A Trial of Bardoxolone Methyl in Patients With CKD at Risk of Rapid Progression (MERLIN): Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for A Trial of Bardoxolone Methyl in Patients With CKD at Risk of Rapid Progression (MERLIN) (NCT04702997), a randomized phase 2 study. The primary outcome is Change From Baseline in Estimated Glomerular Filtration Rate (eGFR) at Week 12.

2. Clinical Question

3. Trial Design

MERLIN was a randomized, parallel-group Phase 2 trial, with triple masking recorded in the registry. The study compared bardoxolone methyl with placebo in people with chronic kidney disease at risk of rapid progression. Its status is completed. The registry lists Biogen as sponsor. The recorded study dates are a start date of 2021-02-09 and a primary completion date of 2021-10-20.

The registry summary describes a planned enrollment of approximately 70 and randomization in a 1:1 ratio. The recorded enrollment was 81. The posted arm sizes for the primary outcome are 39 for bardoxolone methyl and 42 for placebo. The registry record does not explain the difference between the approximate enrollment stated in the summary and the final enrollment.

Participants were assigned to once-daily bardoxolone methyl or placebo for a 12-week dosing period. The bardoxolone methyl dose began at 5 mg and was titrated to a maximum determined by baseline UACR: 20 mg at or below 300 mg/g and 30 mg above 300 mg/g. The placebo group followed the same titration schedule to maintain masking. Both arms were scheduled for the same visits and assessments during treatment, including assessments at Day 1 and Weeks 1, 2, 4, 6, 8, and 12, with telephone contacts also described in the registry summary.

The summary further describes a 5-week off-treatment period after the 12-week dosing period, with assessments intended to characterize eGFR after treatment. The primary endpoint, however, is specified as change from baseline at Week 12. Details of the randomization procedure, allocation concealment, masking roles, and the trial's original sample-size justification are not reported in the registry record.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: Intent-to-treat population (all enrolled patients whether or not they received the study drug)

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

6. Primary Endpoint

The registry lists the primary outcome as Change From Baseline in Estimated Glomerular Filtration Rate (eGFR) at Week 12, measured over Baseline through 12 weeks after participant receives the first dose.

The primary endpoint is change from baseline in estimated glomerular filtration rate at Week 12, measured in mL/min/1.73 m^2. eGFR is an estimate of kidney function derived from blood or serum assessment. The registry states that higher eGFR values represent better or improved kidney function and lower values represent poorer or decreased kidney function. Expressing the outcome as change from baseline focuses the comparison on how the measured value changed over the treatment period, rather than only on the endpoint value.

The registry reports a least-squares mean for each group and a least-squares mean difference between groups. A mean summarizes the group-level average, while the least-squares mean is an estimate from a statistical model. The model specification is not reported in the registry record. The stated analysis population is intent-to-treat: all enrolled patients, whether or not they received study drug. This definition describes who is intended to contribute to the primary analysis, but does not by itself explain how missing Week 12 measurements were handled.

Using eGFR makes the endpoint a continuous measure, so the result describes an average change in a laboratory-derived estimate. It does not describe the number of participants who reached a particular kidney outcome, nor does it establish how individual participants changed. The primary endpoint's timeframe is baseline through 12 weeks after the first dose.

7. Results Posted in the Registry

• Bardoxolone Methyl: mean 6.79 versus -0.92 on control; difference 7.71 (95% CI 5.22 to 10.20), standardized effect d = 1.35; z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is continuous: each participant's eGFR change can take a range of values, and the group result is expressed as a mean. This differs from a binary outcome, such as whether an event occurred, and from a time-to-event outcome, which concerns the timing of an event. The registry reports least-squares means and a least-squares mean difference for the primary comparison. A least-squares mean is generally a model-based estimate of a group mean, potentially accounting for variables specified in the model. Which variables or covariance structures were used in this trial is not reported in the registry record, so the reported estimate cannot be reconstructed from the description alone.

What does the mean difference represent?

The recorded mean changes are 6.79 mL/min/1.73 m^2 in the bardoxolone methyl arm and -0.92 mL/min/1.73 m^2 in the placebo arm. The recalculated contrast is 7.71 mL/min/1.73 m^2, defined as bardoxolone methyl minus placebo. It is an unadjusted calculation from the posted group summaries. In general, a mean difference expresses the average separation between groups on the measured scale. Its interpretation depends on the direction and meaning of that scale: the registry states that higher eGFR represents better or improved kidney function.

