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 Belatacept Early Steroid Withdrawal Trial (NCT01729494), a randomized phase 4 study. The primary outcome is Number of Patients With Composite Endpoint of Experiencing Either Death, Graft Loss, or eGFR < 45ml/Min.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT01729494 |
| Phase | Phase 4 |
| Condition | Renal Transplantation |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | None (open label) |
| Enrollment | 316 |
| Arms in the primary outcome | 3 |
| Lead sponsor | University of Cincinnati |
| Results posted | Yes |
2. Clinical Question
Population
Renal transplant recipients in an intent-to-treat analysis. The registry record lists enrollment of 316 participants.
Intervention
Group A received alemtuzumab, belatacept, mycophenolate mofetil or enteric-coated mycophenolate sodium, and early cessation of steroids. Group B received rabbit antithymocyte globulin, belatacept, the mycophenolate options, and early cessation of steroids.
Comparator
Group C received rabbit antithymocyte globulin, tacrolimus, the mycophenolate options, and early cessation of steroids.
Primary question
At 12 months, how many participants in each group experienced death, graft loss, or eGFR below 45 mL/min, and how did the event risk in each belatacept group compare with Group A?
The study was designed to compare the listed immunosuppressive regimens in renal transplantation. Its registry hypothesis concerns the composite of patient death, graft loss, or reduced renal function, with eGFR below 45 mL/min as the renal-function criterion. Because the composite counts whether a participant experienced any component, its result does not identify which component accounts for a group’s count. The separate outcome records provide some additional context, but they do not replace the prespecified primary comparison.
The clinical question is specific to these regimens, including their induction treatments and early steroid withdrawal. It is not a comparison of belatacept alone with tacrolimus alone. Any interpretation of a group contrast therefore concerns the full treatment strategies as described in the registry record.
3. Trial Design
The registry identifies this as a Phase 4, randomized, open-label, multicenter, parallel-group study. The record lists enrollment of 316 and a completed status. The study began in 2012-09, with primary completion in 2018-12. Masking is listed as none, so the trial was not blinded according to the registry record.
The three named groups differ in induction treatment and maintenance immunosuppression. Group A combines alemtuzumab induction with belatacept. Group B combines rabbit antithymocyte globulin induction with belatacept. Group C combines rabbit antithymocyte globulin induction with tacrolimus. Each regimen includes mycophenolate mofetil or enteric-coated mycophenolate sodium and early cessation of steroids. Thus, Group A versus Group C differs in both induction and the principal immunosuppressive drug, while Group B versus Group C shares the listed induction and differs in the principal immunosuppressive drug.
The primary outcome is a count of participants experiencing a composite event by 12 months, analyzed in the intent-to-treat population. The posted arm counts are 9 of 107 in Group A, 15 of 104 in Group B, and 14 of 105 in Group C. The registry also posts outcomes at 24 months, including death-censored graft loss, a related composite, and eGFR below 45 mL/min/1.73m2. The record lists additional secondary outcomes, including biopsy-proven rejection and de novo donor-specific antibody, but results for all listed outcomes are not present in the posted outcome data.
The original sample-size justification, target power, and planned statistical analysis are not reported in the registry record. The planning illustrations calculated from the observed effects 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.
Overall Study
| Stage | Group A | Group B | Group C |
|---|---|---|---|
| STARTED | 107 | 104 | 105 |
| COMPLETED | 97 | 93 | 94 |
| NOT COMPLETED | 10 | 11 | 11 |
Analysis population for the primary outcome, as defined in the registry: Intent to treat analysis
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.
