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 Irinotecan and Cetuximab With or Without Bevacizumab in Treating Patients With RAS Wild-Type Locally Advanced or Metastatic Colorectal Cancer That Cannot Be Removed by Surgery (NCT02292758), a randomized phase 2 study. The primary outcome is Progression-Free Survival (PFS).
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT02292758 |
| Phase | Phase 2 |
| Condition | Colorectal Adenocarcinoma, RAS Wild Type, Stage IV Colorectal Cancer AJCC v7 |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Double |
| Enrollment | 36 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Academic and Community Cancer Research United |
| Results posted | Yes |
2. Clinical Question
Population
The registry describes people with RAS-wildtype metastatic colorectal cancer that could not be removed by surgery, and the official title further identifies the disease as irinotecan-refractory. The trial enrolled 36 participants: 19 in the bevacizumab arm and 17 in the placebo arm.
Intervention
The experimental regimen combined irinotecan and cetuximab with bevacizumab. The arm description says the three medicines were given intravenously on day 1, with cycles repeating every 14 days in the absence of disease progression or unacceptable toxicity.
Comparator
The comparison regimen used irinotecan and cetuximab with placebo in place of bevacizumab. It was also administered intravenously on day 1, with cycles repeating every 14 days in the absence of disease progression or unacceptable toxicity.
Primary question
The primary question was whether the time from randomization to documented disease progression or death differed between the two groups. The registry reports median progression-free survival and a hazard-ratio analysis, with progression assessed according to RECIST version 1.1 and follow-up described as up to 24 months.
The central statistical contrast is between two multi-drug regimens that share irinotecan and cetuximab and differ by bevacizumab versus placebo. The randomized, double-blind design is intended to make the groups comparable at the start and to reduce the chance that knowledge of assignment affects participant care or outcome assessment. The record identifies a parallel-group phase II study and an enrollment of 36.
The primary endpoint captures the interval until the first of two events: documented progression or death from any cause. This combines disease progression and death into a single time-to-event outcome. The comparison therefore concerns the distribution of time until an event, rather than simply the proportion of participants with an event at one particular assessment.
The registry reports group medians and a hazard ratio for the primary endpoint. Those statistics provide different views of the comparison: medians describe the time at which the estimated event distribution reaches its midpoint, while a hazard ratio summarizes the relative event rate over follow-up under the model used. Neither statistic alone describes every feature of the survival curves. The posted confidence interval and p-value are important to judging the uncertainty in the estimated contrast.
3. Trial Design
BOND-3 is recorded as a randomized, double-blind, parallel-group phase II trial sponsored by Academic and Community Cancer Research United. The record reports enrollment of 36 participants and a completed status. The recorded study start is 2014-12-12, and the primary completion date is 2019-03-20. The record identifies colorectal adenocarcinoma, RAS wild type, and stage IV colorectal cancer among its condition descriptors.
Participants were assigned to one of two regimens. Arm I combined irinotecan, cetuximab, and bevacizumab; Arm II combined irinotecan, cetuximab, and placebo. The arm descriptions specify intravenous administration on day 1, with cycles repeating every 14 days unless disease progression or unacceptable toxicity occurred. The registry lists laboratory biomarker analysis as an intervention as well as the study drugs and placebo, but further details about how biomarker analyses informed treatment or analyses are not reported in the registry record.
The primary outcome was progression-free survival, measured from randomization to the first documented disease progression or death from any cause, assessed up to 24 months. The registry says progression was defined using RECIST version 1.1 and describes Kaplan-Meier estimation of the outcome distribution. It also describes estimating median progression-free survival with confidence intervals and hazard ratios using stratified Cox models, with and without adjustment for baseline clinical or pathological factors.
The registry record does not report the randomization sequence or allocation concealment details, the factors used for stratification, or the specific baseline factors planned for adjustment. The original sample-size justification, the trial's prespecified significance threshold, any interim-analysis plan, and the full statistical analysis plan are not reported in the registry record. The presence of a phase II designation does not, by itself, establish what design assumptions or decision rules were used.
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 | Arm I (Irinotecan, Cetuximab, Bevacizumab) | Arm II (Irinotecan, Cetuximab, Placebo) |
|---|---|---|
| STARTED | 19 | 17 |
| COMPLETED | 19 | 17 |
| NOT COMPLETED | 0 | 0 |
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 | Arm I (Irinotecan, Cetuximab, Bevacizumab) | Arm II (Irinotecan, Cetuximab, Placebo) | Total |
|---|---|---|---|---|
| Participants analysed | 19 | 17 | 36 | |
| Age, Continuous | years | 58 (41 to 71) | 54 (39 to 82) | 55 (39 to 82) |
| Sex: Female, Male: Female | Participants | 9 | 7 | 16 |
| Sex: Female, Male: Male | Participants | 10 | 10 | 20 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 0 | 0 | 0 |
| Race (NIH/OMB): Asian | Participants | 1 | 1 | 2 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 0 | 0 | 0 |
| Race (NIH/OMB): Black or African American | Participants | 2 | 0 | 2 |
| Race (NIH/OMB): White | Participants | 15 | 15 | 30 |
| Race (NIH/OMB): More than one race | Participants | 0 | 0 | 0 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 1 | 1 | 2 |
| ECOG Performance Status: 0 | Participants | 14 | 12 | 26 |
| ECOG Performance Status: 1 | Participants | 5 | 5 | 10 |
6. Primary Endpoint
The registry lists the primary outcome as Progression-Free Survival (PFS), measured over From the date of randomization to the date of 1st documented disease progression or death due to any cause, whichever occurs first, assessed up to 24 months.
| Element | Registry entry |
|---|---|
| Result type | Median |
| Measure of spread | 95% Confidence Interval |
| Unit | months |
| Endpoint classification | Time-to-Event Analysis |
Progression-free survival measures the time from randomization until the first documented disease progression or death from any cause. Participants who have not experienced either event by the last available assessment contribute follow-up information up to that point, rather than being treated as if an event had occurred then. The registry describes assessment up to 24 months.
