Transcript Survival Analysis - SAS Halifax Regional User Group

Survival Analysis
Biomedical Applications
Halifax SAS User Group
April 29/2011
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Why do Survival Analysis
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Aims :
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•
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
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Survival Data
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Time from randomization until time of the event
of interest
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Classified as event time data
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Generally not symmetrical distribution
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Positive skew (tails to right)
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Survival Data
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Example
-Time from onset of cancer to death/remission
-Time from implant of pacemaker to lead survival
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Fixed start point
- recruitment in study
- onset of cancer
- insertion of Pacemaker
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Censoring
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Right: occurs to the right of the last
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Left: actual survival time is less than
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Interval: survival time is between two time
known survival time
observed, common in reoccurrence
points, a and b
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Kaplan-Meier
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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
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Kaplan–Meier Estimate
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Based on life-table methods
Arbitrarily small intervals, continuous
function
Expressed as a probability
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Kaplan-Meier Data
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Time variable
Censoring
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Strata: Categorical variable that represents
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group effect
ex. Flu strain
Factor: Categorical variable that represents
causal effect
ex. Type of treatment
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SAS Proc Lifetest
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Proc Gplot
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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;
run;
quit;
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SURVPLOT MACRO
%survplot (DATA=xxx_aug , TIME=time_death ,
EVENT=death ,CEN_VL=0, CLASS=event_anyshock ,
TESTOP=1, CLASSFT=cchrl , CMARKS=0, PLOTOP=0 , PRINTOP= 0,
POINTS='1 2 5 10' , SCOLOR=black, XDIVISOR=1, LABELS= ,
LABCOL=black, BY= , WHERE= , LEGEND=1 , YAXIS=2, XAXIS=1,
XMAX=15 , LCOL=black red blue, PERCENT=0, FONT=SWISS,
F1=3, F2=3,
F3=3, F4=3, PLOTNAME= , ANNOTATE= ,
RTFEXCL=0,POPTIONS=);
Survplot Macro: Created by Ryan Lennon. 2009 Mayo Clinic College of Medicine.
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Kaplan–Meier Estimate
Product-Limit Survival Estimates
Timelist
365.00
365.00
Survival Failure
0.5634
0.4366
Error
0.0206
# Failed # Left
258
292
Point
95% Confidence Interval
Percent Estimate
[Lower
Upper)
50 1323.00
720.00 1905.00
Mean Standard Error
1398.44
54.91
The estimated probability that a patient will survive for 365 days or
more is 0.56
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Kaplan – Meier Estimate
Test of Equality over Strata
Test
Chi-Square
DF
Pr >
Chi-Square
Log-Rank
6.8529
1
0.0088
Wilcoxon
3.9626
1
0.0465
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Survival Distribution Function
1.00
0.75
0.50
0.25
0.00
0
2
4
6
8
10
12
time_death
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Modeling Survival Data
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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
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Modeling Survival Data
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Obtain an estimate of hazard function for
individual
Estimate the median survival time for
current or future patients
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Cox Regression Modeling
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Proportional hazard assumption
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Semi- Parametric model
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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
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Cox Regression Modeling
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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
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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.
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Violations of PH Assumption
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PH assumes effect of each covariate is
same at all time points
1. Time dependant covariates
2. Stratification
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Survival Distribution Function
1.00
0.75
0.50
0.25
0.00
0
1
2
3
4
5
6
7
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time_death_after439
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Time dependent covariates
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Variables whose value change over time
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No longer proportional hazard model
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Method to deal with violation of PH assumption
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Positive Coefficient: Effect of covariate increases linearly
with time
Example: GVHD in model to look at leukemia relapse
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Surviving Survival Analysis – An Applied Introduction. NESUG 2008. Williams, C.
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Survival Prediction
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Baseline survivor function
Estimate survivor function for any set of
covariates = Mean of covariate method
Adjusted survival curve method
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Mean of Covariate Method
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Mean value of covariate inserted into survival function of
PH model
Limitations regarding mean value and dichotomous
variables
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Calculated for ‘average’ person
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Easily generated from SAS using baseline statement
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Corrected Group Prognosis Method
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Survival curve generated for each unique
combination of covariates
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Actual averaging of survival curves
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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.
http://people.ucalgary.ca/~hquan/Weight.html
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Direct Adjusted Survival Curves
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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
http://www.mcw.edu/FileLibrary/Groups/Biostatistics/Software/AdjustedSurvivalCurves.pd
f
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.
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Competing Risks Models
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Occurrence of one type of event removes individual
from risk of all other types
Ignoring other event can lead to bias in KaplanMeier estimates
Assumption of independence of the distribution of
the time to the competing events does not hold
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Competing Risks Models
Shunt
Failure
Infection
Functioning
Shunt
Shunt
Failure
Blockage
Shunt
Failure
Other Cause
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Cumulative Incidence Analysis
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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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