• Drug-resistant TB (MDR/RR-TB) remains a major global cause of preventable morbidity and mortality.
• People living with HIV (PLHIV) face substantially higher TB risk, and TB is a leading cause of death among PLHIV.
• Clinicians and programs need evidence to choose among new all-oral regimens.

Recent trials introduced short-course, all-oral regimens:

• TB-PRACTECAL (Nyang’wa et al., 2022, 2024)
  • 6-month regimen: 6BPaLM (Bedaquiline + Pretomanid + Linezolid + Moxifloxacin)
  • Non-inferior vs standard care
• endTB (Guglielmetti et al., 2025)
  • 9-month regimens: 9BLMZ, 9BCLLfxZ, 9BDLLfxZ
  • Non-inferior vs standard care

Standard care in each study was

• TB-PRACTECAL: 9–12 or 18–20 month all-oral regimens (region-specific)
• endTB: 18–20 month all-oral regimens (region-specific)

• WHO guidelines recommend multiple all-oral MDR/RR-TB regimens; shorter regimens are appealing for feasibility and adherence.
• However, comparative evidence between 6-month and 9-month regimens is limited, and certainty of evidence is often low.

We have individual patient data (IPD) from two non-inferiority RCTs:

Primary aim: Compare the efficacy of 6BPaLM versus endTB regimen (9BLMZ, 9BCLLfxZ, 9BDLLfxZ).

• Transportability
  • Prior work studies how to transport causal effects from multiple randomized trials to a new target population where experimental data may not be available (Dahabreh et al., 2020; Dahabreh and Hernán, 2019).
  • The core assumption of these methods lies in addressing the covariate distribution shift between the “experiment” and “target” groups.

• We define a target population as the union of participants from endTB and TB-PRACTECAL and focus on cross-trial causal comparison.

Populations:

• \(S \in \{1,2\}\): trial indicator
  
• \(S=1\): endTB
  
• \(S=2\): TB-PRACTECAL
  
• \(\Omega\): target population of interest
  

Target population of interest \(\Omega\): consisting of individuals at risk of TB recurrence in countries hosting enrollment sites for either the endTB or TB-PRACTECAL trials .

\(\Omega = \Omega_{\text{TB-PRACTECAL}} \cup \Omega_{\text{endTB}}\)

The Core Idea: Use randomization within each trial, then take the difference of the estimated effects.

What the traditional approach does:

1. Analyze each trial separately: Calculate within trial effect with data from TB-PRACTECAL and endTB separately.
2. Compare the two results: Take the difference between the two trial-specific effects.

Strength: Uses within trial randomization

Limitation: Assumes negligible differences in standard-care efficacy between endTB and TB-PRACTECAL, as achieved by having a common comparator.

This directly reflects the common comparator: \(\mathbb{E}[Y(c_1) - Y(c_2) \mid \Omega] = 0\)

Estimand: Compare trial-specific treatment-vs-control contrasts, then take the difference.

Define trial-specific causal effects: \[ \tau_a := \mathbb{E}[Y(a) - Y(c_1) \mid S=1], \qquad \tau_b := \mathbb{E}[Y(b) - Y(c_2) \mid S=2] \]

The traditional indirect comparison estimand is \(\tau_a - \tau_b.\)

Theorem 1. Under M1.1–M1.4, \(\tau_a - \tau_b\) is identified: \[ \tau_a = \mathbb{E}[Y\mid A=a, S=1] - \mathbb{E}[Y\mid A=c_1, S=1], \] and analogously for \(\tau_b\). Under M1.5–M1.6, \(\tau_a - \tau_b = \psi(a,b).\)

Within each trial, \(\tau_a\) and \(\tau_b\) can be estimated via:

• IPW: \(\hat{\tau}_a^{\text{IPW}} = \mathbb{P}_{\Omega,n}\!\left[\dfrac{\mathbf{1}(A=a,S=1)}{P(A=a\mid S=1)}Y - \dfrac{\mathbf{1}(A=c_1,S=1)}{P(A=c_1\mid S=1)}Y\right]\)

• G-computation: \(\hat{\tau}_a^{G} = \hat{\mu}_1(a) - \hat{\mu}_1(c_1)\)

• EIF-based (one-step/doubly robust): augments IPW with outcome regression; consistent if either nuisance model is correctly specified.

Core idea: Construct an emulated trial by pooling treated arms across trials and analyzing the data as an observational study, following a target trial emulation protocol while ignoring standard-care arms.

