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Chronic Renal Failure Phase 3 Continuous Endpoint NCT01473420

A Phase 3 Study Comparing the Effects of Subcutaneous Epoetin Hospira and Epoetin Alfa [Epogen] (Amgen) in Patients With Chronic Renal Failure Requiring Hemodialysis and Receiving Epoetin Maintenance Treatment. AiME - Anemia Management With Epoetin: Complete Statistical Analysis

This randomized phase 3 study compared maintenance-period hemoglobin levels with subcutaneous Epoetin Hospira and Epogen in people receiving hemodialysis and ongoing epoetin treatment. The primary result is considered alongside the registry-reported equivalence analysis, a simple unadjusted recalculation, and the available secondary and safety results.

Trial start: 2012-01-17  ·  Enrollment: 320  ·  Sponsor: Pfizer
Scope of this record

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 A Phase 3 Study Comparing the Effects of Subcutaneous Epoetin Hospira and Epoetin Alfa [Epogen] (Amgen) in Patients With Chronic Renal Failure Requiring Hemodialysis and Receiving Epoetin Maintenance Treatment. AiME - Anemia Management With Epoetin (NCT01473420), a randomized phase 3 study. The primary outcome is Mean Weekly Hemoglobin Level From Week 30 to Week 34: Maintenance Period.

320
Enrollment
Phase 3
2
Arms
In the primary outcome
-0.06
Mean difference
Epogen: Maintenance Period
-0.27–0.15
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT01473420
PhasePhase 3
ConditionChronic Renal Failure, Chronic Kidney Disease
AllocationRandomized
Design modelParallel
MaskingQuadruple
Enrollment320
Arms in the primary outcome2
Lead sponsorPfizer
Results postedYes

2. Clinical Question

Population

People with chronic renal failure requiring hemodialysis who were receiving epoetin maintenance treatment for anemia associated with chronic renal failure. The primary outcome population was the intent-to-treat population randomized into the maintenance period.

Intervention

Subcutaneous Epoetin Hospira, a biological intervention, during the maintenance period.

Comparator

Subcutaneous Epogen (Amgen), also a biological intervention, during the maintenance period.

Primary question

Did the groups have similar mean weekly hemoglobin levels from Week 30 up to Week 34 during maintenance? The study’s stated purpose was to assess therapeutic equivalence using hemoglobin maintenance and study-drug dose requirements.

The comparison concerns maintenance of hemoglobin levels in a specific treatment setting: chronic renal failure, hemodialysis, and ongoing epoetin maintenance treatment. It is not a comparison of starting anemia treatment in people who had not previously received epoetin. The primary endpoint covers a defined portion of the maintenance period, while the secondary outcomes include a longer maintenance-period hemoglobin average, dose measures, and the frequency of hemoglobin values within or outside a target range.

The registry record describes therapeutic equivalence as the study aim. That aim is distinct from asking only whether a conventional test detects a difference. An equivalence assessment ordinarily depends on a prespecified range of differences considered compatible with equivalence; that range is not reported in the registry record. The posted primary estimate and interval can therefore be described, but the registry record does not give enough information to establish how its formal equivalence criterion was set.

3. Trial Design

This was a phase 3, randomized, quadruple-masked, parallel-group study sponsored by Pfizer. The registry record lists enrollment of 320 and a completed status. Participants were assigned to Epoetin Hospira or Epogen (Amgen). The registered study title and summary identify the setting as chronic renal failure requiring hemodialysis, with participants already receiving epoetin maintenance treatment for anemia associated with chronic renal failure.

The primary outcome was a continuous measure: mean weekly hemoglobin level, in g/dL, from Week 30 up to Week 34 of the maintenance period. Its population was defined as all participants randomized into the maintenance period under the intent-to-treat description. The posted arm summaries include 124 participants for Epoetin Hospira and 122 for Epogen. Those outcome counts describe the primary endpoint summaries; they should not be treated as the original enrollment or as evidence about how many participants were randomized at an earlier study stage.

The registry lists secondary maintenance outcomes covering mean weekly hemoglobin and study-medication dose from Week 19 up to Week 34, total medication dose, hemoglobin values within or outside the target range, permanent and temporary dose changes, and transient hemoglobin changes greater than 1.0 g/dL. A number of outcome measures and analyses are posted, but the registry record does not report the original protocol’s full statistical analysis plan, allocation-concealment procedures, or the detailed identities of the masked parties.

