Aminophylline to Prevent Acute Kidney Injury in Children After Cardiac Surgery: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Aminophylline to Prevent Acute Kidney Injury in Children After Cardiac Surgery (NCT01245595), a randomized na study. The primary outcome is Acute Kidney Injury Measured by Kidney Diseases: Improving Global Outcomes (KDIGO) AKI Serum Creatinine Criteria.

2. Clinical Question

3. Trial Design

This was a randomized, placebo-controlled, parallel-group trial of aminophylline in children after cardiac surgery with cardiopulmonary bypass. The registry lists quadruple masking, but does not identify the specific people or roles covered by that description. The two assigned groups were aminophylline and normal saline placebo. The aminophylline regimen was an intravenous bolus of 5 mg/kg followed by 1.8 mg/kg intravenously every 6 hours.

Total enrollment was 144, with 72 participants listed in each group. The registry record identifies the study as completed. The listed primary completion date is 2014-05; the start date is 2010-11. The trial's phase is listed as not applicable. The sponsor was Stanford University.

The primary outcome was acute kidney injury measured using the Kidney Diseases: Improving Global Outcomes serum-creatinine criteria. The timeframe was 5 days. The results record reports 43 participants with the outcome in the aminophylline group and 36 in the placebo group. No secondary outcomes are posted in the record, and no analysis entries are listed. The registry record does not report the original sample-size justification, the planned statistical analysis, interim analyses, or further details about the analysis population. Randomization is reported, but the method used to generate or implement the random assignment is not reported in the registry record.

4. Participant Flow and Accounting

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

Overall Study

5. Baseline Characteristics

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

6. Primary Endpoint

The registry lists the primary outcome as Acute Kidney Injury Measured by Kidney Diseases: Improving Global Outcomes (KDIGO) AKI Serum Creatinine Criteria, measured over 5 days.

The primary endpoint counted participants meeting the Kidney Diseases: Improving Global Outcomes (KDIGO) acute kidney injury serum-creatinine criteria. The registry describes KDIGO stage as a measure of acute kidney injury. The outcome is recorded as a number of participants with an event, rather than as a continuous measurement of kidney function. The timeframe attached to this endpoint is 5 days.

General: A clinical endpoint translates a study question into an outcome that can be assessed consistently in participants. A criterion-based endpoint can help define which observations count as an event, while a stated follow-up timeframe clarifies the period being assessed. Serum-creatinine criteria are the specified basis for this endpoint; the registry description does not provide further detail about how creatinine values were collected or how each participant's stage was determined.

The posted result is a count in each randomized group: 43 participants in the aminophylline group and 36 in the placebo group. These counts describe the endpoint as registered. They do not, by themselves, indicate why an event occurred or establish that the intervention caused a difference. The record does not give a separate breakdown by KDIGO stage, nor does it post secondary outcome results.

7. Results Posted in the Registry

• Aminophylline: 59.7% (43/72) versus 50.0% (36/72) on control; risk difference 9.7 percentage points (95% CI -6.5 to 25.9), risk ratio 1.19 (0.89–1.61); unadjusted two-proportion z-test p = 0.241.

8. Statistical Interpretation

9. Statistical Methods Explained

What does the risk difference describe?

General: A risk difference compares the event proportions in two groups by subtracting one group's proportion from the other's. It is expressed on an absolute scale, making the estimate interpretable as the difference in event frequency between assigned groups. The direction depends on which group is subtracted from which. In this registry comparison, the reported risk difference is for aminophylline relative to placebo, and the estimate is positive. The posted counts are 43 of 72 and 36 of 72, respectively. The estimate is based on the unadjusted group results, not a model that accounts for other participant characteristics.

How should the p-value be read?

The unadjusted p-value is 0.241. General: A p-value describes how compatible the observed data are with a specified null hypothesis under the statistical model used for the test. It is not the probability that the null hypothesis is true, and it is not the probability that the result happened “by chance.” A p-value does not measure the size or clinical importance of an effect. Its interpretation also depends on the analysis and assumptions. The registry record does not report the planned testing procedure or whether any adjustments were intended. The posted value is identified as unadjusted, so it should be read as a summary of the unadjusted comparison.

Why do confidence intervals matter?

