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 RAINBOW Study: RAnibizumab Compared With Laser Therapy for the Treatment of INfants BOrn Prematurely With Retinopathy of Prematurity (NCT02375971), a randomized phase 3 study. The primary outcome is Percentage of Participants With Absence of Active ROP and Absence of Unfavorable Structural Outcomes in Both Eyes at Week 24.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT02375971 |
| Phase | Phase 3 |
| Condition | Retinopathy of Prematurity |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | None (open label) |
| Enrollment | 224 |
| Arms in the primary outcome | 3 |
| Lead sponsor | Novartis Pharmaceuticals |
| Results posted | Yes |
2. Clinical Question
Population
Prematurely born infants with retinopathy of prematurity (ROP) were enrolled. The primary analysis population was the Full Analysis Set, defined in the registry record as participants with an observed value.
Intervention
Two intravitreal ranibizumab regimens were studied: 0.2 mg and 0.1 mg. Each regimen specified an injection in both eyes on Day 1, with up to 2 re-treatments allowed for each eye if required.
Comparator
The comparator was laser therapy to each eye on Day 1, with supplementary treatments allowed. The trial was randomized, open-label, and used a parallel-group design.
Primary question
At Week 24, what percentage of participants had absence of active ROP and unfavorable structural outcomes in both eyes, while also meeting the other criteria in the endpoint definition? The registry describes the study purpose as determining whether intravitreal ranibizumab was superior to laser ablation therapy.
This is a combined outcome rather than a measure of one isolated retinal feature. To meet it, participants had to survive, have no intervention with a second modality for ROP, have absence of active ROP, and have absence of unfavorable structural outcome. These criteria combine clinical status with treatment and survival conditions, so the percentage reflects all of them together.
The clinical comparison is therefore about the probability of meeting the complete Week 24 definition under each assigned strategy. It does not, by itself, establish how the treatments compare on each component separately. Nor does the endpoint describe outcomes beyond the stated assessment time. The registry record does not report a separate primary question about longer-term vision or development.
3. Trial Design
RAINBOW was a randomized, controlled, parallel-group Phase 3 study of treatment for retinopathy of prematurity. The registry lists an enrollment of 224 and identifies Novartis Pharmaceuticals as the sponsor. The study is recorded as completed. Its listed start was 2015-12-30, and its primary completion date was 2017-12-14.
Three treatment groups were described: ranibizumab 0.2 mg, ranibizumab 0.1 mg, and laser therapy. Both ranibizumab regimens called for one intravitreal injection in both eyes on Day 1 (Baseline), with up to 2 re-treatments allowed for each eye if required. The laser group received treatment to each eye on Day 1 (Baseline), with supplementary treatments allowed. The registry record does not give further details about the criteria used to decide on retreatment.
Masking was listed as none, so the study was open-label. This matters when interpreting outcomes that may involve clinical judgment, care decisions, or knowledge of assigned treatment. Random allocation can help balance groups, but it does not make an open-label study blinded. The record does not report additional information about allocation concealment or masking of outcome assessment.
The primary outcome was assessed at Week 24. The registry also lists secondary outcomes covering additional ROP interventions, recurrent ROP, events during the study, adverse events, ranibizumab injections, and pharmacokinetic and VEGF measurements. The listed event follow-up runs from Day 1 after treatment initiation to study exit (Day 169). The original statistical design assumptions, the rationale for the enrollment target, and details of the randomization procedure are 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.
Before assignment: One patient was discontinued prior to receiving any study treatment and was later re-randomized; this patient is counted twice in the Randomized Set (FAS) (225). The number of unique participants randomized in the study is 224.
