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.

Validation of Surrogacy Using a Joint Modeling Approach for Two Normally Distributed Endpoints

Validation Using Joint Modeling of a Time-to- Event and a Binary Endpoint

Validation Using a Joint Model for Continuous and Binary Endpoints

Validation Using a Joint Model for Two Binary Endpoints

The Business Model Approach as Commodification Indicator

Hierarchical Modeling Approaches

A Modelling Approach

Thermoviscoelasticity modeling approach for amorphous SMP networks

The Mental Modeling Approach

The Mental Modeling Approach