Reply to Dunning

To the Editor—The commentary by Dunning helpfully raises the question about the sensitivity of estimation of the vaccine efficacy (VE) curve to the choice of the baseline immunogenicity predictor (BIP) that is used. In the Zostavax Efficacy and Safety Trial (ZEST) example in our article the VE curve is estimated as a function of 2 binding antibody markers: fold rise and week 6 titer, in each case using baseline titer as the BIP [1]. We apply several statistical methods for estimating the VE curve, each of which separately estimates 2 terms: the disease risk in vaccine recipients conditional on the marker and the disease risk in placebo recipients conditional on the marker, which for a placebo recipient is the marker that s/he would have had if, contrary to fact, s/he had been assigned to receive the vaccine. We call these risks Vrisk(s) and Prisk(s), respectively, for subgroups with marker level s, where the VE curve is VE(s) = 1 – Vrisk(s)/Prisk(s), which measures VE ranging over subgroups defined by the marker level s. Vrisk(s) can be straightforwardly estimated using regression statistical methods without the need for any BIP, because the marker is observed in vaccinated individuals, such that the key issue is estimation of Prisk(s). In our Discussion, we noted that if Vrisk(s) and Prisk(s) are correctly modeled such that valid estimates are obtained, then the VE curve is accurately (unbiasedly) estimated, and this statement holds for any BIP that is reasonably well correlated with the marker, as it is for the ZEST example [1]. Therefore, we recast the question raised by Dunning as “How does a scientist jointly select the BIP and a model for Prisk(s) to obtain a valid estimate of Prisk(s), and how can one evaluate the validity?”