1. 1 Survival Analysis Biomedical Applications Halifax SAS User Group April 29/2011

2. 2 Why do Survival Analysis Aims : Aims : How does the risk of event occurrence vary with time? How does the risk of event occurrence vary with time? How does the distribution across states change with time? How does the distribution across states change with time? How does the risk of event occurrence depend on explanatory variables? How does the risk of event occurrence depend on explanatory variables? Paul Allison, 2002 Lecture. University of Pennsylvania at Philadelphia Paul Allison, 2002 Lecture. University of Pennsylvania at Philadelphia

3. 3 Survival Data Time from randomization until time of the event of interest Time from randomization until time of the event of interest Classified as event time data Classified as event time data Generally not symmetrical distribution Generally not symmetrical distribution Positive skew (tails to right) Positive skew (tails to right)

4. 4 Survival Data Example Example -Time from onset of cancer to death/remission -Time from onset of cancer to death/remission -Time from implant of pacemaker to lead survival Fixed start point Fixed start point - recruitment in study - onset of cancer - insertion of Pacemaker

5. 5 Censoring Right: occurs to the right of the last known survival time Right: occurs to the right of the last known survival time Left: actual survival time is less than observed, common in reoccurrence Left: actual survival time is less than observed, common in reoccurrence Interval: survival time is between two time points, a and b Interval: survival time is between two time points, a and b

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7. 7 Kaplan-Meier Non-parametric method Non-parametric method Assumes events depend only on time, and censored and non-censored subjects behave the same Assumes events depend only on time, and censored and non-censored subjects behave the same Descriptive method primarily used for exploratory analysis Descriptive method primarily used for exploratory analysis

8. 8 Kaplan–Meier Estimate Based on life-table methods Based on life-table methods Arbitrarily small intervals, continuous function Arbitrarily small intervals, continuous function Expressed as a probability Expressed as a probability

9. 9 Kaplan-Meier Data Time variable Time variable Censoring Censoring Strata: Categorical variable that represents group effect Strata: Categorical variable that represents group effect ex. Flu strain Factor: Categorical variable that represents causal effect Factor: Categorical variable that represents causal effect ex. Type of treatment

10. 10 SAS Proc Lifetest

11. 11 Proc Gplot

12. 12 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;

13. 13 SURVPLOT MACRO %survplot (DATA=xxx_aug, TIME=time_death, EVENT=death,CEN_VL=0, CLASS=event_anyshock, EVENT=death,CEN_VL=0, CLASS=event_anyshock, TESTOP=1, CLASSFT=cchrl, CMARKS=0, PLOTOP=0, PRINTOP= 0, TESTOP=1, CLASSFT=cchrl, CMARKS=0, PLOTOP=0, PRINTOP= 0, POINTS='1 2 5 10', SCOLOR=black, XDIVISOR=1, LABELS=, POINTS='1 2 5 10', SCOLOR=black, XDIVISOR=1, LABELS=, LABCOL=black, BY=, WHERE=, LEGEND=1, YAXIS=2, XAXIS=1, LABCOL=black, BY=, WHERE=, LEGEND=1, YAXIS=2, XAXIS=1, XMAX=15, LCOL=black red blue, PERCENT=0, FONT=SWISS, 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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15. 15 Kaplan–Meier Estimate The estimated probability that a patient will survive for 365 days or more is 0.56 The estimated probability that a patient will survive for 365 days or more is 0.56

16. 16 Kaplan – Meier Estimate Test of Equality over Strata TestChi-SquareDFPr > Chi-Square Log-Rank6.852910.0088 Wilcoxon3.962610.0465

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18. 18 Modeling Survival Data Model the survival “experience” of the patient and the variables 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 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 How explanatory variables affect “FORM” of the hazard function

19. 19 Modeling Survival Data Obtain an estimate of hazard function for individual Obtain an estimate of hazard function for individual Estimate the median survival time for current or future patients Estimate the median survival time for current or future patients

20. 20 Cox Regression Modeling Proportional hazard assumption Proportional hazard assumption Semi- Parametric model Semi- Parametric model Coefficient is the log of the ratio of hazard of death at time t 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 No assumption about shape but restrained to be proportional across covariate levels

21. 21 Cox Regression Modeling Categorical 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

22. 22 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.

23. 23 Violations of PH Assumption PH assumes effect of each covariate is same at all time points PH assumes effect of each covariate is same at all time points 1. Time dependant covariates 2. Stratification

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25. 25 Time dependent covariates Variables whose value change over time Variables whose value change over time No longer proportional hazard model No longer proportional hazard model Method to deal with violation of PH assumption Method to deal with violation of PH assumption Positive Coefficient: Effect of covariate increases linearly with time Positive Coefficient: Effect of covariate increases linearly with time Example: GVHD in model to look at leukemia relapse Example: GVHD in model to look at leukemia relapse

26. 26 Surviving Survival Analysis – An Applied Introduction. NESUG 2008. Williams, C.

27. 27 Survival Prediction Baseline survivor function Baseline survivor function Estimate survivor function for any set of covariates = Mean of covariate method Estimate survivor function for any set of covariates = Mean of covariate method Adjusted survival curve method Adjusted survival curve method

28. 28 Mean of Covariate Method Mean value of covariate inserted into survival function of PH model Mean value of covariate inserted into survival function of PH model Limitations regarding mean value and dichotomous variables Limitations regarding mean value and dichotomous variables Calculated for ‘average’ person Calculated for ‘average’ person Easily generated from SAS using baseline statement Easily generated from SAS using baseline statement

29. 29 Corrected Group Prognosis Method Survival curve generated for each unique combination of covariates Survival curve generated for each unique combination of covariates Actual averaging of survival curves Actual averaging of survival curves Can be computer intensive 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

30. 30 Direct Adjusted Survival Curves Average of individual predicted survival curves Average of individual predicted survival curves Relative risk of survival between treatment arms adjusted for covariates Relative risk of survival between treatment arms adjusted for covariates Beneficial in non-randomized studies Beneficial in non-randomized studies Variance estimation and difference of direct adjusted survival probabilities Variance estimation and difference of direct adjusted survival probabilities SAS Macro %ADJSURV SAS Macro %ADJSURV http://www.mcw.edu/FileLibrary/Groups/Biostatistics/Software/AdjustedSurvivalCurves.p df http://www.mcw.edu/FileLibrary/Groups/Biostatistics/Software/AdjustedSurvivalCurves.p df 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.

31. 31 Competing Risks Models Occurrence of one type of event removes individual from risk of all other types 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 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 Assumption of independence of the distribution of the time to the competing events does not hold

32. 32 Competing Risks Models Functioning Shunt Shunt Failure Infection Shunt Failure Blockage Shunt Failure Other Cause

33. 33 Cumulative Incidence Analysis Create data set with multiple strata per ‘failure’ Create data set with multiple strata per ‘failure’ If K competing risks, then K rows of data If K competing risks, then K rows of data %CumInc Macro %CumInc Macro %CumIncV Macro %CumIncV Macro Allows some covariates to have same effect on several types of outcome event 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.