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 S0819: Carboplatin and Paclitaxel With or Without Bevacizumab and/or Cetuximab in Treating Patients With Stage IV or Recurrent Non-Small Cell Lung Cancer (NCT00946712), a randomized phase 3 study. The primary outcome is Overall Survival (OS) in the Entire Study Population.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT00946712 |
| Phase | Phase 3 |
| Condition | Recurrent Large Cell Lung Carcinoma, Recurrent Lung Adenocarcinoma, Recurrent Squamous Cell Lung Carcinoma |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | None (open label) |
| Enrollment | 1333 |
| Arms in the primary outcome | 2 |
| Lead sponsor | SWOG Cancer Research Network |
| Results posted | Yes |
2. Clinical Question
Population
Patients with stage IV or recurrent non-small cell lung cancer, including the listed large cell, adenocarcinoma, and squamous cell cancer conditions. The primary analysis included all eligible patients.
Intervention
Carboplatin and paclitaxel with cetuximab, with or without bevacizumab. Cetuximab was given on days 1, 8, and 15; treatment repeated every 21 days for up to 6 courses according to the arm description.
Comparator
Carboplatin and paclitaxel without cetuximab, with or without bevacizumab. Bevacizumab was an option in both arms, so the comparison is between the two treatment strategies as described rather than a simple comparison of chemotherapy with and without bevacizumab.
Primary question
How does overall survival compare between the two randomized treatment strategies in the entire study population? The registry record defines overall survival as time from randomization to death from any cause, with patients last known to be alive censored at their last contact.
The study asks whether adding cetuximab to the chemotherapy strategy, while retaining the bevacizumab options described for both arms, is associated with a different time-to-event pattern. The primary endpoint is overall survival rather than a tumor-response measure, so the main comparison concerns the timing of deaths over follow-up. The posted results also include survival in an EGFR FISH-positive group and progression-free survival outcomes, which provide additional views of the treatment comparison but do not replace the primary question.
3. Trial Design
This was a randomized, phase III, parallel-group study with no masking reported. The registry record lists an enrollment of 1333 and status as terminated. It lists the start as 2009-07-15 and primary completion as 2017-08-31. The reason for termination is not reported in the registry record.
The two arms shared a carboplatin-and-paclitaxel backbone. Arm I used chemotherapy with or without bevacizumab; Arm II used chemotherapy and cetuximab, again with or without bevacizumab. The registry record therefore describes a comparison of treatment strategies that differ by cetuximab use, with bevacizumab included as an option in both. It does not establish from the arm summaries alone how bevacizumab use was allocated or how that option was handled in the analysis.
The arm descriptions state that treatment repeated every 21 days for up to 6 courses, subject to disease progression or unacceptable toxicity. The Arm II description specifies cetuximab on days 1, 8, and 15. The descriptions available in the registry record end partway through a sentence about treatment after the courses, so further treatment details should not be inferred.
The primary endpoint was overall survival in the entire study population. Follow-up was described as every 3 weeks during protocol treatment and every 6 months after protocol treatment until death or up to 3 years. The registry record also lists secondary outcomes involving EGFR FISH-positive patients, progression-free survival, response rates, and adverse events. The trial's original sample-size rationale, allocation details beyond randomization, and full statistical analysis plan are not reported in the registry record.
4. Participant Flow and Accounting
The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.
Overall Study
| Stage | Arm I (Chemo +/- Bevacizumab) | Arm II (Chemo, Cetuximab, +/- Bevacizumab) |
|---|---|---|
| STARTED | 671 | 662 |
| COMPLETED | 124 | 0 |
| NOT COMPLETED | 547 | 662 |
Reasons for not completing this period:
| Reason | Arm I (Chemo +/- Bevacizumab) | Arm II (Chemo, Cetuximab, +/- Bevacizumab) |
|---|---|---|
| Adverse Event | 118 | 124 |
| Disease progression | 308 | 404 |
| Death | 21 | 22 |
| No treatment given | 25 | 29 |
| Other reasons | 61 | 73 |
| On Treatment | 0 | 4 |
| Ineligible | 14 | 6 |
Analysis population for the primary outcome, as defined in the registry: All eligible patients are included in the analysis.
5. Baseline Characteristics
The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.