| Characteristic | Unit | Group A | Group B | Group C | Total |
|---|---|---|---|---|---|
| Participants analysed | 107 | 104 | 105 | 316 | |
| Age, Continuous | years | 51.1 (SD 13.1) | 51.6 (SD 11.7) | 51.5 (SD 12.3) | 51.4 (SD 12.1) |
| Sex: Female, Male: Female | Participants | 30 | 38 | 36 | 104 |
| Sex: Female, Male: Male | Participants | 77 | 66 | 69 | 212 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 3 | 1 | 1 | 5 |
| Race (NIH/OMB): Asian | Participants | 5 | 0 | 0 | 5 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 0 | 1 | 0 | 1 |
| Race (NIH/OMB): Black or African American | Participants | 12 | 11 | 19 | 42 |
| Race (NIH/OMB): White | Participants | 82 | 88 | 80 | 250 |
| Race (NIH/OMB): More than one race | Participants | 0 | 0 | 0 | 0 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 5 | 3 | 5 | 13 |
| Region of Enrollment: United States | participants | 107 | 104 | 105 | 316 |
| # Patients with Pre-existing Donor Specific Antibody (DSA) | Participants | 1 | 4 | 1 | 6 |
| calculated panel reactive antibody (cPRA) % | percentage | 4.9 (SD 12.7) | 6.4 (SD 16.4) | 5.9 (SD 15.7) | 5.8 (SD 14.6) |
| Repeat Transplant | Participants | 7 | 2 | 3 | 12 |
| Living related donor | Participants | 25 | 25 | 33 | 83 |
| Living unrelated donor | Participants | 55 | 53 | 47 | 155 |
| Deceased donor | Participants | 27 | 26 | 25 | 78 |
| Pre-emptive transplant | Participants | 37 | 27 | 40 | 104 |
| Cytomegalovirus (CMV) High Risk status (D+/R-) | Participants | 18 | 21 | 25 | 64 |
| Pre-existing diabetes mellitus | Participants | 26 | 33 | 33 | 92 |
6. Primary Endpoint
The registry lists the primary outcome as Number of Patients With Composite Endpoint of Experiencing Either Death, Graft Loss, or eGFR < 45ml/Min, measured over 12 months.
| Element | Registry entry |
|---|---|
| Result type | Count Of Participants |
| Measure of spread | not applicable |
| Unit | Participants |
| Endpoint classification | Binary Endpoint |
The primary endpoint is the number of participants who experienced any of the following by 12 months: death, graft loss, or eGFR below 45 mL/min. The registry describes the renal-function measurement as estimated GFR using the MDRD method and identifies the analysis population as intent to treat. The posted counts are 9 in Group A, 15 in Group B, and 14 in Group C.
A composite endpoint combines several clinically relevant events into a single outcome. This can capture a broader range of unfavorable outcomes than any component alone and can make the comparison less dependent on observing one particular event. The trade-off is that the combined count does not show which component drove the result. Death, graft loss, and a low eGFR are not interchangeable events, so component-level outcomes are important context when available.
The endpoint is expressed as participants with an event, not as a continuous measure of kidney function or a time-to-event estimate. The registry record does not report the separate contribution of each component to the primary composite. Nor does it report a component-specific primary analysis. Consequently, the primary result should be read as a comparison of the composite as defined, rather than as evidence about the pattern or timing of each individual component.
7. Results Posted in the Registry
- Group B: 14.4% (15/104) versus 8.4% (9/107) on control; risk difference 6.0 percentage points (95% CI -2.5 to 14.6), risk ratio 1.71 (0.79–3.74); unadjusted two-proportion z-test p = 0.169.
- Group C: 13.3% (14/105) versus 8.4% (9/107) on control; risk difference 4.9 percentage points (95% CI -3.4 to 13.3), risk ratio 1.59 (0.72–3.50); unadjusted two-proportion z-test p = 0.249.
Risk difference: Group B
95% CI: -2.5 to 14.6 percentage points
Recalculated from the posted summary statistics
8. Secondary Efficacy Endpoints
The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.
| Secondary outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Number of Patients Experiencing a Graft Loss But Not Including Patients Who Died With Functioning Graft (Death-censored Graft Loss) | Binary Endpoint | Risk difference | +1.0 pts (-0.9 to 2.8) | n/a |
| Number of Patients With Composite Endpoint of Either Experiencing Death, Graft Loss, or eGFR < 45ml/Min at 24 Months | Binary Endpoint | Risk difference | +2.2 pts (-6.4 to 10.8) | 3,215 per arm |
| eGFR (MRDRD) < 45 ml/Min/1.73m2 | Binary Endpoint | Risk difference | -0.7 pts (-8.1 to 6.6) | 22,486 per arm |
Number of Patients Experiencing a Graft Loss But Not Including Patients Who Died With Functioning Graft (Death-censored Graft Loss)
- Endpoint type: Binary: the number of participants with the event, compared as proportions.
