Details

Missing Values

Observations with a missing value for either the failure time or the censoring variable are not used in the analysis. If a stratum variable value is missing, survival function estimates are computed for the strata labeled by the missing value, but these data are not used in any rank tests. However, the MISSING option can be used to request that missing values be treated as valid stratum values. If any variable specified in the TEST statement has a missing value, that observation is not used in the calculation of the rank statistics.

Computational Formulas

Product-Limit Method

Let t ₁ <t ₂ < ... < t _k represent the distinct event times. For each i = 1 ,...,k , let n _i be the number of surviving units, the size of the risk set, just prior to t _i . Let d _i be the number of units that fail at t _i , and let s _i = n _i ˆ’ d _i .

The product-limit estimate of the SDF at t _i is the cumulative product

Notice that the estimator is defined to be right continuous; that is, the events at t _i are included in the estimate of S ( t _i ). The corresponding estimate of the standard error is computed using Greenwoods formula (Kalbfleisch and Prentice 1980)as

The first sample quartile of the survival time distribution is given by

Confidence intervals for the quartiles are based on the sign test (Brookmeyer and Crowley 1982). The 100(1 ˆ’ ± )% confidence interval for the first quartile is given by

where c _± is the upper ± percentile of a central chi-squared distribution with 1 degree of freedom. The second and third sample quartiles and the corresponding confidence intervals are calculated by replacing the 0.25 in the last two equations by 0.50 and 0.75, respectively.

The estimated mean survival time is

where t is defined to be zero. When the largest observed time is censored, this sum underestimates the mean. The standard error of is estimated as

where

If the largest observed time is not an event, you can use the TIMELIM= option to specify a time limit L and estimate the mean survival time limited to the time L and its standard error by replacing k by k + 1 with t _{k +1} = L .

Life-Table Method

The life-table estimates are computed by counting the numbers of censored and uncensored observations that fall into each of the time intervals [ t _{i ˆ’ 1} , t _i ), i = 1 , 2 ,...,k + 1, where t = 0 and t _{k +1} = ˆ . Let n _i be the number of units entering the interval [ t _{i ˆ’ 1} , t _i ), and let d _i be the number of events occurring in the interval. Let b _i = t _i ˆ’ t _{i ˆ’ 1} , and let , where w _i is the number of units censored in the interval. The effective sample size of the interval [ t _{i ˆ’ 1} , t _i ) is denoted by . Let t _mi denote the midpoint of [ t _{i ˆ’ 1} , t _i ).

The conditional probability of an event in [ t _{i ˆ’ 1} , t _i ) is estimated by

and its estimated standard error is

where .

The estimate of the survival function at t _i is

and its estimated standard error is

The density function at t _mi is estimated by

and its estimated standard error is

The estimated hazard function at t _mi is

and its estimated standard error is

Let [ t _{j ˆ’ 1} , t _j ) be the interval in which . The median residual lifetime at t _i is estimated by

and the corresponding standard error is estimated by

Interval Determination

If you want to determine the intervals exactly, use the INTERVALS= option in the PROC LIFETEST statement to specify the interval endpoints. Use the WIDTH= option to specify the width of the intervals, thus indirectly determining the number of intervals. If neither the INTERVALS= option nor the WIDTH= option is specified in the life-table estimation, the number of intervals is determined by the NINTERVAL= option. The width of the time intervals is 2, 5, or 10 times an integer (possibly a negative integer) power of 10. Let c = log ₁₀ (maximum observed time/number of intervals), and let b be the largest integer not exceeding c . Let d = 10 ^{c ˆ’ b} and let

with I being the indicator function. The width is then given by

By default, NINTERVAL=10.

Pointwise Confidence Limits Added to the Output Data Set

Pointwise confidence limits are computed for the survivor function, and for the density function and hazard function when the life-table method is used. Let ± be specified by the ALPHA= option. Let z _{± / 2} be the critical value for the standard normal distribution. That is, ( ˆ’ z _{± / 2} ) = ± / 2, where is the cumulative distribution function of the standard normal random variable.