Motivation: Conducting a new head-to-head randomized trial is often infeasible. By discarding control arms and comparing treated groups directly, we extract maximal information from existing trials under explicit causal assumptions.

What this approach does:

• Specify a target trial protocol (eligibility, treatment strategies, outcome, follow-up). <!–

• Restrict data to treated participants. –>

• Pool treated arms across trials to form a single analytic dataset.

• Adjust for baseline covariates to control for possible confounding.

Identification

• Exchangeability is assumed conditional on measured covariates.

• Randomization is no longer used once control arms are discarded.

Limitation

• Because control arms are ignored, identification relies entirely on covariate adjustment rather than randomization.

• Lower sample size due to discarding control arms.

Core idea: Reframe cross-trial evidence synthesis as the emulation of a hypothetical head-to-head RCT (Hernán & Robins, 2016). Pool the treated arms across trials and analyze the combined dataset as an observational study.

Let \(\Omega_{\text{trt}}\) denote the subpopulation of treated participants. The pooled treated dataset is \[ \mathcal{O}^{\text{pool}}_{\text{trt}} = \{(Y_i, A_i, L_i, S_i) : A_i \in \{a, b\},\; i \in \Omega_{\text{trt}}\}. \]

Target estimand in this approach: \[ \tau'_a - \tau'_b, \quad \text{where}\quad \tau'_a := \mathbb{E}[Y(a)\mid\Omega_{\text{trt}}],\quad \tau'_b := \mathbb{E}[Y(b)\mid\Omega_{\text{trt}}]. \]

M2.2 (Exchangeability) requires that, conditional on \(L\), treatment assignment is independent of potential outcomes within \(\Omega_{\text{trt}}\). This is the standard unconfoundedness condition for observational data — not guaranteed by randomization.

Merge the data from TB-PRACTECAL and endTB, and extend inferences from trial participants to the target population of interest (i.e., \(\Omega\)).

Assumption M3.1: Consistency the observed outcome equals the potential outcome under the treatment actually received, which requires well-defined interventions and rules out multiple versions of treatment and interference.

Assumption M3.3: Exchangeability (unconfoundedness)

\[Y(a)\perp\!\!\perp A\mid (L, S=1),\ \text{and}\ Y(b)\perp\!\!\perp A\mid (L, S=2)\]

If we do not have within trial randomization, we need to measure all important patient characteristics (\(L\)) to ensure treatment assignment is independent of potential outcomes.

Assumption M3.4: Transportability (Conditional exchangeability over inclusion): \[Y(a),Y(b)\perp\!\!\perp S\mid L\]

What we learn about a treatment in one trial can be applied to patients in the other trial, given measured covariates.

Information from patients on 6BPaLM in TB-PRACTECAL can tell us what would happen if endTB patients took 6BPaLM, and vice versa.

Assumption M3.5: Positivity — Treatment assignment

Within each trial, everyone must have a non-zero probability to receive each treatment.

Identification of the target casual parameter of interest \(\psi:=\mathbb{E}[Y(a) - Y(b) \mid \Omega],\) \[\begin{align} \psi(a, b) &:= \mathbb{E}[Y(a) - Y(b) \mid \Omega] \nonumber \\ &= \mathbb{E}_{L\mid S=1}[\mathbb{E}(Y \mid A = a, L, S =1)] \color{#E69F00}{\mathbb{P}_{\Omega}(S=1)} \\&\ \ \ \ - \mathbb{E}_{L\mid S=1}[\mathbb{E}(Y \mid A = b, L, S =2)] \color{#E69F00}{\mathbb{P}_{\Omega}(S=1)} \\ &\ \ \ \ + \mathbb{E}_{L\mid S=2}[\mathbb{E}(Y \mid A = a, L, S =1)] \color{#6b72ff}{\mathbb{P}_{\Omega}(S=2)} \nonumber \\ &\ \ \ \ - \mathbb{E}_{L\mid S=2}[\mathbb{E}(Y \mid A = b, L, S =2)] \color{#6b72ff}{\mathbb{P}_{\Omega}(S=2)}, \end{align}\] or equivalently, \(\psi\) can be identified as the following IPW form \[\begin{align}\label{psiid2} \psi(a, b) &= \mathbb{E}\!\left[\frac{\mathbb{I}(A=a)\mathbb{I}(S=1)Y}{\mathbb{P}_{\Omega}(A=a \mid L, S=1)}\right] + \mathbb{E}\!\left[\frac{\mathbb{I}(A=a)\mathbb{I}(S=1)Y\, \delta(L)}{\mathbb{P}_{\Omega}(A=a \mid L, S=1)}\right] \nonumber \\ &\quad - \mathbb{E}\!\left[\frac{\mathbb{I}(A=b)\mathbb{I}(S=2)Y\, \delta^{-1}(L)}{\mathbb{P}_{\Omega}(A=b \mid L, S=2)}\right]- \mathbb{E}\!\left[\frac{\mathbb{I}(A=b)\mathbb{I}(S=2)Y}{\mathbb{P}_{\Omega}(A=b \mid L, S=2)}\right], \end{align}\] where \(\delta(L):= \frac{\mathbb{P}_{\Omega}(S = 2 \mid L)}{\mathbb{P}_{\Omega}(S = 1 \mid L)} = \frac{1 - \mathbb{P}_{\Omega}(S = 1 \mid L)}{\mathbb{P}_{\Omega}(S = 1 \mid L)}.\)