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Group B: 1.0% (1/104) versus 0.0% (0/107) on control; risk difference 1.0 percentage points (95% CI -0.9 to 2.8); unadjusted two-proportion z-test p = 0.309.
- Group C: 1.0% (1/105) versus 0.0% (0/107) on control; risk difference 1.0 percentage points (95% CI -0.9 to 2.8); unadjusted two-proportion z-test p = 0.312.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Group B and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Group C and the control. The interval gives the range of effects that remain compatible with the data.
Number of Patients With Composite Endpoint of Either Experiencing Death, Graft Loss, or eGFR < 45ml/Min at 24 Months
- Endpoint type: Binary: the number of participants with the event, compared as proportions.
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Group B: 12.5% (13/104) versus 10.3% (11/107) on control; risk difference 2.2 percentage points (95% CI -6.4 to 10.8), risk ratio 1.22 (0.57–2.59); unadjusted two-proportion z-test p = 0.612.
- Group C: 20.0% (21/105) versus 10.3% (11/107) on control; risk difference 9.7 percentage points (95% CI 0.1 to 19.3), risk ratio 1.95 (0.99–3.83); unadjusted two-proportion z-test p = 0.048.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Group B and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval excludes no difference, so the proportion with the event is statistically higher for Group C than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
eGFR (MRDRD) < 45 ml/Min/1.73m2
- Endpoint type: Binary: the number of participants with the event, compared as proportions.
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Group B: 7.7% (8/104) versus 8.4% (9/107) on control; risk difference -0.7 percentage points (95% CI -8.1 to 6.6), risk ratio 0.91 (0.37–2.28); unadjusted two-proportion z-test p = 0.848.
- Group C: 19.0% (20/105) versus 8.4% (9/107) on control; risk difference 10.6 percentage points (95% CI 1.5 to 19.8), risk ratio 2.26 (1.08–4.74); unadjusted two-proportion z-test p = 0.024.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Group B and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval excludes no difference, so the proportion with the event is statistically higher for Group C than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The secondary outcomes offer additional but incomplete context for the primary composite. They include a related 24-month composite, eGFR below 45 mL/min/1.73m2, death-censored graft loss, and listed outcomes such as rejection and de novo donor-specific antibody. The posted results do not form a single uniform pattern across these outcomes. Some estimates are near zero, others favor higher observed event risk in a comparison group, and the degree of precision varies substantially. The death-censored graft-loss counts are especially sparse.
The 24-month outcomes relate to the primary result by extending observation or examining a related component-like measure. They are not interchangeable with the 12-month primary composite: the time point differs, and an individual secondary endpoint may include only one part of the primary definition. Differences across endpoints could reflect different event definitions, follow-up times, and random variation. The registry record does not report a component-level breakdown of the 12-month primary composite that would directly reconcile every secondary outcome with it.
Secondary comparisons carry less weight when many outcomes are examined and the analysis does not report a multiplicity adjustment. Each unadjusted test is considered on its own, while the chance of at least one apparently notable result can increase across a collection of tests. The registry record lists multiple secondary outcomes and does not report a multiplicity plan or adjusted secondary analyses. Thus, isolated secondary p-values are better treated as signals that need cautious interpretation than as definitive confirmation of a difference.