Survival Function

When the computation of confidence limits for the survivor function S ( t ) is based on the asymptotic normality of the survival estimator ( t ), the approximate confidence interval may include impossible values outside the range [0,1] at extreme values of t . This problem can be avoided by applying the asymptotic normality to a transformation of S ( t ) for which the range is unrestricted. In addition, certain transformed confidence intervals for S ( t ) perform better than the usual linear confidence intervals (Borgan and Liest l 1990). The CONFTYPE= option enables you to pick one of the following transformations: the log-log function (Kalbfleisch and Prentice 1980), the arcsine-square root function (Nair 1984), the logit function (Meeker and Escobar 1998), the log function, and the linear function.

Let g be the tranformation that is being applied to the survivor function S ( t ). By the delta method, the standard error of g ( ( t )) is estimated by

where g ² is the first derivative of the function g . The 100(1- ± )% confidence interval for S ( t ) is given by

where g ^{ˆ’ 1} is the inverse function of g .

Arcsine-Square Root Transformation

The estimated variance of . The 100(1- ± )% confidence interval for S ( t ) is given by

Linear Transformation

This is the same as having no transformation in which g is the identity. The 100(1 ˆ’ ± )% confidence interval for S ( t ) is given by

Log Transformation

The estimated variance of . The 100(1- ± )% confidence interval for S ( t ) is given by

Log-log Transformation

The estimated variance of . The 100(1- ± )% confidence interval for S ( t ) is given by

Logit Transformation

The estimated variance of . The 100(1- ± )% confidence limits for S ( t ) are given by

Density and Hazard Functions

For the life-table method, a 100(1- ± )% confidence interval for hazard function or density function at time t is computed as

where ( t ) is the estimate of either the hazard function or the density function at time t , and [ ( t )] is the corresponding standard error estimate.

Simultaneous Confidence Intervals for Kaplan-Meier Curve

The pointwise confidence interval for the survivor function S ( t ) is valid for a single fixed time at which the inference is to be made. In some applications, it is of interest to find the upper and lower confidence bands that guarantee, with a given confidence level, that the survivor function falls within the band for all t in some interval. Hall and Wellner (1980) and Nair (1984) provide two different approaches for deriving the confidence bands. An excellent review can be found in Klein and Moeschberger (1997). You can use CONFBAND= option in the SURVIVAL statement to select the confidence bands. The EP confidence band provides confidence bounds that are proportional to the pointwise confidence interval, while those of the HW band are not proportional to the pointwise confidence bounds. The maximum time, t _U , for the bands can be specified by the BANDMAX= option; the minimum time, t _L , can be specified by the BANDMIN= option. Transformations that are used to improve the pointwise confidence intervals can be applied to improve the confidence bands. It may turn out that the upper and lower bounds of the confidence bands are not decreasing in t _L < t < t _U , which is contrary to the nonincreasing characteristic of survivor function. Meeker and Escobar (1998) suggest making an adjustment so that the bounds do not increase: if the upper bound is increasing on the right, it is made flat from the minimum to t _U ; if the lower bound is increasing from the right, it is made flat from t _L to the maximum. PROC LIFETEST does not make any adjustment for the nondecreasing behavior of the confidence bands in the OUT= data set. However, the adjustment was made in the display of the confidence bands using ODS graphics.

For Kaplan-Meier estimation, let t ₁ < t ₂ <...< t _D be the D distinct events times, and that at time t _i , there are d _i events. Let Y _i be the number of individuals who are at risk at time t _i . The variance of ( t ), given by the Greenwood formula, is where

Let t _L < t _U be the time range for the confidence band so that t _U is less than or equal to the largest event time. For the Hall-Wellner band, t _L can be zero, but for the equal precison band, t _L is greater than or equal to the smallest event time. Let

Let { W ( u ) , u 1} be a Brownian bridge.

