Subtitles section Play video Print subtitles 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 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.