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 Phase III Study of ABI-007(Albumin-bound Paclitaxel) Plus Gemcitabine Versus Gemcitabine in Metastatic Adenocarcinoma of the Pancreas (NCT00844649), a randomized phase 3 study. The primary outcome is Overall Survival (OS).
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT00844649 |
| Phase | Phase 3 |
| Condition | Metastatic Pancreatic Cancer |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | None (open label) |
| Enrollment | 861 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Celgene |
| Results posted | Yes |
2. Clinical Question
Population
Participants had metastatic adenocarcinoma of the pancreas. The primary analysis population was the intent-to-treat population, defined in the registry as all randomized participants. The registry reports total enrollment of 861 participants; the outcome summaries list 431 participants in the combination group and 430 in the gemcitabine group.
Intervention
The combination group received albumin-bound paclitaxel (ABI-007) at 125 mg/m2 with gemcitabine at 1000 mg/m2 weekly for 3 weeks, followed by one week of rest.
Comparator
The comparator group received gemcitabine at 1000 mg/m2 weekly for 7 weeks followed by a week of rest in Cycle 1. From Cycle 2 onward, gemcitabine was given weekly for 3 weeks followed by a week of rest.
Primary question
The primary question was whether overall survival, measured from randomization to death from any cause, differed between the two randomized groups. The registry reports median survival by group and a sponsor-reported hazard ratio from a stratified log-rank analysis. These are group-level trial results; they do not describe the outcome an individual participant would experience.
General statistical context: random assignment supports a comparison of outcomes between groups by reducing the influence of baseline differences on average, but it does not ensure that every participant has the same prognosis or treatment experience. The registry identifies the study as randomized, parallel-group, Phase III, and unmasked. It does not report the details of the randomization procedure or the factors used for stratification.
3. Trial Design
The registry describes a randomized, parallel-group Phase III study comparing albumin-bound paclitaxel (ABI-007) plus gemcitabine with gemcitabine alone in metastatic adenocarcinoma of the pancreas. The sponsor was Celgene. The study is marked completed, with enrollment of 861 participants. The registry lists the study start as 2009-03-01 and primary completion as 2012-09-17.
Outcome summaries list 431 participants in the combination group and 430 in the gemcitabine group. The primary outcome analysis used the intent-to-treat population, which the registry defines as all randomized participants. Overall survival was measured from randomization until death from any cause; participants who had not died were censored at the last known time they were alive. The primary outcome timeframe ends at the data cutoff of 17 Sept 2012, and maximum follow-up is reported as 37 months.
The study was unmasked, according to the registry's masking entry. The registry does not report further details about how assignment was generated, allocation concealment, or whether outcome assessors were masked. It describes the combination regimen as weekly treatment for 3 weeks followed by one week of rest. For gemcitabine alone, the schedule differs between Cycle 1 and later cycles, as described in the clinical question.
Progression-free survival was assessed by independent radiological review and was measured from randomization to disease progression or death from any cause. The registry also reports the percentage of participants with an objective confirmed overall response by independent radiological review. The response outcome timeframe extends to a data cutoff of 17 Sept 2013, whereas the overall-survival and progression-free-survival timeframes use a cutoff of 17 Sept 2012. The registry does not report the reason for these different cutoffs.
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: 38 participants were randomized but not treated due to the participants request to withdraw after the randomization results became known. 1 participant was randomized to Gemcitabine and was treated with Albumin-bound paclitaxel ABI-007/Gemcitabine in error and analyzed as treated and included in the intent to treat population (ITT)
Overall Study
| Stage | Albumin-bound Paclitaxel (ABI-007)/Gemcitabine (Gem) | Gemcitabine (Gem) |
|---|---|---|
| STARTED | 431 | 430 |
| Treated Population | 421 | 402 |
| COMPLETED | 26 | 12 |
| NOT COMPLETED | 405 | 418 |
Reasons for not completing this period:
| Reason | Albumin-bound Paclitaxel (ABI-007)/Gemcitabine (Gem) | Gemcitabine (Gem) |
|---|---|---|
| Progressive Disease | 196 | 245 |
| Adverse Event | 128 | 73 |
| Physician Decision | 25 | 18 |
| Protocol Violation | 10 | 6 |
| Withdrawal by Subject | 28 | 39 |
| Other | 7 | 10 |
| Withdrew prior to starting treatment | 11 | 27 |
Analysis population for the primary outcome, as defined in the registry: Intent to Treat population (ITT population) consisted of all randomized participants.