Hall-Wellner Band

The 100(1- ± )% HW band of Hall and Wellner (1980) is

for all t _L t t _U , where h _± ( a _L ,a _U ) is given by

The critical values are computed from the results in Chung (1986).

Note that the given confidence band has a formula similar to that of the (linear) pointwise confidence interval where h _± ( a _L ,a _U ) and in the former correspond to and ( ( t )) in the latter, respectively. You can obtain the other transformations (arcsine-square root, log-log, log, and logit) for the confidence bands by replacing and ( t ) in the corresponding pointwise confidence interval formula by h _± ( a _L , a _U ) and the following ( t ), respectively.

• Arcsine-Square Root Transformation

  

• Log Transformation

  

• Log-log Transformation

  

• Logit Transformation

  

Equal Precision Band

The 100(1- ± )% EP band of Nair (1984)is

for all t _L t t _U , where e _± ( a _L ,a _U ) is given by

PROC LIFETEST uses the approximation of Miller and Siegmund (1982, Equation 8) to approximate the tail probability in which e _± ( a _L ,a _U ) is obtained by solving x in

where () is the standard normal density. Note that the given confidence bounds are proportional to the pointwise confidence intervals. As a matter of fact, this confidence band and the (linear) pointwise confidence interval have the same formula except for the critical values ( for the pointwise confidence interval and e _± ( a _L ,a _U ) for the band). You can obtain the other transformations (arcsine-square root, log-log, log, and logit) for the confidence bands by replacing by e _± ( a _L ,a _U ) in the formulae of the pointwise confidence intervals.

Comparison of Two or More Groups of Survival Data

Let k be the number of groups. Let S _i ( t ) be the underlying surivor function i th group , i = 1 ,...,k . The null and alternative hypotheses to be tested are

versus

respectively, where is the largest observed time. Let t ₁ <t ₂ <...< t _D be the distinct event times in the pooled sample. At time t _i , let W ( t _i ) be a positive weight function, and let n _ij and d _ij be the size of the risk set and the number of events in the j th sample, respectively. Let and s _i = n _i ˆ’ d _i .

Nonparametric tests

The rank statistics (Klein and Moeschberger 1997, Section 7.3) for testing H versus H ₁ have the form of a k -vector v =( v ₁ ,v ₂ ,...,v _k ) ² with

and the estimated covariance matrix, V =( V _jl ), is given by

where _jl is 1 if j = l and 0 otherwise . The term v _j can be interpreted as a weighted sum of observed minus expected numbers of failure under the null hypothesis of identical survival curves. The overall test statistic for homogeneity is v ² V ^ˆ’ v , where V ^ˆ’ denotes a generalized inverse of V . This statistic is treated as having a chi-square distribution with degrees of freedom equal to the rank of V for the purposes of computing an approximate probability level. The choices of the weight function W ( t _i ) are given in the following table:

Test	W ( t i )
log-rank	1.0
Wilcoxon	n i
Tarone-Ware
Peto-Peto
modified Peto-Peto
Harrington-Fleming ( p , q )	[ ( t i )] p [1 ˆ’ ( t i )] q , p , q

where ( t ) is the product-limit estimate at t for the pooled sample, and ( t ) is a survivor function estimate close to ( t ) given by

Likelihood Ratio Test

The likelihood ratio test statistic (Lawless 1982) for test H versus H ₁ assumes that the data in the various samples are exponentially distributed and tests that the scale parameters are equal. The test statistic is computed as

where N _j is the total number of events in the j th stratum, is the total time on test in the j th stratum, and . The approximate probability value is computed by treating Z as having a chi-square distribution with c ˆ’ 1 degrees of freedom.

Trend Tests

Trend tests (Klein and Moeschberger 1997, Section 7.4) have more power to detect ordered alternatives as

Let a ₁ <a ₂ <...<a _k be a sequence of scores associated with the k samples. The test statistic and its standard error are given by

respectively. Under H , the z ˆ’ score

has, asymptotically, a standard normal distribution.

