session_lecture.Rmd
This is the Kaplan-Meier Estimate of the Survival function .
Definition: The survival function at time t, denoted , is the probability of being event-free at t. Equivalently, it is the probability that the survival time is greater than t.
Definition: The cumulative event function at time t, denoted , is the probability that the event has occurred by time t, or equivalently, the probability that the survival time is less than or equal to t. .
Definition: The hazard function is the short-term event rate for subjects who have not yet experienced an event.
Definition: Under the proportional hazards assumption, the hazard ratio does not vary with time. That is, .
In other words, does not vary with time
Multiplicative or additive model?
## Call:
## coxph(formula = Surv(time, cens) ~ group, data = leuk)
##
## n= 42, number of events= 30
##
## coef exp(coef) se(coef) z Pr(>|z|)
## group6 MP -1.5721 0.2076 0.4124 -3.812 0.000138 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## group6 MP 0.2076 4.817 0.09251 0.4659
##
## Concordance= 0.69 (se = 0.041 )
## Likelihood ratio test= 16.35 on 1 df, p=5e-05
## Wald test = 14.53 on 1 df, p=1e-04
## Score (logrank) test = 17.25 on 1 df, p=3e-05
Source: Using Time Dependent Covariates and Time Dependent Coefficients in the Cox Model
survival::coxph
with
survival::survreg