The advanced prostate cancer data described in Section 7 is used for illustration of the analysis for the survival-normal surrogacy setting. The true endpoint is overall survival time and the surrogate endpoint is the logarithm of prostate-specific antigen (PSA), measured at about 28 days. The data structure for the survival-normal setting is shown in Figure 12.36, in which time- to-event (surv) and censoring status (survind) are given to the true endpoint and the continuous response (cont) is the surrogate endpoint.
The SAS Macro °/„NORMSURV
The SAS macro %NORMSURV can be used in order to fit the models specified in (12.36)-(12.37). For the prostate data we use:
%NORMSURV(data=prostate,true=surv,trueind=survind,surrog=cont, trt=treat,trial=center,patid=patientId,copula=hougaard, adjustement=weighted)
The specification of the macro's arguments is the same as the specification presented in Section 5.2.
Data Analysis and Output
The exploratory plots produced by the macro %NORMSURV are shown in Figure 12.37. The histogram in Figure 12.37 (bottom left panel) suggests that the logarithm of PSA at 28 days is normally distributed. The scatter plot for the survival time and the continuous surrogate in Figure 12.37 (bottom right panel) reveal a weak association (ignoring censoring on the true endpoint).
Individual- and trial-level surrogacy, Kendall’s т = 0.2763 (0.2124, 0.3403) and Rrial = 0.0066 (-0.0724, 0.0856), shown in Figure 12.38 indicate that the logarithm of PSA after 28 days is a weak surrogate to overall survival time for the prostate cancer data. The Hougaard copula is presented in the output as well.
Figure 12.39 shows the parameter estimates for the treatment effects for both surrogate and true endpoints that were used to estimate trial-level surrogacy.