"Within-trial" prognostic score adjustment is targeted maximum likelihood estimation
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908629027782656 |
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| author | Højbjerre-Frandsen, Emilie Schuler, Alejandro |
| author_facet | Højbjerre-Frandsen, Emilie Schuler, Alejandro |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_23446 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | "Within-trial" prognostic score adjustment is targeted maximum likelihood estimation Højbjerre-Frandsen, Emilie Schuler, Alejandro Methodology 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. |
| title | "Within-trial" prognostic score adjustment is targeted maximum likelihood estimation |
| topic | Methodology |
| url | https://arxiv.org/abs/2507.23446 |