Outcome-wide longitudinal designs for causal inference: a new template for empirical studies

• The design aims to address unmeasured confounding, investigator discretion in modeling and covariate selection, and false positives associated with repeated p-value testing.The authors note that observational estimates may remain confounded despite extensive covariate control, and that model choices and widespread use of a 0.05 threshold can contribute to biased or false findings (Simmons et al., 2011; Gelman and Loken, 2014; Head et al. 2015).Source: §1 · pp. 2–3
• The outcome-wide longitudinal design applies a single-exposure causal analysis to multiple outcomes measured after exposure, supplemented by metrics for unmeasured confounding and multiple testing.The authors propose using the E-value, making covariate-control and basic modeling decisions simultaneously across outcomes, and employing multiple-testing metrics.Source: §1 · p. 3
• The E-value assesses sensitivity to potential unmeasured confounding, while making covariate-control and basic modeling decisions across outcomes simultaneously is intended to limit outcome-specific investigator discretion.The template also proposes multiple-testing metrics, including Bonferroni correction and new metrics intended to assess evidence across associations and potential effects.Source: §1 · p. 3
• The authors argue that assessing one exposure across numerous outcomes can expand knowledge more rapidly and inform policy and public-health assessment of human flourishing.They advocate examining diverse outcomes, including happiness, mental and physical health, close relationships, and financial security.Source: §1 · pp. 3–4

2.1 Causal Inference Using Confounding Control

• Causal interpretation requires exposed and unexposed groups to be comparable within measured-covariate strata; under this condition, observed associations estimate counterfactual effects.The section expresses this condition as counterfactual outcomes being independent of exposure conditional on covariates, and gives difference- and ratio-scale contrasts.Source: §2.1 · pp. 4–5

2.2 Longitudinal Data and Control for Baseline Outcome

• Longitudinal data establish that exposure precedes outcome, and controlling for baseline outcome often helps mitigate reverse causation, though substantive knowledge can sometimes make it unnecessary.At least two waves are generally needed; retrospective reports can also preserve temporal ordering, although differential misreporting remains a concern.Source: §2.2 · pp. 5–6

2.3 Principles of Confounder Selection

• For total effects, adjust for common causes rather than mediators; the modified disjunctive cause criterion includes pre-exposure causes of exposure or outcome, excludes known instruments, and includes proxies for unmeasured common causes.Its theoretical guarantee applies when some measured-covariate subset suffices to control confounding; it may perform less well when no such subset exists.Source: §2.3 · pp. 6–7

2.4 Common Confounders in Practice in Outcome-Wide Studies

• Outcome-wide analyses should use a substantial shared covariate set covering measured pre-exposure causes of any outcome, including baseline outcomes when appropriate, and are principally suited to large cohorts.The proposed covariates span demographic, health, economic, social, political, and psychological factors; parental warmth, Big Five traits, political affiliation, and religious attendance are often neglected.Source: §2.4 · pp. 7–8
• A rich measured-covariate set can reduce residual confounding, but its sufficiency is uncertain, so outcome-wide studies should assess robustness to unmeasured confounding and other biases.The section suggests omitting covariates one at a time to assess how estimates change.Source: §2.4 · p. 9

2.5 Timing of Confounders

• When covariates are repeatedly measured, using measurements before exposure can help distinguish confounders from mediators; distant prior measures may leave more residual confounding than recent ones.Contemporaneous adjustment risks controlling for mediators, creating a trade-off against using covariates measured too far before exposure.Source: §2.5 · pp. 9–10

2.6 Control for Prior Exposure

• For changing exposures, controlling for prior exposure can clarify change effects and further address reverse causation or unmeasured confounding, but its usefulness depends on exposure variation, recency, and sample size.Prior-exposure adjustment may be unnecessary for stable or uniformly unexposed exposures, and distant measures can introduce time-dependent-confounding concerns.Source: §2.6 · pp. 10–12

