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 the “RMST Estimates” table,

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.

The “RMST Test of Equality” table 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 the “Analysis of Parameter

Estimates” table 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.

As you have seen from this brief presentation,

the restricted mean survival time

is a good alternative to the survival outcome.

Compared to the survival mean and median,

it can be more robustly estimated and is valid

when the proportional hazards assumption is violated.

Starting in SAS/STAT 15.1, you can use the new RMSTREG

procedure to perform regression analysis and the new RMST

option in PROC LIFETEST to perform nonparametric analyses.

You can consider the RMST option in PROC LIFETEST

to be a bonus option because it performs

RMST analysis in addition to the existing functionality in PROC

LIFETEST.

For more information about restricted mean analysis

and other resources, visit our website

at support.sas.com/statistics.

You can find overview papers about new developments

and past SAS Global Forum papers.

You can also sign up for newsletters

and browse through examples.

Thank you for watching!