← Clinical Trials
Colorectal Cancer Phase 3 Time-to-Event Analysis NCT00265850

Cetuximab and/or Bevacizumab Combined With Combination Chemotherapy in Treating Patients With Metastatic Colorectal Cancer: Complete Statistical Analysis

The registry record compares overall survival for bevacizumab- and cetuximab-containing chemotherapy regimens in eligible KRAS wild type patients with metastatic colorectal cancer. The reported hazard ratio is 0.88, with a 95% confidence interval of 0.77 to 1.01 and p = 0.08.

Trial start: 2005-11  ·  Enrollment: 2334  ·  Sponsor: Alliance for Clinical Trials in Oncology
Scope of this record

This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.

1. Trial at a Glance

This page covers the registry results for Cetuximab and/or Bevacizumab Combined With Combination Chemotherapy in Treating Patients With Metastatic Colorectal Cancer (NCT00265850), a randomized phase 3 study. The primary outcome is Overall Survival.

2334
Enrollment
Phase 3
3
Arms
In the primary outcome
0.88
Hazard ratio
Arm A: FOLFOX or FOLFIRI + Bevacizumab v
0.77–1.01
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT00265850
PhasePhase 3
ConditionColorectal Cancer
AllocationRandomized
Design modelParallel
MaskingNone (open label)
Enrollment2334
Arms in the primary outcome3
Lead sponsorAlliance for Clinical Trials in Oncology
Results postedYes

2. Clinical Question

Population

The trial concerned patients with untreated metastatic adenocarcinoma of the colon or rectum. The primary endpoint population was narrower: all eligible KRAS wild type patients who began treatment. The registry record does not give further detail about the eligibility criteria for this endpoint population.

Intervention

One comparison group received FOLFOX or FOLFIRI with bevacizumab. FOLFOX and FOLFIRI are the chemotherapy options named in the registry record. Bevacizumab was administered with the chosen chemotherapy regimen.

Comparator

The comparator group received FOLFOX or FOLFIRI with cetuximab. A third arm combined cetuximab and bevacizumab with chemotherapy, but the posted primary endpoint results do not report an outcome value for that arm.

Primary question

The primary comparison asked whether overall survival differed between the bevacizumab and cetuximab groups among eligible KRAS wild type patients who began treatment. Overall survival was measured from registration to death and estimated using Kaplan-Meier methods. The registry reports a comparison using a log-rank test and a hazard ratio.

This is a randomized phase III trial with parallel groups and no masking. Its stated purpose was to compare regimens combining chemotherapy with cetuximab and/or bevacizumab for metastatic colorectal cancer. The posted primary results address the comparison between the bevacizumab-containing and cetuximab-containing groups, rather than a reported three-way comparison. Although the trial record includes a third combination arm, its primary outcome row has no reported participant count or survival estimate. The main inferential result therefore concerns only the two arms with posted primary estimates. This distinction matters: the reported estimate does not establish what the combined-antibody regimen would have produced relative to either of the other regimens.

3. Trial Design

The registry describes a randomized, open-label, parallel-group phase III trial sponsored by the Alliance for Clinical Trials in Oncology. The overall recorded enrollment was 2334. The record lists colorectal cancer as the condition and describes treatment for patients with untreated metastatic adenocarcinoma of the colon or rectum. The trial status is completed. The recorded start was 2005-11 and primary completion was 2015-02.

The treatment groups relevant to the posted primary result received either FOLFOX or FOLFIRI with bevacizumab, or either chemotherapy option with cetuximab. The record also describes a third group receiving chemotherapy with both antibodies. The primary endpoint analysis, however, includes only the two antibody groups with posted outcome values. For overall survival, the reported analysis population comprised all eligible KRAS wild type patients who began treatment. The registry does not report why the posted outcome sample counts are smaller than the overall enrollment, so no explanation should be inferred from those figures alone.

Overall survival was assessed for up to 5 years post-treatment. The record defines survival time as time from registration to death and says that time-to-event distributions were estimated with the Kaplan-Meier method. The primary comparison was between Arm A, chemotherapy plus bevacizumab, and Arm B, chemotherapy plus cetuximab. The reported inferential method was a log-rank test, with a hazard ratio and 95% confidence interval also reported.

