Chapter_22

### Chapter 22: TARGET TRIAL EMULATION

Chapter Overview
This chapter extends the target trial framework to sustained treatment strategies, providing a unified causal inference approach for both randomized experiments and observational studies. It introduces key causal effects (intention-to-treat and per-protocol effects) and emphasizes the necessity of g-methods for valid estimation when time-varying confounders exist. The chapter also addresses practical challenges in emulating target trials using observational data.

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22.1 Intention-to-treat effect and per-protocol effect

Subsection Content

• Compares two causal effects in randomized trials:
  • Intention-to-treat (ITT) effect: Effect of assignment to treatment ($Z$), agnostic to adherence.
  • Per-protocol effect: Effect of receiving treatment ($A$) as specified in the protocol, requiring full adherence.
• Figure 22.1 illustrates pathways: $Z \rightarrow A \rightarrow Y$ (treatment effect) and $Z \rightarrow Y$ (direct effect, e.g., behavioral changes).
• When the exclusion restriction holds (no $Z \rightarrow Y$), ITT effect simplifies; otherwise, direct effects complicate interpretation.
• Per-protocol effect estimation requires adjustment for confounding (e.g., via g-methods), as non-adherence breaks exchangeability.

Technical Points:

• Core Theory:
  • ITT effect: $Pr[Y^{z=1} = 1]/Pr[Y^{z=0} = 1]$ (unadjusted association valid due to randomization).
  • Per-protocol effect: $Pr[Y^{a=1} = 1]/Pr[Y^{a=0} = 1]$ (requires adjustment for confounders).
• Key Formulas:
  • ITT risk ratio: $\frac{Pr[Y=1|Z=1]}{Pr[Y=1|Z=0]}$
  • Per-protocol risk ratio: $\frac{Pr[Y^{a=1}=1]}{Pr[Y^{a=0}=1]}$ (estimable only with confounder adjustment).
• Application Scenarios:
  • ITT: Pragmatic for null preservation in blinded trials.
  • Per-protocol: Essential for real-world decision-making when adherence is feasible.

Fine Points:

• Exclusion Restriction: Violated if $Z$ directly affects $Y$ (e.g., unblinded trials), invalidating null preservation.
• Biased Analyses:
  • Pseudo-ITT: Restricts to uncensored individuals, risking selection bias.
  • Modified ITT: Includes only initiators, biased without adjustment.
  • Naïve per-protocol: Compares adherent subgroups without confounder adjustment, inducing selection bias.
• Misconceptions:
  • ITT is not always conservative (e.g., head-to-head trials with differential adherence).
  • Efficacy/effectiveness labels are ambiguous; explicit strategy definitions are preferable.

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22.2 A target trial with sustained treatment strategies

Subsection Content

• Defines a pragmatic randomized trial comparing sustained treatment strategies (e.g., continuous antiretroviral therapy vs. no therapy for HIV patients).
• Follow-up starts at assignment ($k=0$), ends at death, censoring, or 60 months.
• ITT effect: Contrasts static strategies ($Z=1$ vs. $Z=0$) with no censoring.
• Per-protocol effect: Contrasts dynamic strategies (e.g., "treat unless toxicity occurs") under full adherence.
• Dynamic strategies require explicit protocol specifications to avoid misclassifying discontinuations as non-adherence.

Technical Points:

• Core Theory:
  • ITT: $Pr[D^{z=1,\bar{c}_k=0}_k = 1] - Pr[D^{z=0,\bar{c}_k=0}_k = 1]$
  • Per-protocol: $Pr[D^{g_1,\bar{c}_k=0}_k = 1] - Pr[D^{g_0,\bar{c}_k=0}_k = 1]$
• Controlled Direct Effects:
  • Defined as $E[Y^{a=1,m}] - E[Y^{a=0,m}]$ (setting mediator $M$ to $m$).
  • Identifiable via sequential randomization or g-methods in observational studies.

Fine Points:

• Protocol Clarity: Ambiguous strategies (e.g., omitting toxicity discontinuation rules) misclassify adherence.
• Alternative Effects: Data from non-adherent participants enable emulation of different target trials (e.g., comparing modified strategies).

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22.3 Emulating a target trial with sustained strategies

Subsection Content

• Observational analogs:
  • ITT analog: Contrasts initiators ($A_0=1$ vs. $A_0=0$), resembling modified ITT.
  • Per-protocol analog: Identical to the target trial definition.
• Explicit strategy definitions prevent non-actionable comparisons (e.g., non-translatable to interventions).
• Efficacy/effectiveness dichotomies are less useful than precise strategy specifications.

Technical Points:

• Estimation Requirements:
  • Per-protocol effects require g-methods for time-varying confounding.
  • Extrapolation beyond observed strategies (e.g., dose-response models) may be needed.

Fine Points:

• Grace Periods: Allow delayed treatment initiation (e.g., 3 months), handled via cloning/censoring/IP weighting.

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22.4 Time zero

Subsection Content

• Start of follow-up must align with the target trial to avoid selection bias.
• **Solutions for non-unique time zero$:
  1. Single eligibility time: Start when criteria first met.
  2. Multiple eligibility times: Emulate sequential trials (e.g., at each time unit).
• Non-unique strategy assignment: Use cloning (create copies for compatible strategies) with IP weighting for censoring bias.

Technical Points:

• Cloning Procedure:
  • Assign clones to feasible strategies.
  • Censor when data deviate from assigned strategy.
  • Adjust variances via bootstrapping.

Fine Points:

• Time-Unit Choice: Coarse units (e.g., months) introduce bias if confounders vary within intervals.

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22.5 A unified approach to answer What If questions with data

Subsection Content

• Unifies counterfactual and causal diagram frameworks via target trial emulation.
• Randomized and observational studies differ only in:
  1. Baseline confounding (absent in randomized trials).
  2. Known randomization probabilities.
  3. Recorded treatment assignments.
• Per-protocol analyses in both settings: Require g-methods for time-varying confounding/selection bias.
• Conventional unadjusted "per-protocol analyses" in trials are often biased.

Technical Points:

• G-Methods: Necessary for per-protocol effects with sustained strategies (e.g., IP weighting, g-formula).
• Variance Adjustment: Bootstrapping for cloned/sequential trial data.

Fine Points:

• Data Integration: Combined randomized/observational data may outperform randomized trials alone when unmeasured effect modifiers exist.
• Optimal Strategies: Observational data can reveal personalized strategies (e.g., treat only high-benefit subgroups).

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Key Takeaways

1. Target Trial Framework: Forces explicit definition of interventions, enhancing causal question clarity.
2. G-Methods: Essential for valid per-protocol effect estimation with time-varying confounders in both trials and observational studies.
3. Time Zero Handling: Critical to avoid selection bias; cloning/IP weighting resolves non-unique strategy assignments.
4. Unified Analysis: Randomized and observational studies require similar adjustment for post-baseline biases when estimating per-protocol effects.

Note: Image content (Figures 22.1–22.4) is referenced but not summarized due to lack of interpretable data.