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

2025/07/31 by Emilie Højbjerre‐Frandsen, Alejandro Schuler, Højbjerre-Frandsen, Emilie +1
Medicine · #Cardiac Imaging and Diagnostics #FOS: Computer and information sciences #Methodology (stat.ME)

paper · pdf · doi:10.48550/arxiv.2507.23446

openalex publication_date 2025/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

Adjustment for ``super'' or ``prognostic'' 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.

Citations

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Related

• Prognostic Adjustment with Efficient Estimators to Unbiasedly Leverage Historical Data in Randomized Trials
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• postcard: An R Package for Marginal Effect Estimation with or without Prognostic Score Adjustment