Validation of Surrogacy Using a Joint Modeling Approach for Two Normally Distributed Endpoints
In this section, we present SAS macros for the setting in which both endpoints are continuous. For all models discussed in this section the agerelated macular degeneration (ARMD) data is used for illustration. Visual acuity at week 52 (Diff52) and visual acuity at week 24 (Diff24) are the true and the surrogate endpoints, respectively. Each line in the data contains information about one patient. A partial print of the data is shown in Figure 12.1.
TABLE 12.1
SAS macros available for the evaluation of surrogate endpoints in randomized clinical trials. Part I.
Surrogacy Setting 
Macro name 
Model 
Surrogacy measures 
Chap ter 12 
Rest of the book 
Case study 
1. Normal/Normal 
CONTCONTFULL CONTCONTRED CONTRANFULL CONTRANRED 
Full fixed Reduced fixed Full random Reduced random 
T)2 тУ2. “'trial’ “"indiv D 2 D 2 “"trial’ “"indiv D 2 D 2 “"trial’ ?“'indiv d 2 p2 “"trial’ “"indiv 


ARMD data True endpoint= Diff52 Surrogate endpoint=Diff24 
2. Survival/Survival 
TWOSTAGEKM TWOSTAGECOX COPULA 
Twostage Twostage joint model 
ту‘2 “"indiv p2 “Hrial d2 p2 “"trial’ “"indiv 


Ovarian data True endpoint= OS Surrogate endpoint=PFS 
3. Survival/Binary 
SURVBIN 
Joint model 
p2 “"trial’ Gl. odds 
12.5 
6.2 
Colorectal data True endpoint=OS Surrogate endpoint=Remission 
4. Survival/Normal 
NORMSURV 
Twostage model 
Kendall’s r p2 '“trial 
12.7 
Ch. 7 
Prostate cancer True endpoint=OS Surrogate endpoint=ln(PSA) 
5. Normal/Binary 
NORMALBIN 
Joint model Normalbinary 
d2 p2 “"trial’ “"indiv 
12.7 
Schizo data True endpoint=PANSS Surrogate endpoint=CGI 
TABLE 12.2
SAS macros available for the evaluation of surrogate endpoints in randomized clinical trials. Part II.
Surrogacy Setting 
Macro name 
Model 
Surrogacy measures 
Chap ter 12 
Rest of the book 
Case study 
6. Binary/Binary 
BINBIN 
Bivariate probit 
D 2 D 2 “"trial’ “indiv 
12.8 
Schizo data True endpoint=CGI Surrogate endpoint=PANSS 

7. Survival/Binary 
SURVBINIT SURVBININFO 
Information theory 
p 2 p 2 ^{л}h 
12.9 
Colorectal data True endpoint=OS Surrogate endpoint=Remission 

8. Normal/В inary 
NORMBINIT 
Information theory 
p2 p2 ^{K}hV ^{K}h 
12.9 
10.6 
Schizo data True endpoint=PANSS Surrogate endpoint=CGI 
9. Binary/Binary 
BINBINIT 
Information theory 
p2 p2 ^{K}hV ^{K}h 
12.9 
10.6 
Schizo data True endpoint=CGI Surrogate endpoint=PANSS 
10. Normal/Normal 
NORMNORMIT 
Information theory 
p2 p2 ^{K}h 
12.9 

ARiViD data True endpoint=Diff52 Surrogate endpoint=Diff24 
FIGURE 12.1
Data snapshot for some patients, when the true and the surrogate endpoints are normally distributed.