The registry record does not report the original sample-size justification, the trial's original statistical design assumptions, interim analyses, or a complete statistical analysis plan. It also does not describe masking beyond indicating that the trial was unmasked. These omissions limit what can be concluded about the planned analysis process, but they do not change the interpretation of the posted comparison itself.

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: From 5/2005 to 9/2009, patients were randomized 1:1:1 to Arms A, B and C. Study was amended in 2009 to include only KRAS wild type patients; then Arm C was closed based on data showing no benefit from chemo with the combination of Bevacizumab and an EGFR antibody. Thereafter, only KRAS wild type patients were randomized 1:1 to Arm A and B.

Overall Study

StageArm A: FOLFOX or FOLFIRI + BevacizumabArm B: FOLFOX or FOLFIRI + CetuximabArm C: FOLFOX or FOLFIRI + Cetuximab + Bevacizumab
STARTED899902533
COMPLETED899902533
NOT COMPLETED000

Analysis population for the primary outcome, as defined in the registry: All eligible KRAS wild type patients that began treatment were included in this endpoint.

5. Baseline Characteristics

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

Population: During the trial, it was learned that KRAS mutation predicted for lack of efficacy of EGFR antibodies; also studies showed no benefit from chemo combined with both Bevacizumab and an EGFR antibody. The trial was amended to 2 arms limited to KRAS wild type patients. Only confirmed and consented KRAS wild type patients were analyzed.

CharacteristicUnitArm A: FOLFOX or FOLFIRI + BevacizumabArm B: FOLFOX or FOLFIRI + CetuximabArm C: FOLFOX or FOLFIRI + Cetuximab + BevacizumabTotal
Participants analysed55957801137
Age, Continuousyears59 (21.8 to 85)59.2 (20.8 to 89.5)—59.1 (20.8 to 89.5)
Sex: Female, Male: FemaleParticipants211229—440
Sex: Female, Male: MaleParticipants348349—697
Region of Enrollment: Canadaparticipants3232—64
Region of Enrollment: United Statesparticipants527546—1073

6. Primary Endpoint

The registry lists the primary outcome as Overall Survival, measured over Up to 5 years post-treatment.

ElementRegistry entry
Result typeMedian
Measure of spread95% Confidence Interval
Unitmonths
Endpoint classificationTime-to-Event Analysis

The primary endpoint is overall survival, measured in months. The registry defines survival time as the interval from registration to death and states that the endpoint was evaluated for up to 5 years post-treatment. Overall survival is a time-to-event outcome: the event is death, and the analysis considers both when events occur and participants whose event time is not observed during follow-up.

This endpoint is used because it describes time until death without requiring a judgment about radiographic tumor response or disease progression. It is a direct measure of survival over follow-up, although it does not by itself explain why survival times differ or capture other dimensions of health and treatment experience. The registry identifies the primary endpoint population as all eligible KRAS wild type patients who began treatment. That population definition should be kept in mind when interpreting the reported median survival and comparison.

The Kaplan-Meier method estimates the time-to-event distribution while accounting for censoring, which occurs when a participant's event time is not observed during the relevant follow-up. The median is the point in the estimated distribution at which half the population is estimated to have experienced the event. The primary result also includes a hazard ratio and confidence interval to compare the groups over the observed time-to-event data. A median is a useful summary, but it does not describe the entire survival curve; the hazard ratio likewise compresses a time-dependent comparison into a single reported value. Neither statistic, by itself, gives the full shape of survival over time.

7. Results Posted in the Registry

Hazard ratio: Arm A: FOLFOX or FOLFIRI + Bevacizumab vs Arm B: FOLFOX or FOLFIRI + Cetuximab

0.88

95% CI: 0.77 to 1.01

As reported in the registry

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Arm A: FOLFOX or FOLFIRI + Be…0.750.800.850.910.971.03hazard ratio (as reported) vs control (95% CI)

8. Secondary Efficacy Endpoints

The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.