Stratified Tests

Suppose the test is to be stratified on M levels of a set of STRATA variables . Based only on the data of the s th stratum ( s = 1 ...M ), let v _s be the test statistic (Klein and Moeschberger 1997, Section 7.5) for the s th stratum, and let V _s be its covariance matrix. A global test statistic is constructed as

Under the null hypothesis, the test statistic has a ² distribution with the same df as the individual test for each stratum.

Rank Tests for the Association of Survival Time with Covariates

The rank tests for the association of covariates (Kalbfleisch and Prentice 1980, Chapter 6) are more general cases of the rank tests for homogeneity. In this section, the index ± is used to label all observations, ± = 1 , 2 , ..., n , and the indices i, j range only over the observations that correspond to events, i, j = 1 , 2 ,..., k . The ordered event times are denoted as t _{( i )} , the corresponding vectors of covariates are denoted as z _{( i )} , and the ordered times, both censored and event times, are denoted as t _± .

The rank test statistics have the form

where n is the total number of observations, c _{± , ±} are rank scores, which can be either log-rank or Wilcoxon rank scores, _± is 1 if the observation is an event and 0 if the observation is censored, and z _± is the vector of covariates in the TEST statement for the ± th observation. Notice that the scores, c _{± , ±} , depend on the censoring pattern and that the terms are summed up over all observations.

The log-rank scores are

and the Wilcoxon scores are

where n _j is the number at risk just prior to t _{( j )} .

The estimates used for the covariance matrix of the log-rank statistics are

where V _i is the corrected sum of squares and crossproducts matrix for the risk set at time _{t (} i ₎ ; that is,

where

The estimate used for the covariance matrix of the Wilcoxon statistics is

where

In the case of tied failure times, the statistics v are averaged over the possible orderings of the tied failure times. The covariance matrices are also averaged over the tied failure times. Averaging the covariance matrices over the tied orderings produces functions with appropriate symmetries for the tied observations; however, the actual variances of the v statistics would be smaller than the preceding estimates. Unless the proportion of ties is large, it is unlikely that this will be a problem.

The univariate tests for each covariate are formed from each component of v and the corresponding diagonal element of V as . These statistics are treated as coming from a chi-square distribution for calculation of probability values.

The statistic v ² V ^ˆ’ v is computed by sweeping each pivot of the V matrix in the order of greatest increase to the statistic. The corresponding sequence of partial statistics is tabulated. Sequential increments for including a given covariate and the corresponding probabilities are also included in the same table. These probabilities are calculated as the tail probabilities of a chi-square distribution with one degree of freedom. Because of the selection process, these probabilities should not be interpreted as p -values.

If desired for data screening purposes, the output data set requested by the OUTTEST= option can be treated as a sum of squares and crossproducts matrix and processed by the REG procedure using the option METHOD=RSQUARE. Then the sets of variables of a given size can be found that give the largest test statistics. Example 40.1 illustrates this process.

Computer Resources

The data are first read and sorted into strata. If the data are originally sorted by failure time and censoring state, with smaller failure times coming first and event values preceding censored values in cases of ties, the data can be processed by strata without additional sorting. Otherwise, the data are read into memory by strata and sorted.

Memory Requirements

For a given BY group, define

N	the total number of observations
V	the number of STRATA variables
C	the number of covariates listed on the TEST statement
L	total length of the ID variables in bytes
S	number of strata
n	maximum number of observations within strata
b	12 + 8 C + L
m 1	(112 + 16 V ) S
m 2	50 b S
m 3	(50 + n ) ( b +4)
m 4	8( C +4) 2
m 5	20 N +8 S ( S +4)

The memory, in bytes, required to process the BY-group is at least

The test of equality of survival functions across strata requires additional memory ( m 5 bytes). However, if this additional memory is not available, PROC LIFETEST skips the test for equality of survival functions and finishes the other computations . Additional memory is required for the PLOTS= option. Temporary storage of 16 n bytes is required to store the product-limit estimates for plotting.