Treatment (Day 1 - Baseline)
| Stage | Ranibizumab 0.2 mg | Ranibizumab 0.1 mg | Laser Therapy |
|---|---|---|---|
| STARTED | 74 | 77 | 74 |
| Safety Set | 73 | 76 | 69 |
| VEGF Set | 19 | 26 | 51 |
| PK Set | 49 | 46 | 0 |
| COMPLETED | 73 | 76 | 69 |
| NOT COMPLETED | 1 | 1 | 5 |
Reasons for not completing this period:
| Reason | Ranibizumab 0.2 mg | Ranibizumab 0.1 mg | Laser Therapy |
|---|---|---|---|
| Subj/Guardian Decision | 0 | 0 | 2 |
| Physician Decision | 1 | 1 | 1 |
| Lost to Follow-up | 0 | 0 | 1 |
| Adverse Event | 0 | 0 | 1 |
Follow-Up Phase (up to Day 169)
| Stage | Ranibizumab 0.2 mg | Ranibizumab 0.1 mg | Laser Therapy |
|---|---|---|---|
| STARTED | 73 | 76 | 69 |
| COMPLETED | 66 | 71 | 64 |
| NOT COMPLETED | 7 | 5 | 5 |
Reasons for not completing this period:
| Reason | Ranibizumab 0.2 mg | Ranibizumab 0.1 mg | Laser Therapy |
|---|---|---|---|
| Adverse Event | 1 | 0 | 0 |
| Subject/Guardian Decision | 1 | 0 | 1 |
| Death | 4 | 4 | 4 |
| Withdrawal of Consent | 1 | 1 | 0 |
Analysis population for the primary outcome, as defined in the registry: The Full Analysis Set (FAS), which consisted of all participants with an observed value, was considered.
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 | Ranibizumab 0.2 mg | Ranibizumab 0.1 mg | Laser Therapy | Total |
|---|---|---|---|---|---|
| Participants analysed | 74 | 77 | 74 | 225 | |
| Age, Continuous | Weeks | 25.8 (SD 2.25) | 26.5 (SD 2.57) | 26.2 (SD 2.59) | 26.1 (SD 2.48) |
| Sex: Female, Male: Female | Participants | 41 | 40 | 37 | 118 |
| Sex: Female, Male: Male | Participants | 33 | 37 | 37 | 107 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 0 | 0 | 0 | 0 |
| Race (NIH/OMB): Asian | Participants | 27 | 22 | 23 | 72 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 0 | 0 | 0 | 0 |
| Race (NIH/OMB): Black or African American | Participants | 0 | 4 | 3 | 7 |
| Race (NIH/OMB): White | Participants | 43 | 45 | 45 | 133 |
| Race (NIH/OMB): More than one race | Participants | 0 | 0 | 0 | 0 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 4 | 6 | 3 | 13 |
6. Primary Endpoint
The registry lists the primary outcome as Percentage of Participants With Absence of Active ROP and Absence of Unfavorable Structural Outcomes in Both Eyes at Week 24, measured over Week 24.
| Element | Registry entry |
|---|---|
| Result type | Number |
| Measure of spread | not applicable |
| Unit | Percentage of Participants |
| Endpoint classification | Binary Endpoint |
The primary endpoint is the percentage of participants with absence of active ROP and absence of unfavorable structural outcomes in both eyes at Week 24. The registry defines success as meeting all of its listed conditions: survival, no intervention with a second modality for ROP, absence of active ROP, and absence of unfavorable structural outcome. A participant who did not meet any one of these conditions would not meet the combined endpoint as described.
A composite endpoint can capture several clinically relevant aspects of a treatment course in one outcome. Here, it incorporates survival, the need for a second treatment modality, active disease, and structural outcome. This gives the result a broader scope than a measure of retinal disease activity alone. It also means that the overall percentage cannot show which component most influenced the result. Separate component results would be needed to distinguish those contributions.
The registry describes the Full Analysis Set as all participants with an observed value. This definition indicates that the reported endpoint analysis was based on participants for whom an outcome value was observed; it does not, on its own, describe how missing values were handled or whether sensitivity analyses were performed. Those details are not reported in the registry record.
The endpoint is specific to the Week 24 assessment and the stated criteria. It does not directly quantify longer-term outcomes, nor does it separately report each eye's status as an independent result. Interpretation should therefore stay tied to the composite definition and assessment time.
7. Results Posted in the Registry
- Ranibizumab 0.1 mg: 75.3% (58/77) versus 79.7% (59/74) on control; risk difference -4.4 percentage points (95% CI -17.7 to 8.9), risk ratio 0.94 (0.80–1.12); unadjusted two-proportion z-test p = 0.517.
- Laser Therapy: 66.2% (49/74) versus 79.7% (59/74) on control; risk difference -13.5 percentage points (95% CI -27.7 to 0.6), risk ratio 0.83 (0.68–1.01); unadjusted two-proportion z-test p = 0.064.
