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Surrogate Package: BinaryOrdinal SettingIn the Surrogate package, the function FixedDiscrDiscrIT() investigates surrogacy where both the surrogate and true outcome are ordinal or one is ordinal and the other binary. This function estimates both trial and individual level surrogacy using the fixedeffects information theory approach summarized in this chapter. Case Study Analysis: Five Trials in SchizophreniaIn this analysis of the Schizophrenia dataset (introduced in Section 2.2.2), we investigate the dichotomized Positive and Negative Syndrome Scale (PANSS) change score as a possible surrogate for Clinical Global Impression (CGI, an ordinal measure of the change in schizophrenia symptoms on a sevenpoint scale). Hence, we evaluate binary S for an ordinal T. PANSS change was dichotomized according to convention as 1: an improvement of 20% or more in the PANSS score from beginning to end of treatment, and 0: otherwise. Lower CGI scores represent an improved psychiatric outcome. We would therefore anticipate a negative association between the binary PANSS surrogate and the ordinal CGI. The Schizophrenia dataset includes five trials  too few to use as the clustering unit in surrogacy evaluation  and so the 198 treating physicians were instead considered as “trials” in the analysis (see Section 2.2.2). As in other settings, observations are deleted if any outcome has a missing value; and if only one treatment group exists for a particular trial, then that trial cannot be included in the calculation of R or . Occasionally models may fail at either level due to very small trial size, again leading to exclusion of a trial. In the current analysis, 47 clusters have only one treatment group and there is further model failure in nine very small trials for Rh and in one trial for Rh_{t}. Therefore, 141 trials are included in calculating Rh and 150 in Rh_{t}. Among trials included in the analysis, there are 88 instances of separation in the trials for binary PANSS and 63 instances for ordinal CGI. These trials are retained in the analysis thanks to the use of penalized likelihood in model estimation. At the trial level, Rj_{it} = 0.45 with 95% confidence interval [0.32; 0.59], indicating that little uncertainty in the treatment effect on CGI is removed through knowledge of binary PANSS. Figure 11.1 illustrates this moderate strength of relationship between treatment effects on the binary PANSS and ordinal CGI. At the individual level, R_{h} = 0.46 with 95% confidence interval [0.10;0.82]. The reduction in uncertainty about CGI through knowledge of binary PANSS is again limited. The wide confidence intervals for R_{h} demonstrate diminished certainty in the findings due to the loss of information in the binary PANSS versus its continuous counterpart. Overall, a binary interpretation of PANSS does not have strong legitimacy as a surrogate for the ordinal CGI measure. Full details of how to run the above analysis in the Surrogate package in R, including the relevant commands, function arguments, and software output, may be found in Chapter 13. FIGURE 11.1 Assessing triallevel surrogacy of binary PANSS change for the ordinal CGI true outcome. Treatment effects are logodds ratios. Summary: BinaryOrdinal SettingThe preceding sections demonstrate that despite the additional computational problems associated with binary and ordinal outcomes in relatively small trials, the informationtheoretic approach may be readily applied to binary S and ordinal T with the aid of the penalized likelihood technique. This in turn may be easily implemented in the Surrogate R package. 
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