Population: Only eligible patients are included in the analysis.
| Characteristic | Unit | Arm I (Chemo +/- Bevacizumab) | Arm II (Chemo, Cetuximab, +/- Bevacizumab) | Total |
|---|---|---|---|---|
| Participants analysed | 657 | 656 | 1313 | |
| Age, Continuous | years | 63 (30 to 86) | 63 (19 to 84) | 63 (19 to 86) |
| Age, Customized: Age, Categorized – Age <= 65 | Participants | 379 | 381 | 760 |
| Age, Customized: Age, Categorized – Age > 65 | Participants | 278 | 275 | 553 |
| Sex: Female, Male: Female | Participants | 298 | 271 | 569 |
| Sex: Female, Male: Male | Participants | 359 | 385 | 744 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 26 | 16 | 42 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 606 | 618 | 1224 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 25 | 22 | 47 |
| Race/Ethnicity, Customized: Race – White | Participants | 565 | 568 | 1133 |
| Race/Ethnicity, Customized: Race – Black | Participants | 61 | 55 | 116 |
| Race/Ethnicity, Customized: Race – Asian | Participants | 10 | 18 | 28 |
| Race/Ethnicity, Customized: Race – Pacific Islander | Participants | 3 | 6 | 9 |
| Race/Ethnicity, Customized: Race – Native American | Participants | 2 | 1 | 3 |
| Race/Ethnicity, Customized: Race – Unknown | Participants | 16 | 8 | 24 |
| M-stage: M1a | Participants | 148 | 150 | 298 |
| M-stage: M1b | Participants | 509 | 506 | 1015 |
| Bevacizumab treatment: Yes | Participants | 277 | 283 | 560 |
| Bevacizumab treatment: No | Participants | 380 | 373 | 753 |
| Smoking History: Current | Participants | 297 | 292 | 589 |
| Smoking History: Former | Participants | 303 | 305 | 608 |
| Smoking History: Never | Participants | 57 | 59 | 116 |
| Histology: Squamous cell carcinoma | Participants | 161 | 160 | 321 |
| Histology: Adenocarcinoma | Participants | 408 | 411 | 819 |
| Histology: Other | Participants | 88 | 85 | 173 |
| Performance Status: 0 | Participants | 229 | 256 | 485 |
| Performance Status: 1 | Participants | 427 | 400 | 827 |
| Performance Status: Missing Data | Participants | 1 | 0 | 1 |
| EGFR (Epidermal Growth Factor Receptor) FISH (Fluorescence In Situ Hybridization) status: Positive | Participants | 201 | 199 | 400 |
| EGFR (Epidermal Growth Factor Receptor) FISH (Fluorescence In Situ Hybridization) status: Negative | Participants | 293 | 283 | 576 |
| EGFR (Epidermal Growth Factor Receptor) FISH (Fluorescence In Situ Hybridization) status: Unknown | Participants | 163 | 174 | 337 |
6. Primary Endpoint
The registry lists the primary outcome as Overall Survival (OS) in the Entire Study Population, measured over Patients will be followed every 3 weeks while on protocol treatment. Once off all protocol treatment, patients will be followed every 6 months until death or up to 3 years.
| Element | Registry entry |
|---|---|
| Result type | Median |
| Measure of spread | 95% Confidence Interval |
| Unit | months |
| Endpoint classification | Time-to-Event Analysis |
The primary endpoint is overall survival in the entire study population. The registry record defines it as the time from randomization until death from any cause. A patient last known to be alive is censored at the date of last contact, meaning that the analysis uses the available follow-up without treating that person's later survival time as known.
Overall survival is a time-to-event endpoint: it considers both whether an event occurred and when it occurred. Its median is the time by which the estimated survival curve reaches the halfway point. The median is a summary of the survival distribution, not a statement that every participant lived for that duration.
This endpoint is used to compare the timing of deaths across the randomized groups. A hazard ratio summarizes the relative event rate over follow-up under the model used for the reported comparison; it is not the ratio of the two median survival times. The registry record reports a Log Rank comparison and a hazard ratio with a confidence interval and p-value. Those statistics should be interpreted together with the medians, their confidence intervals, follow-up information, and the study's limitations. The registry record does not report details of the model assumptions or a fuller analysis plan.
7. Results Posted in the Registry
- Arm I (Chemo +/- Bevacizumab) vs Arm II (Chemo, Cetuximab, +/- Bevacizumab): hazard ratio 0.93 (95% CI 0.83–1.04), reported p = 0.220 (as reported in the registry).