This is a time-to-event endpoint. It uses both the timing of events and information from participants whose event has not been observed during their available follow-up. That makes it different from an endpoint that only counts how many people experienced progression by a fixed date. The registry specifies Kaplan-Meier estimation for the outcome distribution and describes median estimates with confidence intervals.
The median is the time by which half of the estimated population has experienced the event, according to the estimated distribution. The hazard ratio compares event rates between groups over follow-up using a model. A hazard ratio does not directly state how many months an individual participant gains, and the median alone does not capture the whole pattern of the curves. Reading the two together, along with their uncertainty, gives a more complete statistical description.
Progression is defined in the registry according to RECIST version 1.1, including a new lesion or an increase by ≥50% of previously involved sites from nadir. Combining progression with death means the endpoint counts death from any cause as an event even when progression has not first been documented.
7. Results Posted in the Registry
- Arm I (Irinotecan, Cetuximab, Bevacizumab) vs Arm II (Irinotecan, Cetuximab, Placebo): hazard ratio 0.91 (95% CI 0.43–1.93), reported p = 0.761 (as reported in the registry).
- Arm I (Irinotecan, Cetuximab, Bevacizumab) vs Arm II (Irinotecan, Cetuximab, Placebo): hazard ratio 0.64 (95% CI 0.25–1.66) (as reported in the registry).
Hazard ratio: Arm I (Irinotecan, Cetuximab, Bevacizumab) vs Arm II (Irinotecan, Cetuximab, Placebo)
95% CI: 0.43 to 1.93
As reported in the registry
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 |
|---|---|---|---|---|
| Overall Survival (OS) | Time-to-Event Analysis | Hazard ratio | 0.47 (0.21 to 1.06) | 56 events |
| Disease Control Rate (DCR) | Binary Endpoint | Risk difference | +15.5 pts (-16.1 to 47.1) | 156 per arm |
| Overall Response Rate (ORR) | Binary Endpoint | Risk difference | +25.1 pts (-1.5 to 51.6) | 45 per arm |
Overall Survival (OS)
- Endpoint type: Time to event: compared as a hazard ratio.
- Test: Hazard ratio as reported by the sponsor (Log Rank); it was not recalculated.
- Result:
- Arm I (Irinotecan, Cetuximab, Bevacizumab) vs Arm II (Irinotecan, Cetuximab, Placebo): hazard ratio 0.47 (95% CI 0.21–1.06), reported p = 0.045 (as reported in the registry).
- Arm I (Irinotecan, Cetuximab, Bevacizumab) vs Arm II (Irinotecan, Cetuximab, Placebo): hazard ratio 0.41 (95% CI 0.15–1.09) (as reported in the registry).
- Interpretation:
- The 95% confidence interval includes no difference (a ratio of 1), so these data do not show a statistically significant difference between Arm I (Irinotecan, Cetuximab, Bevacizumab) vs Arm II (Irinotecan, Cetuximab, Placebo) and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval includes no difference (a ratio of 1), so these data do not show a statistically significant difference between Arm I (Irinotecan, Cetuximab, Bevacizumab) vs Arm II (Irinotecan, Cetuximab, Placebo) and the control. The interval gives the range of effects that remain compatible with the data.
Disease Control Rate (DCR)
- 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:
- Arm I (Irinotecan, Cetuximab, Bevacizumab): 68.4% (13/19) versus 52.9% (9/17) on control; risk difference 15.5 percentage points (95% CI -16.1 to 47.1), risk ratio 1.29 (0.75–2.22); unadjusted two-proportion z-test p = 0.342.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Arm I (Irinotecan, Cetuximab, Bevacizumab) and the control. The interval gives the range of effects that remain compatible with the data.
Overall Response Rate (ORR)
- 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:
- Arm I (Irinotecan, Cetuximab, Bevacizumab): 36.8% (7/19) versus 11.8% (2/17) on control; risk difference 25.1 percentage points (95% CI -1.5 to 51.6), risk ratio 3.13 (0.75–13.07); unadjusted two-proportion z-test p = 0.083.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Arm I (Irinotecan, Cetuximab, Bevacizumab) and the control. The interval gives the range of effects that remain compatible with the data.
The secondary outcomes provide a broader description of survival, disease control, response, treatment failure, dose intensity, and adverse events. The registry posts numeric results for overall survival, disease control rate, and overall response rate, alongside the primary progression-free survival result. Their directions are not all equivalent in statistical strength: the survival and response point estimates differ between groups, while their uncertainty and reported tests do not offer a uniform basis for firm conclusions.
