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Kidney Transplantation Phase 2, Phase 3 Binary Endpoint NCT01120028

Campath, Calcineurin Inhibitor Reduction and Chronic Allograft Nephropathy: Complete Statistical Analysis

This analysis examines the registry’s primary outcome of biopsy-proven acute rejection after kidney transplantation, comparing alemtuzumab with basiliximab induction while both groups received tacrolimus maintenance. It also considers the registry’s reported time-to-event analysis, secondary outcomes, precision, planning illustrations, and safety data.

Trial start: 2010-09  ·  Enrollment: 852  ·  Sponsor: University of Oxford
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 Campath, Calcineurin Inhibitor Reduction and Chronic Allograft Nephropathy (NCT01120028), a randomized phase 2, phase 3 study. The primary outcome is Number of Participants With Biopsy-proven Acute Rejection at 6-months After Randomization to Induction Therapy.

852
Enrollment
Phase 2, Phase 3
2
Arms
In the primary outcome
+8.7 pts
Risk difference
Period 1: Basiliximab/Tacrolimus
4.4 to 12.9 pts
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT01120028
PhasePhase 2, Phase 3
ConditionKidney Transplantation
AllocationRandomized
Design modelFactorial
MaskingNone (open label)
Enrollment852
Arms in the primary outcome2
Lead sponsorUniversity of Oxford
Results postedYes

2. Clinical Question

Population

Patients receiving kidney transplants in a completed randomized study of renal function preservation. The registry lists an enrollment of 852. It does not give further eligibility details or a fuller description of the analyzed population; those details are not reported in the registry record.

Intervention

For the primary comparison, induction treatment was alemtuzumab, also called Campath-1H, followed by tacrolimus maintenance. In the study’s broader factorial design, alemtuzumab or basiliximab induction was paired with sirolimus or tacrolimus maintenance; maintenance allocation was at 6 months post-transplant.

Comparator

The primary comparison is basiliximab induction followed by tacrolimus maintenance. The posted primary endpoint counts participants with biopsy-proven acute rejection in the two Period 1 groups, each with 426 participants.

Primary question

Among kidney transplant recipients assigned to tacrolimus maintenance, how did the observed number of participants with biopsy-proven acute rejection at 6 months post-transplantation differ between those allocated alemtuzumab and those allocated basiliximab induction? This is a comparison of recorded outcomes, not a statement about an individual patient’s likely outcome.

3. Trial Design

The registry describes a randomized, open-label, multicentre factorial study, with phase listed as Phase 2 and Phase 3. Its official title identifies comparisons of CAMPATH-1H versus basiliximab induction treatment and sirolimus versus tacrolimus maintenance treatment. The study is completed. The registry lists a start of 2010-09 and primary completion of 2014-02.

The four listed treatment combinations pair alemtuzumab or basiliximab induction with sirolimus or tacrolimus maintenance. The primary endpoint concerns Period 1: alemtuzumab/tacrolimus compared with basiliximab/tacrolimus. Each of those groups has 426 participants in the posted primary outcome. For Period 2, the arm descriptions place maintenance allocation at 6 months post-transplantation; the posted maintenance outcome comparisons have 197 participants in each group.

Open-label means masking is listed as none. Random allocation can reduce systematic differences between comparison groups at baseline, but lack of masking can affect behavior, clinical decisions, outcome assessment, or reporting, depending on the outcome and study procedures. Biopsy-proven rejection is a defined clinical event, but the registry record does not describe the biopsy assessment procedures or whether outcome assessment was blinded.

The registry lists University of Oxford as sponsor and kidney transplantation as the condition. It does not report the original sample-size justification, detailed eligibility criteria, allocation procedures, or a full protocol description. Those details should not be inferred from the factorial label or from the number enrolled.

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: 852 participants were randomized for a comparison of Alemtuzumab (426) and Basiliximab (426) based induction therapies. After 6-months, 394 of those participants were re-randomized to either Sirolimus (197) or Tacrolimus (197) based maintenance therapies.

Period 1: Alemtuzumab or Basiliximab

StagePeriod 1: Alemtuzumab/TacrolimusPeriod 1: Basiliximab/TacrolimusPeriod 2: SirolimusPeriod 2: Tacrolimus
STARTED42642600
COMPLETED41240300
NOT COMPLETED142300

Reasons for not completing this period:

ReasonPeriod 1: Alemtuzumab/TacrolimusPeriod 1: Basiliximab/TacrolimusPeriod 2: SirolimusPeriod 2: Tacrolimus
Withdrawal by Subject0500
Not transplanted141800

Period 2: Tacrolimus or Sirolimus

StagePeriod 1: Alemtuzumab/TacrolimusPeriod 1: Basiliximab/TacrolimusPeriod 2: SirolimusPeriod 2: Tacrolimus
STARTED00197197
COMPLETED00197197
NOT COMPLETED0000

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: Period 1: Baseline data (852 participants) at randomization to induction therapy (Alemtuzumab or Basiliximab). Period 2: 6-months post-transplantation, baseline data (394 of the original participants) at re-randomization to maintanence therapy (Sirolimus or Tacrolimus).

