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REVIEW 3 major objections 6 minor 48 references

Precision Mental Health: Predicting Heterogeneous Treatment Effects for Depression through Data Integration

T0 review · 3 major / 6 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read This paper proposes predicting conditional average treatment effects in a target patient population by combining randomized trials through a two-stage meta-analysis, and wrapping each prediction in a 95% interval that accounts for both with

desk verdict A clean extension of meta-analytic prediction intervals to CATEs, with careful simulations, but the real-data application to Duke EHR profiles stretches the method beyond trial support and the intervals are likely too wide to be decision-relevant. read the letter →

arxiv 2509.04604 v1 pith:3HO3I6FV submitted 2025-09-04 stat.AP stat.ME

Carly L. Brantner , Trang Quynh Nguyen , Harsh Parikh , Congwen Zhao , Hwanhee Hong , Elizabeth A. Stuart This is my paper
classification stat.APstat.ME MSC 62P1062G05
keywords DataintegrationMeta-analysisNon-parametricstatisticsPredictionintervalsTreatmenteffectheterogeneityConditionalaveragePrecisionmentalhealth
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Clinicians want to know which depression drug works best for a particular patient, but individual trials are powered for averages, not for patient subgroups. This paper claims that combining several trials through a two-stage meta-analysis can produce a 95% prediction interval for the average treatment effect of a covariate-defined patient profile in a new setting, meaning patients who were not in any trial. Stage 1 estimates the profile-specific effect within each trial using regression, causal forests, or BART; Stage 2 pools the estimates with a random-effects model and adds between-trial variance to the interval. Simulations built on real trial structure show roughly 95% coverage for the target profiles across all first-stage methods, with coverage slipping for extreme ages and under non-normal between-trial distributions. Applied to four trials comparing duloxetine and vortioxetine, the method estimates duloxetine as better for nearly all profiles, but only a small subset has an interval that excludes zero, reflecting the large uncertainty from combining only four trials.

What carries the argument

The central object is the random-effects two-stage meta-analysis prediction interval, τ_{K+1}(X*) ≈ τ̂(X*) ± t_{K−2} √(SE(τ̂(X*))² + θ̂²(X*)), where τ is the conditional average treatment effect for covariate profile X*, SE(τ̂) is the pooled within-trial variance, and θ̂² is the between-trial variance estimated by restricted maximum likelihood. The interval's work is to convert trial-by-trial CATE estimates into a calibrated range for an unseen setting; Assumption 5, the exchangeability of the target CATE with the trial CATEs, is what licenses interpreting θ̂² as transferable to the target.

What would settle it

Hold out one trial at a time, fit the two-stage method on the remaining trials, and record whether the held-out trial's per-profile CATE estimates fall inside the predicted 95% intervals; over enough replications, long-run coverage well below 95% would refute the interval's calibration. A direct simulation version is to generate a target setting whose true CATEs are shifted relative to the trials and observe coverage dropping below nominal.

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Extended reading notes

Core claim

The paper's central claim is that uncertainty about a conditional average treatment effect in a new target setting can be quantified by a prediction interval built from a two-stage meta-analysis of trial-level CATE estimates. In Stage 1, each trial contributes an estimate τ̂_s(X*) and its variance for a covariate profile X*; in Stage 2, a random-effects model pools these into τ̂(X*), a between-trial variance θ̂²(X*), and the interval τ̂(X*) ± t_{K−2}√(SE(τ̂(X*))² + θ̂²(X*)). Under the paper's Assumption 5, that the target setting's CATE is a draw from the same normal distribution as the trials' CATEs, this interval is claimed to have approximately 95% coverage for the target CATE. Simulation

Load-bearing premise

The load-bearing premise is that the target patients come from the same universe as the trial patients in the specific sense that, at every covariate profile, the target's true treatment effect is just another random draw from the same bell-shaped distribution as the trial effects; if that is false, the intervals are not calibrated, and with only four trials the interval width is dominated by the estimate of between-study spread.