Risk difference: Ranibizumab 0.1 mg
95% CI: -17.7 to 8.9 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 |
|---|---|---|---|---|
| Percentage of Participants Requiring Interventions With a Second Modality for ROP at Week 24 | Binary Endpoint | Risk difference | +2.0 pts (-9.6 to 13.7) | 5,146 per arm |
| Number of Participants Experiencing an Event, From the First Study Treatment to the Last Study Visit | Binary Endpoint | Risk difference | +4.5 pts (-8.5 to 17.5) | 1,317 per arm |
Percentage of Participants Requiring Interventions With a Second Modality for ROP at Week 24
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Ranibizumab 0.1 mg: 16.9% (13/77) versus 14.9% (11/74) on control; risk difference 2.0 percentage points (95% CI -9.6 to 13.7), risk ratio 1.14 (0.54–2.37); unadjusted two-proportion z-test p = 0.735.
- Laser Therapy: 24.3% (18/74) versus 14.9% (11/74) on control; risk difference 9.5 percentage points (95% CI -3.2 to 22.2), risk ratio 1.64 (0.83–3.22); unadjusted two-proportion z-test p = 0.147.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Ranibizumab 0.1 mg and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Laser Therapy and the control. The interval gives the range of effects that remain compatible with the data.
Number of Participants Experiencing an Event, From the First Study Treatment to the Last Study Visit
- 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:
- Ranibizumab 0.1 mg: 23.4% (18/77) versus 18.9% (14/74) on control; risk difference 4.5 percentage points (95% CI -8.5 to 17.5), risk ratio 1.24 (0.66–2.30); unadjusted two-proportion z-test p = 0.503.
- Laser Therapy: 31.1% (23/74) versus 18.9% (14/74) on control; risk difference 12.2 percentage points (95% CI -1.7 to 26.0), risk ratio 1.64 (0.92–2.94); unadjusted two-proportion z-test p = 0.088.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Ranibizumab 0.1 mg and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Laser Therapy and the control. The interval gives the range of effects that remain compatible with the data.
The registry lists secondary outcomes spanning treatment escalation, recurrence, events during follow-up, adverse events, pharmacokinetic measurements, VEGF levels, and injection counts. The available arm-level numerical details cover only some of those outcomes. Across the secondary comparisons with recalculated results, the estimates are not uniformly decisive: the intervals include the no-difference value. The numerical pattern therefore does not provide a consistent, independently conclusive extension of the primary comparison.
These secondary outcomes address different questions from the primary composite. A second-modality intervention concerns treatment escalation; recurrence concerns later disease activity and intervention; an event count during follow-up is broader; and concentration or VEGF measurements are laboratory measures. These should not be treated as interchangeable measures of the Week 24 combined outcome. The registry lists 11 secondary outcomes, but numerical results for every listed measure are not reported in the registry record considered in these results.
Secondary analyses are often interpreted with less weight than a prespecified primary analysis, particularly when many outcomes or comparisons are examined. With multiple opportunities to find a small p-value, the chance of at least one apparently unusual result can increase unless multiplicity is addressed. The registry record does not report a multiplicity adjustment or a hierarchy for interpreting secondary outcomes. This does not make the secondary outcomes irrelevant; it means isolated secondary findings need cautious interpretation and should be considered alongside their estimates, precision, and role in the analysis plan.
They also do not resolve the discrepancy between the sponsor's primary analysis and the simple primary re-calculations. The secondary findings have different endpoints and should not be used as a substitute for clarifying the primary analysis method or its reported contrast.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Percentage of Participants Requiring Interventions With a Second Modality for ROP at Week 24
- Number of Participants Experiencing an Event, From the First Study Treatment to the Last Study Visit
- Percentage of Participants Having Recurrent ROP and Receiving Any Post-baseline Intervention at or Before Week 24
- Percent of Participants With Ocular Adverse Events by Primary System Organ (SOCs) at Week 24
- Mean Change in Ranibizumab Concentration in Pharmacokinetic Serum Samples Over Time at Day 1, Day 15 and Day 29
- Mean Change in Vascular Endothelial Growth Factor (VEGF) Levels Over Time at Day 1, Day 15 and Day 29
- Total Number of Ranibizumab Injections Received at Week 24
- Percent of Participants With Non-Ocular Adverse Events by Primary System Organ (SOCs) at Week 24
9. Statistical Interpretation
For the primary outcome, the posted percentages were 80.0 for ranibizumab 0.2 mg, 75.0 for ranibizumab 0.1 mg, and 66.2 for laser therapy. These are the percentages meeting the full Week 24 composite definition, not percentages meeting one component in isolation. The posted arm summaries show numerically higher endpoint values for both ranibizumab groups than for laser.