CharacteristicUnitPeriod 1: Alemtuzumab/TacrolimusPeriod 1: Basiliximab/TacrolimusPeriod 2: SirolimusPeriod 2: TacrolimusTotal
Participants analysed4264261971971246
Age, Categorical: Age, Period 1 – <=18 yearsParticipants00000
Age, Categorical: Age, Period 1 – Between 18 and 65 yearsParticipants34735000697
Age, Categorical: Age, Period 1 – >=65 yearsParticipants797600155
Age, Categorical: Age, Period 2 – <=18 yearsParticipants00000
Age, Categorical: Age, Period 2 – Between 18 and 65 yearsParticipants00163162325
Age, Categorical: Age, Period 2 – >=65 yearsParticipants00343569
Age, Continuous: Age, Continuous, Period 1years52.1 (SD 13.3)51.8 (SD 13.3)——51.9 (SD 13.3)
Age, Continuous: Age, Continuous, Period 2years——51.7 (SD 13.0)52.0 (SD 12.9)51.8 (SD 13.0)
Sex: Female, Male: Sex, Period 1 – FemaleParticipants14915100300
Sex: Female, Male: Sex, Period 1 – MaleParticipants27727500552
Sex: Female, Male: Sex, Period 2 – FemaleParticipants006565130
Sex: Female, Male: Sex, Period 2 – MaleParticipants00132132264
Race/Ethnicity, Customized: Ethnic origin, Period 1 – WhiteParticipants37037200742
Race/Ethnicity, Customized: Ethnic origin, Period 1 – BlackParticipants21210042
Race/Ethnicity, Customized: Ethnic origin, Period 1 – AsianParticipants30230053
Race/Ethnicity, Customized: Ethnic origin, Period 1 – OtherParticipants5100015
Race/Ethnicity, Customized: Ethnic origin, Period 2 – WhiteParticipants00174173347
Race/Ethnicity, Customized: Ethnic origin, Period 2 – BlackParticipants005712
Race/Ethnicity, Customized: Ethnic origin, Period 2 – AsianParticipants00131528
Race/Ethnicity, Customized: Ethnic origin, Period 2 – OtherParticipants00527
Region of Enrollment: United Kingdom – Period 1: United KingdomParticipants42642600852
Region of Enrollment: United Kingdom – Period 2: United KingdomParticipants00197197394
Primary Renal Disease: Primary Renal Disease: Period 1 – Diabetic kidney diseaseParticipants514900100
Primary Renal Disease: Primary Renal Disease: Period 1 – GlomerulonephritisParticipants928900181
Primary Renal Disease: Primary Renal Disease: Period 1 – Polycystic kidney diseaseParticipants687300141
Primary Renal Disease: Primary Renal Disease: Period 1 – Chronic pyelonephritisParticipants23160039
Primary Renal Disease: Primary Renal Disease: Period 1 – HypertensionParticipants42420084
Primary Renal Disease: Primary Renal Disease: Period 1 – Renovascular diseaseParticipants760013
Primary Renal Disease: Primary Renal Disease: Period 1 – OtherParticipants14315100294
Primary Renal Disease: Primary renal disease, Period 2 – Diabetic kidney diseaseParticipants00152136
Primary Renal Disease: Primary renal disease, Period 2 – GlomerulonephritisParticipants00504090
Primary Renal Disease: Primary renal disease, Period 2 – Polycystic kidney diseaseParticipants00473481
Primary Renal Disease: Primary renal disease, Period 2 – Chronic pyelonephritisParticipants005914
Primary Renal Disease: Primary renal disease, Period 2 – HypertensionParticipants00142438
Primary Renal Disease: Primary renal disease, Period 2 – Renovascular diseaseParticipants00347
Primary Renal Disease: Primary renal disease, Period 2 – OtherParticipants006365128
Other Previous Disease: Diabetesparticipants7467——141
Other Previous Disease: Vascular Diseaseparticipants5749——106
Other Previous Disease: Cancerparticipants185——23
Previous renal replacement: HaemodialysisParticipants24321400457
Previous renal replacement: Peritoneal dialysisParticipants10410600210
Previous renal replacement: TransplantParticipants33006
Previous renal replacement: NoneParticipants7610300179
HLA mismatch level: HLA mismatch level, Period 1 – Level 1Participants45470092
HLA mismatch level: HLA mismatch level, Period 1 – Level 2Participants949400188
HLA mismatch level: HLA mismatch level, Period 1 – Level 3Participants19619300389
HLA mismatch level: HLA mismatch level, Period 1 – Level 4Participants919200183
HLA mismatch level: HLA mismatch level, Period 2 – Level 1Participants00232245
HLA mismatch level: HLA mismatch level, Period 2 – Level 2Participants00424284
HLA mismatch level: HLA mismatch level, Period 2 – Level 3Participants008990179
HLA mismatch level: HLA mismatch level, Period 2 – Level 4Participants00434386
Previous transplant: Previous transplant, Period 1 – NoneParticipants39039200782
Previous transplant: Previous transplant, Period 1 – ≥1Participants36340070
Previous transplant: Previous transplant, Period 2 – NoneParticipants00181181362
Previous transplant: Previous transplant, Period 2 – ≥1Participants00161632
Highly sensitised: Highly sensitized, Period 1 – YesParticipants16150031
Highly sensitised: Highly sensitized, Period 1 – NoParticipants41041100821
Highly sensitised: Highly sensitized, Period 2 – YesParticipants004711
Highly sensitised: Highly sensitized, Period 2 – NoParticipants00193190383
Virology serology: CMV-positive donor to negative recipientParticipants104102——206

