Change scores, trajectories, and responder-threshold estimands
No. Baseline is pre-treatment, so the target follow-up and change contrasts are one quantity under any adjustment. Across 24 scenarios, MAIC and G-computation never diverged beyond Monte Carlo error, and were identical to machine precision in unanchored comparisons. The only divergence was in naive unanchored comparisons, equal to 1.00 times the baseline shift and independent of the baseline-by-treatment interaction. Read the study below.
Statement
Mixing endpoint and change-score results in a population-adjusted comparison is an estimand and variance-handling choice rather than an unprincipled conversion: the change-score treatment contrast equals the endpoint contrast minus the baseline contrast, and the baseline-endpoint correlation is required for the variance of a change score, not for its mean contrast. Under randomization the baseline contrast is zero in expectation, so endpoint and change analyses can target the same follow-up effect, and meta-epidemiological work across 21 meta-analyses, 189 trials and 41,256 patients found combining them in conventional meta-analysis generally valid, with a mean difference in standardized mean differences of -0.04 (95% CI -0.13 to 0.06) (pmid:23747228). What remains unresolved is the adjustment step: baseline severity is often itself an effect modifier and regression to the mean acts differently in populations with different baseline distributions, and neither target-standardized mean trajectories nor latent-model responder probabilities has an established population-adjusted formulation.
Why it is open
The unresolved part is the population-adjustment step rather than the combination itself: where baseline severity modifies the effect, change and endpoint analyses can imply different effect-modification structures, so the representation interacts with the adjustment instead of being a fixed offset. Trials measure the outcome repeatedly and on several scales, and joint repeated-measures models need compatible time definitions and within-trial covariances that aggregate publications do not report. Target-standardized trajectories and model-derived responder probabilities are optional estimands with no established formulation under population adjustment, and dichotomizing a reported mean remains invalid without the outcome distribution. cpaic, the unreleased development package on GitHub that is not installable from CRAN, models one Gaussian outcome and a raw mean difference with no trajectory or responder path.
What has been tried
| Work | What it contributes |
|---|---|
| da Costa et al. 2013, Combining follow-up and change data is valid in meta-analyses of continuous outcomes: a meta-epidemiological study, Journal of Clinical Epidemiology (PMID 23747228) | 21 meta-analyses, 189 trials and 41,256 patients; finds no relevant difference between follow-up and change standardized mean differences and concludes that combining them in meta-analysis is generally valid, with the choice prespecified in the protocol; it does not address population adjustment |
Probable solution or research direction
Prespecify whether the analysis uses change or endpoint data, following the meta-epidemiological guidance, and handle the variance correctly rather than converting between representations by ad hoc rescaling. Where baseline severity is a plausible effect modifier or more than one timepoint matters, model baseline and follow-up jointly so the adjustment and the estimand stay consistent. Treat target-standardized trajectories and responder probabilities as declared optional estimands, deriving responder probabilities from directly standardized individual-level indicators where individual patient data allow it and from a latent model only where they do not, and keep a prespecified decision-relevant timepoint alongside any trajectory.
Our study
Change scores and endpoints do not diverge under population adjustment
The question put to it. When baseline severity modifies the treatment effect, do change-score and endpoint analyses give different target-population contrasts after population adjustment, in proportion to the product of the interaction and the baseline shift?
What it found. No. Baseline is pre-treatment, so the target follow-up and change contrasts are one quantity under any adjustment. Across 24 scenarios, MAIC and G-computation never diverged beyond Monte Carlo error, and were identical to machine precision in unanchored comparisons. The only divergence was in naive unanchored comparisons, equal to 1.00 times the baseline shift and independent of the baseline-by-treatment interaction.
Results.
- Adjusted estimators: largest mean endpoint-minus-change difference 0.0068, within 3 Monte Carlo SE of zero in every scenario; in unanchored comparisons the per-replicate difference was at most 4e-13.
- Naive unanchored comparisons: difference = 1.001 (SE 0.002) x shift + 0.007 (SE 0.007) x interaction x shift. Endpoint bias is (b + beta) shift and change bias (b + beta - 1) shift.
