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  • 00:00:00,000 --> 00:00:02,910 Hello, my name is Changbin Guo.

  • I work for SAS R & D in statistical software

  • development, specializing in survival and event history

  • analysis.

  • In this video I would like to talk to you

  • about some new features available in SAS/STAT 15.1 that

  • let you analyze the restricted mean survival time.

  • The LIFETEST and PHREG procedures in SAS/STAT software

  • provide popular survival analysis tools.

  • The LIFETEST procedure focuses on nonparametric analysis,

  • and it provides the Kaplan-Meier method

  • for estimating the survival function and the log-rank test

  • for comparing the survival functions

  • from different populations.

  • The PHREG procedure, on the other hand,

  • focuses on regression modeling and supports the popular Cox

  • proportional hazards model.

  • The proportional hazards, or PH, assumption

  • plays a fundamental role in both the log-rank test and the Cox

  • regression.

  • The proportional hazards assumption

  • is the basis of the Cox regression.

  • The log-rank test can be derived as a score test of the Cox

  • model and has the highest power when the assumption is true.

  • Any violation of the PH assumption

  • influences the performances of the log-rank test and the Cox

  • regression.

  • Unfortunately, however, non-proportional hazards

  • are often encountered in practice.

  • A typical violation of the PH assumption

  • occurs when the two survival curves cross.

  • This implies that the corresponding hazard

  • functions would also cross and therefore violates

  • the PH assumption.

  • Because the log-rank statistic is essentially

  • a weighted sum of the hazard function over time,

  • the log-rank test can lose much of its power

  • to detect the true difference in survival.

  • Results from the Cox PH regression

  • have the same problem.

  • When the true hazard ratio changes over time,

  • the estimated hazard ratio from the fitted model

  • ends up being a weighted average of the time-varying hazard

  • ratios and can be interpreted as such.

  • The problem is that the weights depend on the underlying

  • survival and censoring distributions and therefore

  • cannot be generalized straightforwardly.

  • The restricted mean survival time, or RMST,

  • is defined as the expected value of the restricted survival time

  • from time zero to tau.

  • The RMST is related to the survival mean.

  • When tau goes to infinity, the RMST becomes the survival mean.

  • The RMST can be more reliably estimated

  • than the mean or median.

  • For example, if the last observation is censored,

  • then the mean becomes inestimable;

  • and when the survival does not drop below 0.5,

  • the median is undefined.

  • You can perform essentially the same types

  • of inferences with respect to the RMST

  • as you can in the classical setting.

  • To compare two groups, you can compare their RMSTs

  • given the same tau value.

  • For regression modeling, you can model

  • the RMST via linear or log-linear models.

  • These models enable you to study the effects in the RMST

  • directly.

  • 00:03:32,650 --> 00:03:36,810 Starting in SAS/STAT 15.1, new, dedicated features

  • are available for analyzing the RMST.

  • You can use the RMST option in the LIFETEST procedure

  • to perform nonparametric analysis with respect

  • to the RMST.

  • You can also use the new RMSTREG procedure

  • to fit linear and log-linear models of the RMST.

  • In PROC LIFETEST, you can perform RMST analysis

  • by specifying the RMST option in the PROC LIFETEST statement.

  • When there are multiple groups, you

  • can specify the STRATA statement to compute the RMST

  • for each level of the STRATA variable.

  • In addition to generating the survival plot,

  • you can also request the RMST curve by specifying the PLOTS=

  • option.

  • You can use the MAXTIME= option to set the upper limit

  • of the time axis for these plots.

  • You use the DIFF option in the STRATA statement

  • to compute the paired differences

  • of the RMST among the groups.

  • To protect yourself from falsely significant results,

  • you use the ADJ= option to make multiple-comparison adjustments

  • to the p-values.

  • 00:04:50,730 --> 00:04:53,470 Results from the RMST analyses are

  • displayed following the existing analyses in PROC LIFETEST.

  • By default, PROC LIFETEST uses the smallest value

  • among the largest observed times across the groups

  • as the tau value for the analysis.

  • As you can see from theRMST Estimatestable,

  • the Large and Squamous groups appear to have larger RMST

  • estimates than the Adeno and Small groups.

  • You can interpret the RMST estimates as expected survival

  • time for the first 186 days.

  • TheRMST Test of Equalitytable displays results from

  • the homogeneity test that show whether the RMSTs are the same

  • among the groups.

  • As the p-value indicates, the RMSTs

  • appear to be different among the groups.

  • The RMST curve plots the estimated RMST

  • against different values of tau.

  • Because the RMST can be computed only for tau values smaller

  • than the largest observed times, the ranges of the RMST curves

  • vary among the groups, with the Adeno group having the shortest

  • range.

  • You can read the estimated RMST values

  • for a specific tau value from the plotted curve

  • by drawing a vertical line.

  • 00:06:14,700 --> 00:06:17,032 Results from pairwise comparisons

  • suggest that you can divide the four risk

  • groups into two classes.

  • The first class consists of the Small and Adeno groups,

  • and there is no significant difference in the RMST between

  • them (p = 1.0000).

  • The second class consists of the Large and Squamous groups,

  • and the paired comparison is not significant (p = 0.9572).

  • However, there is a significant difference

  • in any paired comparison between the two classes.

  • You can use the new RMSTREG procedure

  • to perform regression analysis of the RMST.

  • The RMSTREG procedure is a new addition

  • to the SAS/STAT family for modeling time-to-event data.

  • It compares most closely to PROC LIFEREG and PROC PHREG.

  • But the three procedures have different focuses and support

  • different functionality.

  • PROC LIFEREG focuses on the time to event

  • and fits accelerated failure time models

  • by maximizing the likelihood function.

  • PROC PHREG focuses on the hazard function

  • and fits the popular Cox proportional hazards models

  • by maximizing the partial likelihood function.

  • By contrast, PROC RMSTREG focuses on the RMST

  • and fits certain generalized linear models.

  • Its estimation technique is based on estimating equations.

  • PROC RMSTREG can handle right-censored data,

  • just as PROC PHREG does.

  • It can fit linear and log-linear models to the RMST.

  • You can use two estimation techniques,

  • the pseudovalue regression technique

  • and the inverse probability censoring weighting technique,

  • with pseudovalue regression being

  • the default model-fitting method.

  • After you fit a model, you can perform many types

  • of postfitting analyses, just as you can do

  • with generalized linear models.

  • Consider fitting a model for the RMST at a tau value of 10 years

  • with three independent variables--age, bilirubin,

  • and Edema.

  • As the code shows, you can specify the tau value

  • for the analysis by using the TAU= option in PROC RMSTREG.

  • You can include categorical variables in the model

  • by specifying them in the CLASS statement.

  • You can use pseudovalue regression to fit the model

  • by specifying METHOD=PV.

  • The LINK=LINEAR option specifies the linear model.

  • As the equation shows, the model to be analyzed

  • contains a total of five regression parameters

  • that need to be estimated.

  • Outputs from PROC RMSTREG look like outputs

  • from a standard modeling procedure.

  • The Type 3 test results in theAnalysis of Parameter

  • Estimatestable indicate that all three variables are strong

  • predictors of the RMST at 10 years.

  • Because a linear model of the RMST has been fitted,

  • the estimates are in fact on the RMST scale

  • and you can interpret them straightforwardly.

  • For example, on average the RMST is

  • reduced by 0.0686 years with a one-year increase in age.