Output Data Sets

OUTSURV= Data Set

You can specify either the OUTSURV= option in the PROC LIFETEST statement to create an output data set containing the following columns :

• any specified BY variables

• any specified STRATA variables, their values coming from either their original values or the midpoints of the stratum intervals if endpoints are used to define strata (semi-infinite intervals are labeled by their finite endpoint)

• STRATUM , a numeric variable that numbers the strata

• the time variable as given in the TIME statement. In the case of the product-limit estimates, it contains the observed failure or censored times. For the life-table estimates, it contains the lower endpoints of the time intervals.

• SURVIVAL , a variable containing the survivor function estimates

• CONFTYPE , a variable containing the name of the transformation applied to the survival time in the computation of confidence intervals (if the OUT= option is specified in the SURVIVAL statement)

• SDF_ LCL , a variable containing the lower limits of the pointwise confidence intervals for the survivor function

• SDF_ UCL , a variable containing the upper limits of the pointwise confidence intervals for the survivor function

If the estimation uses the product-limit method, then the data set also contains

• _ CENSOR_ , an indicator variable that has a value 1 for a censored observation and a value 0 for an event observation

If the estimation uses the life-table method, then the data set also contains

• MIDPOINT, a variable containing the value of the midpoint of the time interval

• PDF , a variable containing the density function estimates

• PDF_ LCL , a variable containing the lower endpoint of the PDF confidence interval

• PDF_ UCL , a variable containing the upper endpoint of the PDF confidence interval

• HAZARD , a variable containing the hazard estimates

• HAZ_ LCL , a variable containing the lower endpoint of the hazard confidence interval

• HAZ_ UCL , a variable containing the upper endpoint of the hazard confidence interval

Each survival function contains an initial observation with the value 1 for the SDF and the value 0 for the time. The output data set contains an observation for each distinct failure time if the product-limit method is used or an observation for each time interval if the life-table method is used. The product-limit survival estimates are defined to be right continuous; that is, the estimates at a given time include the factor for the failure events that occur at that time.

Labels are assigned to all the variables in the output data set except the BY variable and the STRATA variable.

OUT= Data Set

The OUT= option in the SURVIVAL statement creates an output data set containing all the variables listed in the OUTSURV= data set specified in the PROC LIFETEST statement with the additional variable

• CONFTYPE , a variable containing the type of transform used in the computation of the confidence intervals and bands for the survivor function

If the product-limit method is used, the OUT= data set also contains

• SDF_ STDERR , a variable containing the standard error of the survivor function estimator (if the STDERR option is specified in the SURVIVAL statement)

• HW_ LCL , a variable containing the lower limits of the Hall-Wellner confidence bands (if the CONFBAND=HW or CONFBAND=ALL is specified in the SURVIVAL statement)

• HW_ UCL , a variable containing the upper limits of the Hall-Wellner confidence bands (if the CONFBAND=HW or CONFBAND=ALL is specified in the SURVIVAL statement)

• EP_ LCL , a variable containing the lower limits of the equal precision confidence bands (if the CONFBAND=EP or CONFBAND=ALL is specified in the SURVIVAL statement)

• EP_ UCL , a variable containing the upper limits of the equal precision confidence bands (if the CONFBAND=EP or CONFBAND=ALL is specified in the SURVIVAL statement)

In this release, the OUTSURV= data set is not created if you specify both the OUTSURV= option in the PROC LIFETEST statement and the OUT= option in the PROC statement.

OUTTEST= Data Set

The OUTTEST= option in the LIFETEST statement creates an output data set containing the rank statistics for testing the association of failure time with covariates. It contains

• any specified BY variables

• _ TYPE_ , a character variable of length 8 that labels the type of rank test, either LOG-RANK or WILCOXON

• _ NAME_ , a character variable of length 8 that labels the rows of the covariance matrix and the test statistics

• the TIME variable, containing the overall test statistic in the observation that has _ NAME_ equal to the name of the time variable and the univariate test statistics under their respective covariates.