\[\begin{align}\label{psiid} \psi(a, b) &:= \mathbb{E}[Y(a) - Y(b) \mid \Omega] \nonumber \\ &= \mathbb{E}_{L\mid S=1}[\mathbb{E}(Y \mid A = a, L, S =1)] \color{#E69F00}{\mathbb{P}_{\Omega}(S=1)} \\&\ \ \ \ - \mathbb{E}_{L\mid S=1}[\mathbb{E}(Y \mid A = b, L, S =2)] \color{#E69F00}{\mathbb{P}_{\Omega}(S=1)} \\ &\ \ \ \ + \mathbb{E}_{L\mid S=2}[\mathbb{E}(Y \mid A = a, L, S =1)] \color{#6b72ff}{\mathbb{P}_{\Omega}(S=2)} \nonumber \\ &\ \ \ \ - \mathbb{E}_{L\mid S=2}[\mathbb{E}(Y \mid A = b, L, S =2)] \color{#6b72ff}{\mathbb{P}_{\Omega}(S=2)}, \end{align}\] where \(\color{#E69F00}{\mathbb{P}_{\Omega}(S=1)}\) is the marginal probability of being selected into trial 1 within the target population.

The first term is the standard G-computation result of the trial 1,

\[\begin{align} \psi(a, b) &:= \mathbb{E}[Y(a) - Y(b) \mid \Omega] \nonumber \\ &= \color{#6b72ff}{\mathbb{E}_{L\mid S=1}}[ \mathbb{E}(Y \mid A = a, L, S =1)] \color{#E69F00}{\mathbb{P}_{\Omega}(S=1)} \\&\ \ \ \ - \dots \\ &\ \ \ \ + \dots \nonumber \\ &\ \ \ \ - \dots, \end{align}\] where subgroup-specific conditional means, i.e., \(\color{#6b72ff}{\mathbb{E}(Y \mid A = a, L, S =1)}\), are used to estimate the treatment effect for patients in trial 1.

\(\color{#6b72ff}{\mathbb{E}_{L\mid S=1}}[ \mathbb{E}(Y \mid A = a, L, S =1)]\) is

\[\begin{align} {\color{#6b72ff}{\sum_{l: \mathbb{P}(l, S=1) \neq 0 }\mathbb{E}(Y \mid A = a, L = l, S =1)} * \mathbb{P}(L = l \mid S=1)}. \end{align}\]

The second term uses the transportability of the trial 2 for the trial 1,

\[\begin{align} \psi(a, b) &:= \mathbb{E}[Y(a) - Y(b) \mid \Omega] \nonumber \\ &= \dots \\&\ \ \ \ - \color{#6b72ff}{\mathbb{E}_{L\mid S=1}}[ {\color{#FF6B6B}{\mathbb{E}(Y \mid A = b, L, S =2)}}] \color{#E69F00}{\mathbb{P}_{\Omega}(S=1)} \\ &\ \ \ \ + \dots \nonumber \\ &\ \ \ \ - \dots, \end{align}\] where subgroup-specific conditional means, i.e., \(\color{#FF6B6B}{\mathbb{E}(Y \mid A = b, L, S =2)}\), are fitted/estimated using data from trial 2.

