survival analysis project
TRANSCRIPT
![Page 1: Survival Analysis Project](https://reader036.vdocuments.mx/reader036/viewer/2022062503/589b5a681a28ab606f8b54f9/html5/thumbnails/1.jpg)
German Breast Cancer Survival
AnalysisDavid Schuler, Ankur Verma, Udyot Kumar,
Uma Lalitha-Chockalingham
![Page 2: Survival Analysis Project](https://reader036.vdocuments.mx/reader036/viewer/2022062503/589b5a681a28ab606f8b54f9/html5/thumbnails/2.jpg)
Objectives
●Understand the length of time between breast cancer diagnoses and specific events
●Understand what factors play a role in determining these lengths
![Page 3: Survival Analysis Project](https://reader036.vdocuments.mx/reader036/viewer/2022062503/589b5a681a28ab606f8b54f9/html5/thumbnails/3.jpg)
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
![Page 4: Survival Analysis Project](https://reader036.vdocuments.mx/reader036/viewer/2022062503/589b5a681a28ab606f8b54f9/html5/thumbnails/4.jpg)
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
![Page 5: Survival Analysis Project](https://reader036.vdocuments.mx/reader036/viewer/2022062503/589b5a681a28ab606f8b54f9/html5/thumbnails/5.jpg)
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)
![Page 6: Survival Analysis Project](https://reader036.vdocuments.mx/reader036/viewer/2022062503/589b5a681a28ab606f8b54f9/html5/thumbnails/6.jpg)
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
![Page 7: Survival Analysis Project](https://reader036.vdocuments.mx/reader036/viewer/2022062503/589b5a681a28ab606f8b54f9/html5/thumbnails/7.jpg)
![Page 8: Survival Analysis Project](https://reader036.vdocuments.mx/reader036/viewer/2022062503/589b5a681a28ab606f8b54f9/html5/thumbnails/8.jpg)
Exploratory Data Analysis
![Page 9: Survival Analysis Project](https://reader036.vdocuments.mx/reader036/viewer/2022062503/589b5a681a28ab606f8b54f9/html5/thumbnails/9.jpg)
![Page 10: Survival Analysis Project](https://reader036.vdocuments.mx/reader036/viewer/2022062503/589b5a681a28ab606f8b54f9/html5/thumbnails/10.jpg)
Correlation
● menopause and age
● Estrogen and Progesterone
![Page 11: Survival Analysis Project](https://reader036.vdocuments.mx/reader036/viewer/2022062503/589b5a681a28ab606f8b54f9/html5/thumbnails/11.jpg)
Preliminary Survival Analysis - KM Curves
![Page 12: Survival Analysis Project](https://reader036.vdocuments.mx/reader036/viewer/2022062503/589b5a681a28ab606f8b54f9/html5/thumbnails/12.jpg)
Preliminary Survival Analysis - KM Curves
![Page 13: Survival Analysis Project](https://reader036.vdocuments.mx/reader036/viewer/2022062503/589b5a681a28ab606f8b54f9/html5/thumbnails/13.jpg)
![Page 14: Survival Analysis Project](https://reader036.vdocuments.mx/reader036/viewer/2022062503/589b5a681a28ab606f8b54f9/html5/thumbnails/14.jpg)
![Page 15: Survival Analysis Project](https://reader036.vdocuments.mx/reader036/viewer/2022062503/589b5a681a28ab606f8b54f9/html5/thumbnails/15.jpg)
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
![Page 16: Survival Analysis Project](https://reader036.vdocuments.mx/reader036/viewer/2022062503/589b5a681a28ab606f8b54f9/html5/thumbnails/16.jpg)
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]
![Page 17: Survival Analysis Project](https://reader036.vdocuments.mx/reader036/viewer/2022062503/589b5a681a28ab606f8b54f9/html5/thumbnails/17.jpg)
COX Regression Modelling with phreg in SAS
![Page 18: Survival Analysis Project](https://reader036.vdocuments.mx/reader036/viewer/2022062503/589b5a681a28ab606f8b54f9/html5/thumbnails/18.jpg)
Survival Curve Estimate ( Test Data - 3 rows)
![Page 19: Survival Analysis Project](https://reader036.vdocuments.mx/reader036/viewer/2022062503/589b5a681a28ab606f8b54f9/html5/thumbnails/19.jpg)
Comparing R, Python & SAS Code
![Page 20: Survival Analysis Project](https://reader036.vdocuments.mx/reader036/viewer/2022062503/589b5a681a28ab606f8b54f9/html5/thumbnails/20.jpg)
Comparing R, Python, & SAS: Plots
![Page 21: Survival Analysis Project](https://reader036.vdocuments.mx/reader036/viewer/2022062503/589b5a681a28ab606f8b54f9/html5/thumbnails/21.jpg)
SAS Plot
![Page 22: Survival Analysis Project](https://reader036.vdocuments.mx/reader036/viewer/2022062503/589b5a681a28ab606f8b54f9/html5/thumbnails/22.jpg)
Comparing Regression Models: Tumor Grade
![Page 23: Survival Analysis Project](https://reader036.vdocuments.mx/reader036/viewer/2022062503/589b5a681a28ab606f8b54f9/html5/thumbnails/23.jpg)
Comparing Regression Models: Hormone
![Page 24: Survival Analysis Project](https://reader036.vdocuments.mx/reader036/viewer/2022062503/589b5a681a28ab606f8b54f9/html5/thumbnails/24.jpg)
Comparing Regression Models: Menopause
![Page 25: Survival Analysis Project](https://reader036.vdocuments.mx/reader036/viewer/2022062503/589b5a681a28ab606f8b54f9/html5/thumbnails/25.jpg)
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