Secondary outcomeTypeEffect measureEstimate (95% CI)Planning size, 80% power
Progression-free Survival (PFS)Time-to-Event AnalysisHazard ratio0.95 (0.84 to 1.08)11,933 events
Time to Treatment FailureTime-to-Event AnalysisHazard ratio0.96 (0.85 to 1.07)18,840 events
Duration of Tumor ResponseTime-to-Event AnalysisHazard ratio0.92 (0.79 to 1.08)4,516 events

Progression-free Survival (PFS)

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Arm A: FOLFOX or FOLFIRI + Be…0.820.870.930.981.041.10hazard ratio (as reported) vs control (95% CI)

Time to Treatment Failure

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Arm A: FOLFOX or FOLFIRI + Be…0.830.880.930.981.031.09hazard ratio (as reported) vs control (95% CI)

Duration of Tumor Response

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Arm A: FOLFOX or FOLFIRI + Be…0.770.830.890.961.031.11hazard ratio (as reported) vs control (95% CI)

The posted secondary outcomes cover progression-free survival, time to treatment failure, and duration of tumor response. Across these measures, the reported comparisons do not provide a consistent strong statistical signal separating the two analyzed groups. Their hazard-ratio confidence intervals include 1, and their p-values are above the conventional 0.05 threshold. The secondary results therefore broadly align with the primary result's uncertain comparison, rather than supplying clear evidence that resolves it.

These outcomes capture different aspects of the clinical course and are not interchangeable with overall survival. Progression-free survival concerns time to disease progression or death; treatment failure and response duration address other time-based outcomes. The registry record names these endpoints but does not provide further definitions for every event or detailed analysis rules. Their interpretation should remain tied to the definitions and estimates posted in the record.

Secondary results usually carry less inferential weight than a designated primary endpoint, particularly when several outcomes are examined. Each additional test creates another opportunity for a nominally unusual result to arise by chance. The registry record does not report a multiplicity adjustment or a hierarchy for these secondary tests, so their p-values should be treated as unadjusted evidence rather than as confirmatory proof. A result that appears notable among several outcomes would need cautious interpretation, and a nonsignificant result does not establish that the endpoint is identical between groups.

The secondary outcomes provide context around the primary comparison but do not overturn it. They also do not establish a three-arm result: the posted secondary comparisons are between the bevacizumab and cetuximab arms, and the registry record does not provide a corresponding outcome estimate for the combination-antibody arm across these results.

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

9. Statistical Interpretation

Clinical Biostats interpretation

The median overall survival was 29.0 months in the bevacizumab group, with a 95% confidence interval of 25.6 to 31.2 months. In the cetuximab group, the median was 30.0 months, with a 95% confidence interval of 27.5 to 32.8 months. These are estimated medians, not guarantees about an individual participant's survival time. The registry's primary comparison reports a hazard ratio of 0.88, a 95% confidence interval of 0.77 to 1.01, and p = 0.08 using the log-rank method.

The point estimate is below 1, but the confidence interval includes 1. The interval is compatible with a range of relative hazard values that includes no difference as well as values on either side of it. The p-value is above the conventional 0.05 threshold, so the posted result does not provide strong evidence against the null hypothesis of no difference in the comparison. This does not establish that the regimens are equivalent, nor does it prove that their survival distributions are identical. It means that the reported data do not distinguish the groups with high statistical certainty under the stated comparison.

The confidence interval is important alongside the p-value. It conveys uncertainty about the hazard-ratio estimate and indicates that the data are compatible with more than one interpretation of the relative comparison. A single point estimate should not be treated as a definitive ranking. The median estimates are close, but comparing medians alone is not a substitute for the reported time-to-event analysis, which uses information across follow-up.

The primary result applies to the two analyzed groups and to the endpoint population stated in the record: eligible KRAS wild type patients who began treatment. It does not report a primary survival estimate for the third group receiving both antibodies. Nor does the result address every patient with metastatic colorectal cancer, every chemotherapy regimen, or outcomes beyond those posted. The registry gives no basis for attributing the result to a particular biological mechanism or for making a clinical recommendation.

In statistical terms, the central finding is an imprecise comparison that does not cross the conventional significance threshold. The estimate and interval should be read together, with the population and endpoint definition kept in view. The posted findings describe the trial's reported comparison; they do not by themselves establish causation beyond the randomized comparison or settle whether small or moderate differences are absent.

10. Statistical Methods Explained

The primary outcome is a time-to-event measure. In general, time-to-event methods are useful when the outcome is not simply whether an event occurred, but also the timing of that event. Participants may have different lengths of follow-up, and some may not have an observed event by the end of observation. Such participants contribute information until the time their follow-up ends; their unobserved event times are treated as censored rather than as if the event never occurred.

What does Kaplan-Meier estimation do?

