This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.
1. Trial at a Glance
This page covers the registry results for Dose-Finding Study of Vadadustat in Japanese Subjects With Anemia Secondary to Dialysis-Dependent Chronic Kidney Disease (DD-CKD) (NCT03054350), a randomized phase 2 study. The primary outcome is Mean Change in Hemoglobin (Hb) Levels From Pre-treatment to the End of the Primary Efficacy Period.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT03054350 |
| Phase | Phase 2 |
| Condition | Anemia, Dialysis Dependent Chronic Kidney Disease |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Triple |
| Enrollment | 60 |
| Arms in the primary outcome | 4 |
| Lead sponsor | Akebia Therapeutics |
| Results posted | Yes |
2. Clinical Question
Population
Japanese participants with anemia secondary to dialysis-dependent chronic kidney disease. The primary analysis population was the modified Intent-to-Treat population: randomized participants who received at least 1 dose, had a pre-treatment hemoglobin average, and had at least one post-Baseline hemoglobin measurement.
Intervention
Daily oral vadadustat, assigned at 150 mg, 300 mg, or 600 mg.
Comparator
Daily oral placebo.
Primary question
How did mean hemoglobin change from the pre-treatment average to Week 6 in each vadadustat dose group compared with placebo?
The endpoint is a continuous measure of hemoglobin concentration, expressed in grams per deciliter. The registry record describes the pre-treatment value as the average of 3 measurements: the qualifying screening value and the Baseline value, with a third value included in the stated average. Change was defined as the Week 6 value minus the pre-treatment average. A positive change therefore indicates a higher Week 6 value than the pre-treatment average, while a negative change indicates a lower value.
The central statistical question is about the average difference between assigned groups over this endpoint and the precision of that estimate. It is not, by itself, a complete assessment of the treatment’s safety, longer-term outcomes, or effects beyond the measured study period. The listed primary efficacy period ends at Week 6; the registry also lists additional outcomes across later study periods.
3. Trial Design
This was a Phase 2, randomized, double-blind, placebo-controlled, dose-finding study of orally administered vadadustat. The registry describes a parallel-group design and triple masking. The study enrolled 60 participants and is recorded as completed. The listed start is 2016-12, and the primary completion date is 2017-10-24.
Participants were assigned to daily oral vadadustat at 150 mg, 300 mg, or 600 mg, or to daily oral placebo. The primary outcome analysis reports group sizes of 15 for vadadustat 150 mg, 15 for vadadustat 300 mg, 14 for vadadustat 600 mg, and 14 for placebo. These are the analysis counts shown for the endpoint, not a reconstruction of every participant’s path through the trial. The record does not report the original sample-size justification or the planned allocation ratio.
The primary endpoint compares mean hemoglobin change from the pre-treatment average to Week 6. The endpoint’s population is the modified Intent-to-Treat population, defined in the registry by randomization, receipt of at least 1 dose, a pre-treatment average, and at least one post-Baseline hemoglobin measurement. The sponsor’s reported group comparisons used ANCOVA and are described as least-squares mean differences.
The study’s dose-finding purpose and the inclusion of three active-dose groups make the dose-specific estimates important to read separately. The registry record does not report the covariates used in the ANCOVA, the original power target, or the planned approach to interim analyses. Such details should not be inferred from the results or from the displayed planning illustrations.
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.
Before assignment: Participants who had not recently received erythropoiesis-stimulating agent (ESA) therapy participated in 2 screening visits (SVs). Participants who had recently received ESA therapy and otherwise met the eligibility criteria were required to washout from ESA therapy prior to evaluation of screening hemoglobin levels and participate in 3 SVs.
Primary Efficacy Period (6 Weeks)
| Stage | Vadadustat 150 mg | Vadadustat 300 mg | Vadadustat 600 mg | Placebo to Vadadustat 150 mg | Placebo to Vadadustat 300 mg | Placebo to Vadadustat 600 mg |
|---|---|---|---|---|---|---|
| STARTED | 15 | 15 | 15 | 5 | 5 | 5 |
| COMPLETED | 11 | 13 | 13 | 3 | 1 | 2 |
| NOT COMPLETED | 4 | 2 | 2 | 2 | 4 | 3 |
Reasons for not completing this period:
| Reason | Vadadustat 150 mg | Vadadustat 300 mg | Vadadustat 600 mg | Placebo to Vadadustat 150 mg | Placebo to Vadadustat 300 mg | Placebo to Vadadustat 600 mg |
|---|---|---|---|---|---|---|
| ESA Rescue/Blood Transfusion for Anemia | 4 | 2 | 1 | 2 | 4 | 3 |
| Withdrawal by Subject | 0 | 0 | 1 | 0 | 0 | 0 |
Dose Adjustment and Maintenance Period
| Stage | Vadadustat 150 mg | Vadadustat 300 mg | Vadadustat 600 mg | Placebo to Vadadustat 150 mg | Placebo to Vadadustat 300 mg | Placebo to Vadadustat 600 mg |
|---|---|---|---|---|---|---|
| STARTED | 11 | 13 | 13 | 3 | 1 | 2 |
| COMPLETED | 10 | 13 | 12 | 2 | 1 | 2 |
| NOT COMPLETED | 1 | 0 | 1 | 1 | 0 | 0 |
Reasons for not completing this period:
| Reason | Vadadustat 150 mg | Vadadustat 300 mg | Vadadustat 600 mg | Placebo to Vadadustat 150 mg | Placebo to Vadadustat 300 mg | Placebo to Vadadustat 600 mg |
|---|---|---|---|---|---|---|
| ESA Rescue/Blood Transfusion for Anemia | 1 | 0 | 0 | 1 | 0 | 0 |
| Captured as Other | 0 | 0 | 1 | 0 | 0 | 0 |
Analysis population for the primary outcome, as defined in the registry: Modified Intent-to-Treat Population (mITT): all randomized participants who received at least 1 dose of study medication, had a pre-treatment Hb average, and at least one post-Baseline Hb measurement. The mITT Population was based on the treatment to which participants were randomized.