What does the standard error describe?

The posted group dispersion values are standard errors: 0.925 for bardoxolone methyl and 0.868 for placebo. In general, a standard error describes the sampling uncertainty of an estimated statistic, such as a mean; it is not the same as the spread of individual participant measurements. Smaller standard errors generally indicate more precise estimates under the statistical model and sampling assumptions. The registry does not post the individual observations or the standard deviations for the outcome, so the recalculation uses an approximate standard deviation derived from the reported standard errors and group sizes. That approximation is identified in the statistical calculation and is not a direct summary of the observed participant-level variability.

How should the p-value be read?

A p-value describes how compatible the data are with a specified null hypothesis under the statistical model and its assumptions. It is not the probability that the null hypothesis is true, nor does it measure the size or clinical importance of an effect. The recalculated unadjusted p-value is <0.001; the sponsor's Mixed Models Analysis reports p < 0.001. These are results from different analyses and should be read with their methods in mind. The exact model details for the sponsor's analysis are not reported in the registry record.

Why can a model-based estimate differ from an unadjusted calculation?

In general, a model-based analysis may account for repeated measurements, baseline values, or other prespecified factors, while an unadjusted calculation uses only a simpler comparison of the posted summaries. This trial's reported method is Mixed Models Analysis, but the registry record does not describe its model terms, covariance structure, or estimation details. The sponsor's contrast is 7.71, matching the recalculated point estimate as posted, while the reported confidence limits differ slightly from the recalculated interval. A matching point estimate does not mean the uncertainty calculations or analysis procedures are identical.

What is over-dispersion, and is it relevant?

In general, over-dispersion occurs when the observed variability in data exceeds what a statistical model assumes. It is especially discussed for count outcomes and some binary-data models, where underestimating variability can make uncertainty appear too small. The primary endpoint in MERLIN is continuous eGFR change, and the registry does not report an over-dispersion assessment. It would therefore be inappropriate to claim that over-dispersion was present or that a correction was used. More generally, any model's uncertainty estimate depends on whether its assumptions reasonably describe the data.

What does randomization contribute?

In general, random assignment is intended to make the treatment groups comparable on average with respect to measured and unmeasured baseline characteristics. The registry identifies the study as randomized, but does not report the sequence generation method, allocation concealment details, or group-specific baseline characteristics in the information summarized for this analysis. Randomization supports a comparative interpretation but does not remove the need to examine conduct, adherence, missing outcome data, and analysis methods.

The statistical methods described by the registry are limited to the reported Mixed Models Analysis, the primary endpoint, and its posted result. The model specification, handling of missing data, any covariate adjustment, analysis diagnostics, and any interim analyses are not reported in the registry record. General explanations of statistical concepts do not fill in those trial-specific details.

10. Confidence Intervals and Precision

The sponsor's reported estimate is a least-squares mean difference of 7.71 mL/min/1.73 m^2, with a 95% confidence interval from 5.18 to 10.24. The unadjusted recalculation gives the same point estimate, 7.71, with a 95% confidence interval from 5.224 to 10.2. Both intervals are entirely above zero. The limits differ because the sponsor's Mixed Models Analysis and the simple recalculation use different reported or inferred uncertainty calculations; the registry does not provide enough model detail to reproduce the sponsor's interval.

In general, a confidence interval conveys uncertainty around an estimate by identifying values that remain compatible with the data and the analysis assumptions. It is not a guarantee that the true value lies in the interval, nor does it describe the range of individual participant outcomes. A narrower interval indicates greater statistical precision than a wider interval, all else being comparable. Precision depends on factors including sample size, variability, and the analysis approach.

The posted arm sizes are 39 and 42, and the standard errors of the arm means are 0.925 and 0.868. Those summaries indicate that the reported average changes are estimated with finite uncertainty. The interval's width should be interpreted alongside the measured scale and the trial's limitations; it does not by itself establish whether a difference is clinically important. The registry record does not report a clinically meaningful threshold for the eGFR contrast.

The sponsor's interval is the reported model-based result, while the recalculated interval is an approximate, unadjusted check. Since the registry indicates no discrepancy flag, the two results are broadly aligned in their point estimate and direction. They are not interchangeable: their methods and uncertainty limits should remain identified separately.

11. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

The planning estimates are illustrative calculations based on the observed effect, not the trial's original design justification. For this continuous outcome, the reported planning figures are participants per arm, not total events. The calculation assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each planning row uses a stated fraction of the observed effect: 100%, 75%, or 50%.

For planning at 100% of the observed effect, the estimate is 9 participants per arm for 80% power and 12 participants per arm for 90% power. At 75% of the observed effect, the estimates are 16 participants per arm for 80% power and 21 participants per arm for 90% power. At 50% of the observed effect, they are 35 participants per arm for 80% power and 46 participants per arm for 90% power.

Power is the probability, under a specified effect and statistical assumptions, that a planned study will detect an effect of that size at the chosen significance level. The 80% column represents a planning target with an 80% chance of detecting the assumed effect under those assumptions; the 90% column uses a higher target. Smaller effects require more participants to distinguish them from random variation with comparable power, which is why the estimates increase as the assumed fraction decreases.

These are planning illustrations based on the observed effect and are not observed power. The trial's original sample-size justification and its original planning assumptions are not reported in the registry record. These illustrations should not be treated as evidence that the completed trial was designed using the listed assumptions or participant counts.

12. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = 7.710; pooled standard deviation σ = 5.699.
2. n = 2 × (1.96 + 0.842)² × 5.699² / 7.710² = 8.6, rounded up to 9 participants per arm for 80% power.

The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
delta <- 7.71                      # observed difference in means
sigma <- 5.6985811891751                     # pooled standard deviation
n_per_arm <- function(power, frac = 1) {
  ceiling(round(2 * (z_a + qnorm(power))^2 * sigma^2 / (delta * frac)^2, 6))
}
for (f in c(1, 0.75, 0.5))
  cat(sprintf("%3.0f%% of observed effect: n per arm = %s (80%% power), %s (90%% power)\n", 100 * f,
              format(n_per_arm(0.80, f), big.mark = ","), format(n_per_arm(0.90, f), big.mark = ",")))

# Check against R's built-in function (t-based, so very slightly larger)
cat("power.t.test:", round(power.t.test(delta = delta, sd = sigma, power = 0.80)$n, 1), "\n")

# Simulation: exact two-sample t-test using simulated means and variances
set.seed(4702997)
n    <- n_per_arm(0.80)
reps <- 20000
m_diff <- rnorm(reps, delta, sigma * sqrt(2 / n))             # difference in sample means
s2     <- sigma^2 * rchisq(reps, 2 * (n - 1)) / (2 * (n - 1))   # pooled sample variance
tstat  <- m_diff / sqrt(s2 * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(tstat) > qt(0.975, 2 * (n - 1))), reps))

Output from running the code

100% of observed effect: n per arm = 9 (80% power), 12 (90% power)
 75% of observed effect: n per arm = 16 (80% power), 21 (90% power)
 50% of observed effect: n per arm = 35 (80% power), 46 (90% power)
power.t.test: 9.6 
Simulated power at n = 9 per arm: 0.770 (20000 replicates)

The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

13. Analyses Reported by the Sponsor

The sponsor's reported primary analysis is a Mixed Models Analysis. It gives a least-squares mean difference of 7.71 mL/min/1.73 m^2, a 95% confidence interval from 5.18 to 10.24, and p < 0.001. The registry classifies this as a superiority analysis. This is the sponsor's model-based analysis and is the result to use when describing the sponsor's reported inference.

The recalculation is a simple unadjusted comparison based on the posted arm means, standard errors, and sample sizes. It estimates the same mean difference, 7.71, with a 95% confidence interval from 5.224 to 10.2 and an unadjusted p-value of <0.001. The point estimates agree as posted, while the confidence limits and p-values differ. The recalculation is not a replacement for the sponsor's analysis and does not reproduce the Mixed Models Analysis.

The registry does not report the full model specification, so the source of the difference in uncertainty estimates cannot be determined from the record. The two analyses are directionally aligned and both report intervals above zero. Their distinct methods and outputs should nevertheless be kept clear: the sponsor's analysis is the registry-reported result, and the recalculation is an approximate, unadjusted cross-check.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists one primary outcome measure and one reported analysis for the comparison. It records no posted secondary outcome analyses. The information available does not describe whether additional endpoints, time points, subgroup comparisons, or other hypotheses were assessed outside the posted result. A multiplicity adjustment plan, if any, is not reported in the registry record.

