Integrated TS+TT: Ethical & Causal Framework

• Integrated TS+TT is a framework that combines ethically grounded target studies with target trials to rigorously estimate intervention effects and group disparities.
• It uses stratified sampling on allowable covariates and within-group randomization to ensure both ethical balance and robust causal inference.
• The framework employs semiparametric G-computation for continuous and stochastic interventions, with practical applications in evaluating device bias and treatment disparities.

An Integrated Target Study plus Target Trial (TS+TT) framework is an emerging paradigm for generating ethically interpretable and causally rigorous evidence on intervention effects—particularly on disparities—by explicitly combining the design principles of ethically grounded target studies with the causal inference capabilities of randomized (or emulated) target trials. The approach is designed to enable not just valid causal effect estimation, but also careful quantification of group disparities under interventions, ensuring both ethical interpretability and methodological soundness in policy-relevant areas such as bias mitigation in clinical devices or algorithms (Sun et al., 20 Aug 2025).

1. Framework Composition and Theoretical Rationale

The TS+TT framework combines two methodological innovations:

• Target Study (TS): Focuses on defining and achieving “ethical balance” via stratified sampling. Here, social groups (e.g., those defined by race, ethnicity, or other protected characteristics) are aligned on a set of “allowable” covariates—variables representing differences considered fair or ethically acceptable (such as clinical need). This ensures that any disparity contrast reflects differences beyond such fair attributes, yielding an interpretable measure of inequity.
• Target Trial (TT): Implements within-group randomization and emulates a hypothetical randomized controlled trial, ensuring that both allowable and non-allowable (i.e., potentially confounding) covariates are balanced across experimental arms within each social group. This enables causal inference on intervention effects—both overall and on disparity contrasts—by minimizing confounding and allowing robust estimation even in complex, real-world settings where actual trial data may not be available.

The dual-balance approach ensures that both ethical and causal forms of balance are achieved. TS guarantees that comparisons are made between ethically comparable populations, while TT ensures that comparisons within each group are unconfounded by both observed and unobserved factors, to the extent achievable by the design and data.

2. Ethical Balance: Stratified Sampling on Allowable Covariates

Ethical balance is central to the TS component and is established through stratified sampling. For each predefined social group (e.g., Non-Hispanic Black [NHB] and Non-Hispanic White [NHW]), the sampling aims to align the distribution of allowable covariates (Aₖ) to that of a standard population T=1 (often, but not always, the disadvantaged group). Allowable covariates typically capture clinical need or other non-discriminatory factors relevant to outcome interpretation.

This approach ensures that the contrast in outcomes between groups reflects non-allowable (i.e., unfair) differences, thereby providing a meaningful measure of disparity. The mathematical representation for the standardized average potential outcome in group $g$ under intervention arm $z$ is:

$$u_{k}(g) = \int E[Y^{+}_{k} \mid Z, A_{k}, N_{k}, k, G=g] f_{A_{k}}(A_{k} \mid T=1)\ dA_{k}$$

where $f_{A_{k}}(A_{k} \mid T=1)$ is the reference distribution of allowable covariates, and $Y^{+}_{k}$ is the potential outcome under intervention.

3. Causal Balance: Within-Group Randomization

To achieve causal balance, the TT component randomizes the intervention within each stratum defined by social group and allowable covariates. This process balances the full covariate set (both Aₖ and non-allowable Nₖ) across arms, rendering the intervention effect on disparity unconfounded. The emulated randomization is particularly critical when using observational data, as it allows for model-based approaches (e.g., G-computation) to mimic the statistical properties of an RCT.

The disparity under a given intervention strategy $ž$ is:

$V_{k}(ž) = u_{k}(G=1) - u_{k}(G=0)$

and the “intervention effect on disparity” is defined by:

$T_{k}(ž) = V_{k}(ž) - V_{k}(ž_{0})$

where $ž_{0}$ denotes a reference strategy.

4. Protocol Components and Emulation

A rigorous TS+TT protocol specification includes the following:

• EnroLLMent Windows: Short, well-defined time intervals during which eligibility is assessed.
• EnroLLMent Groups: Pre-specification of social groups for disparity analysis.
• Allowable Covariate Definition: Selection of Aₖ for ethical standardization.
• Standard Population: Choice of reference distribution for stratification.
• Stratified Sampling: Matching or weighting individuals within each group to the standard.
• Within-Group Randomization: Assignment (or emulated assignment) to intervention arms after stratification.
• Outcome Assessment: Measurement of clinical, behavioral, or other relevant endpoints post-intervention.

Practical emulation is conducted using real-world electronic medical records (EMR) or similar datasets, mapping each part of the protocol onto observable variables. Sequential regression, standardization, and marginalization (as in semiparametric G-computation) are implemented to estimate disparities and intervention effects.

5. Continuous-Time and Stochastic Intervention Methods

The framework extends semiparametric G-computation to accommodate continuous-time and stochastic interventions, which is especially relevant for time-to-event outcomes (e.g., time-to-treatment or restricted mean survival time, RMST). This extension allows intervention effects to be estimated for both deterministic and continuous, distributional interventions (such as adjusting device bias parameters).

A simplified outcome model in the continuous time G-computation is:

$$h(E[Y^{+}_{k} | G=g, Z, A_{k}, N_{k}, k]) = \alpha_{0} + \alpha_{z}Z + \alpha_{zA}A_{k} + \alpha_{gN}N_{k} + \alpha_{4}k$$

This enables estimation of counterfactual means under hypothetical interventions with complex parameterizations (e.g., varying device bias by group).

6. Application: Pulse Oximeter Bias and Treatment Disparities

The motivating example in the literature applies TS+TT to evaluate the effect of pulse oximeter racial bias on disparities in dexamethasone treatment receipt for COVID-19. Intervention arms correspond to devices with specific bias characteristics; disparity is measured in RMST to treatment between NHB and NHW groups standardized on clinical need.

By sequentially emulating protocol steps—assignment of hypothetical device errors, outcome modeling, group standardization, and marginalization—TS+TT estimates the disparity under different intervention scenarios, directly informing policy on medical device regulatory standards.

7. Versatility, Implications, and Policy Relevance

The TS+TT framework is generalizable to:

• Arbitrary intervention types (binary/deterministic, continuous/stochastic, or dynamic)
• Multiple outcome domains (binary, time-to-event, continuous)
• A wide spectrum of disparity analyses (including algorithmic or device bias)

This versatility enables its deployment across clinical, public health, and regulatory settings. By generating ethically interpretable and causally sound estimates, TS+TT avoids interventions that might inadvertently exacerbate disparities, thereby informing policies geared toward disparity elimination. The mathematical underpinnings—explicit standardization, within-group randomization, and modern semiparametric inference—reinforce its robustness as a platform for both methodological and applied disparity research (Sun et al., 20 Aug 2025).

Key mathematical expressions:

• Standardized average potential outcome: $$u_{k}(g) = \int E[Y^{+}_{k}|Z, A_{k}, N_{k}, k, G=g]f_{A_{k}}(A_{k}|T=1)dA_{k}$$
• Disparity: $V_{k}(ž) = u_{k}(1) - u_{k}(0)$
• Intervention effect on disparity: $T_{k}(ž) = V_{k}(ž) - V_{k}(ž_{0})$

This integrated structure ensures that interventions are evaluated with attention to both fairness and causal effect, aligning evidence generation in health disparities research with contemporary ethical and scientific standards.