Editorial extensions

If this is right

  • Decision-makers can present a patient profile with a 95% range for the expected difference between treatments, rather than a point estimate from one trial.
  • The interval width automatically grows when trials disagree about the effect, preventing false precision, and shrinks toward the pooled estimate when trials agree.
  • The same two-stage recipe works whether the first stage is a linear regression, a causal forest, or BART, so the uncertainty machinery is decoupled from the choice of CATE learner.
  • In the four-trial duloxetine versus vortioxetine analysis, almost every profile's interval crosses zero, meaning the data do not support personalized choice between these drugs except possibly for a small set of older, higher-comorbidity profiles.
  • The approach can be applied to any collection of trials and any target sample's covariate profiles, producing prediction intervals without observing outcomes in the target setting.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • An immediate consequence the authors do not draw: with only four trials, the t_2 multiplier makes the interval so wide that the method will rarely declare one drug better; its practical value lies more in flagging when uncertainty is too large for a decision than in ranking drugs.
  • A testable extension is to replace or check the normal-exchangeability assumption with a nonparametric prediction interval or a conformal calibration step using held-out trials, which would let the intervals hold under weaker assumptions.
  • Because the center of the interval estimates the average CATE across trials, not the target-specific CATE, clinicians should treat the interval as a plausible range for a future trial-like setting; for covariate profiles far from trial support, the paper's own simulations show coverage degrading.
  • The framework could be extended to more than two treatments or to non-normal between-trial distributions, given the paper's finding that coverage is robust but slightly below nominal under uniform trial-effects distributions.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper proposes a two-stage meta-analytic method for constructing 95% prediction intervals for conditional average treatment effects (CATEs) in a target population not represented in the original randomized trials. Stage 1 estimates trial-specific CATEs and standard errors at target covariate profiles using parametric regression, causal forests, or BART. Stage 2 combines these estimates with a random-effects meta-analysis and forms the interval in Eq. (6), τ̂(X*) ± t_{K−2}√(SE² + θ̂²). The method is evaluated in simulations calibrated to four duloxetine-vortioxetine trials and applied to Duke EHR patient profiles. The paper reports high simulated coverage and finds that, in the real data, prediction intervals are wide and mostly cross zero, with only a small subgroup having intervals entirely above zero.

Significance. If valid, the method would provide a principled way to propagate between-study heterogeneity into individualized treatment predictions outside trial populations, a useful contribution to precision mental health. The manuscript is clearly written, states Assumptions 1–5 explicitly, and provides reproducible code and simulations. The two-stage random-effects derivation is standard. However, the simulation design does not actually evaluate coverage over new target settings, and the real-data application faces a serious covariate-overlap problem. These issues affect the central calibration claim and need to be resolved before the results can be accepted.

major comments (3)
  1. [§5.1–5.2 (simulation design)] The target setting is generated once and held fixed across all 500 replications; only the K trial datasets are redrawn. Eq. (6) is a prediction interval for a new τ_{K+1}(X*) drawn from the superpopulation in Assumption 5, so its nominal coverage should be evaluated by redrawing the target setting (or marginalizing over target draws) in each replication. Conditioning on one fixed target realization evaluates P(τ_{K+1}^{fixed} ∈ PI | trials), not the predictive coverage claimed in the paper. If the fixed target deviation from the mean is smaller than the between-study SD, coverage will be artificially high; the near-100% coverage in several scenarios in Fig. 3 is consistent with this artifact. Because all 100 target profiles share the same b_target and c_target, they are not independent checks. The simulations should be rerun with independent target draws.
  2. [§3.1 (Assumption 4) and §4.4 (Eq. 6)] The calibration of Eq. (6) requires the Stage 1 estimates τ̂_s(X*) to be unbiased for τ_s(X*) at each target profile. Assumption 4 only asserts P(S=s|X=x*)>0; it does not require the trial data to contain comparable treated and control units near x*. For causal forest and BART, prediction at profiles outside or at the edge of trial covariate support is extrapolation whose bias is not captured by SE(τ̂_s). In the application, Table 1 shows that Duke EHR prevalences of anxiety (61.0%), diabetes (20.7%), and antidepressant use (58.2%) are far higher than in any of the four trials (max 3.8%, 4.8%, 33.5%), so many target profiles lie in sparse or unsupported regions. The paper's own simulations show degraded coverage for extreme age profiles (§5.2 and Discussion). Since target outcomes are not used, this miscalibration is undetectable from the data. The paper should report overlap diagnostics
  3. [§4.4, §6.2] The real-data analysis uses K=4, so θ̂²(X*) is estimated with only two degrees of freedom and Eq. (6) uses t_{2}=4.303. The reported average prediction interval length (8.51) is more than three times the average CATE estimate (2.52), and only 1.75% of profiles have intervals excluding zero. This is not an error in the derivation, but it is a serious limitation for the stated goal of leveraging these intervals for treatment decisions. To support the real-data demonstration, the paper should present the K=4 simulation results in the main text and discuss the operating characteristics at this K, and it should show whether the target conclusions are stable across the three Stage 1 methods rather than only the honest causal forest.
minor comments (6)
  1. [§4.2.1, Eq. (3)] The term X_modA should be written as X_mod × A or with an explicit product symbol for readability; the current notation is confusing.
  2. [§5.2] The statement that coverage was 'around 95% or higher' is too broad given the simulation design issue described above. Please clarify that the reported numbers are conditional on the fixed target draw.
  3. [§6.2] The results section focuses on the honest causal forest only. Please state clearly that the numerical summaries in this section are for that model, and note whether the conclusions are robust to the other Stage 1 estimators.
  4. [§6.2, Table 2] The comparison between the two groups in Table 2 is descriptive and untested, as the authors note. To avoid over-interpretation, consider adding a sentence that no statistical inference is intended for these subgroup differences.
  5. [§7, Discussion] The sentence about the t-statistic says 'more studies will decrease the t-value'; it would be more precise to say 'decrease the critical value of the t-distribution'.
  6. [General] Several typographical artifacts appear in the text (e.g., 'V ortioxetine', 'Y ariable covariate distributions'). A careful proofread is recommended.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: Eq. (6) is derived from the stated random-effects model, and self-citations are contextual rather than load-bearing.