These secondary findings do not supersede the primary result. They can help describe patterns that may merit further study, but they were not the endpoint designated as primary in the record. The overall-survival comparison has a reported p-value of 0.045 while its 95% confidence interval includes 1; the response and disease-control comparisons have reported p-values of 0.128 and 0.342. Such results need to be interpreted in the context of the limited enrollment and the number of outcomes examined.
When multiple outcomes are tested, the chance of obtaining at least one apparently notable result by chance can increase. Without a reported multiplicity strategy, unadjusted secondary p-values carry less weight than a single prespecified primary test. The registry lists 12 outcome measures, 10 analyses, and 8 posted secondary outcomes, but a complete account of which hypotheses were prespecified or how testing was controlled is not reported. The secondary endpoints are therefore best treated as descriptive and exploratory unless the missing analysis details clarify otherwise.
The registry lists 12-month, 18-month, and 24-month overall-survival rates, duration of response, treatment failure at 6 months, and relative dose intensity among secondary outcomes. Results for these listed outcomes are not reported in the record details available for this analysis. Their absence limits the ability to assess the full secondary-outcome pattern and should not be interpreted as a zero effect or as evidence that an outcome was not measured.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Number of Participants Who Experienced at Least One Grade 3 or Higher Adverse Events
- Overall Survival (OS)
- 12-month, 18-month, and 24-month Overall Survival (OS) Rates
- Disease Control Rate (DCR)
- Overall Response Rate (ORR)
- Duration of Response (DOR)
- Percentage of Participants With Treatment Failure at 6 Months
- Relative Dose Intensity (RDI)
9. Statistical Interpretation
For the primary endpoint, median progression-free survival was 9.7 months in the irinotecan, cetuximab, and bevacizumab group, with a 95% confidence interval of 7.1 to 13.7 months. In the irinotecan, cetuximab, and placebo group, the median was 5.5 months, with a 95% confidence interval of 3.8 to 10.2 months. The registry reports a hazard ratio of 0.912, with a 95% confidence interval of 0.431 to 1.930 and a Log Rank p-value of 0.761.
The hazard-ratio estimate is near 1, while its confidence interval includes 1 and spans values on either side. The reported p-value is not small under conventional interpretations. Taken together, the posted primary statistics do not establish a clear difference between the groups in progression-free survival. The median estimates are separated, but their uncertainty and the reported comparative analysis matter; the medians should not be read as a definitive treatment effect in isolation.
The registry also contains a second reported hazard-ratio result for the primary endpoint: 0.642, with a 95% confidence interval of 0.249 to 1.656. A p-value and method are not reported for that result. The record describes stratified Cox estimates both without and with adjustment for baseline clinical or pathological factors, but it does not identify which posted estimate corresponds to which analysis or provide enough detail to assign a specific interpretation to each. The sponsor's reported analyses take precedence over simple recalculations from summary statistics.
The overall survival results are secondary. The reported medians were 19.7 months in the bevacizumab group, with a 95% confidence interval from 14.9 months to an unreported upper limit, and 10.2 months in the placebo group, with a 95% confidence interval of 7.9 to 16.0 months. The registry reports a hazard ratio of 0.471, a 95% confidence interval of 0.209 to 1.062, and a Log Rank p-value of 0.045. The confidence interval includes 1, so the estimate remains imprecise despite the reported p-value. A second overall-survival hazard ratio is 0.406, with a 95% confidence interval of 0.151 to 1.089; its p-value and method are not reported.
For disease control rate, the posted percentages were 68.4% and 52.9%, with a reported Chi-squared p-value of 0.342. For overall response rate, the percentages were 36.8% and 11.8%, with a reported Fisher Exact p-value of 0.128. These secondary results add descriptive context, but they do not replace the primary endpoint or resolve the uncertainty in its comparative estimate. The record lists additional secondary outcomes, but does not post results for all of them in the outcome details summarized in the record.
10. Statistical Methods Explained
What does a Kaplan-Meier estimate describe?
Kaplan-Meier estimation is a method for describing time-to-event outcomes when participants may have different lengths of observed follow-up. A participant who has not had a recorded event by the end of their observed follow-up is censored at that point: their available time contributes information, but their later event time is unknown. The method uses the timing of events and censoring to estimate the event-free distribution over time. The registry says Kaplan-Meier curves were used to estimate progression-free survival by group and that medians with confidence intervals were estimated from those curves.
A median from a Kaplan-Meier curve is the point where the estimated event-free distribution reaches its midpoint. It is a useful summary, but it compresses a whole curve into one value. Curves can have different shapes even when their medians are similar, and medians can differ while the comparative evidence remains uncertain. The posted medians should therefore be read alongside the confidence intervals and the comparative analysis.
What does a hazard ratio mean?
A hazard ratio is a relative comparison of event rates at a given time among participants who have not yet had the event, as represented by the fitted model. A value of 1 corresponds to equal modeled hazards; values below or above 1 indicate that the estimated hazard is lower or higher in the first group relative to the reference group, according to the stated comparison. It is not a direct estimate of a difference in median survival time, nor does it give an individual's probability of an event.
The registry describes stratified Cox models for estimating hazard ratios, with and without adjustment for baseline clinical or pathological factors. Stratification permits the model to account for specified strata in the baseline hazard, while adjustment includes selected variables as covariates. The registry does not name the stratification factors or the adjusted factors, and does not link the two posted hazard-ratio estimates to particular model specifications. Those details are not reported in the registry record, so the two estimates cannot be fully distinguished by their adjustment status from the record alone.