Although the study’s stated purpose was therapeutic equivalence, the registry record does not report the original sample-size justification or the equivalence margin used in planning. The planning illustrations associated with the posted effect are separate from the trial’s original design rationale.

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.

Titration Period (18 Weeks)

StageEpoetin HospiraEpogen
STARTED160160
Treated8086
COMPLETED124122
NOT COMPLETED3638

Reasons for not completing this period:

ReasonEpoetin HospiraEpogen
Adverse Event46
Did not meet criteria3232

Maintenance Period (16 Weeks)

StageEpoetin HospiraEpogen
STARTED124122
COMPLETED106105
NOT COMPLETED1817

Reasons for not completing this period:

ReasonEpoetin HospiraEpogen
Adverse Event32
Physician Decision12
Did not meet criteria02
Kidney transplant31
Lost to Follow-up12
Withdrawal by Subject46
Site closure31
Started Peritoneal Dialysis10
Long term hospitalization01
Sponsor's Decision10
Elevated Hemoglobin10

Analysis population for the primary outcome, as defined in the registry: This outcome measure was planned not to be analyzed in titration period. Intent-to-treat (ITT) population included all participants who were randomized into the maintenance period.

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: Analysis population included all participants who were enrolled.

CharacteristicUnitEpoetin HospiraEpogenTotal
Participants analysed160160320
Age, Categorical: <=18 yearsParticipants000
Age, Categorical: Between 18 and 65 yearsParticipants109117226
Age, Categorical: >=65 yearsParticipants514394
Sex: Female, Male: FemaleParticipants7784161
Sex: Female, Male: MaleParticipants8376159

6. Primary Endpoint

The registry lists the primary outcome as Mean Weekly Hemoglobin Level From Week 30 to Week 34: Maintenance Period, measured over Week 30 up to Week 34.

ElementRegistry entry
Result typeMean
Measure of spreadStandard Deviation
Unitg/dL
Endpoint classificationContinuous Endpoint

The primary endpoint is the mean weekly hemoglobin level from Week 30 up to Week 34 during the maintenance period. Hemoglobin is measured in g/dL, and the registry describes the endpoint as a mean with standard deviation. The outcome population includes all participants randomized into the maintenance period under the stated intent-to-treat definition. The reported summaries are 10.17 g/dL for Epoetin Hospira and 10.11 g/dL for Epogen, with standard deviations of 0.821 and 0.838, respectively.

Repeated weekly measurements are represented by an average over the stated period, so the endpoint describes the groups’ average hemoglobin levels during that maintenance interval rather than a single measurement at one visit. In general, using an average across repeated measurements can characterize maintenance over time while reducing emphasis on any one measurement. That is a general explanation of the measure, not a claim about the trial’s unreported analysis procedures.

This endpoint was relevant to the registered question because the study aimed to compare maintenance of hemoglobin levels between two epoetin products in people already receiving maintenance treatment. The registry also identifies dose requirements as part of the study purpose, but dose is not the primary endpoint. The primary result should be interpreted as a comparison of average levels over the specified interval. By itself, it does not describe each participant’s response, the full pattern of weekly measurements, or whether a prespecified equivalence criterion was met.

7. Results Posted in the Registry

Mean difference: Epogen: Maintenance Period

-0.06

95% CI: -0.27 to 0.15

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals9.910.010.110.210.310.3Epoetin Hospira: Maintenance … (n=124)Epogen: Maintenance Period (n=122)g/dL (95% CI)
Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Epogen: Maintenance Period-0.30-0.20-0.11-0.010.080.18mean difference vs control (95% CI)

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 outcomeTypeEffect measureEstimate (95% CI)Planning size, 80% power
Mean Weekly Hemoglobin Level From Week 19 to Week 34: Maintenance PeriodContinuous EndpointMean difference0.02 (-0.14 to 0.18)16,330 per arm
Mean Weekly Dosage of Study Medication From Week 19 to Week 34: Maintenance PeriodContinuous EndpointMean difference-6.85 (-27.83 to 14.13)2,349 per arm
Total Dose of Study Medication Administered: Maintenance PeriodContinuous EndpointMean difference-15,525 (-43,711 to 12,662)828 per arm

