Statistically speaking, the biomarker and the clinical endpoint are realizations of random variables. Interest focuses on the joint distribution of these variables, which was assumed bivariate normal in the preceding models. This is, however, seldom the case, because the biomarker and/or the clinical endpoint is often a realization of nonnormally distributed random variables, which can be:
Binary (dichotomous): biomarker value below or above a certain threshold (e.g., CD4 + counts over 500/mm3) or clinical "success" (e.g., tumor shrinkage)
Categorical (polychotomous): biomarker value falling in successive classes (e.g., cholesterol levels < 200 mg/dL, 200-299 mg/dL, 300 + mg/dL) or clinical response (e.g., complete response, partial response, stable disease, progressive disease) Continuous (normally distributed): biomarker (e.g., log PSA level) or clinical measurement (e.g., diastolic blood pressure) Censored continuous: time to biomarker below or above a certain threshold (e.g., time to undetectable viral load) or time to clinical event (e.g., time to cardiovascular death) Longitudinal (repeated measures): biomarker (e.g., CD4 + counts over time) or clinical outcome (e.g., blood pressure over time) Multivariate longitudinal: several biomarkers (e.g., CD4 + and viral load over time) or several clinical measurements (e.g., dimensions of quality of life over time)
The models used to validate a biomarker as a surrogate for a clinical endpoint will depend on the type of variables observed in the problem at hand. In the example below, we will illustrate this by analyzing the same data in three different ways. The clinical endpoint will be survival in all cases, but the biomarker will consist, respectively, of PSA response (binary variable), time to PSA progression (censored continuous variable), and the PSA pattern over time (longitudinal).
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