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.
Population: Baseline data are reported for members of the Safety Population, comprised of all enrolled participants who received at least 1 dose of study medication. The Safety Population was based on the actual treatment that participants received.
Only the first 6 of 7 groups are shown.
| Characteristic | Unit | Vadadustat 150 mg | Vadadustat 300 mg | Vadadustat 600 mg | Placebo to Vadadustat 150 mg | Placebo to Vadadustat 300 mg | Placebo to Vadadustat 600 mg |
|---|---|---|---|---|---|---|---|
| Participants analysed | 15 | 15 | 15 | 5 | 5 | 5 | |
| Age, Continuous | years | 61.5 (SD 11.01) | 64.3 (SD 8.02) | 65.1 (SD 9.05) | 60.8 (SD 12.85) | 61.0 (SD 15.60) | 70.8 (SD 8.23) |
| Sex: Female, Male: Female | Participants | 5 | 2 | 5 | 2 | 3 | 2 |
| Sex: Female, Male: Male | Participants | 10 | 13 | 10 | 3 | 2 | 3 |
| Race and Ethnicity Not Collected | Participants | — | — | — | — | — | — |
| Hemoglobin Levels | grams per deciliter (g/dL) | 8.996 (SD 0.5229) | 8.793 (SD 0.5254) | 9.317 (SD 0.6222) | 8.827 (SD 0.6405) | 8.950 (SD 0.7331) | 9.133 (SD 0.6737) |
6. Primary Endpoint
The registry lists the primary outcome as Mean Change in Hemoglobin (Hb) Levels From Pre-treatment to the End of the Primary Efficacy Period, measured over Pre-treatment; Week 6.
| Element | Registry entry |
|---|---|
| Result type | Least Squares Mean |
| Measure of spread | Standard Error |
| Unit | grams per deciliter (g/dL) |
| Endpoint classification | Continuous Endpoint |
The primary endpoint measures the change in hemoglobin concentration from the pre-treatment average to Week 6. Hemoglobin is recorded in grams per deciliter. The pre-treatment average was defined using 3 values, including the qualifying screening value and Baseline value. For each participant, the change was calculated as the Week 6 value minus the pre-treatment value; the reported group summaries are least-squares means.
A continuous endpoint retains information about the magnitude of change, rather than reducing each participant’s result to a simple yes-or-no threshold. Comparing the group averages can therefore describe how the measured hemoglobin values shifted over the specified interval. The Week 6 endpoint also gives a defined time point for comparing the assigned dose groups with placebo.
As a general statistical point, a mean is useful for describing the center of a distribution, but it does not show the range of individual responses or whether every participant changed in the same direction. Nor does a mean difference alone establish how the endpoint relates to other outcomes or how results might vary beyond the measured interval. The registry record describes this endpoint and its measurement interval; it does not report a clinical threshold for interpreting the size of a group difference.
7. Results Posted in the Registry
- Vadadustat 150 mg: mean -0.28 versus -1.48 on control; difference 1.20 (95% CI 0.58 to 1.82), standardized effect d = 1.42; z-test p = <0.001.
- Vadadustat 300 mg: mean 0.08 versus -1.48 on control; difference 1.56 (95% CI 0.94 to 2.18), standardized effect d = 1.83; z-test p = <0.001.
- Vadadustat 600 mg: mean 0.41 versus -1.48 on control; difference 1.89 (95% CI 1.25 to 2.53), standardized effect d = 2.20; z-test p = <0.001.
Mean difference: Vadadustat 150 mg
95% CI: 0.58 to 1.82
Recalculated from the posted summary statistics
8. Secondary Efficacy Endpoints
The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.
| Secondary outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Number of Participants Who Required Rescue With a RBC Transfusion From Baseline to the End of the Primary Efficacy Period | Binary Endpoint | Risk difference | -21.4 pts (-42.9 to 0.1) | n/a |
| Number of Participants Who Required Rescue With Erythropoiesis-Stimulating Agents (ESAs) From Baseline to the End of the Primary Efficacy Period | Binary Endpoint | Risk difference | -30.5 pts (-64.7 to 3.8) | 40 per arm |
Number of Participants Who Required Rescue With a RBC Transfusion From Baseline to the End of the Primary Efficacy Period
- Endpoint type: Binary: the number of participants with the event, compared as proportions.