Mean Weekly Hemoglobin Level From Week 19 to Week 34: Maintenance Period

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Epogen: Maintenance Period-0.17-0.09-0.020.060.130.21mean difference vs control (95% CI)

Mean Weekly Dosage of Study Medication From Week 19 to Week 34: Maintenance Period

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Epogen: Maintenance Period-31-21-12-1.987.7517mean difference vs control (95% CI)

Total Dose of Study Medication Administered: Maintenance Period

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Epogen: Maintenance Period-48,221-35,143-22,064-8,9854,09317,172mean difference vs control (95% CI)

The posted secondary outcomes broaden the description beyond the primary maintenance-period average. They cover hemoglobin over a longer maintenance interval, weekly and total study-medication dose, target-range status, dose changes, and transient hemoglobin changes. The available continuous-outcome comparisons do not show a clear separation in the corresponding posted tests, and their reported intervals include zero where intervals are posted. These measures provide context about different aspects of maintenance, but they are not substitutes for the primary endpoint.

The secondary outcomes relate to the primary result by examining other measures that could accompany similar average hemoglobin levels, such as medication dose and variation in hemoglobin over time. The registry lists several categorical outcomes and 12 posted secondary outcomes, but does not give full inferential details for every listed measure in the record. The primary outcome remains the most direct test of the stated hemoglobin-maintenance question, while dose and target-range measures address related but distinct questions.

Unadjusted secondary results carry less weight as a group because multiple outcomes create multiple opportunities for an apparently notable result. In general, when many hypotheses are tested, the chance of at least one small p-value can increase unless the analysis plan accounts for multiplicity. The registry record does not report a multiplicity adjustment or a hierarchy that identifies confirmatory secondary hypotheses. Consequently, secondary results are best read as supportive or descriptive context rather than as a collection of independent confirmatory findings.

The registry’s reported p-values for the continuous secondary tests should be interpreted according to their stated methods, not as proof that the groups are identical. The two-sample t-test and Wilcoxon Rank Sum tests address data in different ways. The registry record does not explain the method-selection rationale or provide a complete plan for interpreting the full family of secondary outcomes. The overall pattern can inform the context of the primary comparison, but it cannot fill in missing details about the primary equivalence margin.

Secondary outcomes registered for this trial, for reference (only those above were recalculated):

9. Statistical Interpretation

Clinical Biostats interpretation

For the primary endpoint, the posted mean was 10.17 g/dL in the Epoetin Hospira maintenance group and 10.11 g/dL in the Epogen maintenance group. The registry’s reported analysis gives an LS mean difference of 0.04 g/dL, with a 95% confidence interval from -0.17 to 0.24 g/dL. The registry classifies this as a non-inferiority or equivalence analysis, but does not post a p-value for it. The interval includes zero, so the reported estimate is compatible with no difference as well as with differences in either direction within its bounds.

A simple unadjusted recalculation from the posted group means gives a mean difference of -0.06 g/dL for Epogen relative to Epoetin Hospira, with an unadjusted p-value of 0.571. Its confidence interval also includes zero. This recalculation is not the same quantity as the reported LS mean difference: the estimates differ in value and direction. The registry record does not report enough methodological detail to explain the difference, so the recalculation should be read as a separate, unadjusted summary rather than a replacement for the registry-reported analysis.

A confidence interval that includes zero does not establish that the treatments are equivalent. For a formal equivalence interpretation, the interval must be assessed against a prespecified equivalence margin. That margin is not reported in the registry record. The posted analysis is identified as an equivalence-type analysis, but without the margin and fuller analysis details, the criterion used to reach a formal conclusion cannot be evaluated from the registry record alone.

The secondary outcomes provide context about hemoglobin and dose during maintenance. Their unadjusted comparisons do not supply the missing primary equivalence margin, and they should not be treated as separate proof of equivalence. Several registry-reported secondary tests use named methods, while a number of other outcomes are listed without a reported inferential result in the available record. Taken together, the posted results describe similar group averages for the primary measure and no clear evidence of a difference in the simple unadjusted comparison. They do not, on their own, establish that all clinically relevant differences have been excluded.

The safety information is also descriptive. It reports numbers of participants affected by serious and other adverse events in titration and maintenance periods, along with selected serious-event terms. The listed groups and risk sets differ across periods, and these counts should be read within their stated periods rather than treated as a single overall comparison. Death counts are not reported in the registry record.

