STAT 7780: Survival AnalysisFirst Review

Peng Zeng

Department of Mathematics and StatisticsAuburn University

Fall 2017

Peng Zeng (Auburn University) STAT 7780 – Lecture Notes Fall 2017 1 / 25

Outline

1 Review

2 SAS codes

3 Proc LifeTest

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Review

Quantities

survival function

hazard function

cumulative hazard function

mean residual life

median lifetime

Relationship between these quantities.

express one quantity in terms of the other

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Review

Common Parametric Models

Exponential distribution

Weibull distribution

Gamma distribution

Need to know

density function

mean and variance

basic properties

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Review

Censoring and Truncation

Be able to distinguish the following scenarios

type I censoring & type II censoring

left/right/double/interval censoring

progressive/generalized censoring

left/right truncation

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Review

Likelihood Function

write out likelihood function for different censoring/truncationscenarios

maximum likelihood estimator (MLE)

asymptotic distribution of MLE

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Review

Left-Truncated and Right-Censored Data

Most discussions are presented in terms of right-censored data.

Understand how the formula are adjusted for left-truncated data.

Understand

ti distinct event times

di number of events

Yi number of individuals at risk

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Review

Kaplan-Meier Estimator

Need to understand

product-limit estimator

variance

pointwise confidence interval

confidence band

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Review

Nelson-Aalen Estimator

Need to understand

estimator

variance

pointwise confidence interval

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Review

Mean Survival Time

Need to understand

estimator

variance

confidence interval

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Review

Median Survival Time

Need to understand

estimator

variance

confidence interval

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Review

Hypothesis Testing

one-sample log-rank test

log-rank test and Wilcoxon test

test for trend

Renyi type tests

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Review

Parametric Regression

Three different views

accelerated fail-time model

log-time linear model

distribution of life time

Two distributions

Weibull distribution.

Log-logistic distribution.

Topics include

interpretation of parameters

hypothesis testing (Wald’s test, likelihood ratio test)

AIC

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SAS codes

SAS Code

ods graphics on;proc lifetest data = your-SAS-data more-options;

time T * delta(level-for-censoring);run;

with ods graphics on;, SAS draws a graph for the estimated S(t)

use statement strata to compare groups

use statement ods output ProductLimitEstimates =mySASfile;to output the results of Kaplan-Meier estimators andNelson-Aalen estimator.

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SAS codes

More SAS Options

nelson requests Nelson-Aalen estimators

plots = S(CL CB = EP) plots pointwise confidence intervalband confidence band for S(t)

outsurv = creates a data set for estimated S(t) and more

conftype = linear type of confidence interval, default is loglog.

confband = ep type of confidence band,

stderr outputs standard error of S(t) with outsurv =

alpha = specifies confidence level

adjust = in strata statement for multiple comparison.

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SAS codes

SAS for Parametric Regression

proc lifereg data = SAS-data-set;model time * delta(0) = list-of-variables;output out = new-data keyword = names;

run;

In SAS output, Weibull shape means 1/σ and Weibull scalemeans eµ.

Use option covb for the estimated covariance matrix.

Use option distribution = to specify distribution. It can beexponential, gamma, llogistic, lnormal, weibull.

The keyword in output statement can be cres, sres, xbeta.

probplot statement provides a plot for checking distribution ofresponse.

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SAS codes

SAS Code

proc lifereg data = SAS-data-set;model (lower, upper) = list-of-variables;

run;

The censoring status is determined by whether the two values areequal and whether either is coded as missing data:

Uncensored LOWER and UPPER are both present and equal.Interval Censored LOWER and UPPER are present and different.Right Censored LOWER is present, but UPPER is missing.Left Censored LOWER is missing, but UPPER is present.

Observations are also excluded if times are 0 or negative or bothUPPER and LOWER are missing or if LOWER > UPPER.

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Proc LifeTest

LifeTest Procedure

LIFETEST procedure can be used to

Estimate survival curves

Compare different populations

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Proc LifeTest

Syntax

PROC LIFETEST options;BY variables;FREQ variable;ID variables;STRATA variables;TEST variables;TIME variable;WEIGHT variables;

Some comments.

proc lifetest and time statements are required and the remainingstatements are optional.

Most statements have many options.

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Proc LifeTest

Commonly-used Statements

The TIME statement specifies the variables that define thesurvival time and censoring indicator.

The STRATA statement specifies a variable or set of variablesthat define the strata for the analysis.

The TEST statement specifies a list of numeric covariates to betested for their association with the response survival time. Eachvariable is tested individually, and a joint test statistic is alsocomputed.

The ID statement provides a list of variables whose valuesidentify observations in the product-limit, Breslow, orFleming-Harrington estimates.

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Proc LifeTest

OptionsOptions in proc lifetest statements.

nelson or aalen produces the Nelson-Aalen estimates of thecumulative hazards and the corresponding standard errors.

outsurv = names an output data set to contain survivor functionestimates

outtest = names an output data set to contain rank teststatistics for association of survival time with covariatesplots = specifies plots to display. Supported plots include

hazard or H for the estimated hazard functions.loglogS or LLS for the log of negative log of estimated survivorfunctions versus the log of time.logSurv or LS for the negative log of estimated survivorfunctions versus time.survival or S for the estimated survivor functions.

maxtime = specifies the maximum time value for plotting.Peng Zeng (Auburn University) STAT 7780 – Lecture Notes Fall 2017 21 / 25

Proc LifeTest

Example: Lung Cancer

The following variables are available for a corhort of lung cancerpatients.

SurvTime: survival time in days, where negative values indicatecensoring.

Cell: type of cancer cell (squamous, small, adeno, large)

Therapy: type of therapy: 0 = standard or 1 = test

Prior: prior therapy: 0 = no, 10 = yes

Age: age in years

DiagTime: time in months from diagnosis to entry into the trial

Kps: performance status

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Proc LifeTest

Example: Bone Marrow Transplant

Data of 137 bone marrow transplant patients have been saved in thedata set BMT in the sashelp library.

T: represents the disease-free survival time (time to death orrelapse or to the end of the study in days)

Status: the censoring indicator 1 = event time and 0 = censoredtime.

Group: the patient’s risk category (ALL, AML-low, AML-high)

This example highlights a number of features in the survival plot thatuses ODS Graphics. Also shown in this example are comparisons ofsurvival curves based on multiple comparison adjustments.

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Proc LifeTest

Commentsatrisk = suboption of survival curves (plots = S) specifies thetime points at which the at-risk numbers are displayed.

The strata = panel of survival curves (plots = S) specificationrequests that the survival curves be displayed in a panel of threeplots, one for each risk group.

In the strata statement, the adjust = sidak option requests theSidak multiple-comparison adjustment, and by default, all pairedcomparisons are carried out.

Use diff = option in the strata statement to designate one groupas the control and apply a multiple-comparison adjustment tothe p-values for the paired comparison between the controlgroup with each of treatment groups.

The order = internal option in the strata statement enables oneto order the strata by their internal values.

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Proc LifeTest

Example: Life-Table Estimate

The data in this example represent the survival rates of males withangina pectoris.

Survival time is measured as years from the time of diagnosis.

Data are the number of events and number of withdrawals ineach one-year time interval.

Use method = lt for life-table method of computing estimates.

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