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Vadadustat 150 mg: 0.0% (0/15) versus 21.4% (3/14) on control; risk difference -21.4 percentage points (95% CI -42.9 to 0.1); unadjusted two-proportion z-test p = 0.058.
- Vadadustat 300 mg: 0.0% (0/15) versus 21.4% (3/14) on control; risk difference -21.4 percentage points (95% CI -42.9 to 0.1); unadjusted two-proportion z-test p = 0.058.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Vadadustat 150 mg and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Vadadustat 300 mg and the control. The interval gives the range of effects that remain compatible with the data.
Number of Participants Who Required Rescue With Erythropoiesis-Stimulating Agents (ESAs) From Baseline to the End of the Primary Efficacy Period
- Endpoint type: Binary: the number of participants with the event, compared as proportions.
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Vadadustat 150 mg: 26.7% (4/15) versus 57.1% (8/14) on control; risk difference -30.5 percentage points (95% CI -64.7 to 3.8), risk ratio 0.47 (0.18–1.21); unadjusted two-proportion z-test p = 0.096.
- Vadadustat 300 mg: 13.3% (2/15) versus 57.1% (8/14) on control; risk difference -43.8 percentage points (95% CI -74.9 to -12.7), risk ratio 0.23 (0.06–0.92); unadjusted two-proportion z-test p = 0.013.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Vadadustat 150 mg and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval excludes no difference, so the proportion with the event is statistically lower for Vadadustat 300 mg than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The registry record lists a broad set of secondary outcomes, including hemoglobin measures over later study periods, time to a target hemoglobin range, changes in red blood cell measures, hematocrit and reticulocytes, and rescue interventions. Detailed group summaries in the posted results cover two rescue outcomes: red blood cell transfusion and erythropoiesis-stimulating agents. These outcomes address related but distinct questions from the primary continuous hemoglobin endpoint.
In broad terms, the primary endpoint describes mean hemoglobin change over the specified interval, while rescue outcomes record whether participants required particular interventions. Those measures may add context to the primary result, but they are not interchangeable: a group mean does not determine rescue use, and a rescue count does not describe the full distribution of hemoglobin change. The secondary outcomes therefore offer complementary information rather than a direct confirmation of the primary result.
Unadjusted secondary comparisons carry less weight than the sponsor’s primary analysis for several reasons. They are separate outcome tests, and the registry record does not report a multiplicity adjustment for the secondary comparisons. The available event counts are also small, so estimates based on them may be imprecise. Further, detailed results are not present in the record for every listed secondary outcome, so the overall secondary-outcome picture cannot be reconstructed from the available summaries alone.
For these reasons, secondary results should be treated as supporting or exploratory evidence, not as a substitute for the prespecified primary endpoint. The registry record does not report a hierarchy for interpreting secondary endpoints, a family-wise error strategy, or a formal procedure for controlling false-positive findings across the many outcomes. The pattern across outcomes can help frame questions for further study, but it cannot resolve the uncertainty around unreported outcomes or analysis choices.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Time to Reach the Target Hb Level of 10.0 to 12.0 g/dL From Baseline up to Week 16
- Mean Hb Levels at the End of the Primary Efficacy Period
- Mean Hb Levels at the End of the Dose Adjustment and Maintenance Period
- Number of Participants Who Achieved the Target Hb Level of 10.0 to 12.0 g/dL at the End of the Dose Adjustment and Maintenance Period
- Mean Change in Hb Between Pre-treatment and the End of the Dose Adjustment and Maintenance Period
- Mean Change in Red Blood Cell (RBC) Count and Absolute Reticulocyte Count From Baseline to the End of the Primary Efficacy Period
- Mean Change in RBC Count and Absolute Reticulocyte Count From Baseline to the End of the Dose Adjustment and Maintenance Period
- Mean Change in Hematocrit and Reticulocytes From Baseline to the End of the Primary Efficacy Period
9. Statistical Interpretation
The posted group mean changes were -0.28 g/dL for vadadustat 150 mg, 0.08 g/dL for vadadustat 300 mg, 0.41 g/dL for vadadustat 600 mg, and -1.48 g/dL for placebo. These are least-squares mean changes from the pre-treatment average to Week 6. The group summaries show different mean changes across the assigned groups, with the placebo group’s reported mean change lower than the active-dose group means.
The sponsor’s ANCOVA comparisons report least-squares mean differences of 1.19 g/dL for 150 mg versus placebo, 1.56 g/dL for 300 mg versus placebo, and 1.89 g/dL for 600 mg versus placebo. The associated 95% confidence intervals are 0.56 to 1.82, 0.93 to 2.19, and 1.23 to 2.54, respectively. The sponsor reported p-values of < 0.001, < 0.001, and < 0.001. These are the sponsor’s inferential results for the primary endpoint.