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: For the Karnofsky Performance Status (KPS) baseline characteristic, some of the participants did not have a baseline KPS recorded by the clinical site.
| Characteristic | Unit | Albumin-bound Paclitaxel (ABI-007)/Gemcitabine | Gemcitabine | Total |
|---|---|---|---|---|
| Participants analysed | 431 | 430 | 861 | |
| Age, Continuous | years | 61.4 (SD 10.70) | 63.0 (SD 9.27) | 62.2 (SD 10.04) |
| Sex: Female, Male: Female | Participants | 186 | 173 | 359 |
| Sex: Female, Male: Male | Participants | 245 | 257 | 502 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 0 | 0 | 0 |
| Race (NIH/OMB): Asian | Participants | 8 | 9 | 17 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 1 | 0 | 1 |
| Race (NIH/OMB): Black or African American | Participants | 16 | 16 | 32 |
| Race (NIH/OMB): White | Participants | 378 | 375 | 753 |
| Race (NIH/OMB): More than one race | Participants | 25 | 26 | 51 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 3 | 4 | 7 |
| Karnofsky Performance Status (KPS): 100% = normal, no complaints, no signs of disease | participants | 69 | 69 | 138 |
| Karnofsky Performance Status (KPS): 90% = normal activity, few symptoms of disease | participants | 179 | 199 | 378 |
| Karnofsky Performance Status (KPS): 80% = normal activity, some symptoms of disease | participants | 149 | 128 | 277 |
| Karnofsky Performance Status (KPS): 70% = caring for self, unable to work | participants | 30 | 33 | 63 |
| Karnofsky Performance Status (KPS): 60% = needs help, can manage most tasks | participants | 2 | 0 | 2 |
| Karnofsky Performance Status (KPS): 50% = needs help often and medical care | participants | 0 | 0 | 0 |
| Karnofsky Performance Status (KPS): 40% = disabled; requires special care & assistance | participants | 0 | 0 | 0 |
| Karnofsky Performance Status (KPS): 30% = severely disabled; death is imminent | participants | 0 | 0 | 0 |
| Karnofsky Performance Status (KPS): 20% = hospitalized; requires supportive treatment | participants | 0 | 0 | 0 |
| Karnofsky Performance Status (KPS): 10% = Moribund, fatal processes progressing fast | participants | 0 | 0 | 0 |
| Pancreatic Primary Tumor Location: Head | participants | 191 | 180 | 371 |
| Pancreatic Primary Tumor Location: Body | participants | 132 | 136 | 268 |
| Pancreatic Primary Tumor Location: Tail | participants | 105 | 110 | 215 |
| Pancreatic Primary Tumor Location: Unknown = not specified | participants | 3 | 4 | 7 |
| Number of Baseline Lesions (Target + Non-Target): 1 | participants | 1 | 0 | 1 |
| Number of Baseline Lesions (Target + Non-Target): 2 | participants | 32 | 25 | 57 |
| Number of Baseline Lesions (Target + Non-Target): 3 | participants | 7 | 7 | 14 |
| Number of Baseline Lesions (Target + Non-Target): 4 | participants | 37 | 43 | 80 |
| Number of Baseline Lesions (Target + Non-Target): 5 | participants | 8 | 8 | 16 |
| Number of Baseline Lesions (Target + Non-Target): >5 | participants | 276 | 262 | 538 |
6. Primary Endpoint
The registry lists the primary outcome as Overall Survival (OS), measured over From randomization to death; until the data cut off 17 Sept 2012. The maximum time in follow up was 37 months..
| Element | Registry entry |
|---|---|
| Result type | Median |
| Measure of spread | 95% Confidence Interval |
| Unit | months |
| Endpoint classification | Time-to-Event Analysis |
Overall survival was the primary endpoint. It measures the time from randomization until death from any cause. Participants who had not died by the time of their last known contact were censored at that last known time alive. The registry states that survival was summarized with Kaplan-Meier methods.
General statistical context: overall survival is a time-to-event endpoint. It uses information about both whether an event occurred and how long participants were followed before death or censoring. Censoring does not mean that a participant had no event; it means that the exact event time was not observed during the available follow-up. The registry's definition makes death from any cause the event, rather than limiting the endpoint to a particular cause of death.
The median is the time by which half of the estimated survival distribution has experienced the event. It is a summary of the middle of the survival-time distribution, not a description of every participant's survival time or of the full pattern of events over follow-up. The hazard ratio provides a separate comparison of the event rates over time under the model and analysis used; it should not be read as a direct comparison of the medians.