Hazard ratio: Arm I (Chemo +/- Bevacizumab) vs Arm II (Chemo, Cetuximab, +/- Bevacizumab)
95% CI: 0.83 to 1.04
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) of EGFR FISH-positive Patients | Time-to-Event Analysis | Hazard ratio | 0.81 (0.66 to 1.00) | 708 events |
| Progression-Free Survival (PFS) of the Entire Study Population by Institutional Review | Time-to-Event Analysis | Hazard ratio | 0.99 (0.88 to 1.10) | 310,819 events |
Overall Survival (OS) of EGFR FISH-positive Patients
- 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 (Chemo +/- Bevacizumab) vs Arm II (Chemo, Cetuximab, +/- Bevacizumab): hazard ratio 0.81 (95% CI 0.66–1.00), reported p = 0.054 (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 (Chemo +/- Bevacizumab) vs Arm II (Chemo, Cetuximab, +/- Bevacizumab) and the control. The interval gives the range of effects that remain compatible with the data.
Progression-Free Survival (PFS) of the Entire Study Population by Institutional Review
- 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 (Chemo +/- Bevacizumab) vs Arm II (Chemo, Cetuximab, +/- Bevacizumab): hazard ratio 0.99 (95% CI 0.88–1.10), reported p = 0.830 (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 (Chemo +/- Bevacizumab) vs Arm II (Chemo, Cetuximab, +/- Bevacizumab) and the control. The interval gives the range of effects that remain compatible with the data.
The posted secondary results span a biomarker-defined population and a different time-to-event endpoint in the entire study population. They offer additional context, but they should not be read as independent confirmation of the primary result. A subgroup analysis asks a narrower question and may have less information; progression-free survival measures a different event process from overall survival.
The registry record lists other secondary outcomes, including centrally reviewed progression-free survival, response rates, and adverse events. The numerical summaries do not provide a complete account of results for every listed secondary outcome. The record does not report a multiplicity adjustment for the family of secondary analyses.
In general, when many outcomes or subgroups are examined, some results may appear noteworthy by chance even if there is no underlying effect. Unadjusted secondary results therefore carry less weight than a prespecified primary analysis, particularly when there is no reported multiplicity strategy or full analysis plan. They can be useful for describing patterns and generating questions, but their apparent strength should not be treated as definitive evidence on its own.
The overall pattern should be considered alongside the primary analysis rather than by selecting whichever endpoint appears most favorable. The primary overall-survival comparison remains the central result for the entire study population. Secondary analyses differ in population, endpoint, and review method, and their interpretation is limited by the information available in the registry record. No secondary result can establish an effect that the primary comparison does not demonstrate, and the record does not report a formal procedure for drawing a combined conclusion across endpoints.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Overall Survival (OS) of EGFR FISH-positive Patients
- Progression-Free Survival (PFS) of EGFR FISH-positive Patients by Centralized Review
- Progression-Free Survival (PFS) of the Entire Study Population by Institutional Review
- Progression-Free Survival (PFS) of the Entire Study Population by Centralized Review
- Response Rate (Confirmed Plus Unconfirmed, Complete and Partial Responses) in the Subset of Patients With Measurable Disease in EGFR FISH-positive Patients
- Response Rate (Confirmed Plus Unconfirmed, Complete and Partial Responses) in the Subset of Patients With Measurable Disease in the Entire Study Population
- Number of Patients With Gr 3 Through 5 Adverse Events That Are Related to Study Drugs
9. Statistical Interpretation
For overall survival in the entire study population, the posted median was 9.2 months in Arm I and 10.9 months in Arm II. The corresponding 95% confidence intervals were 8.7 to 10.3 months and 9.5 to 12.0 months. These are estimates of the medians, and the intervals show that each estimate has uncertainty.
The registry record reports a hazard ratio of 0.93, with a 95% confidence interval from 0.83 to 1.04, and a Log Rank p-value of 0.22. The interval includes 1.00, the value representing no relative difference in the hazard under the usual interpretation of a hazard ratio. The p-value does not provide evidence against the no-difference reference at conventional thresholds. This is not proof that the treatment strategies are identical: the estimate and its interval remain compatible with a range of relative effects.
The hazard ratio and the medians summarize different features of the survival data. The medians describe the estimated time at which each survival curve reaches its midpoint. The hazard ratio summarizes the relative event rate over the follow-up period, as represented by the reported analysis. It is not a direct comparison of the medians, and it should not be read as a percentage change in median survival.
The trial's secondary results offer context, but they do not overturn or settle the primary result. In the EGFR FISH-positive subgroup, the posted overall-survival medians were 9.8 months and 13.4 months, with a reported hazard ratio of 0.81, a 95% confidence interval from 0.66 to 1.00, and p=0.054. For progression-free survival of the entire study population by institutional review, the medians were 4.5 months and 4.6 months; the reported hazard ratio was 0.99, with a 95% confidence interval from 0.88 to 1.10 and p=0.83. These endpoints and populations differ from the primary analysis. The registry record does not report a multiplicity adjustment, so secondary findings warrant caution.