Unadjusted recalculations from the posted group summaries estimate mean differences of 1.2, 1.56, and 1.89 g/dL for the three dose comparisons, respectively. Their recalculated 95% confidence intervals are 0.585 to 1.815, 0.939 to 2.181, and 1.254 to 2.526; the corresponding unadjusted p-values are all <0.001. These recalculations are simple comparisons based on posted summaries, not replacements for the sponsor’s ANCOVA. The recalculated values are close to the sponsor’s reported estimates, but they arise from different calculations and should be distinguished when interpreting the results.
The estimates describe average differences over the primary endpoint’s defined interval. They do not establish that each participant experienced the group-average change, and they do not by themselves address longer-term outcomes, safety, or the importance of a particular difference to patients. Statistical evidence against a null difference is also not the same as evidence about the size or practical meaning of an effect. The registry record does not report a threshold that would define a clinically important hemoglobin difference.
These findings should be read within the trial’s dose-finding context. The endpoint analysis includes modest group sizes, and uncertainty remains around each estimated comparison, as reflected by the confidence intervals. The registry record also does not describe multiplicity adjustment across the dose comparisons. Consequently, the estimates and p-values are best understood as the reported evidence for the primary endpoint, with attention to the study design and the stated analysis population rather than as a stand-alone conclusion about treatment.
10. Statistical Methods Explained
The primary endpoint is continuous: it is a change in hemoglobin concentration measured in grams per deciliter. The registry reports least-squares mean changes by group and sponsor comparisons using ANCOVA. In general, a least-squares mean is a model-based group mean, potentially adjusted for covariates included in the model. The record does not report which covariates were used, so the specific adjustment cannot be reconstructed from the registry description.
What does ANCOVA contribute?
As a general statistical method, analysis of covariance compares group outcomes while accounting for specified covariates. When the relevant covariates and model are reported, this can provide an adjusted comparison that may improve precision or account for baseline differences. Here, the sponsor reports ANCOVA and least-squares mean differences, but the registry record does not identify the covariates, model specification, or assumptions used. The reported analysis should therefore be read as the sponsor’s stated model-based comparison, without attributing particular adjustments that are not described.
What do the mean changes describe?
The group values describe average changes from the pre-treatment average to Week 6. A value below zero represents a lower Week 6 value than the pre-treatment average on average; a value above zero represents a higher value on average. A mean compresses the distribution of individual values into one summary. It does not reveal the spread of individual changes, the number of participants moving in each direction, or whether outliers influence the mean. The registry reports a standard error for each group mean, which describes uncertainty in the estimated mean rather than the spread of individual observations.
How should the recalculations be read?
The unadjusted recalculations compare posted summary statistics for each vadadustat group with placebo. They are based on the group means and standard errors, with the pooled standard deviation approximated from those standard errors. This produces a simple, unadjusted comparison rather than the sponsor’s ANCOVA estimate. The recalculated p-values are also unadjusted. They do not account for potential multiplicity across the three dose comparisons or across the study’s broader set of outcomes.
The sponsor’s reported estimates and confidence intervals remain the principal inferential results for the trial’s primary endpoint. When recalculations and sponsor results differ, the sponsor’s own analysis takes precedence; in this record, the discrepancy flag is false and the estimates are broadly similar. Similarity does not make the methods identical: the sponsor’s model-based analysis and the unadjusted recalculation answer closely related but not necessarily identical statistical questions.
Why do confidence intervals matter?
In general, a confidence interval expresses uncertainty around an estimated quantity under the method used to calculate it. A narrower interval indicates greater precision under that method, while a wider interval indicates less precision. The sponsor reports 95% confidence intervals for all three primary comparisons. The recalculations also include confidence intervals, but those are based on the simpler summary-statistic approach. The limits should not be read as a range containing every participant’s response.
A p-value summarizes how compatible the observed data are with a specified null hypothesis under the statistical model. A small p-value is not the probability that the null hypothesis is true, nor does it measure the clinical importance of the estimate. The sponsor reports p-values for the primary comparisons; the recalculated p-values are unadjusted and should be interpreted with that distinction in mind.
What cannot be determined from the registry description?
The original sample-size justification, target power, assumed treatment effect, and planned significance level are not reported in the registry record. The record also does not report whether interim analyses were planned, how missing primary endpoint measurements were handled, or whether the primary analysis used a particular imputation method. The mITT population definition is stated, but the record does not describe additional sensitivity analyses or the reasons participants may have been excluded from that population.
As a general point, missing-data methods can matter when outcome availability differs across participants or groups. Different assumptions about unobserved outcomes can lead to different estimates. Because the registry record does not describe the handling of missing primary measurements, no particular missing-data assumption should be attributed to the sponsor. Likewise, the trial’s randomization and masking are design features; they do not reveal the unreported details of the analysis model or its implementation.
