Miscellanea: "Within-trial" prognostic score adjustment is targeted maximum likelihood estimation

Abstract: Adjustment for super'' orprognostic'' composite covariates has become more popular in randomized trials recently. These prognostic covariates are often constructed from historical data by fitting a predictive model of the outcome on the raw covariates. A natural question that we have been asked by applied researchers is whether this can be done without the historical data: can the prognostic covariate be constructed or derived from the trial data itself, possibly using different folds of the data, before adjusting for it? Here we clarify that such ``within-trial'' prognostic adjustment is nothing more than a form of targeted maximum likelihood estimation (TMLE), a well-studied procedure for optimal inference. We demonstrate the equivalence with a simulation study and discuss the pros and cons of within-trial prognostic adjustment (standard efficient estimation) relative to standard TMLE and standard prognostic adjustment with historical data.