How should the log-rank result be read?
The log-rank test compares event-time distributions between groups over follow-up. It tests evidence of a difference, rather than estimating the size of a clinically meaningful time gain. Its p-value is interpreted together with the estimated hazard ratio, confidence interval, group medians, and trial context. A p-value does not express the probability that a treatment is effective or ineffective. The primary endpoint's reported Log Rank p-value is 0.761; the registry reports 0.045 for the first overall-survival comparison.
Different methods can produce different summaries because they target different features of the data or use different assumptions. Kaplan-Meier medians summarize the estimated distribution; a Cox model estimates a relative hazard; and the log-rank test evaluates evidence of a group difference. Their results are related, but are not interchangeable. A model's interpretation also depends on its specification and assumptions. The registry record does not report diagnostics or enough details to assess those assumptions in this trial.
What do confidence intervals add?
A confidence interval expresses statistical uncertainty around an estimate under the method used to calculate it. A wider interval indicates less precision than a narrower interval, all else equal. For hazard ratios, an interval that includes 1 is compatible with no difference under the model at the stated confidence level, as well as with values on either side of 1. This does not prove that the groups are identical. It indicates that the data and method do not pin down the relative effect precisely enough to exclude those possibilities at that confidence level.
For medians, confidence intervals describe uncertainty in the estimated median, not the range of individual participants' survival times. A median confidence interval should not be treated as a test of the hazard ratio. Overlap or non-overlap between separate group intervals is not a substitute for the reported comparative analysis.
Why do the simple recalculations differ in role from the sponsor's analyses?
Unadjusted recalculations from posted summary statistics are descriptive checks, not replacements for participant-level analyses. They cannot account for covariates, censoring details, stratification, or other features not available in summary data. The registry supplies sponsor-reported time-to-event hazard ratios, and those analyses take precedence over any simple unadjusted recalculation. Where the record lists a second hazard ratio but no method or p-value, its exact analytic role is not reported.
General statistical practice treats trial analyses as dependent on prespecified methods, outcome definitions, follow-up, and handling of incomplete observations. Those details affect how results should be interpreted. Here, the registry describes some planned methods for the primary endpoint but does not report the full analysis plan, analysis populations, missing-data procedures, or interim-analysis details. These absences limit how completely the analyses can be independently reconstructed from the registry record.
11. Confidence Intervals and Precision
The primary hazard-ratio estimate is 0.912, with a 95% confidence interval from 0.431 to 1.930. This interval is broad and includes 1. It is compatible with a range of relative hazard estimates, including values below and above 1; therefore, the point estimate alone gives an incomplete account of the uncertainty. The reported p-value, 0.761, is consistent with the lack of clear comparative evidence for the primary endpoint in this small trial.
The group-specific median estimates also have uncertainty. Progression-free survival medians were 9.7 months, with a 95% confidence interval of 7.1 to 13.7, and 5.5 months, with a 95% confidence interval of 3.8 to 10.2. These intervals show that the median estimates are not exact values. They are not confidence intervals for the difference between medians, and comparing their endpoints does not replace the reported hazard-ratio analysis.
The overall-survival hazard-ratio confidence interval is 0.209 to 1.062 around an estimate of 0.471. It includes 1, while the posted Log Rank p-value is 0.045. The distinction between a point estimate, an interval, and a test result matters: the point estimate suggests a contrast in one direction, but the interval indicates uncertainty that includes a value corresponding to equal hazards. The upper confidence limit for the bevacizumab group's median overall survival is not reported in the registry record.
With 19 and 17 participants in the two groups, estimates are based on a limited enrollment. The record does not provide event counts for the primary endpoint or enough detail to assess follow-up completeness. Consequently, the precision of the estimates should be judged from the posted intervals and not inferred from the trial's phase label or the direction of the point estimates.
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 (log scale) | Hazard ratio | Events, 80% power | Events, 90% power |
|---|---|---|---|
| 100% of the observed effect | 0.91 | 3,701 | 4,954 |
| 75% of the observed effect | 0.93 | 6,578 | 8,806 |
| 50% of the observed effect | 0.95 | 14,801 | 19,814 |
The sample-size illustrations are based on the observed effects, not on the trial's original design assumptions. For the time-to-event outcomes, the figures are total numbers of events, not participants per arm. For other outcomes, the figures are participants per arm. The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation; the effect to detect is the stated fraction of the observed effect. The time-to-event illustrations use the Schoenfeld approach.
The 80% power column describes the illustrative number of events or participants that would be needed for an 80% chance of detecting the specified effect under those planning assumptions, if the assumed effect and other conditions held. The 90% power column applies the same idea at a higher target chance of detection and therefore generally requires more information. For example, the disease-control illustration for planning for 100% of the observed effect lists 156 participants per arm for 80% power and 208 for 90% power. Planning for 50% of that observed effect lists 642 participants per arm for 80% power and 859 for 90% power. Smaller effects need more participants or events to distinguish them from random variation at the same target power.
For progression-free survival, the illustrations are stated in total events. The figures differ across the two posted hazard-ratio estimates; the registry does not explain the distinction between those estimates or identify a separate original design target. These calculations are planning illustrations, not observed power, and do not show the probability that this completed trial detected an effect.