11. Confidence Intervals and Precision
The sponsor’s 95% confidence intervals for the primary comparisons are 0.56 to 1.82 g/dL for vadadustat 150 mg versus placebo, 0.93 to 2.19 g/dL for 300 mg versus placebo, and 1.23 to 2.54 g/dL for 600 mg versus placebo. Each interval is reported around a positive least-squares mean difference. The intervals communicate uncertainty in the estimated group differences under the sponsor’s ANCOVA analysis; they do not describe the range of individual participant outcomes.
The unadjusted recalculations give 95% confidence intervals of 0.585 to 1.815, 0.939 to 2.181, and 1.254 to 2.526 for the same dose comparisons. These are based on posted summary statistics and an approximate pooled standard deviation. They are not the sponsor’s model-based intervals, even where their limits are similar. The recalculated values should therefore be read as a separate, simpler analysis.
In general, confidence intervals help distinguish the estimated effect from its precision. An interval gives a set of values compatible with the data and statistical method at the stated confidence level; it does not guarantee that the true value lies inside the interval, and it is not a prediction interval for individual responses. Width depends on factors such as variability and the amount of information available. The registry reports standard errors for the group means and confidence limits for the comparisons, but the analysis population is not large, so the estimates should not be treated as exact.
All three sponsor intervals exclude zero, consistent with the sponsor’s reported p-values for the stated comparisons. This describes statistical evidence under the reported analysis, not clinical importance. The registry record does not report a threshold for a meaningful difference, and it does not describe adjustment for testing multiple doses or outcomes.
12. 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.
| Effect to detect | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 8 | 11 |
| 75% of the observed effect | 14 | 19 |
| 50% of the observed effect | 32 | 42 |
The planning illustrations use the observed effect as a starting point and show how many participants per arm would be needed under specified assumptions to detect the stated fraction of that effect. The binary outcome illustration for rescue with erythropoiesis-stimulating agents also reports participants per arm. No time-to-event planning illustration is described in the posted results; in general, time-to-event planning figures, when present, are total event counts rather than participants per arm.
The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each planning scenario targets the stated fraction of the observed effect. The columns for 80% and 90% power mean, in plain language, the planned number of participants per arm under those assumptions to have the specified chance of detecting the assumed effect if that effect is present. For the primary continuous endpoint, the illustrations are shown for each vadadustat dose compared with placebo. The secondary binary-outcome illustration applies to the reported ESA-rescue comparison; no such illustration is reported for the RBC-transfusion outcome.
Smaller assumed effects require more participants to distinguish them from random variation under the same planning assumptions. The scenarios based on 75% or 50% of the observed effect therefore illustrate the consequences of targeting less pronounced effects than the observed estimate. These figures are planning illustrations, not the trial’s original design calculations. The original sample-size assumptions are not reported in the registry record. They are not observed power: observed effects from a completed study do not establish the probability that the study had to detect its result.
13. 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 z1−α/2 = 1.960) and the desired power (z1−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
- Observed difference Δ = 1.200; pooled standard deviation σ = 0.845.
- n = 2 × (1.96 + 0.842)2 × 0.8452 / 1.2002 = 7.8, rounded up to 8 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 <- 1.2 # observed difference in means
sigma <- 0.844938568882487 # 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(3054350)
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 = 8 (80% power), 11 (90% power)
75% of observed effect: n per arm = 14 (80% power), 19 (90% power)
50% of observed effect: n per arm = 32 (80% power), 42 (90% power)
power.t.test: 8.9
Simulated power at n = 8 per arm: 0.755 (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.
14. Analyses Reported by the Sponsor
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| ANCOVA | Least squares mean difference 1.19 | 0.56 to 1.82 | < 0.001 |
| ANCOVA | Least squares mean difference 1.56 | 0.93 to 2.19 | < 0.001 |
| ANCOVA | Least squares mean difference 1.89 | 1.23 to 2.54 | < 0.001 |
The sponsor’s primary analysis used ANCOVA and reported least-squares mean differences with 95% confidence intervals and p-values. For vadadustat 150 mg, the reported difference versus placebo was 1.19 g/dL, with a 95% confidence interval of 0.56 to 1.82 and p < 0.001. For 300 mg, it was 1.56 g/dL, with a 95% confidence interval of 0.93 to 2.19 and p < 0.001. For 600 mg, it was 1.89 g/dL, with a 95% confidence interval of 1.23 to 2.54 and p < 0.001.
The unadjusted recalculations from posted summaries produce estimates of 1.2, 1.56, and 1.89 g/dL, with their own confidence intervals and p-values. They are a transparent check based on group summaries, not a reproduction of the sponsor’s ANCOVA. Their close correspondence with the reported estimates does not establish that the models or inferential procedures are interchangeable. The registry record does not identify the ANCOVA covariates, preventing a full reconstruction of the sponsor’s model.
The record does not flag a discrepancy between the sponsor analysis and recalculations. The sponsor’s model-based results remain the primary reported analysis; recalculations are supplementary and unadjusted. The p-values from the recalculations should not be confused with the sponsor’s p-values or interpreted as multiplicity-adjusted results.