The registry says overall survival distributions were estimated with the Kaplan-Meier method. In general, Kaplan-Meier estimation constructs an estimate of the event-free proportion over time, updating that estimate at observed event times and accounting for censoring. It can describe the survival experience over follow-up without requiring every participant to have an observed death. The method relies on assumptions about censoring and follow-up; the registry record does not describe diagnostic checks or details about those assumptions.

The reported median is read from the estimated survival distribution. It identifies the time at which the estimated proportion surviving reaches the median point. A median is easy to communicate, but it leaves out detail about the shape of the distribution and can conceal differences at particular portions of follow-up. The registry reports median survival and its 95% confidence interval for the two arms, along with a separate comparison statistic.

What does the log-rank test compare?

The log-rank test is a general method for comparing time-to-event distributions between groups. It uses the timing of events over follow-up and compares observed events with the events expected under a no-difference hypothesis. Its result is not a direct measure of the size of a treatment effect; the hazard ratio supplies a relative effect estimate, while the p-value indicates how compatible the observed test statistic is with the null hypothesis under the test's assumptions.

The registry reports the log-rank method for the primary comparison and reports a hazard ratio of 0.88, with a 95% confidence interval of 0.77 to 1.01 and p = 0.08. The interval includes 1, the value corresponding to no relative difference in a hazard ratio. As a result, the point estimate should not be read in isolation as conclusive evidence of a difference. The registry record does not report further details about the exact model or the handling of potential departures from assumptions.

How should a hazard ratio be understood?

In general, a hazard is the instantaneous event rate among participants who have not yet experienced the event, conditional on reaching a given time without the event. A hazard ratio compares hazards between groups over time. It is not a ratio of median survival times, and it is not a direct statement about the probability that an individual participant will experience an event. The reported ratio is a single summary of the comparison and is most straightforward to interpret when the relative hazards are reasonably stable over time. The registry record does not report whether this assumption was assessed.

A confidence interval expresses uncertainty about the estimated hazard ratio under the analysis. If an interval includes 1, the estimate is compatible with no relative difference at the confidence level used, as well as with some values below and above 1. The interval does not assign probabilities to individual possible values, and it is not a range that must contain the true value. Its width is relevant to precision: a wider interval leaves more uncertainty about the size and direction of the comparison.

What can the p-value establish?

In general, a p-value measures how unusual the observed data, or data more extreme, would be if the null hypothesis and analysis assumptions were true. It does not give the probability that the null hypothesis is true, and it does not measure the clinical importance of a result. The reported p = 0.08 is above the conventional 0.05 threshold. This result does not amount to proof of no difference; rather, the analysis does not reject the no-difference hypothesis at that conventional threshold.

The endpoint and population definitions also affect interpretation. The primary analysis was for eligible KRAS wild type patients who began treatment, not all enrolled participants. The registry identifies the primary comparison as Arm A versus Arm B and provides no primary outcome value for Arm C. The registry record does not report whether additional adjusted models, subgroup analyses, or sensitivity analyses were planned or conducted. Accordingly, the interpretation should stay with the reported analysis and avoid assuming analyses that are not described.

11. Confidence Intervals and Precision

The primary hazard-ratio estimate is 0.88, with a 95% confidence interval from 0.77 to 1.01. This interval is the main guide to the precision of the reported comparison. It includes 1, so the data are compatible with no relative difference under the hazard-ratio scale. It also includes values below and above 1, leaving uncertainty about the direction and magnitude of the relative comparison. The point estimate alone gives a narrower impression than the interval supports.

The arm-specific median estimates also have uncertainty. The bevacizumab group median is 29.0 months, with a 95% confidence interval of 25.6 to 31.2 months; the cetuximab group median is 30.0 months, with a 95% confidence interval of 27.5 to 32.8 months. These intervals describe uncertainty in each arm's median estimate. They are not a direct confidence interval for the difference between medians, and their overlap should not be used as a replacement for the reported log-rank comparison.

In general, a 95% confidence interval is produced by a method that, over repeated studies under its assumptions, would contain the target parameter in 95% of such intervals. It does not mean there is a 95% probability that this particular interval contains the fixed true value. The interval's width reflects both the information available and the analysis method; it does not capture every possible source of uncertainty, such as biases or limitations in the record.

