lifetime,status==1)~ ulcer+log(thickn,2)+age, data=melanoma)
summary(cox.mel)
# Omit age (which has largest P value among the remaining)
cox.mel<- coxph(Surv(lifetime,status==1)~ ulcer+log(thickn,2), data=melanoma)
summary(cox.mel)
# We end up with a model with log2-thickness and ulceration
# This model ought to be checked for proportional hazards
# and possible interaction(s), but that is a theme for later lectures
# and exercises