Mammary Cancer Survival Analysis

Survival analysis

In medicine, especially but not only in oncology, it is very important to analyse overall survival, recurrence-free survival and perform other time-to-event analyses. In this example, using simulated data, we will analyse overall mammary cancer survival. We will try to see if survival is associated with a few predictive variables.

The dataset

For every woman, we have data about

date of cancer diagnosis
date of last follow up visit
survival at last follow up visit
possible predictors of survival: BMI, cancer stage, neo_adiuvant_therapy


suppressWarnings(suppressMessages(library(dplyr, quiet = T)))

set.seed(111)
# Upload data (I created the data, it's not real!)
db = read.csv("mammary_cancer_data.csv") %>% select(-X) %>% 
filter(as.Date(date_diagnosis,format="%d/%m/%Y")>as.Date("01/01/1900",format="%d/%m/%Y"))

db = db %>% 
# simulate stage data and neo_adiuvant_therapy data accordingly
mutate(stage = sample(1:4, nrow(db), replace = T),
       neo_adiuvant_therapy = ifelse(stage %in% c(3,4), 1, neo_adiuvant_therapy),
# calculate survival time after diagnosis
	   survival_time = abs(as.numeric(as.Date(last_visit,format="%d/%m/%Y") - as.Date(date_diagnosis,format="%d/%m/%Y")-sample(1:5000, nrow(db)))), 
       survival_factor = as.factor(survival),
       neo_adiuvant_therapy = as.factor(neo_adiuvant_therapy), 
       stage = as.factor(stage), 
       BMI_cat = ifelse(BMI > 30, "Obese", "Not Obese"))
head(db)

Data summary

BMI, stage and neoadiuvant therapy are not significantly associated with survival status at bivariate analysis, but time has not yet been considered.

# Summary of data
install.packages("arsenal", quiet = T)
library(arsenal, quiet = T)
as.data.frame(summary(tableby(survival_factor ~ BMI + neo_adiuvant_therapy + stage, data = db), text = T))

Kaplan-Meier Analysis

Overall Kaplan-Meier survival curve shows a median survival of more than 4000 days, which is more than 10 years.

library(survival, quiet = T)
library(ggplot2, quiet = T)
suppressWarnings(suppressMessages(install.packages("survminer", quiet = T)))
suppressWarnings(suppressMessages(library(survminer, quiet = T)))
# overall survival
sop <- Surv(db$survival_time, db$survival)
fitkm <- survfit(sop ~ 1, type="kaplan-meier")

ggsurvplot(
  fitkm,
  data = db,
  conf.int = TRUE,
  xlab = "Days", ylab = "",
  ggtheme = theme_light(),
  surv.median.line = "hv",  legend.labs = c("Overall survival"),
  legend.title = "",risk.table = F,
  palette = c("#8C3F4D"), font.y = 15, font.x = 15, font.tickslab = 10, font.legend = 12)

Bivariate and Multivariate Analysis

BMI is associated with survival at bivariate analysis while neoadiuvant therapy and stage seem not (remember this is fake data!!)

listavariabili<-list("BMI_cat", "stage", "neo_adiuvant_therapy")
listatitoli<- c("BMI", "Cancer stage", "Neo-adiuvant therapy")
listaetichette <- list(c("Not Obese", "Obese"), c("1", "2", "3", "4"), c("No", "Yes"))
formulae <- lapply(listavariabili, function(x) as.formula(paste0("sop ~ ", x)))
fits <- surv_fit(formulae, data = db)

p1_st <- ggsurvplot(fits, data = db,
  pval = TRUE,
  #pval.coord = c(200, 0.10),
  xlab = "Days", ylab = "",
  ggtheme = theme_light(),
  #surv.median.line = "hv",
  title = "",
  legend.title=listatitoli, tables.height = 0.28, tables.theme = theme_cleantable(),  conf.int = F, tables.col = "strata", tables.y.text = F, censor = T,
  palette = c("#8C3F4D", "#3E606F", "#6476a1", "red"), font.y = 7, font.x = 7, font.tickslab = 10, font.legend = 12, legend.labs = listaetichette,
  risk.table = T, risk.table.title = "", risk.table.fontsize = 3
  )
options(repr.plot.width=10, repr.plot.height=20)
arrange_ggsurvplots(p1_st, ncol = 1, nrow = 3, print = TRUE, title = "Kaplan-Meier plots for survival in mammary cancer stratified by Body Mass Index, neoadiuvant therapy and stage.\nLog rank test p values are shown for each group.")