Some listed secondary outcomes have no posted results in the available outcome record. Their absence should not be read as evidence that no events occurred or that groups were alike. It means the record does not provide results to interpret for those outcomes. The primary comparison remains the principal basis for the trial’s stated question, and the secondary outcomes are supportive context rather than a replacement for it.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Number of Patients Experiencing a Graft Loss But Not Including Patients Who Died With Functioning Graft (Death-censored Graft Loss)
- Number of Patients With Composite Endpoint of Either Experiencing Death, Graft Loss, or eGFR < 45ml/Min at 24 Months
- eGFR (MRDRD) < 45 ml/Min/1.73m2
- Biopsy Proven Acute Rejection
- Biopsy Proven Acute Cellular Rejection
- Biopsy Proven Acute Antibody Mediated Rejection
- Biopsy Proven Mixed Acute Rejection
- Number of Patients Developing Denovo Donor Specific Antibody (DSA) Post-transplant
9. Statistical Interpretation
Group A is the reference group for the posted comparisons. At 12 months, the composite event count was 9 of 107 in Group A, 15 of 104 in Group B, and 14 of 105 in Group C. The unadjusted risk difference was 0.060 for Group B versus Group A, with a 95% confidence interval from -0.025 to 0.146 and p = 0.169. For Group C versus Group A, the risk difference was 0.049, with a 95% confidence interval from -0.034 to 0.133 and p = 0.249. Both point estimates are positive, meaning the observed composite event risk was higher in the comparison group than in Group A. Both intervals include zero, and the posted unadjusted p-values do not provide clear evidence against no risk difference.
These estimates are not precise enough to rule out a range of possible differences. For either comparison, the interval is compatible with a modest difference in either direction as well as a larger positive difference. The observed counts alone should not be treated as proof that one regimen is better or worse. The registry record does not provide an adjusted primary analysis or additional model-based results to supplement the unadjusted comparisons.
The 24-month outcome records add context but do not establish a consistent pattern across every endpoint. For the 24-month composite, the posted comparison of Group C with Group A has a risk difference of 0.097, a confidence interval from 0.002 to 0.193, and an unadjusted p-value of 0.048. The Group B comparison has a risk difference of 0.022, a confidence interval from -0.064 to 0.108, and an unadjusted p-value of 0.612. For eGFR below 45 mL/min/1.73m2 at 24 months, the Group C comparison has a risk difference of 0.106, with a confidence interval from 0.015 to 0.198 and an unadjusted p-value of 0.024; the Group B comparison has a risk difference of -0.007, with a confidence interval from -0.081 to 0.066 and an unadjusted p-value of 0.848. The death-censored graft-loss counts are small, and their comparisons are also imprecise.
The 24-month p-values are unadjusted. The registry record does not report a multiplicity procedure, and multiple secondary outcomes are listed. A nominal p-value below 0.05 in a secondary comparison therefore warrants caution: it is a signal in the posted data, not a substitute for a prespecified, multiplicity-controlled analysis. The distinction between the primary result and secondary results matters. The primary endpoint comparisons do not show a clear difference, while some secondary comparisons have different observed patterns. Taken together, these data support describing what was recorded and how uncertain the estimates are, rather than making a broad claim about the comparative effects of the regimens.
10. Statistical Methods Explained
What does a risk difference represent?
A risk difference compares the proportion of participants with an event in one group with the corresponding proportion in another group. It is expressed on the probability scale. A positive value in these comparisons means the event risk is higher in the named group than in Group A; a negative value means it is lower. A value of zero corresponds to equal observed risks. The posted primary risk differences are 0.060 for Group B versus Group A and 0.049 for Group C versus Group A. These estimates are unadjusted comparisons based on the posted group counts.
The risk difference is an absolute contrast, not a relative measure. Relative risks and odds ratios are also listed in some outcome comparisons, but each uses a different scale and interpretation. Neither a relative measure nor a risk difference removes uncertainty from sparse event data. The comparison should be read together with its confidence interval and the way the endpoint was defined.
How should the confidence intervals and p-values be read?
A confidence interval describes the range of effects reasonably compatible with the data under the analysis method. It is not a guarantee that the true effect lies within the interval, and it does not describe the probability that a treatment is effective. For the primary comparisons, both intervals extend across zero. That means the posted data are compatible with no risk difference as well as with differences in either direction. The intervals are also wide enough to include positive differences that could be important, so a non-small p-value does not demonstrate equivalence.
A p-value measures how unusual data at least as inconsistent with the no-difference hypothesis would be under that hypothesis and the stated statistical model. It is not the probability that the no-difference hypothesis is true. The primary p-values, 0.169 and 0.249, are unadjusted. The registry record does not report the sponsor’s detailed statistical model or a separate adjusted analysis. Results should therefore be described as posted unadjusted comparisons rather than as model-adjusted estimates.