full rationale

The paper's central claim is a two-stage meta-analytic prediction interval. Eq. (6) follows directly from the random-effects model in Eq. (5) and the standard meta-analysis prediction interval formula (Riley et al. 2011; Higgins et al. 2009), not from any fitted constant or self-citation. Assumption 5 states the exchangeability/normality condition under which the interval is calibrated; the interval is not defined in terms of the target outcome, so there is no self-definitional loop. First-stage estimates are inputs to Stage 2, but they are not renamed as predictions: the prediction target is τ_{K+1}(X*), a distinct quantity. Simulations generate target truths from the same distribution assumed by the model, which is a validation exercise rather than circular derivation; the paper also reports sensitivity to non-normal study effects and overlap violations. The citations to Brantner et al. (2023, 2024) are background/context for causal assumptions and trial descriptions, and the load-bearing statistical results (prediction interval formula, REML recommendation, t_{K-2} degrees of freedom) are external. The paper itself flags limitations in Section 7 about overlap and Assumption 5, but those are correctness/robustness concerns, not circularity. No circular step can be exhibited.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

No new physical or conceptual entities are introduced. The method rests on standard causal assumptions and a random-effects superpopulation assumption. The main fitted quantities are the pooled CATE and between-study variance per covariate profile, plus routine hyperparameter choices for the machine-learning first-stage estimators.

free parameters (3)
  • tau(X*) (pooled CATE for each profile) = Not reported per profile; mean over EHR profiles 2.52
    Estimated by inverse-variance weighted average across four trials in Eq. 5-6. This is the standard meta-analytic estimand, not an ad hoc constant.
  • theta^2(X*) (between-study variance) = Not reported; REML estimate per profile
    Controls prediction interval width and is estimated from only K=4 studies, making it highly uncertain.
  • Causal forest hyperparameters = grf defaults except num.trees=1000
    The number of trees was chosen by hand for computational ease and can affect the first-stage variance estimates.
assumptions (5)
  • domain assumption Consistency, unconfoundedness, and positivity within each trial (Assumptions 1-3)
    Standard causal inference conditions for RCTs; Section 3.1.
  • domain assumption Target setting coverage: every target covariate profile has positive probability in each trial (Assumption 4)
    Required for transporting CATE estimates to the target population; Section 3.1.
  • domain assumption CATEs across settings follow a normal superpopulation distribution, tau_s(X*) ~ N(tau(X*), theta^2(X*)) for s=1..K,K+1 (Assumption 5)
    The core exchangeability assumption making the target CATE estimable from trial data; Section 3.1 and Section 4.3.
  • standard math Prediction interval uses a t-distribution with K-2 degrees of freedom and REML estimate of theta^2
    Approximation recommended by Higgins et al. 2009; Section 4.4.
  • standard math BART posterior draws can be summarized by mean and variance to approximate a normal sampling distribution for the CATE variance
    Appendix A; used for the BART first-stage standard error.