10. Statistical Methods Explained

What does the mean difference describe?

The primary endpoint is continuous, and its posted arm summaries are means with standard deviations. A mean describes the average level in a group; a standard deviation describes the spread of individual measurements around that group’s mean. The primary means are 10.17 g/dL for Epoetin Hospira and 10.11 g/dL for Epogen. The standard deviations are 0.821 and 0.838. These summaries describe the maintenance-period outcome in the registry-defined population, not every participant’s individual course.

The unadjusted comparison is a direct contrast of the posted group means. Its estimate is -0.06 g/dL for Epogen relative to Epoetin Hospira, and its unadjusted p-value is 0.571. This simple comparison does not adjust for other participant characteristics or incorporate a model beyond the recalculation from the summary statistics. No additional adjustment should be assumed.

What is a confidence interval?

In general, a confidence interval gives a range of values compatible with the data and the method used to calculate it. It conveys uncertainty around an estimate; it is not a guarantee that the true value lies inside the interval, nor does it show the probability that a particular value is correct. The registry-reported primary interval is -0.17 to 0.24 g/dL at the 95% level. The unadjusted recalculation also has an interval that includes zero. The registry record does not report the recalculated interval’s bounds in a form needed for a precise report.

For a conventional difference test, an interval spanning zero is consistent with no difference at the corresponding level of testing. But a failure to detect a difference is not the same as demonstrating equivalence. Equivalence requires a margin defined in advance and an interval narrow enough to fall within that margin under the chosen procedure. The margin and the detailed decision rule are not reported in the registry record.

How does an equivalence analysis differ from a difference test?

In general, a superiority-style test asks whether the data provide evidence of a difference in a specified direction or in either direction. An equivalence analysis instead asks whether the plausible difference is sufficiently constrained to lie within two prespecified boundaries. A non-inferiority analysis typically uses a one-sided boundary. The registry labels its primary reported analysis as non-inferiority or equivalence, but the method field is not reported and the margin is not reported. The interval and estimate can be described, while the exact decision procedure cannot be reconstructed from the registry record.

The registry-reported primary estimate is an LS mean difference of 0.04 g/dL, with a 95% interval from -0.17 to 0.24 g/dL. “LS mean” refers generally to a model-based least-squares mean, but the model specification and covariates are not reported in the registry record. Therefore, the reported estimate should not be assumed to be an unadjusted contrast of the posted raw means. The recalculated mean difference is explicitly unadjusted and is a distinct estimate.

Why do analysis populations matter?

The primary outcome description states that the intent-to-treat population included all participants randomized into the maintenance period. This is the population definition attached to the primary outcome in the registry. It does not establish that every participant had a complete measurement at every weekly visit or explain how missing observations were handled. The missing-data procedures, exclusions, and analysis population details for the secondary outcomes are not reported in the registry record.

In general, the choice of analysis population can affect an equivalence assessment. Excluding participants or handling missing outcomes differently can change the estimated contrast and its uncertainty. Because the registry does not describe the missing-data method or provide the full analysis plan, those aspects cannot be independently assessed from the posted record.

What do the secondary tests tell us?

The registry reports a two-sample t-test for mean weekly hemoglobin from Week 19 up to Week 34, with p = 0.834. It reports Wilcoxon Rank Sum tests for mean weekly study-medication dosage and total dose, with p = 0.690 and p = 0.918, respectively. A two-sample t-test generally compares group means under its assumptions. A Wilcoxon Rank Sum test generally compares the distributions or ranks of observations and does not directly test a difference in means in the same way. These are general descriptions; further details of the trial’s implementation are not reported.

The posted mean difference for weekly dosage is -6.85 U/kg/week, with an interval from -27.83 to 14.13. For total dose, the posted mean difference is -15520 units, with an interval from -43710 to 12660. Both intervals include zero. The registry’s selected test results are not interchangeable with the unadjusted recalculated p-values, and the registry record does not report adjusted analyses for these comparisons. The outcome distributions and the rationale for choosing each test are not described in sufficient detail to assess all assumptions.

In general, over-dispersion means that observed variability is greater than a model assumes. When that occurs, standard errors can be too small and tests can be too optimistic unless the method accounts for the extra variation. The available outcomes include dose measures with substantial standard deviations relative to their means, but the registry record does not report a distributional assessment or an over-dispersion analysis. No claim about an unreported model or diagnostic is warranted.

