The Delta likelihood ratio does not incorporate study power. Author response

Abstract

Imputation of the observed P-value and effect size within the likelihood ratio and power function are together a maneuver to recenter the H A distribution about the observed estimate ð b dÞ. As the authors imply, this effectively reconfigures their alternative hypothesis from the composite H A : dO0 to the simple HThe resulting likelihood ratio (their dLR) is thus maximized and represents an upper bound on the evidence against H 0 for the one-sided case. Furthermore, reparameterization of the power function in this manner fixes ''marginal power'' at 0.5 for all cases, invalidating the authors' assertion that ''the dLR incorporates study power,'' as it is merely a transformation of the P-value.Similar approaches to determining the Bayes factor bound for a given P-value have been longstanding in the Bayesian literature [7e9], where distributed priors yield average power ð1 À bÞ in the predata expressions [4]. In the present case, however, evaluation of the evidence relative to the a posteriori H 0 A divorces inference from any prior effect estimate, from which power would have been computed. Recognition of the dLR as a bound for the a priori composite H A will prevent its misinterpretation as an externally valid (regarding priors) measure of evidence.