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Pith. "Pith review of Precision Mental Health: Predicting Heterogeneous Treatment Effects for Depression through Data Integration." pith.science (2026). https://pith.science/paper/3HO3I6FV

@misc{pith2026250904604,
  author       = {Pith},
  title        = {Pith review of: Precision Mental Health: Predicting Heterogeneous Treatment Effects for Depression through Data Integration},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3HO3I6FV}},
  note         = {Machine review of arXiv:2509.04604}
}
read the original abstract

When treating depression, clinicians are interested in determining the optimal treatment for a given patient, which is challenging given the amount of treatments available. To advance individualized treatment allocation, integrating data across multiple randomized controlled trials (RCTs) can enhance our understanding of treatment effect heterogeneity by increasing available information. However, extending these inferences to individuals outside of the original RCTs remains crucial for clinical decision-making. We introduce a two-stage meta-analytic method that predicts conditional average treatment effects (CATEs) in target patient populations by leveraging the distribution of CATEs across RCTs. Our approach generates 95\% prediction intervals for CATEs in target settings using first-stage models that can incorporate parametric regression or non-parametric methods such as causal forests or Bayesian additive regression trees (BART). We validate our method through simulation studies and operationalize it to integrate multiple RCTs comparing depression treatments, duloxetine and vortioxetine, to generate prediction intervals for target patient profiles. Our analysis reveals no strong evidence of effect heterogeneity across trials, with the exception of potential age-related variability. Importantly, we show that CATE prediction intervals capture broader uncertainty than study-specific confidence intervals when warranted, reflecting both within-study and between-study variability.

Figures

Figures reproduced from arXiv: 2509.04604 by the authors.

Figure 1
Figure 1. Depiction of overaching assumption of a superpopulation of settings from which we have setting-specific [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. A schematic of two-stage meta-analysis for CATE estimation. [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Distributions of coverage for each covariate profile in the target setting across each method and data generation [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Distributions of average interval length for each covariate profile in the target setting across each method and [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: 95% prediction intervals for treatment effects in target setting.* [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]
Figure 6
Figure 6. Figure 6: Study-specific confidence intervals and target prediction interval for a random subset of six covariate profiles [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]

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Works this paper leans on

48 extracted references · 35 canonical work pages

  1. [1]

    Athey, J

    S. Athey, J. Tibshirani, and S. Wager. Generalized random forests. The Annals of Statistics, 47 0 (2): 0 1148--1178, 2019

    work page 2019

  2. [2]

    D. S. Baldwin, H. Loft, and M. Dragheim. A randomised, double-blind, placebo controlled, duloxetine-referenced, fixed-dose study of three dosages of lu aa21004 in acute treatment of major depressive disorder (mdd). European Neuropsychopharmacology, 22 0 (7): 0 482--491, 2012

    work page 2012

  3. [3]

    Boulenger, H

    J.-P. Boulenger, H. Loft, and C. K. Olsen. Efficacy and safety of vortioxetine ( Lu AA21004 ), 15 and 20 mg/day: a randomized, double-blind, placebo-controlled, duloxetine-referenced study in the acute treatment of adult patients with major depressive disorder. International Clinical Psychopharmacology, 29 0 (3): 0 138--149, May 2014. ISSN 0268-1315. doi:...

    work page arXiv 2014

  4. [4]

    C. L. Brantner, T.-H. Chang, T. Q. Nguyen, H. Hong, L. Di Stefano, and E. A. Stuart. Methods for integrating trials and non-experimental data to examine treatment effect heterogeneity. Statistical Science, 38 0 (4): 0 640--654, 2023

    work page 2023

  5. [5]

    C. L. Brantner, T. Q. Nguyen, T. Tang, C. Zhao, H. Hong, and E. A. Stuart. Comparison of methods that combine multiple randomized trials to estimate heterogeneous treatment effects. Statistics in Medicine, 2024

    work page 2024

  6. [6]