How should p-values be read?

In general, a p-value measures how unusual data at least as extreme as those observed would be under a specified null model and its assumptions. It is not the probability that the null hypothesis is true, nor a measure of clinical importance. The unadjusted primary recalculation has p = 0.571; the registry does not post a p-value for its primary equivalence-type result. The secondary p-values are tests for their respective outcomes, and the registry record does not report a multiplicity adjustment.

The interpretation of any p-value depends on the hypothesis and method used. A non-small p-value does not prove that two groups are identical. In an equivalence setting, the confidence interval relative to prespecified boundaries is central. Because the boundaries and detailed statistical plan are not reported, the p-values and intervals should be interpreted as evidence summaries rather than as a complete account of the trial’s decision rule.

11. Confidence Intervals and Precision

The primary registry-reported estimate is an LS mean difference of 0.04 g/dL, with a 95% confidence interval from -0.17 to 0.24 g/dL. The interval crosses zero and extends in both directions. This indicates that the estimate is not precise enough to identify only a positive or only a negative difference under the reported analysis. The interval’s width is also relevant to equivalence: whether it is sufficiently narrow depends on the prespecified equivalence boundaries, which are not reported in the registry record.

The unadjusted recalculation gives a mean difference of -0.06 g/dL and p = 0.571. Its confidence interval includes zero as well. The recalculated contrast is based on the posted group means and is not the same estimand as the LS mean difference. The registry-reported and recalculated estimates should therefore remain distinct when considering precision. The record does not give the full model details needed to explain their difference.

For the secondary mean weekly hemoglobin outcome from Week 19 up to Week 34, the posted mean difference is 0.02 g/dL and the reported interval extends from -0.142 to 0.182. The intervals for the weekly dosage and total-dose comparisons also include zero. The dosage estimates are less straightforward to interpret from the means alone because the posted standard deviations are large; uncertainty and distribution shape matter as well as the point estimates.

In general, a confidence interval reflects both the estimated contrast and the uncertainty in that estimate. A narrow interval can be more informative about the plausible range of differences than a point estimate alone. Precision does not establish clinical importance, and statistical precision does not substitute for an equivalence margin. The registry record does not report a margin or a complete decision rule, so the precision of the primary interval can be described but not judged against the study’s formal equivalence criterion.

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 detectParticipants per arm, 80% powerParticipants per arm, 90% power
100% of the observed effect3,0014,017
75% of the observed effect5,3347,141
50% of the observed effect12,00116,066
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect2,0005,00010,00020,00050,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Treat these figures cautiously. The observed difference is imprecise: its confidence interval includes no difference at all. A sample size built on a noisy estimate can be far too small or too large, so the smaller-effect rows are the more cautious guide.
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, two-sample comparison of means with the pooled standard deviation. Calculated for the comparison: Epogen: Maintenance Period.

The planning illustrations are expressed as participants per arm for the continuous outcomes; they are not total event counts. They use the observed effect as a starting point and show planning for 100%, 75%, and 50% of that observed effect. The listed assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. These are assumptions for the planning illustration, not necessarily the assumptions used when the trial was originally designed.

The 80% power column describes the number of participants per arm that the illustration estimates would be needed to have an 80% chance of detecting the stated effect under those assumptions, if that effect were the true effect and the statistical model assumptions held. The 90% power column uses a higher target chance of detecting that effect and therefore gives a larger planning requirement. These are prospective planning quantities, not evidence about the chance that the completed trial detected its observed result.

For the primary endpoint, the illustrations show that planning for smaller fractions of the observed effect requires more participants per arm than planning for the full observed effect. This is the expected pattern: smaller effects are harder to distinguish from random variation, so more information is needed. The same direction of change appears in the secondary continuous-outcome illustrations.

The trial’s original sample-size justification, chosen target effect, and original design assumptions are not reported in the registry record. These illustrations are based on the observed effect and should not be used to infer the trial’s intended power or whether enrollment met a design target. This is not observed power.