• all variables listed in the TEST statement

The output is in the form of a symmetric matrix formed by the covariance matrix of the rank statistics bordered by the rank statistics and the overall chi-square statistic. If the value of _ NAME_ is the name of a variable in the TEST statement, the observation contains a row of the covariance matrix and the value of the rank statistic in the time variable. If the value of _ NAME_ is the name of the TIME variable, the observation contains the values of the rank statistics in the variables from the TEST list and the value of the overall chi-square test statistic in the TIME variable.

Two complete sets of statistics labeled by the _ TYPE_ variable are produced, one for the log-rank test and one for the Wilcoxon test.

Displayed Output

If you use the NOPRINT option in the PROC LIFETEST statement, the procedure does not display any output.

For each stratum, the LIFETEST procedure displays the following unless the NOTABLE option is specified.

• if you specify the STRATA statement, the values of the stratum variables

• if you request the product-limit estimate, the Product-Limit Survival Estimates table, which displays

  • the observed (event or censored) time

  • the estimate of the survivor function

  • the estimate of the cumulative distribution function of the failure time

  • the standard error estimate of the estimated survivor function

  • the number of event times that have been observed

  • the number of event or censored times that remain to be observed

  • if you specify the FREQ statement, the frequency of the observed event or censored times

  • if you specify the ID statement, the values of the ID variables

• if you request the product-limit estimate, the Quartile Estimates table, which contains

  • point estimates of the quartiles of the failure times

  • lower and upper confidence limits for the quartiles

• if you requested the product-limit estimate, the estimated mean survival time and its estimated standard error

• if you requested the life-table estimate, the Life Table Survival Estimates table, which displays

  • time intervals into which the failure and censored times are distributed; each interval is from the lower limit, up to but not including the upper limit. If the upper limit is infinity, the missing value is printed.

  • the number of events that occur in the interval

  • the number of censored observations that fall into the interval

  • the effective sample size for the interval

  • the estimate of conditional probability of events (failures) in the interval

  • the standard error of the estimated conditional probability of events

  • the estimate of the survival function at the beginning of the interval

  • the estimate of the cumulative distribution function of the failure time at the beginning of the interval

  • the standard error estimate of the estimated survival function

  • the estimate of the median residual lifetime, which is the amount of time elapsed before reducing the number of at-risk units to one-half. This is also known as the median future lifetime in Elandt-Johnson and Johnson (1980).

  • the estimated standard error of the estimated median residual lifetime

  • the density function estimated at the midpoint of the interval

  • the standard error estimate of the estimated density

  • the hazard rate estimated at the midpoint of the interval

  • the standard error estimate of the estimated hazard

The following results, processed across all strata, are displayed:

• the Summary of the Number of Censored and Uncensored Values table, which contains

  • if the STRATA statement is specified, the stratum identification

  • the total number of observations

  • the number of event observations

  • the number of censored observations

  • the percentage of censored observations

• the Rank Statistics table that contains the test statistics of the nonparametric k -sample tests or stratified k -sample tests

• the covariance matrix for the LOGRANK k -sample statistics

• the covariance matrix for the WILCOXON k -sample statistics

• the covariance matrix for the TARONE k -sample statistics (if requested)

• the covariance matrix for the PETO k -sample statistics (if requested)

• the covariance matrix for the MODPETO k -sample statistics (if requested)

• the covariance matrix for the FLEMING k -sample statistics (if requested)

• the Test of Equality over Strata table, which displays the results of the nonparametric k -sample test and the likelihood ratio test that is based on the exponential distribution (if the GROUP= option is not specified in the STRATA statement)

• the Stratified Test of Equality over Group table, which displays the results of the stratified k -sample tests for the GROUP= variable (if the GROUP= option in the STRATA statement is specified)

• the Scores for Trend Test tables, which displays the set of scores used to contruct the trend tests (if the TREND option is specified in the STRATA statement)

• the Trend Tests tables, which displays the results of the trend tests (if the TREND option is specified in the STRATA statement)

• the line printer plot or traditional high resolution graph of the estimated survivor function against failure time (if requested)