The trial's original sample-size justification and design assumptions are not reported in the registry record. These illustrations should not be interpreted as the enrollment target used by the investigators, nor as evidence that the actual trial had a particular 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
d is the total number of events needed (Schoenfeld's formula) with 1:1 allocation and proportional hazards.
Worked calculation for this trial
- Hazard ratio HR = 0.912, so ln(HR) = -0.0921.
- d = 4 × (1.96 + 0.842)2 / [ln(0.912)]2 = 3,700.0, rounded up to 3,701 events in total 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
hr <- 0.912 # observed hazard ratio
events_needed <- function(power, frac = 1) ceiling(round(4 * (z_a + qnorm(power))^2 / log(hr^frac)^2, 6)) # Schoenfeld, 1:1 allocation
for (f in c(1, 0.75, 0.5))
cat(sprintf("%3.0f%% of observed effect: events = %s (80%% power), %s (90%% power)\n", 100 * f,
format(events_needed(0.80, f), big.mark = ","), format(events_needed(0.90, f), big.mark = ",")))
# Simulation: given d total events under proportional hazards, events in the treatment arm are Binomial(d, hr / (1 + hr)).
# The score (log-rank type) statistic is (D1 - d / 2) / sqrt(d / 4).
set.seed(2292758)
d <- events_needed(0.80)
reps <- 20000
D1 <- rbinom(reps, d, hr / (1 + hr))
z <- (D1 - d / 2) / sqrt(d / 4)
cat(sprintf("Simulated power with %s events: %.3f (%d replicates)\n", format(d, big.mark = ","), mean(abs(z) > z_a), reps))
Output from running the code
100% of observed effect: events = 3,701 (80% power), 4,954 (90% power)
75% of observed effect: events = 6,578 (80% power), 8,806 (90% power)
50% of observed effect: events = 14,801 (80% power), 19,814 (90% power)
Simulated power with 3,701 events: 0.796 (20000 replicates)
The simulation uses the fact that, with d events in total and proportional hazards, the number of events in the treatment arm is binomial. It is an approximation that conditions on the total number of events, and it should land close to the target power.
14. Group-Sequential Design Analysis
Many time-to-event trials, especially in oncology, stop or report early when interim data are overwhelming, so a single fixed-sample number understates the real design problem. The calculation below is an illustrative group-sequential design built from this trial's posted control median and hazard ratio. The registry record does not state the planned number of looks or the spending function, so the design is a planning illustration, not a reconstruction of the protocol. Assumed: one-sided α = 0.025, 90% power, three equally spaced looks on information, Lan-DeMets O'Brien-Fleming spending, 24 months of accrual, 60 months in total and a 1% monthly dropout hazard.
Under these assumptions the design needs about 5,444 participants in total, with the boundaries below.
| Analysis | Calendar time (months) | Events | Efficacy boundary (z) | Nominal one-sided p | Cumulative alpha spent |
|---|---|---|---|---|---|
| Look 1 | 14.5 | 1,670 | 3.710 | 0.0001 | 0.0001 |
| Look 2 | 23.3 | 3,341 | 2.511 | 0.0060 | 0.0060 |
| Look 3 | 60.0 | 5,011 | 1.993 | 0.0231 | 0.0250 |
Fixed design versus group-sequential alternatives
| Design | Power | Events at final analysis | Participants | Study length (months) |
|---|---|---|---|---|
| Fixed design, one analysis | 80% | 3,699 | 4,019 | 60.0 |
| Two looks, O'Brien-Fleming | 80% | 3,713 | 4,034 | 60.0 |
| Three looks, O'Brien-Fleming | 80% | 3,747 | 4,070 | 60.0 |
| Three looks, Pocock | 80% | 4,330 | 4,704 | 60.0 |
| Fixed design, one analysis | 90% | 4,953 | 5,380 | 60.0 |
| Two looks, O'Brien-Fleming | 90% | 4,970 | 5,399 | 60.0 |
| Three looks, O'Brien-Fleming | 90% | 5,011 | 5,444 | 60.0 |
| Three looks, Pocock | 90% | 5,716 | 6,210 | 60.0 |
Group-sequential designs cost a small increase in maximum sample size and events compared with the fixed design, in exchange for the chance to stop early for overwhelming efficacy. O'Brien-Fleming spending keeps early boundaries very conservative and the final boundary close to the fixed-design value, whereas Pocock spending spends more alpha early.
Sensitivity to a smaller true effect
Planning for exactly the observed effect is optimistic, because observed effects in published trials tend to be somewhat larger than the true effect. The table repeats the main design (three looks, O'Brien-Fleming spending, 90% power) for smaller true hazard ratios.
| True effect assumed | Hazard ratio | Events at final analysis | Participants |
|---|---|---|---|
| 100% of the observed effect | 0.912 | 5,011 | 5,444 |
| 75% of the observed effect | 0.933 | 8,909 | 9,668 |
| 50% of the observed effect | 0.955 | 20,046 | 21,729 |
For context, this trial enrolled 36 participants.
Cross-check, upper boundaries: gsDesign 3.71, 2.511, 1.993 | rpact 3.71, 2.511, 1.993. Agreement between the two packages confirms the boundary calculation.