15. Multiplicity, Missing Data and Analysis Populations
The record reports three sponsor comparisons of vadadustat doses with placebo for the primary endpoint. It does not report whether the p-values were adjusted for testing multiple doses. The record also lists many secondary outcomes, but does not report a multiplicity-control strategy or a formal testing hierarchy. Without such information, the reported p-values should be read as the results of the stated comparisons, not as evidence that the chance of a false-positive finding was controlled across all tested outcomes.
The registry record defines the modified Intent-to-Treat population for the primary endpoint as randomized participants who received at least 1 dose, had a pre-treatment hemoglobin average, and had at least one post-Baseline hemoglobin measurement. The record does not report how many randomized participants lacked one or more of these requirements, why any measurements were missing, or what methods were used to handle missing outcomes. It also does not describe sensitivity analyses for missing data.
As a general statistical matter, a modified Intent-to-Treat definition can differ from a population including every randomized participant. The reported eligibility criteria make clear that the primary analysis required exposure and available hemoglobin measurements. This is important context when considering how broadly the result applies to all randomized participants. It does not, on its own, reveal whether exclusions affected the comparison.
The original statistical analysis plan, sample-size justification, planned interim analyses, and detailed model specification are not reported in the registry record. The covariates used in ANCOVA and the procedures for handling protocol deviations are also not reported in the registry record. These omissions limit the ability to independently reconstruct every design and analysis decision. They should be treated as unknowns, rather than filled in from standard practice or inferred from the posted estimates.
16. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Primary Efficacy Period: 150 mg Vadadustat | 0 | 15 | 0.0% |
| Primary Efficacy Period: 300 mg Vadadustat | 0 | 15 | 0.0% |
| Primary Efficacy Period: 600 mg Vadadustat | 3 | 15 | 20.0% |
| Primary Efficacy Period: Placebo Matched to 150 mg Vadadustat | 0 | 5 | 0.0% |
| Primary Efficacy Period: Placebo Matched to 300 mg Vadadustat | 1 | 5 | 20.0% |
| Primary Efficacy Period: Placebo Matched to 600 mg Vadadustat | 0 | 5 | 0.0% |
| Dose Adjustment and Maintenance: 150 mg Vadadustat | 1 | 15 | 6.7% |
| Dose Adjustment and Maintenance: 300 mg Vadadustat | 1 | 15 | 6.7% |
| Dose Adjustment and Maintenance: 600 mg Vadadustat | 1 | 15 | 6.7% |
| Dose Adjustment and Maintenance: Placebo to 150 mg Vadadustat | 0 | 5 | 0.0% |
| Dose Adjustment and Maintenance: Placebo to 300 mg Vadadustat | 0 | 5 | 0.0% |
| Dose Adjustment and Maintenance: Placebo to 600 mg Vadadustat | 0 | 5 | 0.0% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Primary Efficacy Period: 150 mg Vadadustat | 8 of 15 |
| Primary Efficacy Period: 300 mg Vadadustat | 11 of 15 |
| Primary Efficacy Period: 600 mg Vadadustat | 6 of 15 |
| Primary Efficacy Period: Placebo Matched to 150 mg Vadadustat | 2 of 5 |
| Primary Efficacy Period: Placebo Matched to 300 mg Vadadustat | 2 of 5 |
| Primary Efficacy Period: Placebo Matched to 600 mg Vadadustat | 2 of 5 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 5% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Primary Efficacy Period: 150 mg Vadadustat | 8 of 15 |
| Primary Efficacy Period: 300 mg Vadadustat | 11 of 15 |
| Primary Efficacy Period: 600 mg Vadadustat | 5 of 15 |
| Primary Efficacy Period: Placebo Matched to 150 mg Vadadustat | 2 of 5 |
| Primary Efficacy Period: Placebo Matched to 300 mg Vadadustat | 2 of 5 |
| Primary Efficacy Period: Placebo Matched to 600 mg Vadadustat | 2 of 5 |
Most frequent serious adverse event terms
| Event term | Organ system | Primary Efficacy Period: 150 mg Vadadustat | Primary Efficacy Period: 300 mg Vadadustat | Primary Efficacy Period: 600 mg Vadadustat | Primary Efficacy Period: Placebo Matched to 150 mg Vadadustat | Primary Efficacy Period: Placebo Matched to 300 mg Vadadustat | Primary Efficacy Period: Placebo Matched to 600 mg Vadadustat |
|---|---|---|---|---|---|---|---|
| Pericarditis | Cardiac disorders | 0 of 15 | 0 of 15 | 1 of 15 | 0 of 5 | 0 of 5 | 0 of 5 |