The posted primary comparison is consistent with uncertainty about the relative overall-survival pattern rather than a precise demonstration of a difference. Interpretation should remain anchored to the randomized comparison as recorded, the width of the confidence interval, the study's treatment options, and the limits of the registry-level information. It does not by itself establish the effect of cetuximab independently of all other treatment features.
10. Statistical Methods Explained
What does the reported median describe?
Overall survival is measured from randomization until death from any cause. The posted medians summarize the estimated survival distribution in each arm: 9.2 months for Arm I and 10.9 months for Arm II. A median is the point at which the estimated proportion surviving has reached one half. It does not mean that all participants experienced the event at that time, nor does it describe the experience of a particular participant.
Time-to-event analyses can use information from participants who have not experienced the event by the end of their observed follow-up. Under the registry definition, patients last known to be alive are censored at their last contact. Censoring records that an event had not been observed by that point; it does not imply that the participant remained alive indefinitely. The registry record gives this censoring rule but does not describe further checks or sensitivity analyses for censoring.
How should the hazard ratio be read?
The posted comparison uses a hazard ratio, reported as 0.93, and a Log Rank method. In general, a hazard is the rate at which an event occurs among people who have not yet experienced it at a given time. A hazard ratio compares those rates between groups over follow-up, subject to the method and assumptions used. A value near 1 represents similar relative event rates under that summary. A hazard ratio is not a comparison of the median times and does not directly say how many months an individual gains or loses.
The comparison is labeled Arm I versus Arm II, but the registry summary does not spell out the coding convention for the hazard ratio's numerator and reference group. The result is therefore best quoted as the reported hazard ratio and interval, rather than assigning a direction to the estimate beyond what the record explicitly states. The registry record does not report whether proportional hazards were assessed or how any departure from that assumption would be handled.
What does the confidence interval add?
The 95% confidence interval for the primary hazard ratio is 0.83 to 1.04. In general, a confidence interval represents the range of values reasonably compatible with the data and the analysis method, while reflecting sampling uncertainty. It is not a guarantee that the true value lies in that particular interval. Its width helps show the precision of the estimate. Because the interval includes 1.00, the data are compatible with no relative hazard difference as well as with values on either side of that reference.
The median confidence intervals answer a related but distinct question: they quantify uncertainty around each arm's median. Arm I's interval is 8.7 to 10.3 months, and Arm II's is 9.5 to 12.0 months. Overlap between arm-specific intervals is not, on its own, a formal test of the difference between arms. The reported hazard-ratio analysis is the registry's direct comparison.
What does the Log Rank test contribute?
The Log Rank test compares event-time patterns between groups across follow-up. The reported p-value for the primary comparison is 0.22. In general, a p-value describes how unusual the observed data, or data more extreme, would be under a specified null model. It is not the probability that the null hypothesis is true, and it does not measure the size or clinical importance of an effect. A p-value should be read alongside the estimated effect and its interval, not in isolation.
The registry record names the Log Rank method and reports the hazard ratio, but does not describe further model specifications, covariate adjustment, or checks of assumptions. The posted results therefore support interpretation of the reported comparison, not reconstruction of every analytic decision.
Why do analysis populations and endpoints matter?
The primary endpoint is reported for all eligible patients. The secondary overall-survival analysis concerns EGFR FISH-positive patients, a subset rather than the entire study population. Progression-free survival is a different endpoint, and the posted result cited was assessed by institutional review. Results from these analyses are not interchangeable: they involve different populations or event definitions, and may have different precision.
For the primary comparison, the arm summaries include 657.0 participants in Arm I and 656.0 in Arm II. These figures describe the groups in the posted results and should not be confused with the total enrollment alone. The registry record does not report additional detail about exclusions from the eligible-patient analysis, the handling of missing data beyond the stated censoring rule, or the trial's original sample-size justification.
General statistical interpretation is that time-to-event analyses preserve information about event timing and censoring, while a single median reduces an entire curve to one summary. The curve and table on this page should therefore be read together: the curve shows the estimated pattern over time, while the posted medians and hazard ratio summarize selected aspects of that pattern. Neither summary captures every feature of the data.