R code and output
suppressWarnings(suppressMessages({ library(gsDesign); library(rpact) }))
med_control <- 5.5 # control-arm median, months (converted from the posted unit)
hr <- 0.912 # hazard ratio used for planning
lambdaC <- log(2) / med_control
eta <- 0.01 # dropout hazard per month (assumption)
acc_months <- 24 # accrual duration (assumption)
study_months<- 60 # total study duration (assumption)
design <- function(k, sfu, beta, h = hr) gsSurv(k = k, test.type = 1, alpha = 0.025, beta = beta, sfu = sfu,
lambdaC = lambdaC, hr = h, hr0 = 1, eta = eta, gamma = 1, R = acc_months, T = study_months, minfup = study_months - acc_months)
# Main design: 3 looks, Lan-DeMets O'Brien-Fleming spending, one-sided alpha 0.025, 90% power
x <- design(3, sfLDOF, 0.10)
cat(sprintf("N_TOTAL|%s\n", format(ceiling(sum(x$gamma * x$R)), big.mark = ",")))
for (i in 1:3) cat(sprintf("GS|%d|%.1f|%.0f|%.3f|%.5f|%.5f\n", i, x$T[i], x$n.I[i], x$upper$bound[i], pnorm(-x$upper$bound[i]), cumsum(x$upper$spend)[i]))
cat("\n"); print(gsBoundSummary(x))
# Comparison of designs
cmp <- list(list("Fixed design, one analysis", 1, sfLDOF), list("Two looks, O'Brien-Fleming", 2, sfLDOF),
list("Three looks, O'Brien-Fleming", 3, sfLDOF), list("Three looks, Pocock", 3, sfLDPocock))
cat("\n")
for (b in c(0.20, 0.10)) for (d in cmp) {
y <- design(d[[2]], d[[3]], b)
cat(sprintf("DES|%s|%d|%.0f|%s|%.1f\n", d[[1]], round(100 * (1 - b)), tail(y$n.I, 1), format(ceiling(sum(y$gamma * y$R)), big.mark = ","), tail(y$T, 1)))
}
# Sensitivity: what if the true effect is smaller than the observed one? (3 looks, O'Brien-Fleming, 90% power)
cat("\n")
for (fr in c(1, 0.75, 0.5)) {
y <- design(3, sfLDOF, 0.10, exp(log(hr) * fr))
cat(sprintf("SENS|%.2f|%.3f|%.0f|%s\n", fr, exp(log(hr) * fr), tail(y$n.I, 1), format(ceiling(sum(y$gamma * y$R)), big.mark = ",")))
}
# Independent cross-check of the boundaries with rpact
r <- getDesignGroupSequential(kMax = 3, alpha = 0.025, beta = 0.10, sided = 1, typeOfDesign = "asOF", informationRates = x$timing)
cat(sprintf("\nCross-check, upper boundaries: gsDesign %s | rpact %s\n", paste(round(x$upper$bound, 3), collapse = ", "), paste(round(r$criticalValues, 3), collapse = ", ")))
Method: LachinFoulkes
Analysis Value Efficacy
IA 1: 33% Z 3.7103
N: 3286 p (1-sided) 0.0001
Events: 1671 ~HR at bound 0.8340
Month: 14 P(Cross) if HR=1 0.0001
P(Cross) if HR=0.91 0.0338
IA 2: 67% Z 2.5114
N: 5276 p (1-sided) 0.0060
Events: 3341 ~HR at bound 0.9168
Month: 23 P(Cross) if HR=1 0.0060
P(Cross) if HR=0.91 0.5603
Final Z 1.9930
N: 5444 p (1-sided) 0.0231
Events: 5012 ~HR at bound 0.9452
Month: 60 P(Cross) if HR=1 0.0250
P(Cross) if HR=0.91 0.9000
Cross-check, upper boundaries: gsDesign 3.71, 2.511, 1.993 | rpact 3.71, 2.511, 1.993
15. Analyses Reported by the Sponsor
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| Log Rank | Hazard Ratio (HR) 0.912 | 0.431 to 1.930 | 0.761 |
| not stated | Hazard Ratio (HR) 0.642 | 0.249 to 1.656 | not reported |
The registry reports sponsor analyses for the primary time-to-event endpoint, including a Log Rank comparison with a hazard ratio of 0.912, a 95% confidence interval of 0.431 to 1.930, and p = 0.761. It also posts a second hazard ratio of 0.642, with a 95% confidence interval of 0.249 to 1.656, but does not give a method or p-value for that result. The description of the primary analysis mentions stratified Cox models with and without adjustment, yet the record does not identify which estimate corresponds to which version.
Simple recalculations from posted summary statistics are unadjusted and cannot reproduce a participant-level time-to-event analysis. They do not incorporate the underlying event times, censoring pattern, model stratification, or covariate adjustment. For that reason, the sponsor's reported analysis takes precedence over a simple recalculation. There is no discrepancy flag in the registry data.
The sponsor's analysis is not automatically free of uncertainty: its estimate and confidence interval still need to be interpreted together, and missing methodological details constrain independent assessment. For the primary outcome, the reported interval includes 1 and the reported p-value does not indicate clear evidence of a group difference. The second posted estimate has an interval that also includes 1, and its associated test details are not reported.