Overall survival is useful for describing how long participants lived after randomization, while preserving the timing of events and censoring. It is distinct from progression-free survival, which also counts progression as an event, and from objective response, which records whether a confirmed response was observed. The registry identifies overall survival as the primary endpoint and lists the intent-to-treat population for that analysis.
7. Results Posted in the Registry
- Albumin-bound Paclitaxel (ABI-007)/Gemcitabine vs Gemcitabine: hazard ratio 0.72 (95% CI 0.62–0.83), reported p < 0.001 (as reported in the registry).
Hazard ratio: Albumin-bound Paclitaxel (ABI-007)/Gemcitabine vs Gemcitabine
95% CI: 0.62 to 0.83
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 |
|---|---|---|---|---|
| Progression-free Survival (PFS) by Independent Radiological Review (IRR) | Time-to-Event Analysis | Hazard ratio | 0.69 (0.58 to 0.82) | 229 events |
| Percentage of Participants Who Achieved an Objective Confirmed Overall Response by Independent Radiological Review (IRR) | Binary Endpoint | Risk difference | -16.0 pts (-20.6 to -11.3) | 77 per arm |
Progression-free Survival (PFS) by Independent Radiological Review (IRR)
- Endpoint type: Time to event: compared as a hazard ratio.
- Test: Hazard ratio as reported by the sponsor (Stratified Log-rank Test); it was not recalculated.
- Result:
- Albumin-bound Paclitaxel (ABI-007)/Gemcitabine vs Gemcitabine: hazard ratio 0.69 (95% CI 0.58–0.82), reported p < 0.001 (as reported in the registry).
- Interpretation:
- The 95% confidence interval excludes no difference (a ratio of 1), so the hazard of the event is statistically lower for Albumin-bound Paclitaxel (ABI-007)/Gemcitabine vs Gemcitabine than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Percentage of Participants Who Achieved an Objective Confirmed Overall Response by Independent Radiological Review (IRR)
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Gemcitabine: 7.0% (30/430) versus 23.0% (99/431) on control; risk difference -16.0 percentage points (95% CI -20.6 to -11.3), risk ratio 0.30 (0.21–0.45); unadjusted two-proportion z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the proportion with the event is statistically lower for Gemcitabine than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The two posted secondary outcomes describe different aspects of the trial. Progression-free survival captures time to progression or death, while confirmed objective response records whether a radiologically reviewed response was confirmed. The reported directions are consistent with the primary overall-survival comparison: the combination group has a lower reported hazard ratio for progression-free survival and a higher reported response percentage. These outcomes are supportive descriptions, not substitutes for the primary endpoint.
Interpretation should account for the fact that progression-free survival and response were assessed by independent radiological review, while overall survival records death from any cause. They also have different timeframes in the registry: the time-to-event outcomes use the 17 Sept 2012 data cutoff, and the response outcome uses the 17 Sept 2013 cutoff. The registry does not explain the different cutoffs. Differences in endpoint definitions and observation windows mean that the results should not be collapsed into a single measure of effect.
General statistical context: testing several outcomes creates a multiplicity issue. When multiple hypotheses are examined, the chance of at least one apparently unusual result can increase unless the analysis plan accounts for that testing. The registry does not report whether secondary-outcome p-values were adjusted, how the secondary endpoints were ordered, or whether a testing hierarchy was planned. The reported secondary p-values should therefore be read as individual reported analyses rather than as proof that all multiplicity concerns were addressed.
The sponsor reports a chi-squared analysis and response rate ratio for objective response, and a stratified log-rank analysis and hazard ratio for progression-free survival. Those methods answer different statistical questions. The registry does not report the detailed analysis plan or enough information to evaluate the secondary analyses under alternative methods. Their role is to add context around the primary result while retaining their distinct definitions and the uncertainty associated with multiple outcomes.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Progression-free Survival (PFS) by Independent Radiological Review (IRR)
- Percentage of Participants Who Achieved an Objective Confirmed Overall Response by Independent Radiological Review (IRR)
9. Statistical Interpretation
The posted primary results show a median overall survival of 8.5 months for albumin-bound paclitaxel plus gemcitabine, with a 95% confidence interval of 7.89 to 9.53 months. The gemcitabine group had a median of 6.7 months, with a 95% confidence interval of 6.01 to 7.23 months. The sponsor-reported hazard ratio for the combination compared with gemcitabine was 0.72, with a 95% confidence interval of 0.617 to 0.835 and p < 0.001, using a stratified log-rank test.