The simple unadjusted re-calculations compare each other group with ranibizumab 0.2 mg. For ranibizumab 0.1 mg, the recalculated risk difference is -0.044, with a confidence interval from -0.177 to 0.089. For laser therapy, it is -0.135, with a confidence interval from -0.277 to 0.006. These are unadjusted calculations from the posted summary statistics, not the sponsor's own analysis. Each interval includes the no-difference value, so these calculations do not establish a clear difference between the compared groups on their own.
The registry also reports a sponsor analysis using the Cochran-Mantel-Haenszel method, with an odds ratio of 2.19, a 95% confidence interval from 0.993 to 4.824, and p = 0.025. It labels the analysis as superiority. The analysis lists all three groups, and the record does not give enough detail to reconstruct the exact contrasts, coding, or adjustment. The reported interval lies close to the odds-ratio null value, while the reported p-value is below 0.05. The apparent difference between that reported result and the simple re-calculations cannot be resolved from the registry entries. Because a discrepancy is flagged, the sponsor's own analysis takes precedence over the unadjusted re-calculations.
The sponsor's result should still be read with its precision in mind. The confidence interval is broad and its lower endpoint is close to the null value, indicating that the estimate is not sharply determined. The posted result also does not describe the individual endpoint components, so it cannot establish whether the treatment groups differed in survival, retreatment, active ROP, or structural outcomes separately.
Overall, the registry record contains both arm-level percentages and a sponsor-reported superiority analysis, but they are not interchangeable summaries. The percentages are descriptive; the re-calculated risk differences are simple unadjusted comparisons; and the sponsor's analysis uses a named statistical method and is the stated trial analysis. The record does not report the full model specification, covariates, or additional analyses needed to explain their differing results. Neither the re-calculation nor the sponsor's statistical result should be treated as a complete account of clinical benefit or harm.
10. Statistical Methods Explained
The primary outcome is binary at the participant level: the participant either meets the combined Week 24 criteria or does not. Reporting a percentage makes the result interpretable as the share of the analysis group meeting that definition. The arm percentages describe observed results; they do not alone quantify how certain the comparison is.
What does a risk difference describe?
A risk difference expresses the difference between two event proportions on the original probability scale. In these re-calculations, the event is meeting the favorable primary endpoint, and ranibizumab 0.2 mg is the reference group. The estimates are shown as the other group's proportion minus the reference group's proportion. A negative estimate therefore corresponds to a lower observed percentage meeting the endpoint in the compared group. The risk difference is unadjusted: it is calculated from the posted arm summaries rather than from the sponsor's reported analysis method.
Keeping the scale in view is important. A risk difference speaks to absolute separation in proportions, whereas a relative measure such as a risk ratio or odds ratio describes a comparison on a different scale. These measures can look different numerically and should not be treated as if they were the same quantity. The registry's sponsor result is an odds ratio, while the simple re-calculations discussed alongside it are risk differences.
What does the confidence interval add?
A confidence interval describes the range of estimates compatible with the data under the method used to construct it. It conveys uncertainty around an estimate, rather than guaranteeing that the true value lies within a particular range. For a risk difference, an interval that includes the no-difference value indicates that the data and calculation are compatible with no difference as well as with values on either side. The interval's width also matters: a wider interval reflects less precision than a narrower interval.
A p-value addresses how unusual the observed data, or data more extreme, would be under a specified null hypothesis and model. It is not the probability that the null hypothesis is true, and it does not measure clinical importance. A p-value alone also does not provide the size or precision of an effect; estimates and intervals are needed for that context.
What is the sponsor's method?
The registry identifies the sponsor's analysis as Cochran-Mantel-Haenszel and reports an odds ratio. In general, the Cochran-Mantel-Haenszel approach can combine information across strata to estimate an association while accounting for those strata. The registry entries cited for this result do not describe the strata, coding, or exact contrast used. It is therefore not possible to reproduce or fully explain the sponsor estimate from the arm percentages alone. The sponsor's reported analysis and a simple unadjusted re-calculation answer related but not necessarily identical statistical questions.