- Naive anchored comparisons agree in expectation across representations but are both biased by the unadjusted modification.
- The design’s proposed product structure was derived from a misreading: with baseline as a covariate, the treatment and treatment-by-baseline coefficients of a linear model are identical for follow-up and change.
Design.
- Estimand
- Target-population mean difference in follow-up, B versus A
- Methods compared
- naive, MAIC on the baseline mean, G-computation with baseline as covariate, each in endpoint and change representation
- Data-generating mechanism
- Anchored and unanchored comparisons, individual data on A versus C and arm means on B versus C, 24 scenarios crossing baseline shift (0, 0.5, 1 SD), baseline-by-treatment interaction (0, 0.3) and baseline-to-follow-up correlation (0.4, 0.8), 300 per arm.
- Replicates
- 1000 per scenario, 24,000 in total
What this does not answer. Continuous outcome with a linear conditional mean only; nonlinear links, threshold-based responder estimands and joint repeated-measures models are not tested. Peer review has not been done.
Peer review. Not yet done. The result stands on the study alone until it is.
Read it: PDF · Markdown · OpenDocument · Code and data: studies/OUT-06-baseline-severity-as-a-modifier-of-its-own-adjustment · Protocol: registered before the run
Verification
Verdict. Overstated. 2 independent auditors judged the claim as stated too strong. In population-adjusted comparisons the change-versus-endpoint representation is an estimand choice that interacts with baseline severity as an effect modifier, and neither target-standardised mean trajectories nor latent-model responder probabilities have an established formulation; empirical meta-epidemiological work finds that simply combining change and follow-up estimates in conventional meta-analysis is generally valid, so the unresolved part is the adjustment step, not the combination itself.
The source said. “Continuous outcomes in population-adjusted comparisons are reduced to a single-timepoint summary that is sometimes a change from baseline and sometimes an endpoint value, combined without a principled conversion. The report instead calls for target-standardized mean trajectories, multivariate models for repeated measures and multiple scales, and responder probabilities derived from a latent outcome model.”
What was wrong with it. The source treated change-versus-endpoint combination as unresolved and said conversion between them requires the baseline-endpoint correlation; the literature auditor produced da Costa et al. (pmid:23747228, doi:10.1016/j.jclinepi.2013.03.009), which finds combining them generally valid and recommends prespecifying which is used, and the code auditor showed the correlation claim is mathematically wrong as written, since the correlation governs the variance rather than the mean contrast. The code auditor also rejected the claim that responder probabilities must come from a latent continuous model, because with individual patient data responder indicators can be formed and standardized directly.
Revised by the full-text reading. Applied 2026-07-26 full-text reading of the consolidated library (687 papers).
- closure-upheld
- 7 findings from the reading assert this problem is open; the closure was re-examined and stands Put to an independent reviewer with the closing auditors’ reasoning, the work they relied on, and the new findings in view together. The new evidence documents exactly the residual the closure retained: baseline imbalance and effect modification can make change and endpoint representations differ in a population-adjusted analysis, while missing correlations make change-score variances uncertain. The 2025 threshold variation finding also supports the already-conceded absence of an established population-adjusted responder-probability formulation. None of the papers rebuts the algebraic relation between change and endpoint treatment contrasts or the meta-epidemiological evidence that conventional synthesis of the two is generally valid. Examples of unpropagated correlation imputation and inconsistent responder definitions demonstrate poor practice and unresolved extensions, not that the closed universal claim should be restored. (reviewer confidence: high)
- Flagged for reopening
-
9 findings from the reading assert this problem is open while the registry carries
overstatedFlagged, not applied: reversing an earlier audit’s closure needs the closure’s own evidence re-examined alongside this, which the reading did not do. See documentation/audit/reading/PROPOSED.md. - Literature and prior-art check
- open / overstated. Retrieved da Costa et al., ‘Combining follow-up and change data is valid in meta-analyses of continuous outcomes: a meta-epidemiological study’ (J Clin Epidemiol 2013; PMID 23747228; doi 10.1016/j.jclinepi.2013.03.009), 21 meta-analyses, 189 trials, 41,256 patients. It directly addresses the change-versus-endpoint question the entry frames as unresolved and concludes combining them is generally valid, with a mean difference in SMDs of only -0.04 (95% CI -0.13 to 0.06). The entry’s framing that the two are ‘combined without a principled conversion’ therefore overstates the problem for conventional synthesis; the empirically supported guidance is to prespecify which is used. What remains genuinely open is the population-adjustment-specific part: baseline severity as an effect modifier, regression to the mean differing across covariate distributions, and target-standardised mean trajectories or latent-model responder probabilities, none of which da Costa addresses and for which I found no PAIC literature.