\(\color{#6b72ff}{\mathbb{E}_{L\mid S=1}}[ {\color{#FF6B6B}{\mathbb{E}(Y \mid A = b, L, S =2)}}]\) is

\[\begin{align} \color{#6b72ff}{\sum_{l: \mathbb{P}(l, S=1) \neq 0 } } \color{#FF6B6B}{ \mathbb{E}(Y \mid A = b, L = l, S =2)} * \color{#6b72ff}{\mathbb{P}(L = l \mid S=1)}. \end{align}\]

We implement the Direct Method using three estimation method (1) g-computation (2) IPW and (3) one-step/doubly-robust estimation, where the one-step estimator is \[\begin{align} \hat{\psi}_{\text{1step}}(a, b) = \mathbb{P}_{\Omega, n}\{\varphi[\hat{\mu}_s(z, L), \hat{\pi}_s(z, L), \hat{g}(L)]\}, \end{align}\] \[\begin{align*} \varphi({\hat{\mu}}_s, \hat{\pi}_{s}, \hat{g}): & = \frac{\mathbb{I}(A = a, S = 1) }{\hat{\pi}_{1}(a, L)}\left[Y - \hat{\mu}_1(a, L) \right] + \mathbb{I}(S=1)\hat{\mu}_1(a, L) \\ &\ \ \ \ \ - \left[ \frac{\mathbb{I}(A = b, S = 2)}{\hat{\pi}_2(b, L)}\left[Y - \hat{\mu}_2(b, L) \right] + \mathbb{I}(S=2)\hat{\mu}_2(b, L) \right] \\ &\ \ + \frac{\mathbb{I}(A = a, S = 1) [1 - \hat{g}(L)] }{\hat{\pi}_1(a, L)\hat{g}(L)}\left[Y - \hat{\mu}_1(a, L) \right] + \mathbb{I}(S=2)\hat{\mu}_1(a, L) \\ &\ \ \ \ \ - \left[\frac{\mathbb{I}(A = b, S = 2) \hat{g}(L) }{\hat{\pi}_2(b, L) [1 - \hat{g}(L)] }\left[Y - \hat{\mu}_2(b, L) \right] + \mathbb{I}(S=1)\hat{\mu}_2(b, L) \right], \end{align*}\] \(\hat{g}(L):=\hat{\mathbb{P}}_{\Omega}(S = 1 \mid L),\) and \(\hat{\delta}(L) = \frac{1 - \hat{g}(L)}{\hat{g}(L)}\).

Statistical properities of one-step estimator, such as consistency and asymptotic normality, are established under standard regularity conditions.

We focus on a causal machine learning estimator in the main analysis.

• Can flexibly incorporate modern machine learning methods for nuisance estimation.
• Provides valid large-sample inference under standard regularity conditions.

One-step estimation:

Doubly-Robust: The one-step estimator is consistent if either the outcome model or the inclusion and treatment model is correctly specified.

1. Outcome Model: Predicts what the outcome would be under each treatment, given patient characteristics, \(\mu_s(z, L) = \E(Y\mid L,A=z,S=s)\) for any \((s, z) \in \{(1, a), (2, b)\}.\)

2. Inclusion and Treatment Model: The trial inclusion (i.e., \(g(L) := \mathbb{P}_{\Omega}(S=1\mid L)\)) and treatment mechanism (i.e., \(\mathbb{P}_{\Omega}(A=z\mid L,S=s)\)) are consistently estimated.

Instead of directly comparing 6BPaLM vs. 9-month regimens, we can decompose the total difference into two components: (1) the difference in treatment effects, and (2) the difference in standard care arms across trials.

• Component 1: Treatment Effect Difference (\(\theta\))
  • Captures how much better each investigational regimen is compared to its own control, i.e., \(\theta := \mathbb{E}[Y(a)-Y(c_1)\mid\Omega] - \mathbb{E}[Y(b)-Y(c_2)\mid\Omega]\)
• \((\text{Effect of 6BPaLM vs. SC1}) - (\text{Effect of 9-month regimen vs. SC2})\)

• (A4.1) Consistency
  

• (A4.2) No trial engagement effects: for every treatment \(z\) and every trial \(s\), \(Y(s, z) = Y(z)\).

• (A4.3) Exchangeability within each trial

  • Trial 1: \(Y(a), Y(c_1)\perp\!\!\perp A \mid L,S=1\)
    
  • Trial 2: \(Y(b), Y(c_2)\perp\!\!\perp A \mid L,S=2\)

• (A4.4) Positivity of treatment within trial

• (A4.5) Transportability :

  • for \(\phi,\) \(Y(c_1),Y(c_2)\perp\!\!\perp S\mid V\); where \(V=\text{country};\) (standard-of-care is typically defined at the national level, often guided by WHO, and implemented through country-specific clinical guidelines.)
  • for \(\theta,\) \(Y(a),Y(b)\perp\!\!\perp S\mid L\)

• (A4.6) Positivity of trial inclusion

  • For any covariate profile \(L\), a subject must have a non-zeor probability to be in both trials.