11. Confidence Intervals and Precision
The primary median estimates are 9.2 months for Arm I and 10.9 months for Arm II. Their 95% confidence intervals are 8.7 to 10.3 months and 9.5 to 12.0 months, respectively. These intervals communicate uncertainty around each median; they are not ranges containing most individual survival times.
For the between-arm comparison, the reported hazard ratio is 0.93, with a 95% confidence interval from 0.83 to 1.04. The interval includes 1.00, so the posted analysis does not pin down a relative hazard difference with high precision around one direction. It remains compatible with a range of effects around the no-difference reference. The p-value of 0.22 is consistent with that uncertainty, but the interval is more informative about the range of estimates compatible with the analysis.
Confidence intervals are not a probability statement about where the true effect lies after observing the data. In general, they describe the long-run performance of an interval-generating method and, in an individual study, offer a useful summary of statistical precision under the analysis assumptions. They do not account automatically for unreported biases, model misspecification, missing information, or multiple testing.
The median intervals and hazard-ratio interval refer to different estimands, so their widths should not be directly compared as though they measured the same quantity. Nor does overlap between the two median intervals substitute for the reported treatment comparison. The hazard-ratio interval is the direct comparative summary in the registry record. Its bounds should be understood in the context of the reported Log Rank analysis and the lack of further details about model assumptions.
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 | 0.93 | 5,962 | 7,981 |
| 75% of the observed effect | 0.95 | 10,598 | 14,188 |
| 50% of the observed effect | 0.96 | 23,846 | 31,923 |
The sample-size section is a planning illustration based on the observed effect, not a reconstruction of the trial's original design. Because the outcome is time-to-event, its table gives the total number of events required, not participants per arm. The values are calculated under the listed assumptions: a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is the stated fraction of the observed effect.
The 80% power column describes a hypothetical design that would have an 80% chance of detecting the specified effect under those assumptions if that effect were true. The 90% power column describes the corresponding planning target with a 90% chance. These are design probabilities, not probabilities that the observed finding is correct. The displayed event totals are not the number of participants enrolled in this trial.
The table shows planning at 100%, 75%, and 50% of the observed effect. A smaller effect is harder to distinguish from random variation, so planning to detect a smaller effect requires more events. That pattern is visible in the table. The effect used for the illustration comes from the posted result, so it should not be treated as an independently established target or as proof that the observed effect will recur.
This is not observed power. It is a hypothetical planning exercise using the stated assumptions and the observed effect as its starting point. The trial's own sample-size justification and original design assumptions are not reported in the registry record. The planning figures should therefore be read as illustrations of how event requirements change with the target effect and desired power, not as a judgement about whether the completed trial was adequately designed.
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 = 0.930, so ln(HR) = -0.0726.
- d = 4 × (1.96 + 0.842)2 / [ln(0.930)]2 = 5,961.4, rounded up to 5,962 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 <- 0.93 # 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(946712)
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 = 5,962 (80% power), 7,981 (90% power)
75% of observed effect: events = 10,598 (80% power), 14,188 (90% power)
50% of observed effect: events = 23,846 (80% power), 31,923 (90% power)
Simulated power with 5,962 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 9,395 participants in total, with the boundaries below.
| Analysis | Calendar time (months) | Events | Efficacy boundary (z) | Nominal one-sided p | Cumulative alpha spent |
|---|---|---|---|---|---|
| Look 1 | 16.9 | 2,691 | 3.710 | 0.0001 | 0.0001 |
| Look 2 | 26.7 | 5,382 | 2.511 | 0.0060 | 0.0060 |
| Look 3 | 60.0 | 8,074 | 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% | 5,960 | 6,936 | 60.0 |
| Two looks, O'Brien-Fleming | 80% | 5,982 | 6,962 | 60.0 |
| Three looks, O'Brien-Fleming | 80% | 6,036 | 7,024 | 60.0 |
| Three looks, Pocock | 80% | 6,976 | 8,118 | 60.0 |
| Fixed design, one analysis | 90% | 7,979 | 9,285 | 60.0 |
| Two looks, O'Brien-Fleming | 90% | 8,007 | 9,317 | 60.0 |
| Three looks, O'Brien-Fleming | 90% | 8,074 | 9,395 | 60.0 |
| Three looks, Pocock | 90% | 9,210 | 10,717 | 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 | 0.930 | 8,074 | 9,395 |
| 75% of the observed effect | 0.947 | 14,354 | 16,673 |
| 50% of the observed effect | 0.964 | 32,298 | 37,448 |
For context, this trial enrolled 1,333 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 <- 9.2 # control-arm median, months (converted from the posted unit)
hr <- 0.93 # 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: 6630 p (1-sided) 0.0001
Events: 2692 ~HR at bound 0.8667
Month: 17 P(Cross) if HR=1 0.0001
P(Cross) if HR=0.93 0.0338
IA 2: 67% Z 2.5114
N: 9396 p (1-sided) 0.0060
Events: 5383 ~HR at bound 0.9338
Month: 27 P(Cross) if HR=1 0.0060
P(Cross) if HR=0.93 0.5603
Final Z 1.9930
N: 9396 p (1-sided) 0.0231
Events: 8074 ~HR at bound 0.9566
Month: 60 P(Cross) if HR=1 0.0250
P(Cross) if HR=0.93 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) 0.93 | 0.83 to 1.04 | 0.220 |
The registry record reports the primary comparison as a Log Rank hazard ratio of 0.93, with a 95% confidence interval from 0.83 to 1.04 and p=0.22. Those are the sponsor's posted analysis results and are the primary basis for interpretation. The simple summary-statistic recalculation does not identify a discrepancy with that reported result, so there is no conflicting estimate to resolve.