6. Primary Endpoint

The registry lists the primary outcome as Number of Participants With Biopsy-proven Acute Rejection at 6-months After Randomization to Induction Therapy, measured over 6 months post-transplantation.

ElementRegistry entry
Result typeCount Of Participants
Measure of spreadnot applicable
UnitParticipants
Endpoint classificationBinary Endpoint

The primary endpoint counts participants with biopsy-proven acute rejection at 6 months post-transplantation. The registry describes the endpoint as the occurrence of biopsy-proven acute rejection events at 6 months after transplantation during Period 1, when participants were randomized to induction therapy while receiving tacrolimus. In the posted results, 31 of 426 participants in the alemtuzumab/tacrolimus group and 68 of 426 in the basiliximab/tacrolimus group had the endpoint.

A binary participant-count endpoint records whether a participant had at least one qualifying event during the specified period; it does not, by itself, describe the number of repeated events, their timing, or their severity. The registry’s endpoint is therefore useful for comparing how many participants experienced biopsy-proven rejection, but it does not provide a complete account of all aspects of rejection or graft health.

Biopsy confirmation gives the endpoint a specified diagnostic basis. General statistical context: a clear endpoint definition helps make a comparison interpretable, while the quality and consistency of its ascertainment still matter. The registry record does not report detailed rules for biopsy, event adjudication, or handling of participants without an observed biopsy result.

7. Results Posted in the Registry

Risk difference: Period 1: Basiliximab/Tacrolimus

+8.7

95% CI: 4.4 to 12.9 percentage points

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals3.77.210.714.217.721.2Period 1: Alemtuzumab/Tacroli… (n=426)Period 1: Basiliximab/Tacroli… (n=426)% of participants (95% CI)
Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Period 1: Basiliximab/Tacroli…-1.041.974.977.981114risk difference (percentage points) 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
Number of Participants With Graft Failure (at 6-months After Randomization to Induction Therapy)Binary EndpointRisk difference-0.7 pts (-3.1 to 1.7)10,406 per arm
Number of Participants With Graft Failure (at 18-Months After Randomization to Maintenance Therapy)Binary EndpointRisk difference-2.0 pts (-5.4 to 1.4)1,124 per arm
Number of Participants With Serious Infection (at 6-months After Randomization to Induction Therapy)Binary EndpointRisk difference+0.2 pts (-6.0 to 6.5)617,906 per arm

Number of Participants With Graft Failure (at 6-months After Randomization to Induction Therapy)

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Period 1: Basiliximab/Tacroli…-3.53-2.40-1.27-0.140.992.12risk difference (percentage points) vs control (95% CI)

Number of Participants With Graft Failure (at 18-Months After Randomization to Maintenance Therapy)

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Period 2: Tacrolimus-5.96-4.39-2.82-1.240.331.90risk difference (percentage points) vs control (95% CI)

Number of Participants With Serious Infection (at 6-months After Randomization to Induction Therapy)

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Period 1: Basiliximab/Tacroli…-7.02-4.12-1.221.694.597.49risk difference (percentage points) vs control (95% CI)

The registry lists secondary outcomes covering graft failure, serious infection, cancer, and major vascular events, with outcomes assessed in the induction and maintenance periods. Numerical comparisons are available in the posted results for graft failure after induction, graft failure after maintenance, and serious infection after induction. For cancer and major vascular events, numerical results are not reported in the registry record. The record lists serious infection after maintenance among its secondary outcomes, but a numerical result for that outcome is not included in the posted comparisons.

