Package 'benchexcal'

Three RCT-DUPLICATE / ENCORE agreement metrics

Description

For an RCT-database study pair (or RCT vs. emulation), computes the three pre-specified binary agreement metrics used in RCT-DUPLICATE (Wang et al., JAMA 2023) and ENCORE (Weberpals et al., CPT 2026): statistical significance agreement (SA), estimate agreement (EA), and standardized difference / SMD agreement (SD).

Usage

agreement(
  rct_hr,
  rct_lower,
  rct_upper,
  rwe_hr,
  rwe_lower,
  rwe_upper,
  trial_type = c("superiority", "noninferiority"),
  ni_margin = NULL
)

Arguments

rct_hr	Numeric. Point estimate (HR) from the RCT.
rct_lower, rct_upper	Numeric. 95% CI bounds for the RCT HR.
rwe_hr	Numeric. Point estimate (HR) from the database study.
rwe_lower, rwe_upper	Numeric. 95% CI bounds for the RWE HR.
trial_type	One of "superiority" (default) or "noninferiority". If "noninferiority", ni_margin should also be supplied to enable partial significance agreement (SAP).
ni_margin	Numeric on the HR scale (e.g. 1.3). The non-inferiority margin defined by the trial protocol. Only used when trial_type = "noninferiority".

Details

Metric definitions follow Wang et al. (JAMA 2023):

• SA (statistical significance agreement): TRUE when both point estimates AND both 95% CIs sit on the same side of the null (HR = 1). For non-inferiority trials, partial SA (SAP) is flagged if the database upper bound lies below the NI margin, even when the RCT was not powered for superiority.

• EA (estimate agreement): TRUE when the database point estimate falls inside the RCT 95% CI.

• SD (standardized difference): TRUE when |z| < 1.96, where

  $z = \frac{\log(\mathrm{HR}_{RCT}) - \log(\mathrm{HR}_{RWE})}{\sqrt{\mathrm{var}(\log\mathrm{HR}_{RCT}) + \mathrm{var}(\log\mathrm{HR}_{RWE})}}$

  and each variance is derived from its 95% CI via SE = (log(UL) - log(LL)) / (2 * 1.96).

Value

An object of class bx_agreement (a list). Use print() or summary() for formatted output.

References

Wang SV, Schneeweiss S, RCT-DUPLICATE Initiative. Emulation of randomized clinical trials with nonrandomized database analyses: results of 32 clinical trials. JAMA. 2023;329(16):1376-1385.

Weberpals J, Schneeweiss S, et al. Emulating Comparative Oncology Trials With Real-World Evidence Studies (ENCORE). Clin Pharmacol Ther. 2026.

Examples

# LEADER trial (Wang et al., JAMA 2023, Table 1, study #1)
agreement(
  rct_hr = 0.87, rct_lower = 0.78, rct_upper = 0.97,
  rwe_hr = 0.82, rwe_lower = 0.76, rwe_upper = 0.87
)

# PRONOUNCE (noninferiority, NI margin 1.225)
agreement(
  rct_hr = 1.28, rct_lower = 0.59, rct_upper = 2.79,
  rwe_hr = 1.35, rwe_lower = 0.94, rwe_upper = 1.93,
  trial_type = "noninferiority", ni_margin = 1.225
)

---

BenchExCal calibration of a Stage 2 RWE estimate

Description

Implements the Benchmark, Expand, Calibrate (BenchExCal) framework (Wang et al., Clin Pharmacol Ther 2025): uses the divergence observed between a Stage 1 RCT and its database emulation to calibrate the point estimate and 95% CI of a Stage 2 database study designed to inform a supplemental indication (no Stage 2 RCT yet).

Usage

calibrate(
  stage1_rct_hr,
  stage1_rct_lower,
  stage1_rct_upper,
  stage1_rwe_hr,
  stage1_rwe_lower,
  stage1_rwe_upper,
  stage2_rwe_hr,
  stage2_rwe_lower,
  stage2_rwe_upper,
  check_benchmark = TRUE
)

Arguments

stage1_rct_hr, stage1_rct_lower, stage1_rct_upper	Stage 1 RCT HR and 95% CI.
stage1_rwe_hr, stage1_rwe_lower, stage1_rwe_upper	Stage 1 database study HR and 95% CI (emulation of the Stage 1 RCT).
stage2_rwe_hr, stage2_rwe_lower, stage2_rwe_upper	Stage 2 database study HR and 95% CI (the supplemental indication).
check_benchmark	Logical. If TRUE (default), the Stage 1 RCT-RWE pair is evaluated with agreement and a warning is issued if all three agreement metrics fail (per BenchExCal, calibration should not proceed in that case).

