Prognostic Covariate Adjustment in Non-Ideal Conditions: Limitations and Doubly Robust Alternatives

Prognostic covariate adjustment (PROCOVA) incorporates a prognostic score, trained from historical control data, into the analysis of randomized clinical trials (RCTs) to reduce variance, when randomization is appropriate and alignment is strong between the historical model and the current trial control population. However, the performance of PROCOVA under non-ideal conditions, such as improper randomization, prognostic misalignment, or multicollinearity, remains less understood. In this work, we develop a projection representation illustrating how these non-ideal conditions can induce bias or inflate variance in PROCOVA.
Motivated by this, we evaluate doubly robust estimators, augmented inverse probability weighting (AIPTW) and targeted maximum likelihood estimation (TMLE), to mitigate PROCOVA-induced bias and variance inflation. Simulations demonstrate that PROCOVA regression performs well under ideal conditions, but can induce bias, inflate variance, or deliver minimal precision gain in non-ideal conditions. In contrast, AIPTW and TMLE remain valid and achieve improved efficiency across all scenarios.
These findings provide practical guidance for applying PROCOVA, particularly in pre-specified trials at the design stage. Our results support incorporating prognostic scores within doubly robust estimators to enhance robustness while preserving efficiency. TMLE is especially attractive in settings that use regularized or high-dimensional nuisance modeling, and it can offer more stable performance than AIPTW.