The interval is consistent with a result that is not sufficiently precise to establish a clear difference at the conventional threshold. A nonsignificant result is not proof of equivalence. Equivalence would require an appropriate design and prespecified margins, neither of which is reported in the registry record. The posted estimates therefore support a cautious reading: the comparison is uncertain, and the range of values remains relevant to interpretation.

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 ratioEvents, 80% powerEvents, 90% power
100% of the observed effect0.881,9222,572
75% of the observed effect0.913,4164,573
50% of the observed effect0.947,68510,288
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect2,0005,00010,00020,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: events required (total))
Treat these figures cautiously. The observed difference is imprecise: its confidence interval includes no difference at all. A sample size built on a noisy estimate can be far too small or too large, so the smaller-effect rows are the more cautious guide.
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, Schoenfeld approximation for the log-rank test or Cox model. The answer is the total number of events, not participants; the number of participants depends on how quickly events accrue. Calculated for the comparison: Arm A: FOLFOX or FOLFIRI + Bevacizumab vs Arm B: FOLFOX or FOLFIRI + Cetuximab.

The sample-size illustrations are planning calculations based on the observed effect, not the trial's original design justification. For these time-to-event comparisons, the displayed quantities are total events, not participants per arm. The calculations use a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. They use the Schoenfeld approach, with the target effect set to the stated fraction of the observed effect. The trial's own original sample-size assumptions are not reported in the registry record.

The 80% power column describes the total number of events that a hypothetical future study would need, under those planning assumptions, to have an 80% chance of detecting the specified effect if that effect were the true one. The 90% power column makes the corresponding illustration for a 90% chance. These are planning targets, not estimates of the probability that the completed trial detected an effect. This is not observed power.

Rows that plan for 100%, 75%, or 50% of the observed effect illustrate how the assumed effect size changes the required event target. Smaller effects are harder to distinguish from chance variation and therefore require more events under the same planning assumptions. This relationship is general to the calculation, not evidence that a future study will achieve a particular result.

Because the entries count total events, they should not be read as the number of participants needed in each arm. Event totals depend on how many participants experience the event during follow-up, so they are not interchangeable with enrollment totals. The illustrations also do not reproduce the trial's design, since the registry record does not report its original sample-size justification or full analysis plan. They are best read as conditional planning examples tied to the stated assumptions, rather than as a retrospective verdict on whether the completed study was adequately sized.

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 = 4 (z1−α/2 + z1−β)2 / [ln(HR)]2

d is the total number of events needed (Schoenfeld's formula) with 1:1 allocation and proportional hazards.

Worked calculation for this trial

  1. Hazard ratio HR = 0.880, so ln(HR) = -0.1278.
  2. d = 4 × (1.96 + 0.842)2 / [ln(0.880)]2 = 1,921.2, rounded up to 1,922 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 <- 0.88                              # 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(265850)
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 = 1,922 (80% power), 2,572 (90% power)
 75% of observed effect: events = 3,416 (80% power), 4,573 (90% power)
 50% of observed effect: events = 7,685 (80% power), 10,288 (90% power)
Simulated power with 1,922 events: 0.804 (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 4,801 participants in total, with the boundaries below.

AnalysisCalendar time (months)EventsEfficacy boundary (z)Nominal one-sided pCumulative alpha spent
Look 122.08673.7100.00010.0001
Look 235.51,7352.5110.00600.0060
Look 360.02,6021.9930.02310.0250
01234z = 3.7122 mo867 eventsz = 2.5136 mo1735 eventsz = 1.9960 mo2602 eventsUpper efficacy boundary (z)

Fixed design versus group-sequential alternatives

DesignPowerEvents at final analysisParticipantsStudy length (months)
Fixed design, one analysis80%1,9213,54460.0
Two looks, O'Brien-Fleming80%1,9283,55760.0
Three looks, O'Brien-Fleming80%1,9453,58960.0
Three looks, Pocock80%2,2484,14860.0
Fixed design, one analysis90%2,5724,74560.0
Two looks, O'Brien-Fleming90%2,5804,76160.0
Three looks, O'Brien-Fleming90%2,6024,80160.0
Three looks, Pocock90%2,9685,47760.0

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 assumedHazard ratioEvents at final analysisParticipants
100% of the observed effect0.8802,6024,801
75% of the observed effect0.9094,6268,455
50% of the observed effect0.93810,40918,846