The available secondary comparisons do not show the same clear statistical pattern as the primary rejection result: their reported uncertainty is broad, and their unadjusted p-values do not indicate a clear difference. This is a general reading of the available estimates, not evidence that the groups are equivalent. In particular, small event counts can leave substantial uncertainty, and the estimates do not rule out potentially relevant differences.

These outcomes address different aspects of transplant follow-up and should not be treated as substitutes for the primary endpoint. The primary result concerns biopsy-proven acute rejection at 6 months post-transplantation; graft failure and serious infection are distinct outcomes. The secondary findings therefore add context but do not directly confirm or negate the primary comparison.

Unadjusted secondary results carry less weight because multiple outcomes and comparisons create more opportunities for chance findings. The registry record does not report a multiplicity adjustment or a prespecified hierarchy that would establish which secondary tests should be considered confirmatory. General statistical context: when many hypotheses are examined, an isolated small p-value is less compelling unless the testing strategy is accounted for. Conversely, non-significant results do not establish no effect, particularly when precision is limited.

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

9. Statistical Interpretation

Clinical Biostats interpretation

The primary posted counts are 31 of 426 participants in the alemtuzumab/tacrolimus group and 68 of 426 in the basiliximab/tacrolimus group. The recalculated unadjusted risk difference, expressed as basiliximab/tacrolimus minus alemtuzumab/tacrolimus, is 0.087, with a 95% confidence interval from 0.044 to 0.130. The unadjusted p-value is <0.001. On this scale, the observed participant-level event proportion was higher in the basiliximab group; the estimate describes the observed contrast and does not establish a treatment effect free of uncertainty or bias.

The registry also reports a log-rank analysis with a hazard ratio of 0.42, a 95% confidence interval from 0.28 to 0.64, and p < 0.001. A hazard ratio is a time-to-event measure, whereas the recalculated risk difference compares the observed participant counts over the endpoint period. These are different summaries, so their values should not be treated as interchangeable. The registry record does not give further detail about the time-to-event model or the event-time data used for that analysis.

The direction of the count contrast is visible without converting it to another scale: fewer participants in the alemtuzumab/tacrolimus group had the recorded primary event than in the basiliximab/tacrolimus group. The confidence interval for the risk difference does not include zero, and the reported unadjusted p-value is small. General statistical context: these features indicate that the observed contrast is not easily explained by random sampling variation under a simple no-difference model, but they do not address every possible source of bias, measurement error, or chance from multiple analyses.

The primary endpoint is an event count at a specified follow-up point. It does not, by itself, answer the broader study question about long-term transplant function or survival. Nor does the primary comparison evaluate all four treatment combinations: it focuses on the two Period 1 groups receiving tacrolimus maintenance. Results for other outcomes and treatment periods require separate interpretation. The registry does not report enough detail to determine how the primary analysis handled missing outcome information or which analysis population was used.

The sponsor’s reported time-to-event result and the unadjusted recalculation both show a statistically notable contrast, but they use different measures and methods. The posted estimates should be understood as evidence about the recorded study outcomes, with the limits imposed by open-label conduct, the endpoint’s ascertainment, and the analysis details that are not reported in the registry record. No treatment recommendation follows from these statistics alone.

10. Statistical Methods Explained

Statistical interpretation depends on the outcome scale and the analysis method. The posted primary outcome is a binary participant count: a participant either appears among those with biopsy-proven acute rejection during the specified period or does not. The recalculated comparison uses the two posted counts and group sizes without adjustment. Its risk difference compares the participant-level event proportions in the basiliximab/tacrolimus and alemtuzumab/tacrolimus groups, in that order.

What does the risk difference describe?

A risk difference is an absolute contrast between two event proportions. A value above zero in the stated comparison direction means the event proportion was higher in the basiliximab/tacrolimus group in these posted data. The recalculated estimate is 0.087. This scale is often straightforward to interpret because it expresses the size of the observed contrast in proportion units. It is not an adjusted estimate, and it does not account for covariates, differences in follow-up, or other design features beyond the two posted counts and group sizes.

The posted recalculation also gives a risk ratio of 2.194, with a 95% confidence interval from 1.466 to 3.282, and an odds ratio of 2.42, with a 95% confidence interval from 1.546 to 3.789. These are relative measures and use different mathematical scales from the risk difference. A risk ratio compares event proportions; an odds ratio compares event odds. Their numerical values should not be read as if they were the same quantity. The registry’s sponsor-reported analysis is a time-to-event analysis, not either of these unadjusted binary comparisons.