For time-to-event outcomes, the recalculation is not a replacement for the sponsor's analysis. The posted hazard ratio comes from the reported Log Rank comparison, whereas medians alone cannot reproduce that comparison: they do not retain the full event-time information or censoring pattern. The sponsor's analysis therefore takes precedence as the reported inferential result.
The recalculation and the posted results serve different purposes. A simple recalculation can help readers understand the information represented in summary statistics, but it cannot recover unreported details about analysis populations, assumptions, or data handling. The registry record does not report enough of the statistical analysis plan to independently reproduce every aspect of the sponsor's procedure. Readers should use the reported estimate, confidence interval, and p-value as the principal comparison, while treating the medians and plotted summaries as complementary descriptions.
16. Multiplicity, Missing Data and Analysis Populations
The registry record lists multiple secondary outcomes, including overall and progression-free survival in the EGFR FISH-positive group, progression-free survival in the full population using different review methods, response rates, and adverse events. Considering several outcomes or subgroups creates a multiplicity issue: even when no true effect exists, repeated testing can increase the chance that at least one result appears unusual. In general, investigators may address this through prespecified testing sequences, adjusted significance thresholds, or other strategies.
A multiplicity plan or adjustment is not reported in the registry record. The record also does not report which secondary analyses, if any, were prioritized in a formal testing hierarchy. Accordingly, secondary p-values should be treated as exploratory or descriptive unless other documentation establishes a confirmatory role. The reported primary endpoint remains the clearest basis for the main study-level interpretation.
For the primary endpoint, the registry defines the eligible-patient analysis and states that participants last known to be alive are censored at their last contact. That is useful information about the event definition and censoring rule. The registry record does not report further detail on missing covariates, incomplete endpoint ascertainment, loss to follow-up, or sensitivity analyses that might assess the influence of missing data.
The record describes follow-up during and after protocol treatment, but does not provide a detailed account of adherence to the planned follow-up schedule or the number of participants with incomplete follow-up. It also does not report interim analyses, stopping boundaries, or whether the termination was related to efficacy, safety, feasibility, or another reason. These items should not be inferred from the terminated status.
The record states that all eligible patients were included in the primary analysis, but it does not give a full account of eligibility exclusions or other analysis-population definitions. The trial's original sample-size rationale and complete statistical analysis plan are not reported in the registry record. These omissions limit independent assessment of prespecification, missing-data handling, and the broader inferential context, without changing the values shown in the posted primary results.
