Data Analysis and Output
Parameter estimates for individual and trial-level surrogacy (shown below) are equal to 0.7108 (0,6852, 0.7364) and 0.7363 (0.6227, 0.8499), respectively, indicating that PANSS is a surrogate of moderate value for CGI at both surrogacy levels. Figure 12.47 shows the estimated treatment effects upon both endpoints with the fitted regression line.
The Schizophrenia Study. Estimation of trial-level surrogacy. Circle areas are proportional to trial size.
SAS Code for the First-Stage Model
The SAS code to fit the reduced fixed-effects model formulated in (12.44) can be written as follows:
proc glimmix data=binbin; class patientid endp trial;
model response(event='1') = endp endp*treat*trial / noint s dist=byobs(endp) link=byobs(lin) cl; random _residual_ / subject=patientid type=un cl; run;
It is assumed that there are two records per subject in the input dataset, one corresponding to the surrogate endpoint and the other to the true endpoint. A partial print of the data is shown in Figure 12.48. The response variable contains the observed categories on both endpoints for each patient. The statement event=1 specifies the event category for both endpoints. The mean structure, for both endpoints, is similar to the mean structure of the reduced fixed-effects model discussed in Section 12.3.2. The option dist=byobs(endp) defines the distribution for each endpoint and the link function to be used is specified by the option link=byobs(lin).
As in the previous section, the statement RANDOM _residual_ specifies the residual covariance structures from which individual-level surrogacy can be
Partial print of the data.
SAS output for selected trials.
derived. The output from the above code is shown in Figure 12.49 for some trials. For the schizophrenia study, the estimated covariance matrix is
Hence, individual-level surrogacy is equal to i??ndiv = 0.84312 = 0.7108.