For context, this trial enrolled 2,334 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 <- 29          # control-arm median, months (converted from the posted unit)
hr          <- 0.88          # 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: 4398         p (1-sided)   0.0001
  Events: 868        ~HR at bound   0.7773
    Month: 22    P(Cross) if HR=1   0.0001
              P(Cross) if HR=0.88   0.0338
    IA 2: 67%                   Z   2.5114
      N: 4802         p (1-sided)   0.0060
 Events: 1735        ~HR at bound   0.8864
    Month: 36    P(Cross) if HR=1   0.0060
              P(Cross) if HR=0.88   0.5603
        Final                   Z   1.9930
      N: 4802         p (1-sided)   0.0231
 Events: 2603        ~HR at bound   0.9248
    Month: 60    P(Cross) if HR=1   0.0250
              P(Cross) if HR=0.88   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

MethodEstimate95% CIP-value
Log RankHazard Ratio (HR) 0.880.77 to 1.010.080

The registry's sponsor-reported primary analysis gives a hazard ratio of 0.88, a 95% confidence interval of 0.77 to 1.01, and p = 0.08 for the comparison of Arm A with Arm B using the log-rank method. The recalculated presentation agrees with these reported values; the registry record identifies no discrepancy between them. The sponsor's own analysis therefore remains the primary inferential result to interpret.

Recalculated values in this context are unadjusted checks based on posted summary statistics. They do not replace the sponsor's analysis, reconstruct individual participant data, or account for details not present in the record. The agreement is useful as a consistency check, but it does not establish that every design or analysis assumption has been independently verified.

The sample-size illustrations are separate from the sponsor's original design calculations. They use the observed effect and stated planning assumptions, while the registry record does not report the trial's original sample-size justification. They should not be used to infer the sponsor's planned enrollment target or to reinterpret the reported p-value. The sponsor-reported estimate, interval, and test result are the basis for the primary statistical reading.

16. Multiplicity, Missing Data and Analysis Populations

The primary endpoint is identified as overall survival, and the registry names three secondary outcomes: progression-free survival, time to treatment failure, and duration of tumor response. The posted results include analyses for the primary and secondary outcomes, but the registry record does not report a multiplicity adjustment, a testing hierarchy, or a plan specifying how conclusions should be controlled across multiple endpoints. Without those details, the secondary p-values should not be interpreted as though each were the sole prespecified confirmatory test.

Multiplicity matters because making several statistical comparisons increases the chance of obtaining at least one apparently unusual result by chance. In general, procedures such as a prespecified hierarchy or adjustment can address that issue, but the record does not say whether any such procedure was used. It also does not report the full statistical analysis plan, including whether other analyses or subgroups were prespecified. The posted results alone cannot establish how all analyses were selected or prioritized.

The primary analysis population is described as all eligible KRAS wild type patients who began treatment. The arm-level counts reported for the primary outcome are 559 and 578. The registry record does not report a complete account of missing outcome data, reasons for exclusion from the endpoint population, censoring patterns, or sensitivity analyses for missingness. It would therefore be inappropriate to assume that missing data were absent or handled in a particular way. Kaplan-Meier analysis can accommodate censoring under its assumptions, but it does not eliminate the need to understand how follow-up ended and whether censoring could be related to prognosis.

The overall enrollment is 2334, while the primary endpoint population is described more narrowly and the posted arm counts are lower. The record does not explain this difference. The proper interpretation is to use the stated endpoint population and avoid treating the enrollment count as the analyzed population. The record also does not report outcome data for the third arm, so the primary findings cannot be generalized to that arm through inference alone.

17. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Arm A: FOLFOX or FOLFIRI + Bevacizumab9855917.5%
Arm B: FOLFOX or FOLFIRI + Cetuximab11157819.2%
Participants with at least one serious adverse event
Serious adverse events by armArm A: FOLFOX or FOLFIRI + Be…17.5%Arm B: FOLFOX or FOLFIRI + Ce…19.2%% of participants with at least one serious adverse event

Other (non-serious) adverse events

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

ArmParticipants affected of at risk
Arm A: FOLFOX or FOLFIRI + Bevacizumab531 of 559
Arm B: FOLFOX or FOLFIRI + Cetuximab548 of 578

