Data description

The data set was collected by Stensjøen et al. (2015).

Idea for this study

Motivation

Stensjøen et al. (2015) pointed out there are obvious variations among patients, say slow growing and fast growing. Also, Mikkelsen et al. (2018) Modeled the association among the grwoth rate, extent of resectin and survival time.

What will we do

Based on the associations between growth pattern and survival time, in the aspect of growth rate,

  • We test the differnce on the survival time based on the grwoth rate, it should be different significantly.

  • Then set up the stochastic model based on grouped data as we have done before.

  • Make comparision of these two models

Work

1. Input data set

The following code input data into R.

library(readxl)
growthdata <- read.csv("C:/Users/ziweima/Desktop/2018summerbio/Growth_data.csv")

a <- read.csv("C:/Users/ziweima/Desktop/2018summerbio/a.csv")
#View(a)

sgr <- read.csv("C:/Users/ziweima/Desktop/2018summerbio/sgr.csv")
#View(sgr)

2. Study on the grwoth rate : histogram and fitting log-normal curve

loga <- log(a[which(a[,1]>0),1])
ha <- hist(a[which(a[,1]>0),1])

hloga <- hist(loga)
axfit <- seq(min(loga),max(loga),length=100)
ayfit <- dnorm(axfit,mean(loga),sd = sd(loga))
ayfit <- ayfit*diff(hloga$mids[1:2])*length(loga)
lines(axfit,ayfit)

* Fit with growth rate from specific growth rate

logsgr <- log(sgr[which(sgr[,1]>0),1])
hsgr <- hist(sgr[which(sgr[,1]>0),1])

hlogsgr <- hist(logsgr)
sgrxfit <- seq(min(logsgr),max(logsgr),length=100)
sgryfit <- dnorm(axfit,mean(loga),sd = sd(loga))
sgryfit <- sgryfit*diff(hlogsgr$mids[1:2])*length(logsgr)
lines(sgrxfit,sgryfit)

Survival analysis

Reference

Mikkelsen, Vilde Elisabeth, Anne Line Stensjøen, Erik Magnus Berntsen, Ivar Skjåk Nordrum, Øyvind Salvesen, Ole Solheim, and Sverre Helge Torp. 2018. “Histopathologic Features in Relation to Pretreatment Tumor Growth in Patients with Glioblastoma.” World Neurosurgery 109 (January): e50–e58. doi:10.1016/j.wneu.2017.09.102.

Stensjøen, Anne Line, Ole Solheim, Kjell Arne Kvistad, Asta K. Håberg, Øyvind Salvesen, and Erik Magnus Berntsen. 2015. “Growth Dynamics of Untreated Glioblastomas in Vivo.” Neuro-Oncology 17 (10): 1402–11. doi:10.1093/neuonc/nov029.