16. Multiplicity, Missing Data and Analysis Populations
The registry identifies progression-free survival as the primary endpoint and lists a range of secondary endpoints. Testing several outcomes can increase the chance that at least one result appears notable even when there is no underlying difference. General statistical practice addresses this issue through a prespecified testing hierarchy, adjusted significance thresholds, or other multiplicity procedures. The multiplicity plan for this trial is not reported in the registry record, so the secondary p-values should not be read as if they were isolated confirmatory tests.
The record states that analyses were conducted using Kaplan-Meier estimation and stratified Cox models for the primary endpoint, including adjusted and unadjusted versions. However, the exact model specification, stratification factors, covariates, and correspondence between the two reported hazard-ratio estimates are not reported. The original statistical analysis plan is not reported in the registry record. This limits assessment of whether the posted analyses followed prespecified choices or reflect different analysis populations or model versions.
The registry does not report the analysis population used for each endpoint, the number of participants included in each analysis, or detailed handling of missing outcome assessments and censoring. General statistical methods for time-to-event data rely on assumptions about censoring and the information contributed by participants who have not experienced an event. Without details on follow-up completeness, losses to follow-up, or missing data, it is not possible to assess those aspects fully.
Interim analyses, stopping rules, and any adjustments related to repeated looks at the data are not reported in the registry record. Nor is the original sample-size justification reported. These omissions do not establish that such procedures were absent; they mean that their use and implications cannot be determined from the registry information. These reporting gaps are particularly relevant when interpreting several outcomes and more than one posted estimate for an endpoint.
17. 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 |
|---|---|---|---|
| Arm I (Irinotecan, Cetuximab, Bevacizumab) | 5 | 19 | 26.3% |
| Arm II (Irinotecan, Cetuximab, Placebo) | 5 | 17 | 29.4% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Arm I (Irinotecan, Cetuximab, Bevacizumab) | 10 of 19 |
| Arm II (Irinotecan, Cetuximab, Placebo) | 17 of 17 |
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 |
|---|---|
| Arm I (Irinotecan, Cetuximab, Bevacizumab) | 19 of 19 |
| Arm II (Irinotecan, Cetuximab, Placebo) | 17 of 17 |
Most frequent serious adverse event terms
| Event term | Organ system | Arm I (Irinotecan, Cetuximab, Bevacizumab) | Arm II (Irinotecan, Cetuximab, Placebo) |
|---|---|---|---|
| Diarrhea | Gastrointestinal disorders | 1 of 19 | 2 of 17 |
| Vomiting | Gastrointestinal disorders | 1 of 19 | 2 of 17 |
| Nausea | Gastrointestinal disorders | 1 of 19 | 1 of 17 |
| Dehydration | Metabolism and nutrition disorders | 2 of 19 | 0 of 17 |
| Back pain | Musculoskeletal and connective tissue disorders | 1 of 19 | 1 of 17 |
| Gastrointestinal disorders - Oth spec | Gastrointestinal disorders | 0 of 19 | 1 of 17 |
| Mucositis oral | Gastrointestinal disorders | 1 of 19 | 0 of 17 |
| Fever | General disorders | 0 of 19 | 1 of 17 |
| Hepatobiliary disorders - Other, specify | Hepatobiliary disorders | 0 of 19 | 1 of 17 |
| Sepsis | Infections and infestations | 1 of 19 | 0 of 17 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Arm I (Irinotecan, Cetuximab, Bevacizumab) | Arm II (Irinotecan, Cetuximab, Placebo) |
|---|---|---|---|
| Rash acneiform | Skin and subcutaneous tissue disorders | 17 of 19 | 15 of 17 |
| Hypertension | Vascular disorders | 17 of 19 | 13 of 17 |
| Rash maculo-papular | Skin and subcutaneous tissue disorders | 14 of 19 | 15 of 17 |
| Diarrhea | Gastrointestinal disorders | 15 of 19 | 12 of 17 |
| Hypomagnesemia | Metabolism and nutrition disorders | 15 of 19 | 12 of 17 |
| Neutrophil count decreased | Investigations | 9 of 19 | 7 of 17 |
| Platelet count decreased | Investigations | 5 of 19 | 5 of 17 |
| Vomiting | Gastrointestinal disorders | 1 of 19 | 1 of 17 |
| Proteinuria | Renal and urinary disorders | 2 of 19 | 0 of 17 |
| Sinus tachycardia | Cardiac disorders | 0 of 19 | 1 of 17 |
Serious events with the highest arm-level rate: diarrhea (11.8%), vomiting (11.8%), dehydration (10.5%), gastrointestinal disorders - oth spec (5.9%), nausea (5.9%).
The registry reports 5 participants with at least one serious adverse event in Arm I, among 19 participants at risk, and 5 in Arm II, among 17 at risk. These are participant counts, not event counts; an individual participant may experience more than one serious event. The record also reports that 19 of 19 participants in Arm I and 17 of 17 in Arm II experienced at least one other adverse event. The meaning of the registry's separate serious and other adverse-event categories should be retained when comparing those figures.
The record lists diarrhea and vomiting at 11.8% each among the most frequently listed serious-event terms, dehydration at 10.5%, gastrointestinal disorders not otherwise specified and nausea at 5.9% each, and fever at 5.9%. These percentages describe listed terms; the registry summary does not provide enough context to infer the event counts or the participants' overlap for each term.