What does the p-value tell the reader?

The unadjusted p-value for the recalculated primary comparison is <0.001. In general, a p-value describes how incompatible the observed data are with a specified statistical model in which there is no difference, assuming that model and its conditions apply. It is not the probability that the null hypothesis is true, nor does it measure the clinical importance of the contrast. A small p-value also does not correct for bias, incomplete data, or multiple testing.

The sponsor’s reported primary analysis uses the log-rank method and gives a hazard ratio of 0.42, a 95% confidence interval from 0.28 to 0.64, and p < 0.001. In general, a log-rank analysis compares event-time patterns between groups, taking account of when events occur and the available follow-up information. A hazard ratio summarizes a relative event rate over time under the analysis framework; it is not an absolute difference in participant proportions. The registry record does not provide details of the model assumptions, censoring rules, or any covariate adjustment for this analysis.

Why are the confidence intervals important?

A confidence interval displays the range of estimates compatible with the observed data under a specified method and its assumptions. The primary recalculated risk-difference interval is 0.044 to 0.130. Its endpoints convey uncertainty around the point estimate, rather than an exact boundary for the true effect. General statistical context: a confidence interval’s width reflects both the amount of information and variability in the data, as well as the method used to calculate it. An interval should be interpreted on the scale of its estimate.

In a randomized study, random allocation supports comparison of groups, but does not guarantee identical groups or prevent all bias. Open-label conduct is relevant because treatment awareness can influence care and outcome ascertainment. Biopsy-proven rejection has a specified diagnostic basis, but the registry does not report whether biopsies were assessed under blinded procedures. These design and reporting considerations are separate from the arithmetic of the recalculated risk difference.

The registry lists a factorial model, which means the design addresses more than one treatment allocation dimension: induction and maintenance. The primary comparison presented in the posted primary outcome holds maintenance at tacrolimus and compares induction assignments. This outcome therefore does not, on its own, estimate the maintenance-treatment contrast or establish whether the effects of induction and maintenance interact. The registry record does not report the factorial analysis plan or interaction results.

Statistical significance is not the same as clinical importance. The primary endpoint measures biopsy-proven acute rejection, while the broader study description refers to preserving renal function and transplant survival. The relationship between this endpoint and those broader aims cannot be quantified from the primary counts alone. The record does not report a threshold for a clinically important difference or a formal sample-size justification.

11. Confidence Intervals and Precision

The recalculated primary risk difference is 0.087, with a 95% confidence interval from 0.044 to 0.130. The estimate compares the basiliximab/tacrolimus group with the alemtuzumab/tacrolimus group. The interval does not include zero, so the posted unadjusted data are compatible with a positive difference on this scale under the calculation method. The interval’s width still matters: it describes a range of values consistent with the data rather than a single exact effect.

General statistical context: a confidence interval is a method-based measure of uncertainty. Under repeated use of the same procedure and its assumptions, intervals constructed in this way would cover the underlying parameter at the stated rate. For a particular study, the interval is not a probability statement that the true value lies within these specific endpoints. Interpretation depends on the estimand, the analysis assumptions, and the quality of the underlying data.

The recalculated relative measures also have intervals: the risk ratio is 2.194, with a 95% confidence interval from 1.466 to 3.282, and the odds ratio is 2.42, with a 95% confidence interval from 1.546 to 3.789. These intervals use relative scales and should not be substituted for the risk-difference interval. The sponsor’s time-to-event estimate has a separate 95% confidence interval from 0.28 to 0.64 around the reported hazard ratio of 0.42; it describes a different analysis quantity.

Precision is not the same as freedom from bias. A narrow interval would not resolve problems in endpoint measurement, missing data, or analysis choices; a wider interval would indicate greater statistical uncertainty. The registry record does not report the missing-data procedures, analysis population, or enough time-to-event details to assess all assumptions behind the sponsor’s interval.

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 effect213285
75% of the observed effect348465
50% of the observed effect711952
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect2005001,0002,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, pooled-variance normal approximation for two proportions (control proportion held at the observed value). Calculated for the comparison: Period 1: Basiliximab/Tacrolimus.

The planning illustrations show participants per arm for the binary outcomes, rather than total events. The listed assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect used for planning is a stated fraction of the observed effect. For time-to-event outcomes, the general convention in the illustrations is total number of events, but the primary endpoint is binary and its figures are participants per arm.

The 80% power column gives the illustrated number of participants per arm for a design that would have an 80% chance of detecting the specified effect under the stated assumptions, if that effect and assumptions were correct. The 90% power column uses a higher target probability of detecting that same specified effect. These are design-planning quantities, not estimates of the probability that the completed study found a true effect.