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 (Chemo +/- Bevacizumab) | 66 | 632 | 10.4% |
| Arm II (Chemo, Cetuximab, +/- Bevacizumab) | 97 | 627 | 15.5% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Arm I (Chemo +/- Bevacizumab) | 593 of 657 |
| Arm II (Chemo, Cetuximab, +/- Bevacizumab) | 570 of 656 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 5% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Arm I (Chemo +/- Bevacizumab) | 619 of 632 |
| Arm II (Chemo, Cetuximab, +/- Bevacizumab) | 611 of 627 |
Most frequent serious adverse event terms
| Event term | Organ system | Arm I (Chemo +/- Bevacizumab) | Arm II (Chemo, Cetuximab, +/- Bevacizumab) |
|---|---|---|---|
| Death - Disease progression NOS | Neoplasms benign, malignant and unspecified (incl cysts and polyps) | 9 of 632 | 17 of 627 |
| Death not associated with CTCAE term - Death NOS | General disorders | 12 of 632 | 12 of 627 |
| Carbon monoxide diffusion capacity (DL(co)) | Investigations | 8 of 632 | 8 of 627 |
| Carbon monoxide diffusion capacity (DL(co)) | Respiratory, thoracic and mediastinal disorders | 8 of 632 | 8 of 627 |
| Dyspnea (shortness of breath) | Respiratory, thoracic and mediastinal disorders | 6 of 632 | 5 of 627 |
| Febrile neutropenia | Blood and lymphatic system disorders | 5 of 632 | 3 of 627 |
| Allergic reaction/hypersensitivity | Immune system disorders | 0 of 632 | 8 of 627 |
| Thrombosis/thrombus/embolism | Vascular disorders | 4 of 632 | 4 of 627 |
| Cardiac General-Other | Cardiac disorders | 3 of 632 | 3 of 627 |
| Inf (clin/microbio) w/Gr 3-4 neuts - Blood | Infections and infestations | 0 of 632 | 5 of 627 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Arm I (Chemo +/- Bevacizumab) | Arm II (Chemo, Cetuximab, +/- Bevacizumab) |
|---|---|---|---|
| Fatigue (asthenia, lethargy, malaise) | General disorders | 494 of 632 | 474 of 627 |
| Hemoglobin | Blood and lymphatic system disorders | 434 of 632 | 384 of 627 |
| Neuropathy: sensory | Nervous system disorders | 386 of 632 | 368 of 627 |
| Nausea | Gastrointestinal disorders | 304 of 632 | 318 of 627 |
| Hair loss/Alopecia (scalp or body) | Skin and subcutaneous tissue disorders | 315 of 632 | 293 of 627 |
| Dyspnea (shortness of breath) | Respiratory, thoracic and mediastinal disorders | 285 of 632 | 290 of 627 |
| Constipation | Gastrointestinal disorders | 261 of 632 | 302 of 627 |
| Neutrophils/granulocytes (ANC/AGC) | Investigations | 252 of 632 | 305 of 627 |
| Glucose, serum-high (hyperglycemia) | Metabolism and nutrition disorders | 290 of 632 | 266 of 627 |
| Magnesium, serum-low (hypomagnesemia) | Metabolism and nutrition disorders | 201 of 632 | 349 of 627 |
Serious events with the highest arm-level rate: death - disease progression nos (2.7%), death not associated with ctcae term - death nos (1.9%), allergic reaction/hypersensitivity (1.3%), carbon monoxide diffusion capacity (dl(co)) (1.3%), dyspnea (shortness of breath) (0.9%).
The registry record reports serious adverse event figures for 632 participants at risk in Arm I, of whom 66 were affected, and 627 at risk in Arm II, of whom 97 were affected. For other adverse events, the corresponding figures are 619 of 632 and 611 of 627. The record also lists deaths as 593 in Arm I and 570 in Arm II. These are posted counts with their stated at-risk denominators; they are not adjusted comparisons.
The serious-event terms listed most often include death due to disease progression, death not associated with a CTCAE term, allergic reaction or hypersensitivity, carbon monoxide diffusion capacity, dyspnea, and infection with grade 3–4 neutropenia. The registry lists percentages for these terms, ranging from 0.8% to 2.7% in the entries shown. The list is not a complete description of every event, and the record does not establish from these figures alone whether the event counts differ statistically between arms.
The serious-event totals should not be conflated with the separate secondary outcome concerning grade 3 through 5 adverse events related to study drugs. The posted summary does not supply enough detail to determine causality for each event or to make a comparative safety conclusion. These figures describe what the registry reports and should be interpreted with the definitions and collection procedures, which are not fully detailed in the record.
18. What the Result Does, and Does Not, Mean
The posted results describe a randomized comparison of two treatment strategies in advanced or recurrent non-small cell lung cancer. The primary overall-survival estimate is a hazard ratio of 0.93, with a 95% confidence interval from 0.83 to 1.04 and p=0.22. The median estimates were 9.2 months and 10.9 months. Taken together, these results do not provide a precise demonstration of a difference in overall survival between the strategies, while also not proving that the strategies are identical.
The result does not establish the effect of cetuximab in isolation. Bevacizumab was an option in both arms, and the registry record does not explain in the posted summary how its use was allocated or handled analytically. The comparison should therefore be understood as the randomized strategies as recorded, not as a clean test of one drug separated from all other treatment features.