• the line printer plot or traditional high resolution graph of the negative log of the estimated survivor function against failure time (if requested)

• the line printer plot or traditional high resolution graph of the log of the negative log of the estimated survivor function against the log of the failure time (if requested)

• the line printer plot or traditional high resolution graph of the estimated hazard function against failure time (if requested and only for life-table method)

• the line printer plot or traditional high resolution graph of the estimated density function against failure time (if requested and only for life-table method)

If you specify the TEST statement, the PROC LIFETEST also displays

• the Univariate Chi-Squares for the Log-Rank Test table, which contains the log-rank test results for individual variables in the TEST statement

• the Covariance Matrix for the Log-Rank Statistics table

• the Forward Stepwise Sequence of Chi-Squares for the Log-Rank Test table, which contains

  • the sequence of partial chi-square statistics for the log-rank test in the order of the greatest increase to the overall test statistic

  • the degrees of freedom of the partial chi-square statistics

  • the approximate probability values of the partial chi-square statistics

  • the chi-square increments for including the given variables

  • the probability values of the chi-square increments

• the Univariate Chi-Squares for the Wilcoxon Test table, which contains the log-rank test results for individual variables in the TEST statement

• the Covariance Matrix for the Wilcoxon Statistics table

• the Forward Stepwise Sequence of Chi-Squares for the Wilcoxon Test table, which contains

  • the sequence of partial chi-square statistics for the Wilcoxon test in the order of the greatest increase to the overall test statistic

  • the degrees of freedom of the partial chi-square statistics

  • the approximate probability values of the partial chi-square statistics

  • the chi-square increments for including the given variables

  • the probability values of the chi-square increments

ODS Table Names

PROC LIFETEST assigns a name to each table it creates. You can use these names to reference the table when using the Output Delivery System (ODS) to select tables and create output data sets. These names are listed in the following table. For more information on ODS, see Chapter 14, Using the Output Delivery System.

Table 40.3: ODS Tables Produced in PROC LIFETEST

ODS Table Name	Description	Statement	Option
CensorPlot	line printer plot of censored observations	PROC	PLOT=(CSLSLLS), METHOD=PL, and LINEPRINTER
CensoredSummary	number of event and censored observations	PROC	METHOD=PL
DensityPlot	traditional high-resolution or line printer plot of the density function	PROC	PLOT=(D) and METHOD=LT
HazardPlot	traditional high-resolution graph or line printer plot of the hazard function	PROC	PLOT=(H) and METHOD=LT
FlemingHomCov	covariance matrix for k -sample FLEMING statistics	STRATA	TEST=(FLEMING)
HomStats	test statistics for k -sample tests	STRATA
HomTests	results of k -sample tests	STRATA
LifetableEstimates	life-table survival estimates	PROC	METHOD=LT
LogForStepSeq	forward stepwise sequence for the log-rank statistics for association	TEST
LogHomCov	covariance matrix for k -sample LOGRANK statistics	STRATA	TEST=(LOGRANK)
LogLogSurvivalPlot	traditional high-resolution graph or line printer plot of the log of the negative log survivor function	PROC	PLOT=(LLS)
LogSurvivalPlot	GSET or line printer plot of the log survivor function	PROC	PLOT=(LS)
LogTestCov	covariance matrix for log-rank statistics for association	TEST
LogUniChisq	univariate chi-squares for log-rank statistic for association	TEST
Means	mean and Standard Error of survival times	PROC	METHOD=PL
ModPetoHomCov	covariance matrix for k -sample MODPETO statistics	STRATA	TEST=(MODPETO)
NObs	Number of observations default PetoHomCov covariance matrix for k -sample PETO statistics	STRATA	TEST=(PETO)
ProductLimitEstimates	product-limit survival estimates	PROC	METHOD=PL
Quartiles	quartiles of the survival distribution	PROC	METHOD=PL
SurvivalPlot	traditional high-resolution graph or line printer plot of the survivor function	PROC	PLOT=(S)
TaroneHomCov	covariance matrix for k -sample TARONE statistics	STRATA	TEST=(TARONE)
TrendScores	scores used to construct trend tests	STRATA	TREND
TrendTests	results of Trend Tests	STRATA	TREND
WilForStepSeq	forward stepwise sequence for the log-rank statistics for association	TEST
WilHomCov	covariance matrix for k -sample WILCOXON statistics	STRATA	TEST=(WILCOXON)
WilTestCov	covariance matrix for log-rank statistics for association	TEST
WilUniChiSq	univariate chi-squares for Wilcoxon statistic for association	TEST

