In a clinical trial, the treatment effect $\Delta$ is modeled using a profile likelihood. If $L_p(\Delta) = \sup_{\psi} L(\Delta, \psi)$, where $\psi$ is a nuisance parameter, which of the following best describes the advantage of using the profile likelihood ratio statistic $w(\Delta) = -2 \ln(L_p(\Delta) / L_p(\hat{\Delta}))$ compared to the Wald statistic?