| Cholecystitis acute | Hepatobiliary disorders | 0 of 15 | 0 of 15 | 1 of 15 | 0 of 5 | 0 of 5 | 0 of 5 |
| Enteritis infectious | Infections and infestations | 0 of 15 | 0 of 15 | 1 of 15 | 0 of 5 | 0 of 5 | 0 of 5 |
| Arteriovenous fistula site complication | Injury, poisoning and procedural complications | 0 of 15 | 0 of 15 | 0 of 15 | 0 of 5 | 1 of 5 | 0 of 5 |
| Shunt stenosis | Injury, poisoning and procedural complications | 0 of 15 | 0 of 15 | 1 of 15 | 0 of 5 | 0 of 5 | 0 of 5 |
| Toxic encephalopathy | Nervous system disorders | 0 of 15 | 0 of 15 | 1 of 15 | 0 of 5 | 0 of 5 | 0 of 5 |
| Gastric ulcer haemorrhage | Gastrointestinal disorders | 0 of 15 | 0 of 15 | 0 of 15 | 0 of 5 | 0 of 5 | 0 of 5 |
| Cerebral haemorrhage | Nervous system disorders | 0 of 15 | 0 of 15 | 0 of 15 | 0 of 5 | 0 of 5 | 0 of 5 |
| Anxiety | Psychiatric disorders | 0 of 15 | 0 of 15 | 0 of 15 | 0 of 5 | 0 of 5 | 0 of 5 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Primary Efficacy Period: 150 mg Vadadustat | Primary Efficacy Period: 300 mg Vadadustat | Primary Efficacy Period: 600 mg Vadadustat | Primary Efficacy Period: Placebo Matched to 150 mg Vadadustat | Primary Efficacy Period: Placebo Matched to 300 mg Vadadustat | Primary Efficacy Period: Placebo Matched to 600 mg Vadadustat |
|---|---|---|---|---|---|---|---|
| Nasopharyngitis | Infections and infestations | 1 of 15 | 5 of 15 | 1 of 15 | 0 of 5 | 0 of 5 | 0 of 5 |
| Diarrhoea | Gastrointestinal disorders | 0 of 15 | 2 of 15 | 2 of 15 | 1 of 5 | 0 of 5 | 0 of 5 |
| Constipation | Gastrointestinal disorders | 1 of 15 | 1 of 15 | 0 of 15 | 0 of 5 | 0 of 5 | 0 of 5 |
| Contusion | Injury, poisoning and procedural complications | 0 of 15 | 0 of 15 | 1 of 15 | 0 of 5 | 1 of 5 | 0 of 5 |
| Shunt stenosis | Injury, poisoning and procedural complications | 1 of 15 | 0 of 15 | 1 of 15 | 0 of 5 | 0 of 5 | 0 of 5 |
| Arthralgia | Musculoskeletal and connective tissue disorders | 1 of 15 | 0 of 15 | 0 of 15 | 1 of 5 | 0 of 5 | 0 of 5 |
| Pruritus | Skin and subcutaneous tissue disorders | 0 of 15 | 1 of 15 | 0 of 15 | 0 of 5 | 0 of 5 | 1 of 5 |
| Abdominal pain | Gastrointestinal disorders | 0 of 15 | 0 of 15 | 1 of 15 | 0 of 5 | 0 of 5 | 0 of 5 |
| Faeces soft | Gastrointestinal disorders | 0 of 15 | 1 of 15 | 0 of 15 | 0 of 5 | 0 of 5 | 0 of 5 |
| Nausea | Gastrointestinal disorders | 0 of 15 | 1 of 15 | 0 of 15 | 0 of 5 | 0 of 5 | 0 of 5 |
Serious events with the highest arm-level rate: arteriovenous fistula site complication (20.0%), pericarditis (6.7%), gastric ulcer haemorrhage (6.7%), cholecystitis acute (6.7%), enteritis infectious (6.7%).
The registry’s adverse-event summaries divide counts across a primary efficacy period and a dose-adjustment and maintenance period. In the primary efficacy period, the vadadustat groups list 15 participants at risk for each dose, with serious adverse events affecting 0, 0, and 3 participants for the 150 mg, 300 mg, and 600 mg groups, respectively. The placebo-matched groups list 5 participants at risk each, with serious adverse events affecting 0, 1, and 0 participants, respectively.
For the dose-adjustment and maintenance period, the three vadadustat groups each list 15 at risk and 1 affected by serious adverse events. The placebo groups list 5 at risk each, with 0, 0, and 0 affected, respectively. The record also lists counts labelled deaths for each group and period. Those entries should be read as registry-record counts; the information does not establish cause, timing beyond the stated periods, or relationship to study treatment.
The serious-event terms listed include arteriovenous fistula site complication at 20.0%, and pericarditis, gastric ulcer haemorrhage, acute cholecystitis, infectious enteritis, and shunt stenosis at 6.7% each. These summaries do not establish that an event was caused by a study drug. Small group counts and the separate period-specific reporting should be kept in mind when comparing groups. The registry record does not provide a causal assessment in these figures.
17. What the Result Does, and Does Not, Mean
The primary result describes mean hemoglobin change from the pre-treatment average to Week 6 and the sponsor’s estimated differences between each vadadustat dose group and placebo. The posted estimates are positive for all three dose comparisons, with sponsor-reported 95% confidence intervals that exclude zero. This is a statement about the measured endpoint and the reported analysis over the specified interval.