In general, multiplicity arises when several statistical hypotheses are tested. Conducting more tests can increase the chance that at least one result appears statistically notable by chance, so a prespecified testing strategy or adjustment may be important. Whether such an issue applies depends on the full set of analyses and their intended interpretation. The registry's single listed primary analysis does not establish that no other analyses were conducted; their status is not reported in the registry record.

The stated primary population is intent-to-treat, defined in the record as all enrolled patients whether or not they received study drug. The registry reports arm sizes of 39 and 42 for the primary outcome. It does not report the number with an observed Week 12 measurement, the amount or pattern of missing outcome data, reasons for missingness, or the method used to handle missing values. The term intent-to-treat describes the analysis population but does not alone specify how incomplete measurements were included in a model or otherwise addressed.

Details of exclusions, protocol deviations, treatment adherence, and sensitivity analyses are not reported in the registry record. The Mixed Models Analysis is named, but the model's assumptions about repeated measures and missing data are not described. In general, conclusions from an analysis can depend on whether missingness and model assumptions are reasonable. Without the relevant details, these aspects cannot be evaluated from the registry entry.

The record also does not report interim analyses, stopping rules, or a detailed statistical analysis plan. These omissions should be understood as limits on what can be assessed from the registry record, not as evidence that any particular method was or was not used.

15. Safety Results

The registry reports serious adverse events as affected participants divided by participants at risk.

Deaths

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 2% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: gastrooesophageal reflux disease (2.6%), biliary dyskinesia (2.6%), acute kidney injury (2.6%), small intestinal obstruction (2.4%).

The registry reports serious adverse events for 3 of the 39 participants at risk in the bardoxolone methyl group and 1 of the 42 participants at risk in the placebo group. It reports zero deaths in each group. These figures describe participants with at least one serious adverse event as recorded in the registry, not the total number of all adverse events or a comparison adjusted for exposure time.

The listed serious adverse event terms and percentages are gastrooesophageal reflux disease at 2.6%, biliary dyskinesia at 2.6%, acute kidney injury at 2.6%, and small intestinal obstruction at 2.4%. The registry listing does not identify the arm for each of these terms in the information, so they should not be assigned to a particular group. Percentages and counts also describe different aspects of event reporting: the counts give participants affected by any serious adverse event in each group, while the term list reports specific entries.

In general, safety counts in a trial of this size describe events observed during the recorded study period; they do not establish the likelihood of uncommon or later events. The registry entries do not provide event timing, duration, relatedness assessments, or exposure-adjusted comparisons. No conclusion about comparative safety beyond these recorded figures is warranted from these data alone.

16. What the Result Does, and Does Not, Mean

The primary result is an estimated difference in mean Week 12 eGFR change between the bardoxolone methyl and placebo groups. The posted means are 6.79 mL/min/1.73 m^2 and -0.92 mL/min/1.73 m^2, respectively, and the sponsor reports a least-squares mean difference of 7.71. Its 95% confidence interval is 5.18 to 10.24, with p < 0.001. The unadjusted recalculation gives the same point estimate and an interval from 5.224 to 10.2, with p <0.001.

These results describe an average difference on the measured eGFR scale in the recorded intent-to-treat population. They do not state that every participant experienced the group-average change, and they do not describe the distribution of individual responses. The registry explains that higher eGFR represents better or improved kidney function, but the primary endpoint remains a laboratory-derived estimate rather than a complete description of kidney health or a direct count of clinical events.

The result does not establish what happened after the Week 12 primary endpoint, despite the registry summary's description of a later off-treatment assessment period. No secondary outcome analysis is posted in the record. The result also does not establish effects in groups defined by age, kidney disease cause, UACR, or other characteristics; subgroup estimates are not reported in the registry record.

Statistical evidence against a zero mean difference is not equivalent to proof of clinical importance. The registry does not report a threshold for a clinically meaningful difference. Nor do the confidence intervals address every potential source of uncertainty, including missing data, model assumptions, trial conduct, or the applicability of the enrolled population to other settings.

MERLIN was a completed Phase 2 trial with 81 enrolled participants and a 12-week dosing period. Its result is evidence about the recorded comparison and endpoint in that trial. It should not be extended beyond the measured outcome, time period, and population without additional evidence.