Why is the composite endpoint relevant to interpretation?
The endpoint pools death, graft loss, and eGFR below 45 mL/min into a participant-level event count. A participant meeting any component contributes to the composite. This approach can increase the number of events available for comparing groups, but it can also conceal differences among components. The registry record does not show the primary composite count broken down by component. The secondary outcomes include some related measures, but those do not fully provide a component-level decomposition of the primary endpoint.
What can be concluded from a count comparison?
The posted counts describe the number of participants recorded with an event and the number in each group. The risk-difference calculations place the group contrast on an absolute scale. Neither the counts nor the calculated contrasts establish causation beyond the randomized comparison, and interpretation depends on follow-up, endpoint ascertainment, and analysis choices. Random allocation is recorded, but details about adherence, handling of protocol deviations, and missing outcome data are not reported in the registry record.
The primary population is explicitly described as intent to treat. This generally means participants are analyzed according to their randomized group, regardless of treatment received after allocation, but the registry record does not describe implementation details or how missing observations were handled. The posted denominators are the group sizes used in the outcome summaries; they do not by themselves explain whether any outcomes were unavailable or how they were treated.
What do the planning calculations mean?
The planning illustrations use the observed effect as their starting point and estimate the number of participants per arm associated with specified power targets under stated assumptions. The estimates are sensitive to the effect chosen: planning for a smaller fraction of the observed effect requires more participants. They are not a reconstruction of the trial’s original design, and the original design assumptions are not reported in the registry record. Since they use the observed effect, they should be read as hypothetical planning aids rather than as evidence about the trial’s probability of detecting an effect.
For a binary endpoint, sparse event counts can make estimates unstable and intervals wide. The small death-censored graft-loss counts at 24 months are a clear reason to interpret that comparison cautiously. More generally, a point estimate may move substantially when a small number of outcomes change. This does not invalidate the calculation, but it limits how much certainty should be attached to a single estimate. The reported effects, intervals, and p-values are best considered together, with attention to the endpoint and the limited precision of the available counts.
11. Confidence Intervals and Precision
The primary risk-difference estimates are positive, but their confidence intervals extend across zero. For Group B versus Group A, the estimate is 0.060 and the 95% confidence interval is -0.025 to 0.146. For Group C versus Group A, the estimate is 0.049 and the 95% confidence interval is -0.034 to 0.133. These intervals indicate substantial uncertainty about the magnitude and direction of the underlying risk differences.
The intervals do not establish that the groups are equivalent. Equivalence requires a prespecified margin and an analysis designed to assess whether the uncertainty is contained within that margin; such a margin and analysis are not reported in the registry record. Likewise, failure to exclude zero is not proof that there is no effect. It means the data do not clearly distinguish the observed contrast from no difference under the posted unadjusted analysis.
The 24-month secondary comparisons vary in precision. For death-censored graft loss, the observed counts are 0 in Group A, 1 in Group B, and 1 in Group C; the confidence intervals for the risk differences include zero. Such sparse counts provide limited information about the size of a group difference. The 24-month composite and eGFR comparisons have wider uncertainty than a single point estimate might suggest, even where the interval lies just above zero.
Confidence intervals quantify sampling uncertainty under the calculation method. They do not account automatically for multiplicity, missing outcomes, measurement error, or other sources of uncertainty. The registry record does not report enough detail to assess all of those issues. Precision should therefore be judged from the intervals alongside the design and outcome reporting, not from the point estimates alone.
12. Planning a Similar Trial: Sample Size
This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.
| Effect to detect | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 439 | 586 |
| 75% of the observed effect | 735 | 983 |
| 50% of the observed effect | 1,551 | 2,076 |
The planning figures are participants per arm, not total participants across the trial. They use a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set to the stated fraction of the observed effect. The original trial’s own sample-size assumptions are not reported in the registry record. For the binary outcomes in these planning illustrations, the figures are participants per arm; time-to-event planning tables, when present, instead report total events.