General: A confidence interval gives a range of effect values compatible with the data under a particular statistical method. It communicates uncertainty around an estimate, rather than merely labeling a result as statistically significant or not. Here, the risk-difference interval includes zero, so it includes no difference as one value compatible with the data. It also extends to values on either side of zero, meaning the direction is not settled by this estimate. The interval is wide enough to leave meaningful uncertainty about the magnitude of the comparison. Its interpretation is tied to the method used; the registry does not report a detailed analysis plan or confidence-interval procedure.

Why are risk ratios and odds ratios also reported?

General: A risk ratio compares event proportions as a ratio, while an odds ratio compares event odds. These relative measures use different scales from a risk difference, so their numerical values should not be interpreted interchangeably. The posted risk ratio is 1.194, with an interval from 0.886 to 1.611. The posted odds ratio is 1.483, with an interval from 0.767 to 2.868. Each interval includes the null value for its measure. These values are additional summaries of the same group comparison, not independent replications of the finding.

What do randomization and masking contribute?

General: Random assignment is intended to make treatment groups comparable on average, including with respect to factors that may not be measured. Masking can reduce the influence of knowledge about assignment on care, outcome assessment, or reporting. The record identifies the trial as randomized and quadruple-masked, but does not describe the randomization procedure or specify who was masked. The registry's labels therefore establish the stated design features, but do not provide enough detail to evaluate their implementation.

What does over-dispersion mean for this outcome?

General: Over-dispersion arises when the variability in data is greater than a statistical model assumes. It can lead a model to understate uncertainty if the extra variability is ignored. This trial's primary outcome is a binary event count by group, not a count of repeated events per participant. The registry does not report an over-dispersion assessment or a model-based analysis. It would therefore be inappropriate to claim that over-dispersion was present, or that a method to address it was used.

The displayed recalculations are simple, unadjusted summaries from the posted counts. The registry record does not report an analysis plan, analysis populations, missing-data procedures, covariate adjustments, or interim analyses. These absences limit what can be said about analytic choices beyond the reported estimates. The sponsor's own analysis takes precedence if a discrepancy is reported; no discrepancy is recorded for this comparison.

10. Confidence Intervals and Precision

The primary risk-difference confidence interval includes zero. That means the posted data are compatible with no difference between groups under the interval's statistical method. The interval also includes values indicating a lower event frequency with aminophylline and values indicating a higher event frequency. Consequently, the estimate does not settle the direction of the group difference.

General: Precision concerns how narrowly a study estimates an effect. A narrower interval indicates less statistical uncertainty around the estimate, while a wider interval leaves a broader range of effect sizes compatible with the data. Precision is distinct from whether an effect is clinically important. The interpretation of an interval also depends on the analysis method and assumptions, which are not fully described in the registry record.

There were 72 participants in each group, and the primary outcome counts were 43 and 36. Those observed counts are the basis for the reported comparison, but they do not make the effect estimate exact. The unadjusted p-value of 0.241 is consistent with the interval's failure to exclude no difference; neither statistic establishes equivalence. The record does not report a prespecified equivalence or non-inferiority margin, so the result cannot be read as showing that the treatments are equivalent.

The posted risk-ratio and odds-ratio intervals also include their respective null values. Together, the different scales describe uncertainty in the same underlying group comparison. None removes the central limitation: the registered outcome data allow a range of plausible comparative effects, and the record does not give more detailed analyses that would narrow that interpretation.

11. Planning a Similar Trial: Sample Size

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

The planning figures are participants per arm, not total events. They are illustrations based on the observed effect, not the trial's original design assumptions; those original assumptions are not reported in the registry record. The calculation assumes a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. It considers detecting the stated share of the observed effect.

For planning at 100% of the observed effect, the listed requirement is 411 participants per arm for 80% power and 549 participants per arm for 90% power. For planning at 75% of the observed effect, the corresponding figures are 734 participants per arm for 80% power and 981 participants per arm for 90% power. For planning at 50% of the observed effect, they are 1,656 participants per arm for 80% power and 2,216 participants per arm for 90% power.

General: Power is the probability that a specified study design will detect an effect of a chosen size if that effect is present, under the stated assumptions. The 80% and 90% columns therefore represent alternative planning targets: the higher target generally requires a larger planned sample. The figures are not observed power. Smaller effects require more participants under these planning assumptions, as reflected by the increasing requirements for the smaller shares of the observed effect. These calculations should not be treated as a reconstruction of how the completed trial was designed.

