survival analysis project
Post on 09-Feb-2017
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German Breast Cancer Survival
AnalysisDavid Schuler, Ankur Verma, Udyot Kumar,
Uma Lalitha-Chockalingham
Objectives
●Understand the length of time between breast cancer diagnoses and specific events
●Understand what factors play a role in determining these lengths
About Survival Analysis
●Predicting the time until an event of interest occurs
●Applications in Medicine, Manufacturing, Sociology, Sports, and many more
●Right Censored Data – an observation where the event has not yet occurred
● Survival Function - probability that at a given time, t, an event of interest has not yet occurred
Kaplan-Meier Estimator
●Non-parametric estimator of the survival function
●Time on the X-axis
●Percentage surviving on Y axis
●Tick marks represent right-censored observations
Cox Proportional Hazard Regression●Used to look at the relationship between the survival of a patient
and various explanatory variables
●Each explanatory variable is given a coefficient
○ HR = 1 : No effect
○ HR < 1 : Reduction in hazard ( Death)
○ HR > 1 : Increase in Hazard ( Death)
German Breast Cancer Data●Retrieved from UMass Amherst’s Statistics website
●Data collected from clinical trials performed by the German Breast Cancer Study Group
●Total of 686 observations conducted between July 1984 and December 1989● 16 variables, including censoring and time-length fields for death and cancer
recurrence
Exploratory Data Analysis
Correlation
● menopause and age
● Estrogen and Progesterone
Preliminary Survival Analysis - KM Curves
Preliminary Survival Analysis - KM Curves
Probability density function f(t)
Survival function S(t) = P(T>=t)
Hazard function h(t) = f(t) / S(t)
A way to compare two hazard functions:Hazard ratio : HR(t) = h0 (t) / h1(t)
Proportional hazard assumption : The hazard ratio does not vary with time, i.e. HR(t) = HR
This is an important assumption for Cox PH model
Preliminary Survival Analysis - Cox PH
○ HR = 1 : No effect
○ HR < 1 : Reduction in hazard ( Death)
○ HR > 1 : Increase in Hazard ( Death)
● Age1 = [21,30]● Age2 = (30,50]● Age3 =(50,80]
COX Regression Modelling with phreg in SAS
Survival Curve Estimate ( Test Data - 3 rows)
Comparing R, Python & SAS Code
Comparing R, Python, & SAS: Plots
SAS Plot
Comparing Regression Models: Tumor Grade
Comparing Regression Models: Hormone
Comparing Regression Models: Menopause
References
●http://www.medicine.ox.ac.uk/bandolier/painres/download/whatis/cox_model.pdf
●https://media.readthedocs.org/pdf/lifelines/latest/lifelines.pdf
●https://www.cscu.cornell.edu/news/statnews/stnews78.pdf
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