For a binary endpoint, a method's treatment of the comparison and analysis population can affect the estimate and its uncertainty. The Full Analysis Set is described as participants with an observed value, but the registry record does not report a fuller missing-data procedure or a model specification that would allow a more exact methodological reconstruction. The analysis method should not be inferred beyond what the record states.
Why can re-calculations differ?
A re-calculation from group-level proportions does not reproduce an analysis that may use a different estimand, adjustment, stratification, or handling of data. The registry flags a discrepancy between the simple calculations and the sponsor analysis. The sponsor's own analysis therefore takes precedence for the trial's reported inferential conclusion. The record does not supply enough methodological detail to identify the source of the discrepancy, and no explanation should be assumed.
These distinctions are particularly important when an interval and p-value appear close to a conventional decision threshold. The estimate, confidence interval, p-value, and method should be read together, with attention to whether they come from the same analysis. Here, the re-calculated intervals belong to the unadjusted risk-difference comparisons, while the sponsor's odds ratio and p-value belong to the reported Cochran-Mantel-Haenszel analysis. They should not be combined into a single internally consistent test without further information.
11. Confidence Intervals and Precision
The precision of a comparison is conveyed by its confidence interval as well as its point estimate. The unadjusted risk-difference interval for ranibizumab 0.1 mg versus ranibizumab 0.2 mg extends from -0.177 to 0.089. The interval for laser therapy versus ranibizumab 0.2 mg extends from -0.277 to 0.006. Both include the no-difference value, and both cover a range of possible effects on either side of that value. The posted summaries therefore do not pin down the direction of the unadjusted difference with high precision.
The sponsor analysis reports an odds ratio of 2.19 with a 95% confidence interval from 0.993 to 4.824. That interval is wide, and its lower endpoint is close to the odds-ratio null value. The estimate is consequently compatible with a range of association sizes. The reported p-value is p = 0.025, but the interval and p-value are from the sponsor's reported analysis and should not be conflated with the intervals from the unadjusted risk-difference calculations.
Confidence intervals are not a measure of clinical importance. A narrow interval can be precise without establishing that an effect matters clinically, and a wide interval can leave substantial uncertainty even when a point estimate appears favorable. The registry does not provide a threshold for a clinically important difference on this endpoint. Nor does it report component-specific intervals that would show precision for the separate parts of the composite.
Because the record flags a discrepancy, the sponsor's own analysis takes precedence for the trial's reported inference. The available details do not resolve why the sponsor result and simple recalculations differ, so that uncertainty about the comparison's precision and interpretation should remain explicit.
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 | 1,409 | 1,885 |
| 75% of the observed effect | 2,461 | 3,294 |
| 50% of the observed effect | 5,437 | 7,278 |
The sample-size displays are planning illustrations based on the observed effect, not the assumptions used to design this trial. For the binary outcomes, the figures are participants per arm. The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each planning row uses the stated fraction of the observed effect as the effect to detect. The registry record does not report the trial's original sample-size justification or design assumptions.
The 80% power column describes the planned number of participants per arm for a design with an 80% chance of detecting the specified effect under the planning assumptions, if that effect and those assumptions held. The 90% power column uses a higher chance of detection and generally requires more participants per arm for the same assumed effect. These are design concepts: power is the probability of detecting an effect under specified conditions, not the probability that a result is true.
The rows that plan for smaller fractions of the observed effect require more participants per arm. Smaller effects are harder to distinguish from random variation, so a larger study is needed to reach the same target power under otherwise similar assumptions. The displayed calculations use the observed effect as a starting point, which makes them sensitive to uncertainty in that observed estimate.
For a time-to-event outcome, the stated convention is total number of events, using the Schoenfeld approach; other outcomes are expressed as participants per arm. That distinction is important when reading a planning display: an event target is not a participant target. These figures are planning illustrations, not observed power.
13. How the Sample Size Is Derived
Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z1−α/2 = 1.960) and the desired power (z1−β = 0.842 for 80% and 1.282 for 90%).
Formula
n 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 = 0.797; treatment proportion p1 = 0.753; average p̄ = 0.775.
- First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.5903 = 1.1570.
- Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.5895 = 0.4961.