17. Why This Trial Matters Statistically

This trial offers a useful example of how a continuous clinical outcome can be summarized by group means and a between-group contrast. The outcome is change in eGFR, and the reported estimate is expressed in the same units as the measurement. That makes the direction and scale of the comparison explicit: the sponsor's estimate is a positive least-squares mean difference of 7.71 mL/min/1.73 m^2.

It also illustrates why a point estimate should be read with its uncertainty. The sponsor's 95% confidence interval ranges from 5.18 to 10.24, while the unadjusted recalculation ranges from 5.224 to 10.2. Both are above zero, but the intervals are not identical because the sponsor's model-based analysis and the approximate unadjusted calculation are not the same procedure. Distinguishing the reported analysis from a simple recalculation is important for transparent interpretation.

The record makes several design features clear: randomization, parallel groups, triple masking, the two interventions, and the primary endpoint. It also leaves important statistical details unreported, including the full mixed-model specification, handling of missing outcomes, and original sample-size justification. This contrast between recorded results and unavailable analytic detail is a practical reminder that precision in a numerical result does not substitute for transparency about methods.

The planning illustrations further show how sample-size estimates depend on the effect assumed for planning. Smaller assumed effects require more participants under the stated calculation assumptions. Because the illustrations use the observed effect and do not represent the trial's original design rationale, they answer a planning question rather than describing the trial's achieved power.

Finally, the serious adverse event figures show why safety summaries need denominators and clear definitions. Counts of participants affected are distinct from event-specific percentages and do not, by themselves, provide an exposure-adjusted or comprehensive assessment. Each statistic answers a particular question, and interpretation depends on keeping those questions separate.

18. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.

The posted primary result is based on 81 enrolled participants, with 39 in the bardoxolone methyl arm and 42 in the placebo arm. The registry describes the study as Phase 2 and a 12-week dosing trial. The result therefore comes from a defined trial population and period; the record does not establish how broadly it applies beyond those conditions.

The registry summary describes eligibility including ages 18-70 years, eGFR from 20 to less than 60 mL/min/1.73 m^2, and other risk factors for rapid progression, with chronic kidney disease from multiple causes. It does not provide the baseline characteristics needed to assess the composition of the enrolled population in detail. The representation of particular kidney disease causes or risk profiles is not reported in the registry record.

Although the sponsor names a Mixed Models Analysis, the registry does not describe the model specification or its assumptions. It also does not report the amount of missing Week 12 data, the method for handling missing measurements, or sensitivity analyses. These gaps limit the ability to reproduce or fully evaluate the sponsor's result. The recalculated interval uses an approximate standard deviation derived from posted standard errors and group sizes, so it is not a participant-level reanalysis.

The record lists only the primary outcome analysis and no posted secondary analyses. Multiplicity procedures, interim analyses, and detailed original sample-size assumptions are not reported in the registry record. The planning illustrations use the observed effect and should not be mistaken for the trial's design calculations.

The safety information includes serious adverse event counts, deaths, and selected event terms, but does not report timing, relatedness, duration, or exposure-adjusted rates in the information summarized. These limitations constrain interpretation of the posted safety figures. The registry summary also describes a 5-week off-treatment period, but no result for that period is included among the posted primary outcome analyses.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: A Trial of Bardoxolone Methyl in Patients With CKD at Risk of Rapid Progression (MERLIN) — NCT04702997.
• Registry record last updated 2025-06-03; status last verified 2025-05.
• Results first posted 2022-12-01.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

22. Record Summary

MERLIN (NCT04702997) is a completed randomized, parallel-group, triple-masked Phase 2 trial sponsored by Biogen. It enrolled 81 participants with chronic kidney disease at risk of rapid progression and compared once-daily bardoxolone methyl with placebo during a 12-week dosing period.

The primary outcome was change from baseline in eGFR at Week 12. The sponsor's Mixed Models Analysis reported a least-squares mean difference of 7.71 mL/min/1.73 m^2, with a 95% confidence interval from 5.18 to 10.24 and p < 0.001. The unadjusted recalculation gave the same point estimate, with a 95% confidence interval from 5.224 to 10.2 and p <0.001.

The registry reports serious adverse events in 3 participants in the bardoxolone methyl group and 1 in the placebo group, with zero deaths in either group. Model details, missing-data methods, and the trial's original sample-size justification are not reported in the registry record.