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Objectives

Factors or covariates associated with survival of an individual diagnosed with breast cancer

Survival and hazard functions

Survival Analysis methods and assumptions: Parametric, Nonparametric and Semiparametric methods

Comparison of survival rates for different groups

Predicting survival time for a patient under given conditions

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Survival Analysis and Censoring

Survival analysis the analysis of data in the form of times from a well-defined time of origin until an event of interest occurs (end-point).

The end-point or the event of interest is death.

All the observations who are still alive or die from a different cause other than breast cancer are censored.

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Data

The data is from the NCI for individuals diagnosed with breast cancer

The choice of variables we use are biological factors associated with the cells and factors

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Distribution Functions

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Estimating survival and hazard functions

Nonparametric Method: Kaplan Meier test
Parametric Methods: Weibull, Exponential, Gamma, Lognormal
Semiparametric Method: Cox PH Model

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Kaplan Meier Method

We can estimate the survival probability for an individual from the population from the Kaplan Meier survival curve.
The probability of surviving beyond 200 months is about 48%.
The Censored percentage is 54.40%

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Parametric Models

These methods assume that the survival times follow a given distribution.
Weibull
Exponential
Gamma
Lognormal

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Goodness of fit Tests

Distribution	Decision	Kolmogorov-Smirnov	Cramer-von Mises	Anderson-Darling	Chi-Square
Exponential	P Value	<0.001	<0.001	<0.001	<0.001
Exponential	Decision	Reject	Reject	Reject	Reject
Lognormal	P Value	<0.001	<0.001	<0.001	<0.001
Lognormal	Decision	Reject	Reject	Reject	Reject
Gamma	P Value	<0.001	<0.001	<0.001	<0.001
Gamma	Decision	Reject	Reject	Reject	Reject
Weibull	P value				<0.001
Weibull	Decision				Reject

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Goodness of fit: Weibull

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Semiparametric Methods�Cox PH Model – the assumptions are violated

Non proportional hazard

Non linearity

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Comparison of Survival Rates

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Comparison of Survival Rates for order of Treatment

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Comparison of Survival Rates among age groups

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Conclusions

By examining assumptions of the different methods and performing a goodness of fit we can decide on the survival analysis methods to use.
From the analysis of survival curves we can see what groups have a higher survival rate.
We do see a statistically significant difference between the order of Treatments and age groups
Individuals who have radiation during surgery have the least survival compared to the other orders.
Individuals over 60 have a lower survival rate

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Reference

Allison P. (2010): Survival Analysis Using SAS; A Practical Guide. Second edition SAS press, 324pp
Cody R., Smith J.,2006 Applied Statistics and the SAS programming Language, fifth edition, Elsevier Science Publishing Company
Collet D. (2014): Modelling Survival Data in Medical Research, third edition, CRC Press, 548pp.
Montgomery D., Peck E., Vining G. (2012): Introduction to Linear Regression Analysis fifth edition, John Wiley& sons, 672pp
The LIFEREG Procedure. (1999). Retrieved from http://www.math.wpi.edu/saspdf/stat/chap36.pdf

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