The rows that plan for 100%, 75%, or 50% of the observed effect illustrate how the assumed effect size changes the required sample size. A smaller effect is harder to detect and therefore needs more participants under the same planning assumptions. The values are planning illustrations calculated from the observed effect, not the trial’s original design calculation. The original design assumptions and sample-size justification are not reported in the registry record. This is not observed power.

Planning figures should not be interpreted as a verdict on whether the study was adequate for every outcome. The primary outcome, secondary outcomes, and time-to-event analyses may have different event frequencies and analysis requirements. The registry record does not report the trial’s original target sample size or any planned adjustment for the factorial design, loss to follow-up, or multiple comparisons.

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 = [ z1−α/2 √(2p̄(1−p̄)) + z1−β √(p0(1−p0) + p1(1−p1)) ]2 / (p1 − p0)2

n is the number of participants in each arm, p0 and p1 are the control and treatment proportions, and p̄ is their average.

Worked calculation for this trial

  1. Control proportion p0 = 0.073; treatment proportion p1 = 0.160; average p̄ = 0.116.
  2. First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.4532 = 0.8883.
  3. Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.4490 = 0.3779.
  4. n = (0.8883 + 0.3779)2 / (0.0869)2 = 212.5, rounded up to 213 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
p0 <- 0.0727699530516432                          # control proportion
p1 <- 0.15962441314554                          # treatment proportion
n_per_arm <- function(power, frac = 1) {
  q1 <- p0 + (p1 - p0) * frac               # smaller effect = fraction of the observed difference
  pbar <- (p0 + q1) / 2
  z_b <- qnorm(power)
  ceiling(round((z_a * sqrt(2 * pbar * (1 - pbar)) + z_b * sqrt(p0 * (1 - p0) + q1 * (1 - q1)))^2 / (q1 - p0)^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 (unrounded n per arm)
cat("power.prop.test:", round(power.prop.test(p1 = p0, p2 = p1, power = 0.80)$n, 1), "\n")

# Simulation: how often does the z-test reject at the 80%-power sample size?
set.seed(1120028)
n    <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z  <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))

Output from running the code

100% of observed effect: n per arm = 213 (80% power), 285 (90% power)
 75% of observed effect: n per arm = 348 (80% power), 465 (90% power)
 50% of observed effect: n per arm = 711 (80% power), 952 (90% power)
power.prop.test: 212.5 
Simulated power at n = 213 per arm: 0.810 (20000 replicates)

The simulation draws many pairs of event counts at the planned sample size and counts how often the two-proportion z-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
Log RankHazard Ratio (HR) 0.420.28 to 0.64< 0.001

The registry reports a sponsor analysis of the primary outcome using the log-rank method. It gives a hazard ratio of 0.42, with a 95% confidence interval from 0.28 to 0.64 and p < 0.001. The posted re-calculation uses the group counts and sizes to produce an unadjusted risk difference of 0.087, with a 95% confidence interval from 0.044 to 0.130 and p <0.001.

These results are not duplicate estimates of the same quantity. The sponsor’s reported analysis is time-to-event based, while the recalculation compares binary participant counts over the endpoint period. The registry record does not report the additional detail needed to reconstruct the sponsor’s method, including event-time handling and model specifications. Differences in the estimates’ scale and method mean that their numerical values should not be compared directly.

The registry does not flag a discrepancy between its posted result and the recalculation. The recalculation is an unadjusted analysis from the posted summary counts; it does not replace the sponsor’s analysis or establish that one method is preferable. Both should be read with attention to their estimands and assumptions, and neither alone resolves questions about missing data, outcome assessment, or multiplicity.

15. Multiplicity, Missing Data and Analysis Populations

The registry lists a primary endpoint alongside multiple secondary outcomes and reports multiple analyses. It does not report whether the statistical plan adjusted for testing multiple endpoints, comparisons, or time points. Nor does it report a prespecified hierarchy or indicate which secondary analyses were intended to be confirmatory. Without that information, the posted secondary p-values should be treated as exploratory or supportive rather than as a family of independent confirmatory tests.

General statistical context: when researchers test many hypotheses, the chance of obtaining at least one apparently notable result by chance can increase. Adjustment methods or a prespecified testing hierarchy can address this issue, but the registry record does not identify such a method. This missing information does not change the reported values; it affects how confidently multiple results can be interpreted together.

The registry record also does not report how missing outcome data were handled, how participants who did not complete follow-up were treated, or which analysis population was used. It is therefore not possible from the record to determine whether the primary comparison was based on all randomized participants, participants with observed endpoint data, or another analysis set. The record does not give reasons for missingness or describe imputation or sensitivity analyses.