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 = 2 (z1−α/2 + z1−β)2 σ2 / Δ2

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 = -0.060; pooled standard deviation σ = 0.829.
  2. n = 2 × (1.96 + 0.842)2 × 0.8292 / -0.0602 = 3,000.1, rounded up to 3,001 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 <- -0.0600000000000005                      # observed difference in means
sigma <- 0.829473877789063                     # 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(1473420)
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 = 3,001 (80% power), 4,017 (90% power)
 75% of observed effect: n per arm = 5,334 (80% power), 7,141 (90% power)
 50% of observed effect: n per arm = 12,001 (80% power), 16,066 (90% power)
power.t.test: 3001.1 
Simulated power at n = 3,001 per arm: 0.794 (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

MethodEstimate95% CIP-value
not statedLS Mean Difference 0.04-0.17 to 0.24not reported

The registry reports a primary LS mean difference of 0.04 g/dL, with a 95% confidence interval from -0.17 to 0.24 g/dL, for the equivalence-type analysis. The method field and p-value for that reported analysis are not reported in the registry record. Separately, the simple recalculation from the posted arm means gives an unadjusted mean difference of -0.06 g/dL for Epogen relative to Epoetin Hospira, with p = 0.571.

The estimates differ in both value and direction. A model-based LS mean difference need not equal a direct difference between the posted raw group means, but the registry record does not report the model specification or other details that would explain the contrast. The recalculation therefore provides a transparent unadjusted comparison, while the registry-reported estimate remains the sponsor’s posted analysis for the primary outcome. Neither estimate should be substituted for the other.

The sponsor’s reported confidence interval includes zero. Whether that interval meets the study’s formal equivalence criterion cannot be determined without the prespecified equivalence margin and decision rule, which are not reported in the registry record. The posted record does not indicate a discrepancy flag for this outcome.

15. Multiplicity, Missing Data and Analysis Populations

The registry record lists multiple outcomes and several analyses. It includes a primary hemoglobin endpoint and secondary measures of hemoglobin, medication dose, target-range status, dose changes, and transient hemoglobin changes. When many outcomes are examined, general statistical practice distinguishes prespecified confirmatory hypotheses from exploratory comparisons and considers how multiplicity will be handled. The registry record does not report whether an adjustment was planned, which outcomes were treated as confirmatory, or how the outcome hierarchy was defined.

The posted secondary test results are therefore unadjusted as reported in the record. Without a stated multiplicity strategy, a p-value for one secondary comparison should not be treated as if it were the only test conducted. This does not make the descriptive outcome summaries unusable; it limits how strongly a collection of separate significance tests can support a single confirmatory conclusion.

The primary outcome population is described as the intent-to-treat population comprising participants randomized into the maintenance period. The registry record does not report how missing weekly hemoglobin measurements were handled, whether all randomized maintenance participants contributed to the endpoint summaries, or whether any sensitivity analyses were performed. It also does not report imputation methods, rules for excluding observations, or the number and reasons for missing primary measurements. Thus, the stated population definition is known, but the handling of incomplete outcome data cannot be assessed.

The registry record does not report the complete statistical analysis plan, the primary equivalence margin, the original sample-size justification, or details of interim analyses. These absences prevent a full assessment of prespecification and of how the reported analyses relate to the original decision rules. They do not demonstrate that such procedures were absent; they mean that they are not reported in the registry record.

Masking is listed as quadruple, but the registry record does not identify the four masked roles or describe when masking may have been broken. Randomization is listed, while details of sequence generation and allocation concealment are not reported. Those procedural details matter to evaluating bias, but no further inference about them is possible from the record.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Epoetin Hospira: Titration Period128015.0%
Epogen: Titration Period228625.6%
Epoetin Hospira: Maintenance Period2312218.9%
Epogen: Maintenance Period3312227.0%
Participants with at least one serious adverse event
Serious adverse events by armEpoetin Hospira: Titration Pe…15.0%Epogen: Titration Period25.6%Epoetin Hospira: Maintenance …18.9%Epogen: Maintenance Period27.0%% of participants with at least one serious adverse event

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 5% reporting threshold.