The result also does not mean that every participant had the median experience, or that a hazard ratio can be translated directly into a difference in months. The confidence interval communicates statistical uncertainty under the reported analysis, but does not account for every possible source of uncertainty or bias. Details of the full analysis plan, sample-size justification, interim analyses, and handling of other missing information are not reported in the registry record.
Secondary outcomes and subgroup findings may help describe additional patterns, but they involve different endpoints or populations and are not substitutes for the primary analysis. The registry record does not report a multiplicity strategy, so secondary results should be treated with appropriate caution. Safety counts likewise describe posted events and denominators, rather than proving a comparative causal effect.
Overall, this is a reading of the posted trial data and their precision, not medical advice or a recommendation about treatment. The statistical result is best understood as an estimate with uncertainty, within the limits of the study design and the information available in the registry record.
19. Why This Trial Matters Statistically
This trial illustrates why a randomized time-to-event result needs more than a single median. The registry reports medians for each arm, but also gives a hazard ratio, a confidence interval, and a Log Rank p-value. Each contributes a different piece of information: the medians summarize survival distributions, while the comparative analysis uses event-time information across follow-up. A careful reading avoids treating the median difference as the whole statistical result.
It also illustrates the distinction between a point estimate and its precision. The hazard ratio is a concise summary, but the confidence interval shows that the data are compatible with a range of relative effects. A p-value alone cannot communicate that range or establish whether a difference is important. In this record, the interval and p-value both reinforce the need to interpret the estimate cautiously rather than to treat it as a definitive answer.
The treatment structure is another important statistical feature. Cetuximab distinguishes the two described strategies, while bevacizumab is an option in both. That structure limits how narrowly one can attribute the overall comparison to a single agent without further information about allocation and analysis. The posted results should be read as a comparison of the randomized strategies, not a simplified one-drug contrast.
Finally, the record shows how secondary endpoints, subgroup analyses, censoring, and missing statistical-plan details affect interpretation. A broad menu of outcomes can produce results that are harder to interpret without prespecification and multiplicity control. Stating what is and is not documented is part of sound statistical communication: it prevents unreported design features from being mistaken for known details and keeps the conclusion proportionate to the posted evidence.
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.
Several limitations specific to this record constrain interpretation. The trial is listed as terminated, but the reason for termination is not reported in the registry record. Termination alone does not indicate whether the decision was driven by efficacy, safety, recruitment, or another consideration. The record lists primary completion as 2017-08-31 but does not provide a detailed account of follow-up completeness or the timing of the posted analyses.
The primary result compares strategies in which bevacizumab could be used in either arm. The registry summaries do not explain how bevacizumab use was assigned, balanced, or incorporated into the analysis. As a result, the primary comparison cannot be reduced to a fully isolated estimate of adding cetuximab without further details.
The posted statistical information names a Log Rank comparison and reports a hazard ratio, but does not give the full model specification, covariate adjustment, or assessment of assumptions. The record does not report a multiplicity plan, interim analyses, the original sample-size rationale, or detailed missing-data sensitivity analyses. These gaps limit independent evaluation of prespecification and robustness.
The primary analysis is described as including all eligible patients, but the record does not provide a full flow of patients through eligibility and analysis. Censoring is described for participants last known to be alive, yet further details about follow-up gaps and incomplete data are not reported. Secondary outcomes vary in population and review method, and numerical results for all listed outcomes are not represented in the summaries. These limitations call for restrained interpretation of the primary and secondary findings.
21. Related Tutorials
22. Related Statistical Calculators
23. Sources
- ClinicalTrials.gov: S0819: Carboplatin and Paclitaxel With or Without Bevacizumab and/or Cetuximab in Treating Patients With Stage IV or Recurrent Non-Small Cell Lung Cancer — NCT00946712.
- Registry record last updated 2023-05-23; status last verified 2023-05.
- Results first posted 2019-03-07.
- 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.
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
This randomized, phase III, parallel-group trial enrolled 1333 participants and is listed as terminated. It compared carboplatin and paclitaxel with or without bevacizumab against the same chemotherapy strategy with cetuximab and with or without bevacizumab. The primary endpoint was overall survival in the entire eligible population.
The posted primary result was a hazard ratio of 0.93, with a 95% confidence interval from 0.83 to 1.04 and p=0.22. Median overall survival was 9.2 months in Arm I and 10.9 months in Arm II. The reported estimate is uncertain and does not establish a clear difference between the strategies.
The registry record does not report the trial's original sample-size justification, full statistical analysis plan, reason for termination, or multiplicity strategy. Secondary and safety results should be interpreted in light of these limits and the differences in populations and endpoints.