The sponsor’s primary result is described as a log-rank analysis, but detailed censoring rules, model assumptions, and any covariate adjustments are not reported in the registry record. For the recalculated binary comparison, only the posted summary counts and group sizes are used. The recalculation cannot recover information about participants whose outcome status is absent or determine how missing follow-up might affect the comparison.

The registry does not report interim analyses or stopping rules. It also does not report the original statistical analysis plan or the protocol’s sample-size justification. These omissions limit assessment of whether the analyses followed a prespecified plan and how the number of tests was considered. They should be treated as reporting gaps, not as evidence that a particular procedure was or was not used.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Period 1: Alemtuzumab/Tacrolimus34142680.0%
Period 1: Basiliximab/Tacrolimus35442683.1%
Period 2: Sirolimus14019771.1%
Period 2: Tacrolimus13419768.0%
Participants with at least one serious adverse event
Serious adverse events by armPeriod 1: Alemtuzumab/Tacroli…80.0%Period 1: Basiliximab/Tacroli…83.1%Period 2: Sirolimus71.1%Period 2: Tacrolimus68.0%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
Period 1: Alemtuzumab/Tacrolimus11 of 426
Period 1: Basiliximab/Tacrolimus6 of 426
Period 2: Sirolimus11 of 197
Period 2: Tacrolimus9 of 197

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 0% reporting threshold.

ArmParticipants affected of at risk
Period 1: Alemtuzumab/Tacrolimus0 of 0
Period 1: Basiliximab/Tacrolimus0 of 0
Period 2: Sirolimus0 of 0
Period 2: Tacrolimus0 of 0

Most frequent serious adverse event terms

Event termOrgan systemPeriod 1: Alemtuzumab/TacrolimusPeriod 1: Basiliximab/TacrolimusPeriod 2: SirolimusPeriod 2: Tacrolimus
Infections and infestationsInfections and infestations158 of 426161 of 42697 of 19774 of 197
Surgical and medical proceduresSurgical and medical procedures190 of 426190 of 42639 of 19735 of 197
InvestigationsInvestigations140 of 426136 of 42624 of 19726 of 197
Injury, poisoning and procedural complicationsInjury, poisoning and procedural complications154 of 426131 of 42613 of 1977 of 197
Immune system disordersImmune system disorders41 of 42670 of 42633 of 1979 of 197
Gastrointestinal disordersGastrointestinal disorders39 of 42640 of 42627 of 19725 of 197
Metabolism and nutrition disordersMetabolism and nutrition disorders20 of 42623 of 42619 of 19718 of 197
Renal and urinary disordersRenal and urinary disorders24 of 42637 of 4267 of 1979 of 197
Blood and lymphatic system disordersBlood and lymphatic system disorders26 of 42615 of 4263 of 1977 of 197
Neoplasms benign, malignant and unspecified (incl cysts and polyps)Neoplasms benign, malignant and unspecified (incl cysts and polyps)6 of 4267 of 42618 of 19717 of 197

Serious events with the highest arm-level rate: infections and infestations (49.2%), surgical and medical procedures (44.6%), injury, poisoning and procedural complications (36.2%), investigations (32.9%), immune system disorders (16.8%).

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 serious adverse event fields list 341 affected participants among 426 at risk in Period 1: alemtuzumab/tacrolimus, and 354 among 426 at risk in Period 1: basiliximab/tacrolimus. For Period 2, the record lists 140 affected among 197 at risk in the sirolimus group and 134 among 197 at risk in the tacrolimus group. These are registry serious-adverse-event counts, distinct from the primary endpoint and from the secondary serious-infection outcome.

The registry also lists deaths of 11 and 6 in the two Period 1 groups, and 11 and 9 in the Period 2 sirolimus and tacrolimus groups, respectively. The record does not provide a comparative statistical analysis for these safety counts in the registry record described. Counts alone do not establish whether events were caused by a treatment, and the groups represent different treatment periods and allocations.

Serious adverse event terms listed most often include infections and infestations (49.2%), surgical and medical procedures (44.6%), injury, poisoning and procedural complications (36.2%), and investigations (32.9%). These categories describe the registry’s reported terms; they do not by themselves quantify treatment-related risk or indicate that categories are mutually exclusive. Safety interpretation also depends on event definitions, follow-up, and attribution details, which are not reported in the registry record.

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

The primary result describes a difference in the posted number of participants with biopsy-proven acute rejection by 6 months post-transplantation. The alemtuzumab/tacrolimus group had 31 events among 426 participants, compared with 68 among 426 in the basiliximab/tacrolimus group. The recalculated risk difference and its confidence interval indicate a higher observed event proportion in the basiliximab group on the stated comparison scale.