- n = (1.1570 + 0.4961)2 / (-0.0441)2 = 1,408.3, rounded up to 1,409 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 <- 0.797297297297297 # control proportion
p1 <- 0.753246753246753 # 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(2375971)
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 = 1,409 (80% power), 1,885 (90% power)
75% of observed effect: n per arm = 2,461 (80% power), 3,294 (90% power)
50% of observed effect: n per arm = 5,437 (80% power), 7,278 (90% power)
power.prop.test: 1408.3
Simulated power at n = 1,409 per arm: 0.801 (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
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| Cochran-Mantel-Haenszel | Odds Ratio (OR) 2.19 | 0.9932 to 4.8235 | 0.025 |
The sponsor's reported primary analysis uses the Cochran-Mantel-Haenszel method and gives an odds ratio of 2.19, a 95% confidence interval from 0.993 to 4.824, and p = 0.025. The registry labels this as a superiority analysis and lists the three treatment groups. It does not provide enough detail in the record to reconstruct the exact contrast, outcome coding, or any strata used by the method.
The simple re-calculations instead compare ranibizumab 0.1 mg and laser therapy separately with ranibizumab 0.2 mg, using unadjusted risk differences from the posted proportions. Their confidence intervals include no difference. These calculations are not a reproduction of the sponsor's analysis and do not replace it. Since the record flags a discrepancy, the sponsor's own analysis takes precedence.
The sponsor's confidence interval has a lower endpoint close to the odds-ratio null, while its reported p-value is below 0.05. The registry entries do not explain this apparent tension or identify a particular cause for the discrepancy. Differences in estimand or analysis method can matter generally, but the record does not establish that any specific difference explains these results. The sponsor's conclusion should be read as the reported trial analysis, with its interval and methodological details kept in view.
15. Multiplicity, Missing Data and Analysis Populations
The registry record lists a primary endpoint and multiple secondary outcomes. Testing several outcomes or treatment comparisons can raise a multiplicity concern: even when each individual test uses a conventional threshold, the chance of at least one apparently positive result can increase across a collection of tests. A prespecified testing hierarchy or adjustment can address some of that concern, but details of such a plan are not reported in the registry record.
The reported sponsor analysis is labelled superiority, but the registry entries do not state how the three-group comparison was handled for multiplicity, whether there were planned pairwise comparisons, or whether any adjustment was made. The simple re-calculations are unadjusted. They are descriptive re-analyses of posted summary statistics and do not provide a multiplicity-controlled alternative to the sponsor analysis.
The primary analysis population is described as the Full Analysis Set, consisting of participants with an observed value. This statement identifies the population definition used for the posted primary outcome, but it does not explain the extent or pattern of missing outcomes, the reasons values were absent, or any imputation or sensitivity-analysis procedures. Those details are not reported in the registry record. Missing outcome data can affect a percentage-based result if the participants with observed values differ from those without observed values; the extent of that possibility cannot be assessed from the available information.
The record also does not report the original statistical analysis plan, interim analyses, sample-size justification, or further model details. Those items should not be inferred from the registry's posted result. In particular, the observed-value definition should not be mistaken for a complete missing-data strategy, and the stated superiority label should not be taken as evidence that every multiplicity issue has been addressed.
16. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Ranibizumab 0.2 mg | 26 | 73 | 35.6% |
| Ranibizumab 0.1 mg | 24 | 76 | 31.6% |
| Laser | 24 | 69 | 34.8% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Ranibizumab 0.2 mg | 4 of 73 |
| Ranibizumab 0.1 mg | 4 of 76 |
| Laser | 4 of 69 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 4% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Ranibizumab 0.2 mg | 43 of 73 |
| Ranibizumab 0.1 mg | 47 of 76 |
| Laser | 37 of 69 |
Most frequent serious adverse event terms
| Event term | Organ system | Ranibizumab 0.2 mg | Ranibizumab 0.1 mg | Laser |
|---|---|---|---|---|
| Retinopathy of prematurity | Eye disorders | 2 of 73 | 1 of 76 | 3 of 69 |
| Bronchiolitis | Infections and infestations | 2 of 73 | 4 of 76 | 0 of 69 |
| Pneumonia | Infections and infestations | 4 of 73 | 0 of 76 | 2 of 69 |