Most frequent serious adverse event terms

Event termOrgan systemArm A: FOLFOX or FOLFIRI + BevacizumabArm B: FOLFOX or FOLFIRI + Cetuximab
Neutrophil count decreasedInvestigations35 of 55936 of 578
ThrombosisVascular disorders14 of 55922 of 578
Vascular access complicationInjury, poisoning and procedural complications2 of 5597 of 578
Death NOSGeneral disorders and administration site conditions5 of 5592 of 578
FatigueGeneral disorders and administration site conditions4 of 5593 of 578
Abdominal painGastrointestinal disorders3 of 5592 of 578
Platelet count decreasedInvestigations2 of 5593 of 578
Blood glucose increasedMetabolism and nutrition disorders1 of 5594 of 578
Serum magnesium decreasedMetabolism and nutrition disorders0 of 5595 of 578
Myocardial ischemiaCardiac disorders3 of 5591 of 578

Most frequent non-serious adverse event terms

Event termOrgan systemArm A: FOLFOX or FOLFIRI + BevacizumabArm B: FOLFOX or FOLFIRI + Cetuximab
FatigueGeneral disorders and administration site conditions397 of 559418 of 578
Peripheral sensory neuropathyNervous system disorders355 of 559344 of 578
DiarrheaGastrointestinal disorders304 of 559346 of 578
Neutrophil count decreasedInvestigations316 of 559334 of 578
Platelet count decreasedInvestigations208 of 559210 of 578
Abdominal painGastrointestinal disorders189 of 559186 of 578
VomitingGastrointestinal disorders174 of 559185 of 578
Serum magnesium decreasedMetabolism and nutrition disorders56 of 559231 of 578
HypertensionVascular disorders179 of 55980 of 578
ProteinuriaRenal and urinary disorders159 of 55943 of 578

Serious events with the highest arm-level rate: neutrophil count decreased (6.3%), thrombosis (3.8%), vascular access complication (1.2%), death nos (0.9%), serum magnesium decreased (0.9%).

Do not overextend the safety comparison. Serious-adverse-event counts are safety observations, not efficacy outcomes, and should not be combined with the primary result into a single benefit-risk number.

The registry lists serious adverse events for the two groups with reported safety counts. There were 98 serious adverse events affected in the bevacizumab group, among 559 at risk, and 111 in the cetuximab group, among 578 at risk. The record also reports other adverse events affecting 531 of 559 at risk in the bevacizumab group and 548 of 578 at risk in the cetuximab group. These are counts as posted; they do not by themselves establish a comparative safety effect.

The most frequently listed serious adverse-event terms include neutrophil count decreased at 6.3%, thrombosis at 3.8%, vascular access complication at 1.2%, Death NOS at 0.9%, serum magnesium decreased at 0.9%, and fatigue at 0.7%. The record presents these terms and percentages but does not specify in the information whether each percentage applies to both groups combined or to a particular group. They should therefore not be assigned to one arm without further detail.

Adverse-event counts can reflect the number of affected participants, while a term-specific percentage describes a reported frequency under the registry's coding and reporting conventions. The record does not provide event-level timing, severity grades for every event, exposure-adjusted rates, or a comparative statistical analysis of these terms. The safety figures are descriptive and should be read alongside those limitations; they do not establish that one regimen is safer than the other.

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

The posted result is a randomized comparison of overall survival between chemotherapy regimens containing bevacizumab and cetuximab among eligible KRAS wild type patients who began treatment. The estimated medians are 29.0 months and 30.0 months, respectively. The reported hazard ratio is 0.88, with a 95% confidence interval of 0.77 to 1.01 and p = 0.08. The interval includes 1, and the p-value is above the conventional 0.05 threshold. Taken together, the data do not provide strong statistical evidence of a difference in the primary comparison.

This finding does not prove the groups have the same survival experience. A failure to reject a no-difference hypothesis is not an equivalence result, and no equivalence margin or equivalence analysis is reported. The confidence interval leaves uncertainty about the relative comparison. It is possible for a study to report a nonsignificant result while remaining compatible with effects that could matter; the interval, rather than the p-value alone, should guide how much uncertainty remains.

The result also does not establish what would happen for every patient with metastatic colorectal cancer. The endpoint population is specified as eligible KRAS wild type patients who began treatment, and the record does not give all details needed to assess how that population relates to other groups. The result does not provide a primary survival estimate for the third arm combining both antibodies. It does not identify mechanisms, explain individual outcomes, or quantify all benefits and harms.