12. How the Sample Size Is Derived

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

Formula

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

Worked calculation for this trial

1. Control proportion p₀ = 0.500; treatment proportion p₁ = 0.597; average p̄ = 0.549.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.7038 = 1.3793.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.7004 = 0.5895.
4. n = (1.3793 + 0.5895)² / (0.0972)² = 410.1, rounded up to 411 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 <- 0.5                          # control proportion
p1 <- 0.597222222222222                          # 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(1245595)
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 = 411 (80% power), 549 (90% power)
 75% of observed effect: n per arm = 734 (80% power), 981 (90% power)
 50% of observed effect: n per arm = 1,656 (80% power), 2,216 (90% power)
power.prop.test: 410.1 
Simulated power at n = 411 per arm: 0.807 (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.

13. Multiplicity, Missing Data and Analysis Populations

The registry record lists one primary outcome measure and no secondary outcome results. It lists no analysis entries. These details do not establish what outcomes or analyses may have been planned in a protocol, but the registry record does not report a multiplicity strategy. It is therefore not possible to determine whether multiple planned comparisons were considered or whether any adjustment for multiple testing was intended.

General: Multiplicity arises when researchers test multiple outcomes, timepoints, subgroups, or treatment contrasts. Repeated testing can increase the chance of a false-positive finding if each test is treated as independent evidence at the same threshold. A prespecified testing hierarchy or adjustment can address some multiplicity concerns. No such approach is reported in the registry record, and the available entry does not allow its use or absence to be assessed.

The record does not report the number of participants with missing primary outcome data, exclusions from analysis, or the method used to handle missing values. Although 72 participants are listed in each arm and the primary event counts are given, the record does not state whether all randomized participants were included in the analysis or whether any participants had incomplete endpoint assessment. The analysis population is not reported in the registry record.

General: Missing outcome data can affect both the precision and the validity of a comparison, particularly if the likelihood of missingness differs between groups or relates to the outcome. Appropriate interpretation depends on knowing how many observations are missing, why they are missing, and which assumptions or methods were used. Those details are not available in the registry record.

The registry also does not report interim analyses, stopping rules, covariate adjustment, or a full statistical analysis plan. These should be treated as unreported rather than presumed absent from the conduct of the study. The posted unadjusted result can be described, but the record does not support a fuller appraisal of multiplicity, missing-data handling, or analysis-population decisions.

14. Safety Results

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

Other (non-serious) adverse events

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

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: low cardiac output requiring cardiopulmonary resuscitation or extracorporeal membrane oxygenation (1.4%), cardiac arrhythmia leading to cardiopulmonary resuscitation (1.4%).

The registry lists serious adverse events in 1 of 72 participants in the aminophylline group and 2 of 72 participants in the placebo group. These are participant counts and denominators, not estimates of the comparative effect of treatment. The record also lists 10 participants with other adverse events in the aminophylline group and 11 in the placebo group; those figures are distinct from the serious-event counts.

The serious-event terms listed include “Low Cardiac Output requiring Cardiopulmonary resuscitation or Extracorporeal Membrane Oxygenation” and “Cardiac Arrhythmia Leading to Cardiopulmonary Resuscitation,” each reported as 1.4%. The record does not clearly assign those terms to a specific treatment group in the listed term summary, so they should not be attributed to one arm. Death counts are not reported in the registry record.

General: Adverse-event counts are descriptive. They do not establish that an event was caused by the assigned intervention, and small counts can make comparative estimates imprecise. The registry entry does not provide an adjusted safety comparison or a detailed account of event ascertainment. The figures should therefore be read as the reported counts, not as a complete assessment of comparative safety.

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

The primary result describes the number of participants meeting the registered KDIGO serum-creatinine criteria for acute kidney injury within 5 days. The posted count was 43 among 72 participants assigned to aminophylline and 36 among 72 assigned to placebo. The unadjusted risk-difference estimate is positive, but its confidence interval includes zero, and the unadjusted p-value is 0.241. The comparison therefore does not provide a statistically clear distinction between the groups.

This finding does not show that the groups are equivalent. The interval remains compatible with differences in either direction, and the record does not report an equivalence or non-inferiority framework. Nor does the observed difference in counts alone establish that the assigned intervention caused the difference. Randomization is an important design feature, but the registry record does not provide all details needed to evaluate outcome completeness, analysis populations, or the original analysis plan.

