Evaluation of Surrogate Endpoint for Two Continuous Endpoints
We use the age-related macular degeneration data for illustration of the analysis for the normal-normal surrogacy setting with the information-theoretic approach. As before, the true endpoint is visual acuity 52 weeks after the start of the treatment (Diff52) and the surrogate endpoint is the visual acuity 24 weeks after the start of treatment (Diff24).
The data structure for the normal-normal setting is shown in Section 12.2.
The SAS Macro %NORMNORMINFO
The models for two normally distributed endpoints can be fitted using the SAS macro %NORMNORMINFO. The macro fits the models formulated in (12.52)- (12.53), to estimate both individual-level and trial-level surrogacy. The call takes the form:
%NORMNORMINFO(data=ARMD,true=Diff54,surrog=Diff24,
treat=treat,trial=center,patid=patientid,weighted=1, model="full",boot=10)
Arguments specific for the %NORMNORMINFO are:
- • model: the model used in (12.52) and (12.53) (“reduced” or “full”).
- • boot: the number of bootstrap samples used to construct the confidence intervals for the parameter estimates of the surrogacy measures.
Other arguments have been defined in Sections 12.2 and 12.4.1.
Data Analysis and Output
The %NORMNORMINFO macro produces exploratory plots, displaying the distribution of the patients per trial (see, for example, Figure 12.3, left panel). Parameter estimates for the LRF and trial-level surrogacy are shown in Figure 12.52.
The estimated individual- and trial-level surrogacy are equal to Rfl = 0.5297 (0.3785, 0.6809), and R2t = 0.7119 (0.5074, 0.8550), respectively. Both surrogacy measures indicate that visual acuity, 24 weeks after the start of
FIGURE 12.50
Individual-level surrogacy and trial-level surrogacy measures with 95% C.I.
treatment, is a moderate surrogate for visual acuity 52 weeks after the start of the treatment.
As a sensitivity analysis, the trial-specific likelihood reduction factor is presented in Figure 12.53.
Note that the macro %NORMNORMINFO uses the same model formulation as the R function FixedContContIT (i.e., fixed-effects models for two continuous endpoints).