    D. L. Burke, J. Ensor, and R. D. Riley. Meta-analysis using individual participant data: one-stage and two-stage approaches, and why they may differ. Statistics in Medicine, 36 0 (5): 0 855--875, feb 2017. ISSN 02776715. doi:10.1002/sim.7141. URL https://onlinelibrary.wiley.com/doi/10.1002/sim.7141

    doi:10.1002/sim.7141 2017

  7. [7]

    Carnegie, V

    N. Carnegie, V. Dorie, and J. L. Hill. Examining treatment effect heterogeneity using BART . Observational Studies, 5 0 (2): 0 52--70, 2019. ISSN 2767-3324. doi:10.1353/obs.2019.0002. URL https://muse.jhu.edu/article/793357

    work page arXiv 2019

  8. [8]

    Chernozhukov, D

    V. Chernozhukov, D. Chetverikov, M. Demirer, E. Duflo, C. Hansen, W. Newey, and J. Robins. Double/debiased machine learning for treatment and structural parameters, 2018

    2018

Show all 48 references
  1. [9]

    Colnet, I

    B. Colnet, I. Mayer, G. Chen, A. Dieng, R. Li, G. Varoquaux, J.-P. Vert, J. Josse, and S. Yang. Causal inference methods for combining randomized trials and observational studies: a review. arXiv:2011.08047 [stat], 2021. URL http://arxiv.org/abs/2011.08047. arXiv: 2011.08047

    2011 arXiv

  2. [10]

    J. M. Currie and W. B. MacLeod. Understanding doctor decision making: The case of depression treatment. Econometrica, 88 0 (3): 0 847--878, 2020

    2020

  3. [11]

    I. J. Dahabreh, L. C. Petito, S. E. Robertson, M. A. Hernán, and J. A. Steingrimsson. Towards causally interpretable meta-analysis: transporting inferences from multiple studies to a target population. arXiv:1903.11455 [stat], 2020. URL http://arxiv.org/abs/1903.11455. arXiv: ...

    1903 arXiv

  4. [12]

    DerSimonian and N

    R. DerSimonian and N. Laird. Meta-analysis in clinical trials. Controlled clinical trials, 7 0 (3): 0 177--188, 1986

    1986

  5. [13]

    J. S. S. Dhaliwal, B. C. Spurling, and M. Molla. Duloxetine, May 2023. URL https://www.ncbi.nlm.nih.gov/books/NBK549806/

    2023

  6. [14]

    Dorie, G

    V. Dorie, G. Perrett, J. L. Hill, and B. Goodrich. Stan and BART for Causal Inference : Estimating Heterogeneous Treatment Effects Using the Power of Stan and the Flexibility of Machine Learning . Entropy, 24 0 (12): 0 1782, Dec. 2022. ISSN 1099-4300. doi:10.3390/e24121782. UR...

    2022 doi

  7. [15]

    Dorie, H

    V. Dorie, H. Chipman, R. McCulloch, A. Dadgar, R. C. Team, G. U. Draheim, M. Bosmans, C. Tournayre, M. Petch, R. de Lucena Valle, et al. Package ‘dbarts’. 2023

    2023

  8. [16]

    V. J. Dzau and G. S. Ginsburg. Realizing the full potential of precision medicine in health and health care. Jama, 316 0 (16): 0 1659--1660, 2016

    2016

  9. [17]

    D’Agostino, C

    A. D’Agostino, C. D. English, and J. A. Rey. Vortioxetine (brintellix): a new serotonergic antidepressant. Pharmacy and Therapeutics, 40 0 (1): 0 36, 2015

    2015

  10. [18]

    Girardi, M

    P. Girardi, M. Pompili, M. Innamorati, M. Mancini, G. Serafini, L. Mazzarini, A. Del Casale, R. Tatarelli, and R. J. Baldessarini. Duloxetine in acute major depression: review of comparisons to placebo and standard antidepressants using dissimilar methods. Human Psychopharmaco...