The result is limited to the specified serum-creatinine endpoint and 5-day timeframe. It does not answer questions about longer-term kidney outcomes, other clinical endpoints, or unreported secondary outcomes. The registry posts no secondary outcome results. The adverse-event counts are separate descriptive data and do not constitute a comprehensive benefit-harm analysis.

General: Statistical uncertainty is not a verdict about clinical importance. A result that does not distinguish groups statistically may reflect a small effect, an imprecise estimate, or both. Conversely, an observed numerical difference is not automatically clinically meaningful. The registry entry does not provide a threshold for clinical importance, so the posted estimates should be interpreted as a description of the registered comparison rather than a treatment recommendation.

16. Why This Trial Matters Statistically

This trial is statistically informative because it pairs a randomized, placebo-controlled design with a clearly named primary endpoint and a defined follow-up timeframe. The registry identifies a parallel-group comparison, quadruple masking, 144 enrolled participants, and 72 participants in each treatment group. Those features provide a basis for reading the primary outcome counts as a comparison between assigned groups.

The result also illustrates why an estimate should be considered alongside its uncertainty. The aminophylline group had 43 participants with the primary outcome, compared with 36 in the placebo group. The unadjusted risk-difference estimate is positive, but its confidence interval includes zero and the unadjusted p-value is 0.241. Reporting the direction of the observed counts without the interval would give an incomplete account of what the data can establish.

The record highlights the distinction between an observed trial result and a planning calculation. The sample-size illustrations use the observed effect and stated planning assumptions; they are not the original trial design rationale. The record does not report its original sample-size justification, so the planning figures should not be mistaken for a historical protocol target or for evidence about the trial's design adequacy.

Finally, the absence of posted secondary results, analysis entries, missing-data procedures, and a detailed statistical plan limits further interpretation. These are not grounds to infer that a particular procedure was or was not used. They mark what the registry record leaves unresolved, and they show why transparent reporting of endpoints, analyses, and data completeness matters when readers assess clinical-trial evidence.

17. 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 comparison is based on the reported event counts and is presented as an unadjusted recalculation. The registry record does not report a full statistical analysis plan, the original sample-size justification, or an adjusted analysis. It also does not report whether interim analyses were conducted. Those features cannot be inferred from the randomized design or from the posted result.

The record does not specify the analysis population, identify exclusions, or report the number of participants with missing endpoint data. The equal group denominators and total enrollment are reported, but do not by themselves confirm complete outcome ascertainment for every randomized participant. The registry also does not provide a breakdown of primary events by KDIGO stage, or additional details about serum-creatinine measurement and outcome assessment.

Only one primary outcome measure is listed, and no secondary outcome results are posted. The record does not report a multiplicity plan, subgroup analyses, or further outcome timepoints. The masking label is quadruple, but the identities of the masked roles and the implementation details are not described. Randomization is listed, but the method for generating and implementing allocation is not specified.

The safety entry gives serious and other adverse-event counts, but does not provide a full comparative safety analysis. The listed serious-event terms are not assigned to a treatment group in the term summary, and death counts are not reported in the registry record. These reporting limits constrain interpretation of both efficacy-related outcomes and safety.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Aminophylline to Prevent Acute Kidney Injury in Children After Cardiac Surgery — NCT01245595.
• Registry record last updated 2015-06-08; status last verified 2015-06.
• Results first posted 2015-06-08.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

21. Record Summary

The registry record describes a completed, randomized, placebo-controlled, parallel-group trial of aminophylline after pediatric cardiac surgery with cardiopulmonary bypass. It lists quadruple masking, 144 enrolled participants, and 72 participants in each group. The aminophylline regimen was an intravenous bolus of 5 mg/kg followed by 1.8 mg/kg intravenously every 6 hours; the comparator was normal saline placebo.

The primary outcome was participants meeting KDIGO acute kidney injury serum-creatinine criteria within 5 days. The posted counts were 43 in the aminophylline group and 36 in the placebo group. The unadjusted risk-difference confidence interval includes zero, and the unadjusted p-value is 0.241. No secondary outcome results or analysis entries are posted. The registry record does not report the original sample-size justification, analysis plan, missing-data handling, or analysis population.