Details

Let $\hat\theta_1$, $\hat\theta^*_1$, and $\hat\theta^*_2$ denote the Stage 1 RCT, Stage 1 RWE, and Stage 2 RWE log hazard ratios, with variances $V_1, V^*_1, V^*_2$. The Stage 1 divergence is

$\hat\xi_1 = \hat\theta^*_1 - \hat\theta_1.$

Following Wang et al. (CPT 2025), the rescaled Stage 2 divergence is

$\hat\xi_2 = \sqrt{V^*_2 / V^*_1}\, \hat\xi_1,$

and the calibrated Stage 2 log HR is

$\hat\theta_{2,\mathrm{cal}} = \hat\theta^*_2 - \hat\xi_2,$

with variance inflated by the Stage 1 divergence uncertainty,

$V_{2,\mathrm{cal}} = V^*_2 + (V^*_1 + V_1)\, \frac{V^*_2}{V^*_1}.$

Sign convention. The paper writes the mean as $\hat\theta^*_2 + \hat\xi_2$. Because $\xi = \theta^* - \theta$ (RWE minus RCT) is defined as the systematic bias, bias correction is a subtraction; this implementation uses $\hat\theta^*_2 - \hat\xi_2$. If you would rather match the paper's formula literally, negate the returned xi_hat_2 before applying.

Value

An object of class bx_calibration.

References

Wang SV, Russo M, Glynn RJ, et al. A Benchmark, Expand, and Calibration (BenchExCal) Trial Emulation Approach for Using Real-World Evidence to Support Indication Expansions. Clin Pharmacol Ther. 2025;117(6):1820-1828.

Examples

# Stage 1: LEADER liraglutide (RCT-DUPLICATE)
# Stage 2: hypothetical expanded indication, RWE only
cal <- calibrate(
  stage1_rct_hr = 0.87, stage1_rct_lower = 0.78, stage1_rct_upper = 0.97,
  stage1_rwe_hr = 0.82, stage1_rwe_lower = 0.76, stage1_rwe_upper = 0.87,
  stage2_rwe_hr = 0.85, stage2_rwe_lower = 0.78, stage2_rwe_upper = 0.93
)
print(cal)

---

Print the inputs required for BenchExCal calibration

Description

A quick reference that prints what you need to supply to calibrate. Call this if you forget which six (or nine) HR/CI values calibrate() expects.

Usage

calibration_inputs()

Value

Invisibly returns NULL. Called for the printed side effect.

Examples

calibration_inputs()

---

Forest plot for a BenchExCal calibration

Description

Plots the Stage 1 RCT, Stage 1 RWE, Stage 2 RWE (uncalibrated), and Stage 2 RWE (calibrated) HRs on a single log-scale forest plot.

Usage

## S3 method for class 'bx_calibration'
plot(x, ...)

Arguments

x	A bx_calibration object.
...	Currently unused.

Value

A ggplot object.

---

Tipping-point plot

Description

Visualises how the Stage 2 calibrated HR (with CI) shifts as a function of the assumed Stage 2 divergence $\xi_2$.

Usage

## S3 method for class 'bx_tipping'
plot(x, ...)

Arguments

x	A bx_tipping object.
...	Currently unused.

Value

A ggplot object.

---

Selected RCT-DUPLICATE trial emulation results

Description

Effect estimates (pooled, adjusted) from selected trials in Wang et al. (JAMA 2023), useful for testing and illustrating agreement and calibrate.

Usage

data(rct_duplicate)

Format

A data frame with the following columns:

trial

Trial acronym.

rct_hr, rct_lower, rct_upper

RCT HR and 95% CI.

rwe_hr, rwe_lower, rwe_upper

Database study (adjusted, pooled) HR and 95% CI.

trial_type

"superiority" or "noninferiority".

ni_margin

NI margin on the HR scale, or NA.

Source

Wang SV et al., JAMA 2023;329:1376-1385, Table 1.

---

Tipping point sensitivity analysis for BenchExCal calibration

Description

Sweeps over a range of plausible Stage 2 divergence values $\xi_2$ (by default from the 5th to the 95th percentile of the BenchExCal prior on $\xi_2$) and reports the calibrated Stage 2 HR at each point. The tipping point is the value of $\xi_2$ at which the calibrated 95% CI just crosses the decision threshold (HR = 1 by default).

Usage

tipping_point(x, n_grid = 200, quantile_range = c(0.05, 0.95), threshold = 1)

Arguments

x	A bx_calibration object returned by calibrate.
n_grid	Integer. Number of grid points to evaluate (default 200).
quantile_range	Length-2 numeric. Quantile range of the $\xi_2$ prior to scan (default c(0.05, 0.95)).
threshold	Numeric on the HR scale. Decision threshold for the tipping point (default 1, i.e., the null).

Details

At each grid value of $\xi_2$, the function computes

$\hat\theta_2(\xi_2) = \log(\hat{\mathrm{HR}}^*_2) - \xi_2$

and constructs a 95% CI using the uncalibrated Stage 2 standard error (the prior uncertainty in $\xi_2$ is already represented by the breadth of the scan itself, so additional variance inflation would double-count). The first grid point at which the relevant CI bound crosses the threshold is returned as the tipping point.

Value

An object of class bx_tipping.

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