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Data Structure

For the analysis presented in this section we use the Schizophrenia study (see Section 2.2.2) for illustration. The true endpoint is the PANSS score. For the binary surrogate we use the CGI, score which was dichotomized in the following way:

Patient’s data appear on a single line. The treatment variable is coded 1 and -1. Note that only trials with at least two patients per treatment arm were included (i.e., data obtained for 99 investigators and 1757 patients); see Figure 12.40.


The SAS macro %NORMALBIN can be used to fit the joint model specified in (12.41). For the Schizophrenia study the macro is called as follows:

%NORMALBIN(data=schizo,true=panss,surrog=cgi,trt=trtmnt, trial=investid,patid=patientid)

The macro’s arguments were defined in Sections 12.2.

Data Analysis and Output

Descriptive plots produced by the macro include the distribution of patients by treatment arm (shown in Figure 12.41, top panel) and the distribution of the PANSS score by treatment arm across the levels of the surrogate endpoint in Figure 12.41 (bottom panel).

Individual- and trial-level surrogacy measures are equal to 0.3761 (0.3403, 0.4119) and 0.3747 (0.2216, 0.5279), respectively, implying that CGI is a poor surrogate to the PANSS score. Note that, due to convergence problems, only trials with at least two patients per treatment arm were included in the analysis. The results presented above are slightly different from those presented in Section 13.5.1, in which information theory was used to calculate the surrogacy measures. Figure 12.43 shows a scatter plot of the trial-specific parameter estimates for the treatment effects used in the second-stage model for the evaluation of trial-level surrogacy.

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