2.7 Outcome-Wide Regression Models and Estimation

• Outcome-wide estimation can use linear regression for continuous outcomes, logistic regression for dichotomous outcomes, and Poisson regression for count outcomes, adjusting for selected covariates and applicable prior measures.Source: §2.7 · p. 12
• Under Yk(a)⊥A |C, outcome-specific regression coefficients estimate causal effects on the model’s scale; logistic odds ratios approximate risk ratios only for rare outcomes.For common outcomes, modified Poisson or log-binomial models can estimate risk ratios directly.Source: §2.7 · p. 13
• Separate regressions will often suffice: multivariate approaches offer at most modest efficiency gains, and shared design matrices yield identical ordinary least squares estimates.Propensity-score subclasses or matched sets formed without reference to outcomes can be reused across outcomes, facilitating automation (Rosenbaum and Rubin, 1983b; Rosenbaum, 2002).Source: §2.7 · p. 13
• Outcome-based covariate matching is harder to apply across outcomes, while doubly robust, machine-learning, and high-dimensional selection methods are promising but need sample-size guidance.Other approaches can standardize effects across outcomes using mean-variance or median-interquartile range measures (Kennedy et al, 2018).Source: §2.7 · p. 13

3.1 Sensitivity Analysis for Unmeasured Confounding

• For each outcome, report E-values for both the estimate and the confidence-interval limit nearest the null to show robustness to unmeasured confounding.The E-value indicates the minimum strength of association that an unmeasured confounder would need with both exposure and outcome, beyond measured covariates, to explain away the observed association.Source: §3.1 · p. 15
• The E-value is conservative: confounding at that strength can explain away an association, but often would not, and its interpretation depends on measured-covariate control.It applies to multiple unmeasured confounders considered together; a large E-value is meaningful only when the measured covariates plausibly control much of the confounding.Source: §3.1 · p. 16

3.2 Skepticism with Regard to Causal Effects from Selection on Observables

• Evidence from covariate adjustment warrants context-sensitive skepticism: rich covariate data and a large E-value can support strong causal evidence, but do not remove the need for critical interpretation.The plausibility of adjustment differs across settings, including because of differences in available covariates and how people select into exposure groups.Source: §3.2 · pp. 17–18

3.3 Sensitivity Analysis for other Types of Bias

• Nondifferential measurement error often biases estimates toward the null, whereas differential error may bias them away; selection from exposure- or outcome-affected sample restriction can cause substantial bias.Correction for exposure measurement error may be feasible outcome-wide, but outcome measurement correction can require distinct parameters; effect estimates themselves bound the differential error needed to explain away an association.Source: §3.3 · pp. 18–20
• For missing data, compare multiple-imputation estimates with complete-case results; when missingness is extensive or results differ substantially, abandon the outcome-wide approach for outcome-specific analyses.The authors advise caution when missingness considerably exceeds 10% for any covariate, exposure, or outcome; major discrepancies may warrant sensitivity analyses for missing-not-at-random scenarios.Source: §3.3 · pp. 19–20

4.1 Bonferroni Correction and Its Properties

• Bonferroni’s a/K threshold supports inference of at least J true associations when J are rejected, with error at most a, and controls the per-family error rate.Unlike controlling the probability of any false positive, Bonferroni also limits the expected number of false positives to fewer than K × a.Source: §4.1 · p. 21
• Bonferroni’s penalty is often modest in large cohorts with moderate numbers of tests, but can be substantial in smaller trials, studies powered for one outcome, or studies testing many outcomes.For K=24, N=3,929, and mean standard error 0.031, the nominal and Bonferroni effect-size thresholds were 0.061 and 0.095. Reporting actual p-values, the test count, and the corrected threshold lets readers assess both nominal and corrected evidence.Source: §4.1 · pp. 21–22

4.2 Additional Metrics Taking into Account Correlations

• Alongside Bonferroni, the authors recommend correlation-aware metrics, including Romano and Wolf resampling and a confidence interval for expected a-level rejections under the global null.For continuous outcomes, comparing observed rejections with the interval’s upper limit can, under specified conditions, provide a lower bound on true associations at least 95% of the time; the NRejections package implements this approach.Source: §4.2 · pp. 22–23

4.3 Comment on Current Practices for Multiple Testing Correction

• Do not discard evidence solely because it misses a multiple-testing threshold: p-values are continuous, and effect sizes and evidence above nominal thresholds can still merit discussion.The authors favor synthesizing evidence across studies, including meta-analysis, and note that evidence is often strongest when replicated across studies, investigators, and populations.Source: §4.3 · pp. 23–24