The 80% power column gives the estimated participants per arm under which the calculation would have an 80% chance of detecting the specified effect if that effect and the assumptions used in the calculation were true. The 90% power column uses a higher target chance of detection under those same conditions, so its participant estimate is larger. For example, for the Group B primary comparison, the illustration gives 439 participants per arm for 80% power and 586 participants per arm for 90% power when planning for 100% of the observed effect. For 75% of the observed effect, it gives 735 and 983 participants per arm; for 50%, it gives 1,551 and 2,076.
Smaller effects are harder to distinguish from random variation, so planning for a smaller fraction of the observed effect requires more participants. These estimates are planning illustrations based on the observed effect, not observed power. Observed power is not a useful substitute for reading the effect estimate and its confidence interval. The illustrations also rely on assumptions that may not capture every feature of a future study, including actual allocation, outcome availability, and analysis choices.
13. How the Sample Size Is Derived
Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z1−α/2 = 1.960) and the desired power (z1−β = 0.842 for 80% and 1.282 for 90%).
Formula
n is the number of participants in each arm, p0 and p1 are the control and treatment proportions, and p̄ is their average.
Worked calculation for this trial
- Control proportion p0 = 0.084; treatment proportion p1 = 0.144; average p̄ = 0.114.
- First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.4497 = 0.8815.
- Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.4477 = 0.3768.
- n = (0.8815 + 0.3768)2 / (0.0601)2 = 438.1, rounded up to 439 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 <- 0.0841121495327103 # control proportion
p1 <- 0.144230769230769 # 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(1729494)
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 = 439 (80% power), 586 (90% power)
75% of observed effect: n per arm = 735 (80% power), 983 (90% power)
50% of observed effect: n per arm = 1,551 (80% power), 2,076 (90% power)
power.prop.test: 438.1
Simulated power at n = 439 per arm: 0.805 (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. Multiplicity, Missing Data and Analysis Populations
The registry record lists a range of secondary outcomes in addition to the primary composite. When several outcomes and group comparisons are examined, the chance of obtaining at least one small p-value by chance can increase. A multiplicity plan can address that issue by specifying which comparisons are confirmatory and how inference is adjusted. No multiplicity procedure is reported in the registry record. The posted secondary p-values should therefore be read as unadjusted, exploratory evidence rather than as a collection of independently confirmatory findings.
The registry identifies the primary population as intent to treat. It does not report detailed rules for missing data, outcome ascertainment, or participants who may have had incomplete follow-up. It is therefore not possible to determine from the registry record whether every randomized participant had complete outcome information, whether any imputation was used, or how any incomplete observations affected the posted denominators. The reported group sizes and event counts are informative, but they do not answer those analytic questions.
The record also does not report the original statistical analysis plan, the planned handling of protocol deviations, covariate adjustment, subgroup analyses, or interim analyses. These details should not be inferred from the posted summary statistics. The sponsor’s detailed primary analysis is not present in the registry record, and no reported analysis entries are listed for the posted secondary outcomes. The comparisons in the record are unadjusted calculations.
These omissions do not show that the trial lacked a protocol or that particular methods were not used. They mean the methods are not reported in the registry record available for interpretation. Consequently, the primary and secondary estimates can be discussed as posted, while judgments about missing-data bias, prespecified analytic choices, and multiplicity control remain limited.
15. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Group A | 58 | 107 | 54.2% |
| Group B | 66 | 104 | 63.5% |
| Group C | 62 | 105 | 59.0% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Group A | 2 of 107 |
| Group B | 4 of 104 |
| Group C | 1 of 105 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 0% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Group A | 91 of 107 |
| Group B | 90 of 104 |
| Group C | 92 of 105 |
Most frequent serious adverse event terms
| Event term | Organ system | Group A | Group B | Group C |
|---|---|---|---|---|
| Renal dysfunction resulting in hospitalization | Renal and urinary disorders | 30 of 107 | 32 of 104 | 28 of 105 |
| Infection Requiring Hospitalization | Infections and infestations | 24 of 107 | 24 of 104 | 23 of 105 |
| Nausea/vomiting or GI requiring hospitalization | Gastrointestinal disorders | 4 of 107 | 7 of 104 | 13 of 105 |
| Malignancy | Immune system disorders | 7 of 107 | 6 of 104 | 7 of 105 |
| Cardiovascular event | Cardiac disorders | 1 of 107 | 9 of 104 | 3 of 105 |
| Mental status changes or neurological AE's | Nervous system disorders | 5 of 107 | 0 of 104 | 5 of 105 |
| PTLD | Blood and lymphatic system disorders | 0 of 107 | 1 of 104 | 0 of 105 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Group A | Group B | Group C |
|---|---|---|---|---|
| Hematologic events | Blood and lymphatic system disorders | 59 of 107 | 55 of 104 | 60 of 105 |
| Gastrointestinal events | Gastrointestinal disorders | 32 of 107 | 34 of 104 | 50 of 105 |
| Nephrotoxicity events | Renal and urinary disorders | 22 of 107 | 28 of 104 | 37 of 105 |
| Electrolyte/metabolic events | Metabolism and nutrition disorders | 15 of 107 | 21 of 104 | 32 of 105 |
| Neurologic events | Nervous system disorders | 14 of 107 | 14 of 104 | 33 of 105 |
| Leukopenia WBC < 2000/mm3 | Blood and lymphatic system disorders | 22 of 107 | 14 of 104 | 15 of 105 |
| Wound healing | Skin and subcutaneous tissue disorders | 7 of 107 | 10 of 104 | 9 of 105 |
| Musculoskeletal/Bone events | Musculoskeletal and connective tissue disorders | 2 of 107 | 6 of 104 | 5 of 105 |
| Anemia (Hg < 7gm/dL) | Blood and lymphatic system disorders | 2 of 107 | 3 of 104 | 6 of 105 |
| Thrombocytopenia (PLT < 50,000/mm3) | Blood and lymphatic system disorders | 5 of 107 | 2 of 104 | 1 of 105 |
Serious events with the highest arm-level rate: renal dysfunction resulting in hospitalization (30.8%), infection requiring hospitalization (23.1%), nausea/vomiting or gi requiring hospitalization (12.4%), cardiovascular event (8.7%), malignancy (6.7%).
The serious adverse event summaries report affected participants and the number at risk for each group. Group A lists 58 affected of 107 at risk, Group B lists 66 of 104, and Group C lists 62 of 105. Deaths are listed as 2, 4, and 1, respectively. The registry also reports other adverse events affecting 91 of 107 in Group A, 90 of 104 in Group B, and 92 of 105 in Group C. These are descriptive counts; they do not by themselves establish whether a difference between groups is meaningful.
The listed serious adverse event terms include renal dysfunction resulting in hospitalization at 30.8%, infection requiring hospitalization at 23.1%, nausea/vomiting or GI requiring hospitalization at 12.4%, cardiovascular event at 8.7%, malignancy at 6.7%, and mental status changes or neurological adverse events at 4.8%. The registry record does not make the denominator for these term percentages clear in the posted summary, so they should be read as reported rather than converted into participant counts or interpreted as group-specific rates.
The summaries do not report comparative statistical analyses of safety outcomes, event timing, severity distributions, or adjusted estimates. They are useful for describing recorded adverse events, but the counts alone do not support a causal or clinical judgment about comparative safety.
16. What the Result Does, and Does Not, Mean
The results show that the 12-month composite event was recorded for 9 participants in Group A, 15 in Group B, and 14 in Group C. The unadjusted risk-difference estimates are positive for both comparisons with Group A, while both confidence intervals include zero. The data therefore do not provide a precise estimate that excludes no difference for either primary comparison. They also do not establish equivalence or rule out potentially meaningful differences.
Some 24-month secondary comparisons have confidence intervals and unadjusted p-values that differ from the primary comparisons. Because these are secondary results among multiple listed outcomes, and no multiplicity adjustment is reported, they should not be taken as definitive evidence on their own. Their patterns are informative context, but they do not override the primary comparison or resolve its uncertainty.