ArmParticipants affected of at risk
Epoetin Hospira: Titration Period16 of 80
Epogen: Titration Period10 of 86
Epoetin Hospira: Maintenance Period27 of 122
Epogen: Maintenance Period24 of 122

Most frequent serious adverse event terms

Event termOrgan systemEpoetin Hospira: Titration PeriodEpogen: Titration PeriodEpoetin Hospira: Maintenance PeriodEpogen: Maintenance Period
PneumoniaInfections and infestations1 of 801 of 863 of 1222 of 122
Non-Cardiac Chest PainGeneral disorders1 of 801 of 862 of 1221 of 122
HyperkalaemiaMetabolism and nutrition disorders1 of 800 of 862 of 1222 of 122
Atrial FibrillationCardiac disorders0 of 801 of 861 of 1222 of 122
Cardiac ArrestCardiac disorders1 of 801 of 862 of 1220 of 122
HypoglycaemiaMetabolism and nutrition disorders0 of 800 of 860 of 1224 of 122
Respiratory FailureRespiratory, thoracic and mediastinal disorders1 of 801 of 861 of 1221 of 122
SepsisInfections and infestations2 of 802 of 860 of 1220 of 122
Impaired Gastric EmptyingGastrointestinal disorders0 of 800 of 861 of 1222 of 122
CellulitisInfections and infestations0 of 801 of 862 of 1220 of 122

Most frequent non-serious adverse event terms

Event termOrgan systemEpoetin Hospira: Titration PeriodEpogen: Titration PeriodEpoetin Hospira: Maintenance PeriodEpogen: Maintenance Period
NauseaGastrointestinal disorders0 of 800 of 8610 of 1228 of 122
DizzinessNervous system disorders4 of 800 of 863 of 1228 of 122
FallInjury, poisoning and procedural complications0 of 800 of 868 of 1223 of 122
Injection Site PainGeneral disorders0 of 800 of 863 of 1228 of 122
PyrexiaGeneral disorders0 of 800 of 868 of 1223 of 122
HeadacheNervous system disorders4 of 804 of 860 of 1220 of 122
Procedural HypotensionInjury, poisoning and procedural complications5 of 802 of 860 of 1220 of 122
HyperkalaemiaMetabolism and nutrition disorders4 of 801 of 860 of 1220 of 122
Muscle SpasmsMusculoskeletal and connective tissue disorders0 of 805 of 860 of 1220 of 122
Eosinophil Count IncreasedInvestigations4 of 800 of 860 of 1220 of 122

Serious events with the highest arm-level rate: hypoglycaemia (3.3%), sepsis (2.5%), uterine leiomyoma (2.5%), vulval cancer (2.5%), vulval cancer stage 0 (2.5%).

Do not overextend the safety comparison. Serious-adverse-event counts are safety observations, not efficacy outcomes, and should not be combined with the primary result into a single benefit-risk number.

The adverse-event summaries distinguish titration and maintenance periods and report participants at risk and participants affected. During titration, serious adverse events affected 12 participants among 80 at risk in the Epoetin Hospira group and 22 among 86 at risk in the Epogen group. In the same period, other adverse events affected 16 among 80 and 10 among 86, respectively. During maintenance, serious adverse events affected 23 among 122 at risk with Epoetin Hospira and 33 among 122 with Epogen; other adverse events affected 27 among 122 and 24 among 122, respectively.

These are period-specific participant counts. The groups at risk differ between the titration and maintenance summaries, so counts across periods should not be combined as though they represented one common follow-up group. The listed serious-event terms include hypoglycaemia at 3.3%, sepsis at 2.5%, uterine leiomyoma at 2.5%, vulval cancer at 2.5%, vulval cancer stage 0 at 2.5%, and menorrhagia at 2.5%. These terms are descriptive entries in the registry; the record does not provide enough detail to establish their relationship to study treatment.

Deaths are not reported in the registry record. The adverse-event counts alone do not establish comparative risk, causation, or the clinical meaning of individual events. They should be read as reported event summaries rather than as a complete safety assessment.

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

The posted primary summaries describe mean weekly hemoglobin levels of 10.17 g/dL with Epoetin Hospira and 10.11 g/dL with Epogen from Week 30 up to Week 34 of maintenance. The registry-reported LS mean difference is 0.04 g/dL, with a 95% confidence interval from -0.17 to 0.24 g/dL. A simple unadjusted recalculation gives a mean difference of -0.06 g/dL and p = 0.571. Both the posted estimate and the recalculation are compatible with no difference, but the recalculation and the reported model-based estimate are not the same analysis.

The result does not establish that the products are identical. Nor does a non-significant unadjusted comparison establish therapeutic equivalence. Equivalence is a specific statistical claim requiring a prespecified margin and an analysis showing that the plausible differences meet that boundary. The margin and complete decision rule are not reported in the registry record. The registry’s classification of its analysis as non-inferiority or equivalence signals the intended analysis type, but it does not supply the information needed to independently verify the criterion.