    2009

  11. [19]

    D. J. Goldstein, Y. Lu, M. J. Detke, C. Wiltse, C. Mallinckrodt, and M. A. Demitrack. Duloxetine in the treatment of depression: a double-blind placebo-controlled comparison with paroxetine. Journal of clinical psychopharmacology, 24 0 (4): 0 389--399, 2004

    2004

  12. [20]

    P. R. Hahn, J. S. Murray, and C. M. Carvalho. Bayesian Regression Tree Models for Causal Inference : Regularization , Confounding , and Heterogeneous Effects (with Discussion ). Bayesian Analysis, 15 0 (3): 0 965--1056, Sept. 2020. ISSN 1936-0975, 1931-6690. doi:10.1214/19-BA1...

    2020 doi

  13. [21]

    Herrmann, S

    N. Herrmann, S. Black, J. Lawrence, C. Szekely, and J. Szalai. The sunnybrook stroke study: a prospective study of depressive symptoms and functional outcome. Stroke, 29 0 (3): 0 618--624, 1998

    1998

  14. [22]

    J. P. T. Higgins, S. G. Thompson, and D. J. Spiegelhalter. A re-evaluation of random-effects meta-analysis. Journal of the Royal Statistical Society: Series A (Statistics in Society), 172 0 (1): 0 137--159, 2009. ISSN 1467-985X. doi:10.1111/j.1467-985X.2008.00552.x. URL https:...

    2009 arXiv

  15. [23]

    J. L. Hill. Bayesian Nonparametric Modeling for Causal Inference . Journal of Computational and Graphical Statistics, 20 0 (1): 0 217--240, Jan. 2011. ISSN 1061-8600, 1537-2715. doi:10.1198/jcgs.2010.08162. URL http://www.tandfonline.com/doi/abs/10.1198/jcgs.2010.08162

    2011 arXiv

  16. [24]

    IntHout, J

    J. IntHout, J. P. Ioannidis, M. M. Rovers, and J. J. Goeman. Plea for routinely presenting prediction intervals in meta-analysis. BMJ open, 6 0 (7): 0 e010247, 2016

    2016

  17. [25]

    M. R. Kosorok and E. B. Laber. Precision medicine. Annual review of statistics and its application, 6 0 (1): 0 263--286, 2019

    2019

  18. [26]

    Kroenke, R

    K. Kroenke, R. L. Spitzer, and J. B. Williams. The phq-9: validity of a brief depression severity measure. Journal of general internal medicine, 16 0 (9): 0 606--613, 2001

    2001

  19. [27]

    S. R. K \"u nzel, J. S. Sekhon, P. J. Bickel, and B. Yu. Metalearners for estimating heterogeneous treatment effects using machine learning. Proceedings of the national academy of sciences, 116 0 (10): 0 4156--4165, 2019

    2019

  20. [28]

    G. Li, X. Wang, and D. Ma. Vortioxetine versus duloxetine in the treatment of patients with major depressive disorder: a meta-analysis of randomized controlled trials. Clinical drug investigation, 36: 0 509--517, 2016

    2016

  21. [29]

    A. R. Mahableshwarkar, P. L. Jacobsen, and Y. Chen. A randomized, double-blind trial of 2.5 mg and 5 mg vortioxetine ( Lu AA21004 ) versus placebo for 8 weeks in adults with major depressive disorder. Current Medical Research and Opinion, 29 0 (3): 0 217--226, Mar. 2013. ISSN ...

    2013

  22. [30]

    A. R. Mahableshwarkar, P. L. Jacobsen, Y. Chen, M. Serenko, and M. H. Trivedi. A randomized, double-blind, duloxetine-referenced study comparing efficacy and tolerability of 2 fixed doses of vortioxetine in the acute treatment of adults with MDD . Psychopharmacology, 232 0 (12...

    doi

  23. [31]

    H. L. Mills, J. P. Higgins, R. W. Morris, D. Kessler, J. Heron, N. Wiles, G. D. Smith, and K. Tilling. Detecting heterogeneity of intervention effects using analysis and meta-analysis of differences in variance between trial arms. Epidemiology (Cambridge, Mass.), 32 0 (6): 0 846, 2021

    2021

  24. [32]

    S. A. Montgomery and M. sberg. A new depression scale designed to be sensitive to change. The British journal of psychiatry, 134 0 (4): 0 382--389, 1979

    1979

  25. [33]

    Mueller and J

    S. Mueller and J. Pearl. Personalized decision making--a conceptual introduction. Journal of Causal Inference, 11 0 (1): 0 20220050, 2023