| Bronchopulmonary dysplasia | Respiratory, thoracic and mediastinal disorders | 2 of 73 | 2 of 76 | 2 of 69 |
| Apnoea | Respiratory, thoracic and mediastinal disorders | 0 of 73 | 2 of 76 | 2 of 69 |
| Respiratory failure | Respiratory, thoracic and mediastinal disorders | 0 of 73 | 3 of 76 | 1 of 69 |
| Inguinal hernia | Gastrointestinal disorders | 1 of 73 | 2 of 76 | 0 of 69 |
| Necrotising colitis | Gastrointestinal disorders | 0 of 73 | 3 of 76 | 0 of 69 |
| Vomiting | Gastrointestinal disorders | 0 of 73 | 1 of 76 | 2 of 69 |
| Sepsis | Infections and infestations | 0 of 73 | 1 of 76 | 2 of 69 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Ranibizumab 0.2 mg | Ranibizumab 0.1 mg | Laser |
|---|---|---|---|---|
| Retinal haemorrhage | Eye disorders | 6 of 73 | 10 of 76 | 7 of 69 |
| Pyrexia | General disorders | 9 of 73 | 6 of 76 | 4 of 69 |
| Dermatitis diaper | Skin and subcutaneous tissue disorders | 8 of 73 | 6 of 76 | 4 of 69 |
| Anaemia | Blood and lymphatic system disorders | 4 of 73 | 8 of 76 | 5 of 69 |
| Nasopharyngitis | Infections and infestations | 7 of 73 | 5 of 76 | 4 of 69 |
| Conjunctival haemorrhage | Eye disorders | 6 of 73 | 6 of 76 | 2 of 69 |
| Gastrooesophageal reflux disease | Gastrointestinal disorders | 5 of 73 | 5 of 76 | 4 of 69 |
| Upper respiratory tract infection | Infections and infestations | 6 of 73 | 3 of 76 | 1 of 69 |
| Conjunctivitis | Infections and infestations | 1 of 73 | 6 of 76 | 2 of 69 |
| Bronchopulmonary dysplasia | Respiratory, thoracic and mediastinal disorders | 2 of 73 | 3 of 76 | 4 of 69 |
Serious events with the highest arm-level rate: pneumonia (5.5%), bronchiolitis (5.3%), retinopathy of prematurity (4.3%), necrotising colitis (3.9%), respiratory failure (3.9%).
The adverse-event listing reports serious adverse events among participants at risk in each group. It records 26 affected among 73 at risk for ranibizumab 0.2 mg, 24 among 76 at risk for ranibizumab 0.1 mg, and 24 among 69 at risk for laser. The registry also lists 4 deaths in each group. These are counts from the adverse-event record; they do not, by themselves, establish whether an event was caused by treatment.
The listed serious-event terms include Pneumonia (5.5%), Bronchiolitis (5.3%), Retinopathy of prematurity (4.3%), Necrotising colitis (3.9%), Respiratory failure (3.9%), and Vomiting (2.9%). The record does not provide enough context in these details to determine how each term was defined, whether events were judged related to treatment, or how severity and timing varied among groups. These figures should therefore be read as safety reporting, not as causal comparisons.
The at-risk denominators differ among the groups and are not the same as the primary outcome analysis denominators. A direct comparison requires attention to the underlying population, follow-up, and event definitions. The registry record does not report a formal comparative analysis of these serious-event figures.
17. What the Result Does, and Does Not, Mean
The primary endpoint captures whether participants met a combined set of survival, treatment, disease-activity, and structural-outcome criteria at Week 24. The arm summaries show higher observed percentages for both ranibizumab regimens than for laser therapy. The sponsor's reported analysis is labelled superiority, and its estimate and p-value are part of the registry's reported trial analysis. Because a discrepancy is flagged, that sponsor analysis takes precedence over the simple unadjusted re-calculations.
This result does not establish that every component of the composite differed between groups. A combined endpoint can be met or missed for different reasons, and the overall percentage does not identify which criterion drove the result. The posted outcome also does not establish a difference in longer-term function or other outcomes not measured by this Week 24 definition. Such conclusions are not reported in the registry record.
The statistical comparison should not be translated into a guarantee for an individual participant. Group-level percentages describe the study groups, while individual outcomes may differ. The result also does not, on its own, establish the cause of any adverse event or fully characterize treatment safety. The adverse-event listings require their own definitions and comparative context.
Interpretation is limited by the open-label design, the available information about missing outcomes, and the absence of detailed analysis-plan information in the registry record. The sponsor's reported inference and the posted arm percentages are useful but answer different statistical questions. The unadjusted re-calculations are not a substitute for the sponsor's method, and the record does not explain the discrepancy. A careful reading keeps the endpoint definition, analysis method, uncertainty, and limits of the record together rather than reducing the evidence to a single p-value or arm ranking.