This result does not by itself establish what would happen for an individual transplant recipient. It is an estimate from a randomized, open-label study and remains subject to uncertainty and limitations in outcome ascertainment, missing-data reporting, and analysis details. A confidence interval characterizes sampling uncertainty under its method; it does not capture every possible source of bias.

The primary outcome is not the same as long-term kidney function, graft survival, or overall transplant success. The study’s broader description concerns preserving renal function and transplant survival, but the primary endpoint is biopsy-proven acute rejection during Period 1. The secondary graft-failure outcomes and other safety outcomes address different questions and have their own uncertainty.

The comparison also does not represent every combination in the factorial design. The primary endpoint compares induction assignments while both groups are listed with tacrolimus maintenance. It does not estimate the sirolimus-versus-tacrolimus maintenance contrast or establish whether induction and maintenance effects depend on one another. The registry record does not report the factorial interaction analysis.

Statistical evidence is not a treatment recommendation. The result should be understood as an estimate of the recorded group contrast, interpreted alongside its precision, endpoint definition, study conduct, secondary outcomes, and the limitations of the registry reporting. It does not prove that one treatment is universally better, or that the observed difference will recur unchanged in another population or setting.

18. Why This Trial Matters Statistically

This study illustrates why an endpoint and its analysis scale need to be read together. A participant count answers how many people experienced a defined event, while a time-to-event analysis uses information about when events occurred and follow-up. The registry reports both an unadjusted recalculation based on counts and a sponsor log-rank result. Their numerical estimates answer related but non-identical statistical questions.

The factorial design also highlights the importance of distinguishing treatment dimensions. Induction treatment and maintenance treatment are different allocations, and the primary comparison focuses on induction among participants assigned tacrolimus maintenance. A headline result from that comparison should not be generalized automatically to the maintenance comparison or to all four combinations.

Precision matters alongside statistical significance. The primary risk-difference interval helps readers judge the range of estimates compatible with the posted data, while the secondary outcomes show why a non-significant result should not be read as proof of equivalence. The planning illustrations further show how sample-size requirements depend on the effect chosen for detection; those illustrations are not the trial’s original design justification.

Finally, the registry’s reporting gaps matter for reproducibility and interpretation. The multiplicity strategy, missing-data handling, analysis population, and original sample-size rationale are not reported in the registry record. Recognizing these limits is part of sound statistical reading: the posted result can be described precisely without claiming more than the record establishes.

19. Limitations

The study is listed as open-label, with no masking. Awareness of allocation can influence care decisions or outcome assessment. The primary endpoint requires biopsy confirmation, but the registry record does not describe biopsy criteria, assessment procedures, or whether adjudication was blinded. These details affect how consistently the outcome may have been measured.

The primary comparison covers the two tacrolimus-maintenance groups in Period 1, rather than all four treatment combinations. The registry record does not report results of an interaction analysis or explain how the factorial design was incorporated into the analysis. It also does not provide enough detail to assess whether the result generalizes across the separate maintenance allocations.

The registry record does not report missing-data procedures, reasons for missing outcomes, or the analysis population. The sponsor-reported time-to-event analysis is identified as log-rank, but its censoring rules and other model details are not reported. The recalculated risk difference is unadjusted and uses the posted counts and group sizes; it cannot address these gaps.

Multiple outcomes and analyses are listed, but the record does not describe a multiplicity strategy or a hierarchy of hypotheses. Numerical secondary results are not available for every listed secondary outcome in the results described. The original sample-size justification, interim analyses, and detailed protocol are also not reported in the registry record. These limits restrict assessment of the prespecification and completeness of the analysis, without changing the values that are posted.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

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23. Record Summary

The registry describes a completed, randomized, open-label, multicentre factorial study of induction and maintenance treatments in kidney transplant recipients. Enrollment is listed as 852, with University of Oxford as sponsor. The primary endpoint is the number of participants with biopsy-proven acute rejection at 6 months post-transplantation.

In the primary Period 1 comparison, 31 of 426 participants in the alemtuzumab/tacrolimus group and 68 of 426 in the basiliximab/tacrolimus group had the endpoint. The recalculated unadjusted risk difference is 0.087, with a 95% confidence interval from 0.044 to 0.130 and p <0.001. The sponsor reports a log-rank hazard ratio of 0.42, with a 95% confidence interval from 0.28 to 0.64 and p < 0.001.

The reported estimates describe different statistical measures. Interpretation is limited by open-label conduct and by registry entries not reported on multiplicity, missing data, analysis populations, and the original sample-size justification.

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