5. DATA ANALYSIS EXAMPLE

• The analysis related recalled childhood parental warmth to 24 mid-life outcomes in a longitudinal subset of 2,984 MIDUS participants, with adjustment for measured covariates and multiple imputation.Warmth was measured in 1995–1996 and outcomes in 2004–2006; outcomes included flourishing measures, depression and anxiety, and adverse health behaviors and states. Continuous outcomes used ordinary least squares; binary outcomes used Poisson regression when prevalence exceeded 10% and logistic regression otherwise.Source: §5 · p. 24
• Each 1-SD increase in childhood parental warmth was associated with 0.20 SD greater composite mid-life flourishing (95% CI: [0.16, 0.24]).The 24 outcome measures had a median correlation magnitude of 0.25 (minimum = 0.0007; maximum = 0.88), reflecting conceptual and arithmetic relationships among outcomes.Source: §5 · p. 24
• 18 of 24 outcomes were significant at a = 0.05 (17 at a = 0.01), and all 24 effect directions linked greater warmth with improved flourishing outcomes.For several flourishing outcomes and depression, the E-value for the confidence interval exceeded 1.5: confounding associated with both warmth and outcome by risk ratios of 1.5 each could shift the interval to the null, but weaker confounding could not.Source: §5 · pp. 24–25
• 15 of 17 continuous outcomes remained significant at a = 0.05 and a = 0.01 under Romano and Wolf correction.Bonferroni left 17 of 24 tests significant (a » 0.002). Against the global null, observed rejections exceeded the 95% null-interval upper bound by 10 at a = 0.05 and by 13 at a = 0.01, supporting moderately sized effects on composite flourishing.Source: §5 · p. 25

6.1 Formatting of Tables

• Use Table 1 for sample demographics, Table 2 for effect estimates, confidence intervals, p-values and testing thresholds, and Table 3 for outcome-specific E-values.Table 2 can separate risk ratios for binary outcomes from regression coefficients for continuous outcomes. Report E-values for both estimates and confidence intervals; standardize continuous outcomes when useful and report their population standard deviations in the paper or supplement.Source: §6.1 · pp. 25–26

6.2 Details of Measures in Online Supplements

• Keep exposure measurement and variable timing in the main text, while placing extensive outcome and covariate measurement details in an online supplement when word limits are tight.With more generous word limits, such as in some social science journals, detailed descriptions may not need to be moved to a supplement.Source: §6.2 · p. 26

6.3 Effect Sizes for Continuous Exposures

• For continuous exposures, report meaningful-scale contrasts, per-standard-deviation effects, or effects across exposure categories, often combining a scale-based approach with categories.Per-standard-deviation changes and categories can aid explanation and E-value reporting, but a standard deviation can represent very different exposure changes across populations; report standard deviations and avoid using standardized measures to compare effects across populations.Source: §6.3 · p. 26

6.4 Effect Size Reporting and Conversions and Comparisons

• For supplemental comparisons, convert continuous outcomes to approximate risk ratios by dichotomizing them, using a median split, or applying RR ≈ exp(0.91*d), but not for primary analyses.For the conversion, the approximate confidence interval is (exp{0.91*d – 1.78*sd}, exp{0.91*d + 1.78*sd}).Source: §6.4 · p. 27

7.1 Conveys More Information

• An outcome-wide analysis conveys evidence on numerous outcomes in one publication, improving efficiency for readers, researchers, and the research community.Considering beneficial and harmful effects together can inform policy and public health; although each outcome may receive less theoretical discussion, empirical findings can contribute to subsequent theorizing.Source: §7.1 · pp. 27–28

7.2 Reporting of Null Results

• An outcome-wide analysis can report null findings alongside results suggesting effects in a single paper, making null results easier to publish.The passage notes that null results can sometimes be as or more informative than findings suggesting an effect.Source: §7.2 · p. 28

7.3 Less Temptation to Choose Models

• Using the same covariates and modeling approach across outcomes can reduce researcher degrees of freedom, but cannot eliminate analytic flexibility or selective outcome reporting.Selecting several outcomes across flourishing domains and preregistering analytic plans may mitigate selective reporting; null results may also help assess whether positive findings reflect unmeasured confounding when outcomes can serve as negative controls.Source: §7.3 · pp. 28–29

7.4 The Comparison of Effect Sizes

• Outcome-wide analyses allow clearer comparisons of exposure effect sizes across outcomes within the same sample, though differences across populations may limit generalization.Repeated studies of the same exposure-outcome relationships in different populations may clarify which outcomes show particularly large effects across populations.Source: §7.4 · p. 29

8.1 Challenges of Exposure-Wide Designs

• Exposure-wide epidemiology is vulnerable because exposures affect downstream exposures: simultaneous adjustment can block total effects and induce collider-stratification bias, whereas outcome-wide studies can control variables preceding a fixed exposure.Each exposure may require a distinct set of confounders; controlling for downstream exposures can estimate only direct effects and can create bias even when an exposure has no effect.Source: §8.1 · pp. 30–31