Finally, a registry result is a record of specified outcomes and analyses, not a substitute for a complete account of trial conduct. The registry does not report the original sample-size justification, complete analysis plan, multiplicity strategy, or detailed missing-data handling. These omissions limit the depth of assessment possible from the posted record. The defensible conclusion is narrow: the reported primary comparison is uncertain and does not meet the conventional significance threshold, while neither equivalence nor a definitive absence of difference is established.

19. Why This Trial Matters Statistically

This trial illustrates why a clinical comparison should be read through its endpoint, population, and analysis together. The overall enrollment is 2334, but the primary endpoint population is explicitly defined as eligible KRAS wild type patients who began treatment. The reported survival estimates apply to that endpoint population, not automatically to everyone enrolled or to every patient with metastatic colorectal cancer. Keeping that distinction visible prevents an overall trial enrollment figure from being mistaken for the analyzed sample.

It also shows why a point estimate and a significance threshold are not enough on their own. The hazard-ratio estimate is 0.88, while its 95% confidence interval reaches 1.01 and the log-rank p-value is 0.08. The estimate, interval, and test result together communicate both the direction of the point estimate and the remaining uncertainty. A nonsignificant result is not proof of equivalence, just as a point estimate below 1 is not, by itself, persuasive evidence of a difference.

The registry includes multiple time-to-event outcomes and a third treatment arm, but the posted primary analysis compares only the two arms with outcome data. This emphasizes the importance of matching the scope of a conclusion to the comparison actually reported. Secondary analyses can help describe consistency across endpoints, yet they do not automatically carry the same confirmatory status as the primary endpoint, especially when a multiplicity plan is not reported.

Finally, the record distinguishes the sponsor's reported analysis from planning illustrations based on observed effects. Planning calculations describe assumptions for hypothetical future studies; they do not measure the probability that the completed trial succeeded. Separating these uses of statistics helps prevent retrospective planning estimates from being mistaken for trial design details or evidence about observed power.

20. Limitations

Several limitations are specific to the registry record and its posted results. The primary comparison is limited to Arm A and Arm B. Although Arm C is described as chemotherapy with both cetuximab and bevacizumab, no primary endpoint participant count or survival estimate is posted for that group. The reported two-arm comparison cannot establish the effect of the combination-antibody regimen.

The primary endpoint population is restricted to eligible KRAS wild type patients who began treatment. The record does not explain how that population was derived from the overall enrollment of 2334, or why the posted primary arm counts are 559 and 578. It also does not describe the effect of exclusions, withdrawals, or missing outcome information. These gaps make it difficult to assess how representative the analyzed population is of all enrolled participants.

The registry provides medians and a hazard-ratio analysis, but it does not report the full survival curves in the registry record for this explanation, tests of the proportional-hazards assumption, or detailed censoring information. The hazard ratio may not summarize every feature of survival if the relative hazards vary over time. The record also does not report the original sample-size justification, the complete statistical analysis plan, interim analyses, or multiplicity procedures.

Safety reporting is similarly limited: the registry gives overall affected counts and selected serious-event terms but does not provide all detail needed to compare event rates by arm or account for treatment exposure. These limitations do not invalidate the posted results, but they define what the record can support. Interpretation should remain confined to the reported populations, endpoints, and comparisons.

21. Related Tutorials

22. Related Statistical Calculators

23. Sources

Continue through the Clinical Biostats statistical pathway

Use this trial's endpoint as a starting point for deeper study of effect measures, confidence intervals, and sample-size planning.

24. Record Summary

The registry describes a completed randomized, open-label, parallel-group phase III trial of chemotherapy with bevacizumab and/or cetuximab for metastatic colorectal cancer. Overall enrollment was 2334. The primary endpoint was overall survival, defined from registration to death and estimated using Kaplan-Meier methods for eligible KRAS wild type patients who began treatment.

The posted primary comparison was between chemotherapy plus bevacizumab and chemotherapy plus cetuximab. Median overall survival was 29.0 months and 30.0 months, respectively. The reported hazard ratio was 0.88, with a 95% confidence interval of 0.77 to 1.01 and p = 0.08. The interval includes 1, and the result does not meet the conventional 0.05 significance threshold. The registry record does not post a primary survival estimate for the third arm or report the complete original statistical design assumptions.

Clinical Biostats