    2023

  26. [34]

    Nie and S

    X. Nie and S. Wager. Quasi-oracle estimation of heterogeneous treatment effects. Biometrika, 108 0 (2): 0 299--319, 2021. ISSN 0006-3444, 1464-3510. doi:10.1093/biomet/asaa076. URL https://academic.oup.com/biomet/article/108/2/299/5911092

    2021 doi

  27. [35]

    The national institute of mental health strategic plan, May 2024

    NIMH. The national institute of mental health strategic plan, May 2024. URL https://www.nimh.nih.gov/about/strategic-planning-reports

    2024

  28. [36]

    R. A. Post and E. R. Van Den Heuvel. Beyond conditional averages: Estimating the individual causal effect distribution. Journal of Causal Inference, 13 0 (1): 0 20240007, 2025

    2025

  29. [37]

    R. A. Post, M. Petkovic, I. L. Van den Heuvel, and E. R. Van den Heuvel. Flexible machine learning estimation of conditional average treatment effects: a blessing and a curse. Epidemiology, 35 0 (1): 0 32--40, 2024

    2024

  30. [38]

    R. D. Riley, J. P. T. Higgins, and J. J. Deeks. Interpretation of random effects meta-analyses. BMJ, 342 0 (feb10 2): 0 d549--d549, Feb. 2011. ISSN 0959-8138, 1468-5833. doi:10.1136/bmj.d549. URL https://www.bmj.com/lookup/doi/10.1136/bmj.d549

    2011 doi

  31. [39]

    R. D. Riley, T. P. Debray, T. P. Morris, and D. Jackson. The Two -stage Approach to IPD Meta - Analysis . In Individual Participant Data Meta - Analysis , pages 87--125. John Wiley & Sons, Ltd, 2021. ISBN 978-1-119-33378-4. doi:10.1002/9781119333784.ch5. URL https://onlinelibr...

    2021 doi

  32. [40]

    Roth and P

    A. Roth and P. Fonagy. What works for whom?: a critical review of psychotherapy research. 2006

    2006

  33. [41]

    D. B. Rubin. Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology, 66 0 (5): 0 688--701, 1974. ISSN 1939-2176. doi:10.1037/h0037350. Place: US Publisher: American Psychological Association

    1974 doi

  34. [42]

    Z. M. Sheffler, P. Patel, and S. Abdijadid. Antidepressants, May 2023. URL https://www.ncbi.nlm.nih.gov/books/NBK538182/

    2023

  35. [43]

    Snaith, F

    R. Snaith, F. Harrop, t. D. Newby, and C. Teale. Grade scores of the montgomery— sberg depression and the clinical anxiety scales. The British journal of psychiatry, 148 0 (5): 0 599--601, 1986

    1986

  36. [44]

    Sobel, D

    M. Sobel, D. Madigan, and W. Wang. Causal Inference for Meta - Analysis and Multi - Level Data Structures , with Application to Randomized Studies of Vioxx . Psychometrika, 82 0 (2): 0 459--474, 2017. ISSN 0033-3123, 1860-0980. doi:10.1007/s11336-016-9507-z. URL http://link.sp...

    2017 doi

  37. [45]

    conditional average treatment effects

    B. G. Vegetabile. On the distinction between" conditional average treatment effects"(cate) and" individual treatment effects"(ite) under ignorability assumptions. arXiv preprint arXiv:2108.04939, 2021

    2021 arXiv

  38. [46]

    Viechtbauer

    W. Viechtbauer. Conducting meta-analyses in R with the metafor package. Journal of Statistical Software, 36 0 (3): 0 1--48, 2010. doi:10.18637/jss.v036.i03

    2010 doi

  39. [47]

    Wager and S

    S. Wager and S. Athey. Estimation and inference of heterogeneous treatment effects using random forests. Journal of the American Statistical Association, 113 0 (523): 0 1228--1242, 2018

    2018

  40. [48]

    Yusuf, J

    S. Yusuf, J. Wittes, J. Probstfield, and H. A. Tyroler. Analysis and interpretation of treatment effects in subgroups of patients in randomized clinical trials. Jama, 266 0 (1): 0 93--98, 1991

    1991

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.