8.2 Lagged Exposure-Wide Designs

• A lagged exposure-wide design fits separate W2-exposure regressions with shared W1 covariates and exposures, enabling common confounding control when waves are close enough to limit time-dependent confounding.A coefficient estimates a causal effect under the stated conditional exchangeability assumption. The design is limited to exposures measured and changeable in the interval, but may inform policy about what can change the outcome at that time.Source: §8.2 · pp. 31–32

8.3 Interaction Outcome-Wide Studies

• With two contemporaneous exposures, outcome-wide models can estimate main effects and interactions across outcomes; noncontemporaneous exposures with intermediate confounding require more complex causal models.The proportion of effects attributable to each exposure alone or to their interaction can also be reported and converted to a difference scale for comparison.Source: §8.3 · p. 32

8.4 Outcome-Wide Studies for Causal Effects of Time-Varying Exposures

• Outcome-wide analyses can target effects of exposure trajectories, with marginal structural models and parametric g-formula approaches generally more feasible than structural nested models.The former approaches may reuse the same models across outcomes, whereas structural nested model estimation can be more challenging because some options require outcome-derived numeric grid searches.Source: §8.4 · pp. 32–33

8.5 Quasi-Experimental Outcome-Wide Designs

• Outcome-wide quasi-experimental analyses are most plausible with randomized instruments or deterministic or randomized regression-discontinuity assignment; outcome-specific assumptions limit plausibility, and interrupted time series are harder.For interrupted time-series designs, trajectories before and after intervention must be assessed for each outcome.Source: §8.5 · p. 33

8.6 Mediator-Wide Studies

• Mediator-wide analyses may be biased when mediators affect one another; they are more plausible for contemporaneous mediators measured shortly after exposure, otherwise joint mediation may be preferable.A mediator-wide design examines potential mediators one at a time, whereas the alternative is to assess mediation through the set jointly.Source: §8.6 · p. 34

9. CONCLUSION

• The design provides a template for assessing one exposure’s effects across numerous subsequent outcomes, with principles for confounding control, unmeasured-confounding metrics, and multiple-testing metrics.The paper presents theoretical justification alongside tentative guidelines that may be refined through further analyses; other causal questions require different approaches and theory.Source: §9 · p. 34
• The authors argue the design could become standard—and often preferable to single exposure-outcome studies—when many outcomes are relevant and longitudinal or panel data support confounding control.They note that careful evaluation of single exposure-outcome relationships will still be needed.Source: §9 · p. 34
• Broad measurement of human flourishing outcomes is critical to the design’s value and enables more objective inference, null-result reporting, confounding assessment, effect-size comparison, and policy and public-health relevance.The authors encourage applying the design and anticipate further refinements and developments.Source: §9 · p. 35

E-value for point

• 1.69 and 1.59 are reported for overall composite flourishing (continuous); the E-value formula is attributed to VanderWeele and Ding (2017).The supplied passage does not label which value corresponds to the point estimate versus another statistic.Source: E-value for point · p. 44
• The complete-case analysis covers parental warmth associations with mid-life health and well-being outcomes, with outcome-specific samples ranging from 2,618 to 2,742.Models controlled for demographic and childhood family factors; Bonferroni correction used a 0.002 cutoff across 24 outcomes.Source: Table S1 · p. 46, E-value for point · p. 46
• The parental-warmth-tertile analysis used multiple imputation and a sample of 2,948 to assess associations with mid-life health and well-being outcomes.Models controlled for age, sex, race, nativity, siblings, and other childhood family factors; the Bonferroni cutoff was 0.002 across 24 outcomes.Source: Table S2 · p. 47, E-value for point · p. 47
• For flourishing, one supplementary analysis converted continuous-outcome estimates to the risk-ratio scale using RR ≈ exp(0.91*B).The estimates came from standardized beta coefficients in linear regression models; models used multiple imputation and adjusted for demographic and childhood family factors.Source: Table S3 · p. 48, E-value for point · p. 48
• A separate flourishing analysis dichotomized continuous outcomes at the median and estimated risk ratios with Poisson regression.It used multiple imputation, adjusted for demographic and childhood family factors, and applied a Bonferroni cutoff of 0.002 across 24 outcomes.Source: E-value for point · pp. 48–49, Table S4 · p. 49