Assignment3

#loading packages
library(survival)
library(survminer)

## Loading required package: ggplot2

## Loading required package: ggpubr

## 
## Attaching package: 'survminer'

## The following object is masked from 'package:survival':
## 
##     myeloma

#loading dataset
data(lung)

## Warning in data(lung): data set 'lung' not found

lung$surv_obj <- Surv(time = lung$time, event = lung$status == 2)

#kaplan meier
km_fit <- survfit(lung$surv_obj ~ 1)
ggsurvplot(km_fit, data = lung, conf.int = TRUE, pval = TRUE)

## Warning in .pvalue(fit, data = data, method = method, pval = pval, pval.coord = pval.coord, : There are no survival curves to be compared. 
##  This is a null model.

#it shows the overall probability overtime for the entire cohort

#nelson aalen
na_fit <- survfit(lung$surv_obj ~ 1, type = "fh")
ggsurvplot(na_fit, data = lung, fun = "cumhaz")

#it shows cumulative hazard function over time an represents the accumulated risk of an event which is death

#long rank test
lung$sex <- factor(lung$sex, labels = c("Male", "Female"))
log_rank_test <- survdiff(lung$surv_obj ~ lung$sex)
log_rank_test

## Call:
## survdiff(formula = lung$surv_obj ~ lung$sex)
## 
##                   N Observed Expected (O-E)^2/E (O-E)^2/V
## lung$sex=Male   138      112     91.6      4.55      10.3
## lung$sex=Female  90       53     73.4      5.68      10.3
## 
##  Chisq= 10.3  on 1 degrees of freedom, p= 0.001

#it shows statistically test for differences in survival between the groups

#cox proportion hazard
cox_model <- coxph(lung$surv_obj ~ age + sex + ph.ecog, data = lung)
summary(cox_model)

## Call:
## coxph(formula = lung$surv_obj ~ age + sex + ph.ecog, data = lung)
## 
##   n= 227, number of events= 164 
##    (1 observation deleted due to missingness)
## 
##                coef exp(coef)  se(coef)      z Pr(>|z|)    
## age        0.011067  1.011128  0.009267  1.194 0.232416    
## sexFemale -0.552612  0.575445  0.167739 -3.294 0.000986 ***
## ph.ecog    0.463728  1.589991  0.113577  4.083 4.45e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##           exp(coef) exp(-coef) lower .95 upper .95
## age          1.0111     0.9890    0.9929    1.0297
## sexFemale    0.5754     1.7378    0.4142    0.7994
## ph.ecog      1.5900     0.6289    1.2727    1.9864
## 
## Concordance= 0.637  (se = 0.025 )
## Likelihood ratio test= 30.5  on 3 df,   p=1e-06
## Wald test            = 29.93  on 3 df,   p=1e-06
## Score (logrank) test = 30.5  on 3 df,   p=1e-06

#it estimates hazard ratios for predictors and tests their significance and also checks the proportional hazard assumption