The trial evaluates complete regimens rather than the isolated effect of a single drug. Group A and Group C differ in both the listed induction treatment and the principal immunosuppressive agent; Group B and Group C share the listed induction but differ in the principal immunosuppressive agent. The observed comparisons thus concern those treatment combinations in this study setting.
The registry record cannot answer every question relevant to interpretation. It does not report the original sample-size justification, detailed missing-data handling, multiplicity plan, or a detailed sponsor analysis. It also does not provide a primary composite breakdown by component. These limits make it inappropriate to infer a specific effect on death, graft loss, or renal function separately from the composite. The statistical findings should be understood as descriptions of the posted outcomes, with uncertainty, rather than as a medical recommendation or a general conclusion about all renal transplant recipients.
17. Why This Trial Matters Statistically
This trial illustrates why effect estimates and their uncertainty matter more than a simple comparison of event counts. The primary counts differ across groups, but the risk-difference confidence intervals extend across zero and allow a range of possible effects. A point estimate alone would conceal that uncertainty. Conversely, a non-small p-value does not show that regimens are equivalent; equivalence requires a specific design and analysis that are not reported in the registry record.
The composite endpoint also highlights a common interpretive trade-off. Combining death, graft loss, and reduced eGFR can capture more events in a single outcome, yet it obscures which component contributes to the result. The posted secondary outcomes partially broaden the picture, but they are not a direct decomposition of the primary outcome and include multiple comparisons.
Finally, the planning illustrations show how sensitive sample-size requirements are to the effect targeted. Planning for smaller effects requires more participants per arm under the stated assumptions. These figures are not evidence of the trial’s achieved power or its original design rationale. Keeping planning calculations separate from the observed trial findings helps prevent a hypothetical calculation from being mistaken for an outcome of the study.
18. Limitations
- The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
- Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.
The primary outcome is a composite, but the registry record does not report how many primary events were deaths, graft losses, or eGFR values below the stated threshold. As a result, the group comparison cannot be attributed to any individual component. The 24-month outcomes provide related information but use different endpoints and a different follow-up time.
Although the study is recorded as randomized and multicenter, it is open label. The registry record does not describe outcome assessment procedures or whether endpoint adjudication was masked. It also does not report the original statistical analysis plan, details of missing-data handling, treatment adherence, or protocol deviations. These omissions limit assessment of potential bias and of how closely the posted analyses follow the planned analyses.
Several secondary comparisons are unadjusted, and no multiplicity procedure is reported. The registry lists more secondary outcomes than are represented in the posted outcome results, so interpretation is incomplete for outcomes without posted findings. Sparse counts for death-censored graft loss limit precision. The record also does not provide a reported sponsor analysis that would clarify whether the posted unadjusted estimates differ from the trial’s primary analysis.
Finally, the groups differ in combinations of induction and maintenance treatments. Comparisons should be interpreted as contrasts between those full regimens, not as isolated effects of a single component. The findings are specific to the trial population and the outcome definitions recorded; the registry record alone does not establish how results apply beyond that setting.
19. Related Tutorials
20. Related Statistical Calculators
21. Sources
- ClinicalTrials.gov: Belatacept Early Steroid Withdrawal Trial — NCT01729494.
- Registry record last updated 2026-07-24; status last verified 2020-08.
- Results first posted 2021-07-28.
- Data retrieved from ClinicalTrials.gov on 2026-11-09.
- Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.
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22. Record Summary
NCT01729494 is a completed, randomized, open-label, multicenter, parallel-group Phase 4 study of early steroid withdrawal regimens in renal transplantation. It compares belatacept-based regimens using alemtuzumab or rabbit antithymocyte globulin induction with a tacrolimus-based regimen using rabbit antithymocyte globulin induction. The registry lists enrollment of 316.
The primary intent-to-treat outcome is the 12-month count of participants experiencing death, graft loss, or eGFR below 45 mL/min. Posted counts are 9 in Group A, 15 in Group B, and 14 in Group C. The unadjusted primary risk-difference intervals include zero. Secondary findings vary and are reported without a stated multiplicity adjustment. The registry record does not report the original sample-size justification or detailed information on missing-data handling and the statistical analysis plan.