# Evaluation of Surrogacy for Survival and Binary Endpoints

We use the colorectal cancer study to illustrate the analysis for the survivalbinary surrogacy setting using the information-theoretic approach. The true endpoint is overall survival and the surrogate endpoint is a two-category tumor response: patients with complete or partial response are considered as responders and patients with stable or progressive disease are considered nonresponders. The data structure for the survival-binary setting is shown in Section 12.5.

### The SAS Macro %SURVBININFO

The information-theoretic approach discussed above can be used to evaluate surrogacy in different settings. In this section, we present the results for the survival-binary setting using the SAS macro %SURVBININFO. The macro fits logistic regression and the Cox proportional hazards model for a binary and survival endpoint, respectively, and uses the models formulated in (12.53) to estimate trial-level surrogacy:

%SURVBININFO(data=colo,true=Surv,trueind=survind,

surrog=responder,treat=treat,trial=center, patid=patientid,weighted=1, model="reduced",boot=10)

Arguments specific to the %SURVBININFO are:

• model: the model used in (12.52) and (12.53) ("Reduced" or "Full").

FIGURE 12.51

*Trial-specific likelihood reduction factor (horizontal line: the overall LRF).*

TABLE 12.3

*SAS macros available for analyses using the information-theoretic approach.*

Surrogacy Setting |
SAS Macro |
Data structure |

N orrnal- N orrnal |
7.N0RMN0RMINF0 |
12.3.1 |

Normal-Binary |
7.N0RMBININF0 |
12.7 |

Survival- Survival |
°/ |
12.4 |

Survival-Binary |
°/ |
12.5 |

Binary-Binary |
7.BINBININF0 |
12.8 |

FIGURE 12.52

*The estimated likelihood reduction factor. Individual-level and trial-level surrogacy measures with 95% C.I.*

FIGURE 12.53

*The Colorectal Cancer Study. Trial-specific and overall LRF (horizontal line).*

sures are equal to i?h = 0.0797 (0.0561, 0.1033), and = 0.3559 (0.1096, 0.6216), respectively. Both surrogacy measures indicate that the binary tumor response is a poor surrogate for the overall survival. As a sensitivity analysis, trial-specific LRF is presented in Figure 12.53.

# Other Surrogacy Settings

SAS macros that were developed for the evaluation of surrogacy using the information-theoretic approach are presented in Table 12.3. Note that, as discussed in previous sections in the chapter, the data structure depends on the surrogacy setting.