The Full Mixed-Effects Model

The full mixed-effects model, discussed in Chapter 4, is a joint model for the surrogate and true endpoint given by

Here, and are fixed intercepts, a and в are the fixed treatment effects on the two endpoints, m_Si and m_Ti are random intercepts, and a* and b_i are trial-specific random treatment effects. As pointed out in Chapter 4, the vector of random effects (m_Si, m_Ti, a_i,b_i) is assumed to follow a normal distribution with zero mean and covariance matrix (4.2). The error terms, ?_Sij and ?_Tij, are assumed to follow a bivariate normal distribution with covariance matrix

FIGURE 12.11

Error terms covariance matrix.

FIGURE 12.12

Error terms covariance matrix.

given in (4.3). Trial- and individual-level surrogacy can be estimated using the variance-covariance elements in the covariance matrices (4.2) and (4.3), respectively. For more detail, see Chapter 4.

The SAS Macro %CONTRANFULL

The %CONTRANFULL macro can be used to perform the analysis and it can be invoked using the following call:

%CONTRANFULL(data=simdata,true=true,surrog=surr,trt=treat, trial=trial,patid=patientId,looa=1).

The macro’s arguments are the same as those presented in Section 12.2.