ODS Graphics (Experimental)

This section describes the use of ODS for creating statistical graphs with the LIFETEST procedure. These graphics are experimental in this release, meaning that both the graphical results and the syntax for specifying them are subject to change in a future release.

To request these graphs you must specify the ODS GRAPHICS statement in addition to the PLOTS= option. For general information about ODS GRAPHICS, see Chapter 15, Statistical Graphics Using ODS.

You can specify the PLOTS=option in the SURVIVAL statement to request graphical displays of survival distribution and related function estimates:

PLOTS= ( type <,type,...,type> )

• requests one or more plots of the survival estimates, where type is the type of plot. The following table shows the valid values of type .

  Type	Plot Description
  CL PCL	pointwise confidence limits for the survival function
  DENSITY PDF	estimated density function (life-table method only)
  EPB	equal precision bands for survivorship (product-limit method only)
  HAZARD HAZ	estimated hazard function (life-table method only)
  HWB	Hall-Wellner confidence bands for survivorship (product-limit method only)
  LOGLOGS LLS	log of negative log of estimated survivor function versus log of time
  LOGSURV LS	negative log of estimated survivor function
  STRATUM	a panel of three plots and a table of summary statistics for each stratum. For the product-limit method, the panel contains a plot of the product-limit estimates, a plot of the Hall-Wellner band, and a plot of the equal precision band. Pointwise confidence limits and the product-limit estimates are also plotted along with the confidence bands. For the life-table method, the panel contains a plot of life-table estimates, a plot of the estimated hazard function, and a plot of the estimated density. Corresponding pointwise confidence limits are also plotted along with the survival estimates.
  SURVIVAL S	estimated survivor function. Censored times are plotted as a plus sign on the product-limit curve.

• You can use the ALPHA=, BANDMIN=, BANDMAX=, and CONFTYPE= options in the SURVIVAL statement to modify the confidence limits and confidence bands. To restrict the display of the plots up to a certain limit on the time scale, specify the following option in the SURVIVAL statement.

MAXTIME= value

• specifies the maximum value of the time variable allowed on the plots so that outlying points do not determine the scale of the time axis of the plots.

ODS Graph Names

PROC LIFETEST assigns a name to each graph it creates using the Output Delivery System (ODS). You can use these names to reference the graphs when using ODS. The names are listed in Table 40.4.

To request these graphs you must specify the ODS GRAPHICS statement in addition to the options indicated in Table 40.4. For more information on the ODS GRAPHICS statement, see Chapter 15, Statistical Graphics Using ODS.

Table 40.4: ODS Graphics Produced by PROC LIFETEST

ODS Graph Name	Plot Description	Statement	PLOTS=(type)
Density	Density estimate based on life-table method	SURVIVAL	PDF
EqualPrecision	Equal precision band overlaid with the estimated survival curve	SURVIVAL	EPB
HallWellner	Hall and Wellner band overlaid with the estimated survival curve	SURVIVAL	HWB
Hazard	Hazard estimate based on the life-table method	SURVIVAL	HAZ
LogNegLogSurvival	Log of negative log of the estimated survival function	SURVIVAL	LLS
NegLogSurvival	Negative log of the estimated survival function	SURVIVAL	LS
Survival	Estimated survival curve	SURVIVAL	S
SurvivalCL	Pointwise confidence limits overlaid with estimated survival curve	SURVIVAL	CL