Deaths are recorded for 10 participants in Arm I and 17 in Arm II. The registry summary does not say that these deaths were caused by treatment, nor does this count alone establish a treatment-related safety difference. Interpretation requires context such as timing, cause, exposure, follow-up, and formal adverse-event attribution, which is not reported in these figures.
18. What the Result Does, and Does Not, Mean
The posted primary results describe a small randomized comparison of two regimens and do not establish a clear difference in progression-free survival. The median estimates favor different times across the groups, but the reported primary hazard-ratio confidence interval is wide and includes 1, and the Log Rank p-value is 0.761. These results are compatible with substantial uncertainty about the comparative effect.
The point estimates and secondary outcomes may describe patterns in this trial, but they are not proof that one regimen causes better outcomes. A hazard ratio is a group-level model estimate, not a promise about an individual participant's experience. A p-value is not the probability that a treatment works, and a confidence interval is not a range containing the true value with certainty. The estimates need to be considered in light of the small enrollment, the duration of follow-up, and incomplete reporting of analysis details.
The registry reports a notable overall-survival point estimate and p-value, but the corresponding confidence interval includes 1. The unadjusted secondary response comparisons also have p-values above conventional thresholds. Because the registry does not report a multiplicity plan, secondary results should not be treated as confirmatory evidence without further context.
The data do not establish that the regimens are equivalent. A failure to demonstrate a clear difference is not proof of no difference, especially when estimates are imprecise. Conversely, differences in observed medians or percentages do not by themselves establish a reliable effect. The registry information supports a cautious description of observed results and their uncertainty, not medical advice or a treatment recommendation.
19. Why This Trial Matters Statistically
This trial illustrates why statistical interpretation should not rest on a single number. The primary medians are separated, but the sponsor-reported hazard ratio has a broad confidence interval that includes 1 and a Log Rank p-value of 0.761. The median, hazard ratio, confidence interval, and p-value address related but distinct questions. Reading them together prevents the point estimates from being mistaken for precise or definitive evidence.
It also highlights the distinction between a primary endpoint and secondary outcomes. The overall-survival and response results add context, but a registry listing several outcomes without a reported multiplicity strategy makes it important to distinguish exploratory patterns from confirmatory findings. A secondary p-value should not be interpreted with the same weight as a single primary test when the testing framework is unknown.
The record's two reported hazard ratios for both progression-free and overall survival make transparent analytic reporting especially important. The primary endpoint description mentions adjusted and unadjusted Cox models, but the record does not map each estimate to a model, and one result for each outcome lacks a reported method and p-value. Clear identification of the analysis population, model specification, stratification factors, and prespecified analysis plan would make the estimates easier to interpret and reproduce.
Finally, the sample-size illustrations show how planning targets depend on the effect size chosen and the amount of information needed. They are not a measure of the trial's observed power, and they are not the original design justification. Keeping planning calculations separate from observed trial results is essential to avoid overstating what a small phase II study can establish.
20. 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 trial enrolled 36 participants, with 19 assigned to the bevacizumab regimen and 17 to the placebo regimen. That enrollment gives limited information for estimating event-time differences and uncommon safety outcomes. The registry does not provide primary endpoint event counts or detailed follow-up completeness, so the amount of observed information behind the survival estimates cannot be fully judged from the record.
The primary endpoint has two posted hazard-ratio estimates, 0.912 and 0.642, with differing reported details. The registry describes Cox analyses with and without adjustment but does not identify which estimate belongs to which analysis. The second estimate has no associated method or p-value in the record. The interpretation is therefore constrained by ambiguity about the analytic specifications.
The upper confidence limit for median overall survival in the bevacizumab group is not reported. Analysis populations, missing-data handling, censoring details, stratification factors, and covariate definitions are also not reported in the registry record. Further, the multiplicity plan and original sample-size justification are not reported, although several secondary outcomes are listed.
The registry gives serious adverse-event participant counts and selected event terms, but those summary figures do not provide attribution, timing, severity detail beyond the reported categories, or participant-level overlap. The death counts likewise do not identify causes or treatment relationship. These limits mean the safety figures should be read as registry summaries rather than as a complete causal comparison.
21. Related Tutorials
22. Related Statistical Calculators
23. Sources
- ClinicalTrials.gov: Irinotecan and Cetuximab With or Without Bevacizumab in Treating Patients With RAS Wild-Type Locally Advanced or Metastatic Colorectal Cancer That Cannot Be Removed by Surgery — NCT02292758.
- Registry record last updated 2022-01-31; status last verified 2019-08.
- Results first posted 2020-02-28.
- 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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24. Record Summary
BOND-3 is a completed, randomized, double-blind phase II trial comparing irinotecan and cetuximab plus bevacizumab with irinotecan and cetuximab plus placebo in RAS-wildtype, irinotecan-refractory metastatic colorectal cancer. The registry reports enrollment of 36 participants and identifies progression-free survival as the primary endpoint.
The posted primary hazard ratio is 0.912, with a 95% confidence interval of 0.431 to 1.930 and a Log Rank p-value of 0.761. This estimate is imprecise and does not establish a clear group difference. Secondary survival and response results provide additional descriptive information, but uncertainty, the number of outcomes, and unreported analysis details limit their weight.
Key details—including the original sample-size justification, multiplicity plan, analysis populations, and handling of missing data—are not reported in the registry record.