18. Why This Trial Matters Statistically
This trial presents several statistical issues that are common in clinical research. First, the primary endpoint is a composite: it combines survival, treatment escalation, disease activity, and structural outcomes. Such an endpoint can capture more than one aspect of a clinical course, but interpretation depends on understanding every component and recognizing that the overall result does not identify which component accounts for the difference.
Second, the trial has three randomized groups, while the sponsor's reported analysis is a Cochran-Mantel-Haenszel odds ratio and the simple recalculations are separate unadjusted risk differences against ranibizumab 0.2 mg. These measures and analysis approaches are not interchangeable. Their contrast, scale, and assumptions need to be clear before estimates are compared. The registry flags a discrepancy, making it especially important to distinguish the reported sponsor analysis from an unadjusted reconstruction.
Third, the reported primary inference sits alongside uncertainty in the estimates. Confidence intervals communicate how much the data constrain possible effects; a p-value alone does not. In this record, the sponsor's interval is broad and close to its null value at the lower end, while the straightforward risk-difference intervals include no difference. The record does not provide enough methodological detail to reconcile these summaries.
Finally, the outcome population is described in terms of observed values, while fuller missing-data and multiplicity procedures are not reported. These features affect how confidently readers can generalize the statistical result. The trial is therefore a useful case for reading an endpoint, analysis method, uncertainty, and registry detail as parts of one interpretation rather than relying on a headline conclusion alone.
19. Limitations
- The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
- Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.
- Participant counts were reconstructed from posted percentages and arm sizes, so small rounding differences are possible.
The study was open-label, with masking listed as none. Knowledge of treatment assignment may matter for clinical decisions, retreatment, or outcome assessments that involve judgment. The record does not report whether outcome assessment was independently masked or how decisions about supplementary laser treatment and ranibizumab re-treatment were standardized.
The primary outcome is a composite measured at Week 24. It combines survival, no second-modality intervention, absence of active ROP, and absence of unfavorable structural outcome. The posted overall percentage does not separate these components, and the registry record does not give component-specific primary results in the details. The outcome therefore has limited ability to show which aspect of the clinical course accounts for the arm-level pattern.
The Full Analysis Set is defined as participants with an observed value, but the record does not report the amount or pattern of missing primary outcome data, reasons for missingness, imputation, or sensitivity analyses. The record also does not give the original sample-size justification, detailed analysis plan, multiplicity strategy, or enough information to reconstruct the sponsor's contrast and explain the flagged discrepancy.
The primary endpoint is assessed at Week 24, and the listed event follow-up extends to study exit (Day 169). The registry entries do not establish longer-term outcomes beyond those periods. Finally, the three treatment strategies permit re-treatment or supplementary treatment under specified conditions, but the criteria and actual use are not fully described in the details. These limitations constrain interpretation of both efficacy comparisons and safety patterns.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: RAINBOW Study: RAnibizumab Compared With Laser Therapy for the Treatment of INfants BOrn Prematurely With Retinopathy of Prematurity — NCT02375971.
- Registry record last updated 2018-11-14; status last verified 2018-10.
- Results first posted 2018-07-31.
- Data retrieved from ClinicalTrials.gov on 2026-11-09.
- Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.
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23. Record Summary
RAINBOW was a randomized, open-label, parallel-group Phase 3 study of ranibizumab 0.2 mg, ranibizumab 0.1 mg, and laser therapy for retinopathy of prematurity. The registry lists enrollment of 224 and records the study as completed.
The primary outcome was the percentage meeting a combined favorable definition in both eyes at Week 24. Posted arm percentages were 80.0 for ranibizumab 0.2 mg, 75.0 for ranibizumab 0.1 mg, and 66.2 for laser therapy. The sponsor reported a Cochran-Mantel-Haenszel superiority analysis with an odds ratio of 2.19, a 95% confidence interval from 0.993 to 4.824, and p = 0.025. A discrepancy is flagged between that result and simple unadjusted re-calculations; the sponsor's own analysis takes precedence.
The registry also lists secondary outcomes and adverse-event information. Important details about the original design assumptions, multiplicity, missing-data handling, and the full analysis specification are not reported in the registry record.