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Survival Analysis Biomedical Applications. Halifax SAS User Group April 29/2011. Why do Survival Analysis. Aims : How does the risk of event occurrence vary with time? How does the distribution across states change with time?

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Survival Analysis Biomedical Applications

Halifax SAS User Group

April 29/2011

Why do Survival Analysis

  • Aims :

    • How does the risk of event occurrence vary with time?

    • How does the distribution across states change with time?

    • How does the risk of event occurrence depend on explanatory variables?

    • Paul Allison, 2002 Lecture. University of Pennsylvania at Philadelphia

Survival Data

  • Time from randomization until time of the event of interest

  • Classified as event time data

  • Generally not symmetrical distribution

  • Positive skew (tails to right)

Survival Data

  • Example

    -Time from onset of cancer to death/remission

    -Time from implant of pacemaker to lead survival

  • Fixed start point

    - recruitment in study

    - onset of cancer

    - insertion of Pacemaker


  • Right: occurs to the right of the last known survival time

  • Left: actual survival time is less than observed, common in reoccurrence

  • Interval: survival time is between two time points, a and b


  • Non-parametric method

  • Assumes events depend only on time, and censored and non-censored subjects behave the same

  • Descriptive method primarily used for exploratory analysis

Kaplan–Meier Estimate

  • Based on life-table methods

  • Arbitrarily small intervals, continuous function

  • Expressed as a probability

Kaplan-Meier Data

  • Time variable

  • Censoring

  • Strata: Categorical variable that represents group effect

    ex. Flu strain

  • Factor: Categorical variable that represents causal effect

    ex. Type of treatment

SAS Proc Lifetest

Proc Gplot

proc gplot data=out3;

title 'Adjusted Survival Curve by Gender';

axis1 label=('Years') order=(0 to 12 by 1);

axis2 label=(angle=90 'Proportion Surviving');* order=(0.6 to 1.0 by 0.1);

plot surv*time=gender / haxis=axis1 vaxis=axis2 legend=legend1;




%survplot (DATA=xxx_aug , TIME=time_death ,

EVENT=death ,CEN_VL=0, CLASS=event_anyshock ,


POINTS='1 2 5 10' , SCOLOR=black, XDIVISOR=1, LABELS= ,


XMAX=15 , LCOL=black red blue, PERCENT=0, FONT=SWISS,


Survplot Macro: Created by Ryan Lennon. 2009 Mayo Clinic College of Medicine.

Kaplan–Meier Estimate

The estimated probability that a patient will survive for 365 days or more is 0.56

Kaplan – Meier Estimate

Modeling Survival Data

  • Model the survival “experience” of the patient and the variables

  • Focus on the risk or hazard of death at anytime after the time origin of the study

  • How explanatory variables affect “FORM” of the hazard function

Modeling Survival Data

  • Obtain an estimate of hazard function for individual

  • Estimate the median survival time for current or future patients

Cox Regression Modeling

  • Proportional hazard assumption

  • Semi- Parametric model

  • Coefficient is the log of the ratio of hazard of death at time t

  • No assumption about shape but restrained to be proportional across covariate levels

Cox Regression Modeling

  • Categorical

    Hazard Ratio: Ratio of estimated hazard for those with Diabetes to those without (controlling for other variables) = 0.250

    The hazard of death for those with diabetes is 25% of the hazard for those without

Hazard Ratio = 2

“ The treatment will cause the patient to progress more quickly, and that a treated patient who has not yet progressed by a certain time has twice the chance of having progressed at the next point in time compared with someone in the control group.”

What are hazard ratios?. Duerden, M. What is series by Hayward Group Ltd, 2009.

Violations of PH Assumption

  • PH assumes effect of each covariate is same at all time points

    1. Time dependant covariates

    2. Stratification

Time dependent covariates

  • Variables whose value change over time

  • No longer proportional hazard model

  • Method to deal with violation of PH assumption

  • Positive Coefficient: Effect of covariate increases linearly with time

  • Example: GVHD in model to look at leukemia relapse

Surviving Survival Analysis – An Applied Introduction. NESUG 2008. Williams, C.

Survival Prediction

  • Baseline survivor function

  • Estimate survivor function for any set of covariates = Mean of covariate method

  • Adjusted survival curve method

Mean of Covariate Method

  • Mean value of covariate inserted into survival function of PH model

  • Limitations regarding mean value and dichotomous variables

  • Calculated for ‘average’ person

  • Easily generated from SAS using baseline statement

Corrected Group Prognosis Method

  • Survival curve generated for each unique combination of covariates

  • Actual averaging of survival curves

  • Can be computer intensive

    Comparison of 2 Methods for Calculating Adjusted Survival Curves from Proportional Hazard models. Ghali, W.A., Quan, H., Brant, R., et al. JAMA. 2001; 286(12):1494-1497.

Direct Adjusted Survival Curves

  • Average of individual predicted survival curves

  • Relative risk of survival between treatment arms adjusted for covariates

  • Beneficial in non-randomized studies

  • Variance estimation and difference of direct adjusted survival probabilities

  • SAS Macro %ADJSURV

    A SAS Macro for Estimation of Direct Adjusted Survival Curves Based on A Stratified Cox Regression Model. Zhang, X., Loberiza, F.R., Klein, J.P. and Zhang, M-J.

Competing Risks Models

  • Occurrence of one type of event removes individual from risk of all other types

  • Ignoring other event can lead to bias in Kaplan-Meier estimates

  • Assumption of independence of the distribution of the time to the competing events does not hold

Shunt Failure


Shunt Failure






Other Cause

Competing Risks Models

Cumulative Incidence Analysis

  • Create data set with multiple strata per ‘failure’

  • If K competing risks, then K rows of data

  • %CumInc Macro

  • %CumIncV Macro

  • Allows some covariates to have same effect on several types of outcome event

    Rosthoj, S., Anderson, P. and Adildstrom, S. SAS macros for estimation of the cumulative incidence functions based on a Cox regression model for competing risks survival data. Computer Methods and Programs in Biomedicine, (2004) 74,69-75.

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