An Appraisal of the Adjusted Association and the Relative Effect
Issues with the Adjusted Association
When both S and T are continuous normally distributed endpoints, there are no issues with the adjusted association (pZ). Indeed, pZ is simply the correlation between S and T adjusted for Z. This quantity has desirable properties, i.e., it always remains within the unit interval, it generally has a small confidence interval (because there is sufficient individual-level replication in most clinical trials), and it is straightforward to compute and interpret.
However, if we move away from the situation were both S and T are contin?uous normally distributed endpoints, it is no longer clear how pZ, the adjusted association, should be quantified. For example, in the mixed continuous-binary setting, i.e., S is continuous and T is binary, a bivariate probit model can be used in which pZ is defined as the correlation between a latent continuous variable that is assumed to underlie the observed discretized endpoint T and the continuous endpoint S. Alternatively, a bivariate Plackett-Dale model can be used in which pZ is defined as the global odds ratio between S and T (Geys, 2005). A variety of other measures have been proposed to quantify pZ in other settings (for details, see Burzykowski, Molenberghs, and Buyse, 2005). It would be desirable to have a single unifying approach to quantify pZ across a wide variety of settings. In Chapter 10, an information-theoretic approach is introduced for this purpose.