It does not show that every participant’s hemoglobin increased, that individual responses were uniform, or that a particular participant would experience the group average. The group means summarize distributions; they do not reveal all individual values. The result also does not establish the clinical importance of the estimated difference, because the registry record does not report a threshold for a meaningful hemoglobin change.
The primary endpoint is not a complete measure of safety or overall health, and the Week 6 comparison does not resolve effects over longer periods. The registry includes other outcomes, but the available summaries do not provide a full account of all those measures. Serious adverse-event counts and rescue outcomes are relevant additional information, yet they answer different questions and do not convert the primary endpoint into a comprehensive assessment of benefit and risk.
Interpretation is also limited by the information not reported in the registry record, including the original sample-size assumptions, multiplicity procedures, detailed ANCOVA specification, and missing-data methods. The analysis population has stated eligibility requirements, so it should not be assumed to include every randomized participant. The result should therefore be understood as a dose-specific, short-interval comparison in the defined analysis population, not as a universal prediction or a stand-alone treatment recommendation.
18. Why This Trial Matters Statistically
This trial is statistically informative because it compares three active doses with placebo using a continuous primary endpoint, allowing the dose-specific estimates to be considered separately. The sponsor’s reported least-squares mean differences and confidence intervals communicate both the estimated separation between groups and the uncertainty around those comparisons. The endpoint is defined with a clear measurement interval, making the estimand more interpretable than an outcome with no specified time point.
The analysis also illustrates why reported results and simple recalculations should be distinguished. Unadjusted calculations from summary statistics can help readers understand the scale of an effect and check its broad consistency with the sponsor’s results. They do not reproduce a model-based ANCOVA when the model details are not fully available. The sponsor’s primary analysis and the supplementary recalculations each have a distinct role.
More broadly, this record highlights important statistical questions for dose-finding studies: how to compare multiple doses, how to express uncertainty, and how to interpret secondary outcomes alongside a primary endpoint. The presence of multiple comparisons makes multiplicity methods relevant, while small group counts and missing analysis details limit what can be concluded from registry summaries alone. The sample-size illustrations further show how planning needs depend on the assumed effect, but they cannot be treated as the trial’s original design rationale.
These are useful distinctions for clinical researchers: estimates, precision, model assumptions, analysis populations, and multiplicity all contribute to interpretation. The record offers primary endpoint results and selected secondary and safety summaries, while leaving several design and analysis details unreported.
19. 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.
Several limitations are specific to interpreting this trial record. The primary endpoint is measured through Week 6, so it cannot by itself describe the durability of the observed differences. Although later-period outcomes are listed, detailed summaries for many listed outcomes are not available in the results. That limits the ability to connect the short-interval primary result with longer-term hemoglobin patterns.
The endpoint group sizes are 15, 15, 14, and 14. With group sizes of this scale, estimates may be sensitive to individual observations, and the confidence intervals remain important to interpretation. The record does not provide individual-level data or distribution summaries sufficient to assess the shape of the outcome distributions or the influence of unusual values.
The sponsor reports ANCOVA, but the covariates and detailed model specification are not reported in the registry record. The missing-data approach, sensitivity analyses, and reasons for any exclusions from the mITT population are also not reported. The stated population definition requires treatment exposure and at least one post-Baseline measurement, so it is not identical by definition to all randomized participants.
The record does not report multiplicity adjustment across the dose comparisons or the wider outcome set, nor does it report the original sample-size justification. Planning illustrations based on observed effects are not a substitute for those original design assumptions. Finally, adverse-event counts are presented separately by group and period, but the registry figures alone do not establish causal relationships or provide a complete account of each event’s clinical context.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Dose-Finding Study of Vadadustat in Japanese Subjects With Anemia Secondary to Dialysis-Dependent Chronic Kidney Disease (DD-CKD) — NCT03054350.
- Registry record last updated 2021-04-08; status last verified 2021-03.
- Results first posted 2021-04-08.
- 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.
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23. Record Summary
NCT03054350 is a completed Phase 2 randomized, double-blind, placebo-controlled dose-finding study of daily oral vadadustat in Japanese participants with anemia secondary to dialysis-dependent chronic kidney disease. The primary endpoint was mean change in hemoglobin from the pre-treatment average to Week 6, analyzed in a defined modified Intent-to-Treat population.
The sponsor reported ANCOVA least-squares mean differences versus placebo for vadadustat 150 mg, 300 mg, and 600 mg, with 95% confidence intervals excluding zero for each comparison. Unadjusted recalculations from posted summaries give broadly similar estimates but are not substitutes for the sponsor’s model-based analysis.
The registry record also includes rescue outcomes, selected safety counts, and other listed secondary measures. Multiplicity procedures, original sample-size assumptions, detailed ANCOVA covariates, and missing-data methods are not reported in the registry record. Results should be interpreted as defined endpoint comparisons over the reported interval, with those limitations in view.