The result also does not establish that all participants had similar hemoglobin trajectories or required similar doses. The primary endpoint is an average over a defined maintenance interval, and the secondary outcomes address some other aspects of maintenance. The available registry summaries do not fully describe individual trajectories, missing measurements, or all analysis methods.

Safety counts describe participants affected by adverse events over specified periods. They do not, by themselves, establish causation or provide a complete account of comparative safety. A balanced interpretation is therefore that the posted primary averages are close, the reported interval spans zero, and the registry’s formal equivalence basis cannot be fully assessed without the unreported margin and analysis details.

18. Why This Trial Matters Statistically

This trial illustrates why the intended statistical question matters. A study designed to assess equivalence is not adequately interpreted by asking only whether a conventional test found a statistically significant difference. The primary estimate and its confidence interval must be judged against a prespecified margin. The registry record identifies an equivalence-type analysis but does not report the margin, so readers can see the estimate’s uncertainty without confirming the formal equivalence decision rule.

It also illustrates the distinction between an unadjusted comparison and a model-based estimate. The raw group means yield an unadjusted contrast, while the registry reports an LS mean difference. Their different values and directions cannot be reconciled from the posted methods because the model details are not reported. Presenting these as separate estimands avoids implying that one is a correction of the other.

The study also has multiple secondary outcomes. These can add useful context about dose and hemoglobin maintenance, but their interpretation depends on how they were prespecified and whether multiplicity was addressed. Those details are not reported in the registry record. Statistical significance or non-significance across individual secondary tests should therefore not be treated as a substitute for a clear primary decision rule.

Finally, the sample-size illustrations show how planning depends on the effect size one wishes to detect. Smaller effects require more participants under the stated planning assumptions. Because these illustrations are based on the observed effect and are not the original design justification, they cannot establish whether the completed trial was planned with adequate precision for its intended equivalence question.

19. Limitations

A central limitation of interpretation is that the registry record does not report the equivalence margin or the detailed decision rule. The primary analysis is labeled as non-inferiority or equivalence, but the reported interval cannot be judged against an unreported boundary. This limits independent assessment of the study’s stated therapeutic-equivalence aim.

The registry reports an LS mean difference but does not give the method for that primary analysis, the model specification, or covariates. The simple recalculation from the posted group means gives a different estimate. The record does not explain why, so the distinction between the two estimates remains unresolved. The recalculation is unadjusted and should not be treated as a substitute for the registry-reported analysis.

Details about missing primary outcome measurements and their handling are not reported. The population is identified as participants randomized into the maintenance period, but the record does not describe imputation, sensitivity analyses, or the completeness of repeated weekly measurements. The original sample-size justification and design assumptions are also not reported; the posted planning illustrations are based on the observed effect and cannot answer that question.

The record lists multiple secondary outcomes but does not report a multiplicity strategy, full analysis hierarchy, or complete inferential results for every listed measure. The number of posted outcome measures is 27 and the number of posted analyses is 5, but those registry counts do not by themselves establish which outcomes were confirmatory or how all outcomes were handled.

Safety summaries are separated by period and use different risk sets. The registry record does not report deaths, and the event listings alone do not provide a complete comparative safety evaluation. These limitations concern what can be established from the registry record; they should not be taken as evidence that unreported analyses or procedures were not performed.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

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Use this trial's endpoint as a starting point for deeper study of effect measures, confidence intervals, and sample-size planning.

23. Record Summary

The registry record describes a completed phase 3 randomized, quadruple-masked, parallel-group study sponsored by Pfizer. It compared subcutaneous Epoetin Hospira with Epogen (Amgen) in people with chronic renal failure requiring hemodialysis and receiving epoetin maintenance treatment.

The primary outcome was mean weekly hemoglobin from Week 30 up to Week 34 of maintenance. The registry reports an LS mean difference of 0.04 g/dL and a 95% confidence interval from -0.17 to 0.24 g/dL for an analysis classified as non-inferiority or equivalence. An unadjusted recalculation gives a mean difference of -0.06 g/dL and p = 0.571. The registry record does not report the equivalence margin or enough method detail to fully reconcile the analyses.

Secondary outcomes and period-specific adverse-event counts provide additional context. The record does not report the full multiplicity plan, missing-data procedures, original sample-size justification, or deaths.

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