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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 age-related 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

  • 12.3.1
  • 12.3.2
  • 12.3.3
  • 12.3.4
  • 4.3.1
  • 4.3.2
  • 4.2
  • 4.3.2

ARMD data

True endpoint= Diff52

Surrogate endpoint=Diff24

2. Survival/Survival

TWOSTAGEKM

TWOSTAGECOX

COPULA

Two-stage Two-stage joint model

ту‘2

-“"indiv

p2

“Hrial d2 p2 -“"trial’ -“"indiv

  • 12.4.1
  • 12.4.2
  • 12.4.3
  • 13.3
  • 5.2

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

Two-stage 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 Normal-binary

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

лh

12.9

Colorectal data

True endpoint=OS

Surrogate endpoint=Remission

8. Normal/В inary

NORMBINIT

Information

theory

p2 p2

KhV Kh

12.9

10.6

Schizo data

True endpoint=PANSS Surrogate endpoint=CGI

9. Binary/Binary

BINBINIT

Information

theory

p2 p2

KhV Kh

12.9

10.6

Schizo data

True endpoint=CGI

Surrogate endpoint=PANSS

10. Normal/Normal

NORMNORMIT

Information

theory

p2 p2

Kh

12.9

  • 13.2.2.1
  • 10.2

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.

 
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