- GPT-5.6 Sol, technical and source-code lens
- open / overstated. C2 is mathematically wrong as written. The treatment contrast in change is the endpoint contrast minus the baseline contrast; baseline-endpoint correlation is required to recover the variance or standard error of a change score, not its mean contrast. Under randomization the baseline contrast is zero in expectation, so endpoint and change analyses can target the same follow-up treatment effect, although finite-sample imbalance, baseline adjustment, and effect modification can matter in PAIC. C3 is therefore possible rather than inevitable. C4 and C6 are reasonable research outputs, but trajectories need not replace a prespecified decision-relevant timepoint and multivariate models require compatible time definitions and covariance information. C5 is right that a reported mean cannot be dichotomized into a responder probability, but a latent continuous model is not the only valid route: with IPD, responder indicators can be formed and standardized directly, while a latent-tail calculation adds distributional assumptions. cpaic currently models one Gaussian outcome and raw MD, with no trajectory or responder path. The unresolved PAIC-specific extensions are real, but the change-versus-endpoint issue and the Medium-high severity are overstated as universal problems.
- Decision path
-
R5:default-open → R8:overstated-majority(n=2)
How the evidence falls in time
9 papers in the reviewed corpus bear on this problem, published 2012 to 2025. Partial progress is on the record, and later work still calls this open. Both belong in view.
This problem is recurrent: three or more papers spanning at least eight years assert it independently. Sustained restatement by authors who mostly do not cite each other is the strongest evidence this reading can offer that a gap is real rather than one group’s framing.
It is also being closed in pieces: partial results come from more than one paper in more than one year, each covering a different part.
| Year | Says | Paper |
|---|---|---|
| 2012 | confirms it is open | A Primer on Network Meta-Analysis for Dental Research |
| 2015 | confirms it is open | From Randomized Controlled Trials of Antidepressant Drugs to the Meta-Analytic Synthesis of Evidence: Methodological Aspects Lead to Discrepant Findings |
| 2016 | partly addresses it | Methods for network meta-analysis of continuous outcomes using individual patient data: a case study in acupuncture for chronic pain |
| 2018 | partly addresses it | Sensitivity analyses for effect modifiers not observed in the target population when generalizing treatment effects from a randomized controlled trial: Assumptions, models, effect scales, data scenarios, and implementation details (Nguyen, Ackerman, Schmid, Cole, Stuart, PLoS ONE 2018;13(12):e0208795) |
| 2019 | confirms it is open | Using Matching-Adjusted Indirect Comparisons and Network Meta-analyses to Compare Efficacy of Brexanolone Injection with Selective Serotonin Reuptake Inhibitors for Treating Postpartum Depression |
| 2022 | confirms it is open | Baseline imbalance and heterogeneity are present in meta-analyses of randomized clinical trials examining the effects of exercise and medicines for blood pressure management |
| 2024 | confirms it is open | Network meta-analysis examining efficacy of components of cognitive behavioural therapy for insomnia |
| 2024 | confirms it is open | The effectiveness of delivery modalities of non-pharmacological diabetes prevention programs: A systematic review and component network meta-analysis |
| 2025 | confirms it is open | Network connectivity, between-study heterogeneity and timepoint challenges in generalized myasthenia gravis: a feasibility assessment of indirect treatment comparisons |
Source
Derived from C:L1537-1545, C:L1548-1555 of the reviewed corpus.