General statistical context: a hazard ratio compares the event rates over follow-up as represented by the analysis; it is not a ratio of the two median survival times, nor does it state how many months an individual participant will live. A value below 1 for the stated comparison indicates that the estimated event rate was lower in the first group under that analysis. The confidence interval expresses uncertainty in the estimated hazard ratio, and the reported p-value indicates that the data were inconsistent with the test's null hypothesis under its assumptions. Neither statistic alone establishes the size or certainty of an individual participant's outcome.
The registry also reports a median progression-free survival of 5.5 months for the combination group and 3.7 months for gemcitabine. Its sponsor-reported hazard ratio is 0.69, with a 95% confidence interval of 0.581 to 0.821 and p < 0.001. For confirmed objective response, the posted percentages are 23.0% and 7.0%, respectively. The sponsor reports a response rate ratio of 3.19, with a 95% confidence interval of 2.178 to 4.662 and p < 0.001.
These are separate endpoints with different definitions and analysis methods. Progression-free survival counts either progression or death, while response records a confirmed radiological outcome. Overall survival remains the primary endpoint and directly concerns death from any cause. The secondary results offer additional descriptions of the trial outcomes, but their interpretation also depends on the measurement and analysis choices for each endpoint.
The reported findings describe the randomized groups and the follow-up available at the stated cutoffs. They do not establish that every participant had the group median outcome, and they do not determine an individual prognosis. The registry does not report the original sample-size justification, a detailed analysis plan, or interim-analysis procedures, so those aspects cannot be used to qualify the results.
10. Statistical Methods Explained
Overall survival was summarized with Kaplan-Meier methods, according to the registry. The sponsor compared survival between groups with a stratified log-rank test and reported a hazard ratio. The registry does not identify the stratification factors or give further detail about the model used to estimate the hazard ratio.
What does a Kaplan-Meier summary do?
General statistical explanation: Kaplan-Meier methods estimate the probability of remaining event-free over follow-up while accounting for participants whose event time is not observed because they are censored. Each observed event contributes information up to its event time, and a censored participant contributes information up to the last known time they were observed. The resulting curve describes the estimated pattern over time; the median is the point at which the estimated event-free probability reaches its midpoint. It is not an arithmetic average of individual follow-up times.
The registry defines censoring for overall survival as occurring at the last known time a participant was alive if the participant did not die. That definition is important because a participant who is censored is not counted as having died at the censoring time. The registry does not report additional details about how censoring was handled for progression-free survival or objective response.
How should the hazard ratio be understood?
General statistical explanation: a hazard ratio compares the event rates between groups over the observed follow-up, conditional on the analysis model. It is a relative, time-to-event summary, not a difference in median months and not an individual-level prediction. The sponsor-reported overall-survival estimate compares albumin-bound paclitaxel plus gemcitabine with gemcitabine. The reported value is 0.72, and its 95% confidence interval is 0.617 to 0.835. The sponsor used a stratified log-rank test; the registry does not report the strata or enough detail to reconstruct that analysis independently.
A log-rank test compares the observed event pattern between groups over follow-up, taking account of the timing of events and censoring. Stratification can account for specified grouping factors in the comparison, but the factors used in this study are not reported in the registry record. A p-value is a measure of how compatible the observed data are with a null hypothesis under the test assumptions. It does not measure the probability that the null hypothesis is true, and it does not give the probability that a treatment will benefit a particular person.
How do the endpoints differ?
Overall survival counts death from any cause as the event. Progression-free survival counts disease progression or death from any cause, with progression assessed by independent radiological review. An objective confirmed overall response is a binary outcome: the registry reports the percentage of participants who achieved a confirmed response based on independent radiological review. These endpoints answer related but distinct questions. A result for one cannot be substituted for a result on another.
The reported secondary endpoint analysis for response uses a chi-squared method and reports a response rate ratio. The reported time-to-event analyses use the stratified log-rank test and hazard ratios. These statistics have different meanings and should not be compared as if they were the same measure. The registry does not report whether secondary analyses were adjusted for other factors, nor whether an adjustment for multiple testing was planned or applied.
What do the confidence intervals and p-values add?
General statistical explanation: a confidence interval gives a range of estimates compatible with the observed data and the method's assumptions. It helps show the precision of an estimate, while a p-value addresses a null-hypothesis test. Neither replaces the point estimate, and neither describes the range of outcomes among individual participants. For time-to-event measures, the interval around a hazard ratio describes uncertainty in that relative comparison; the intervals around medians describe uncertainty in the median estimates.
The registry reports 95% confidence intervals for the primary and secondary outcomes. It reports p < 0.001 for the primary hazard-ratio analysis and the progression-free-survival hazard-ratio analysis; the response analysis reports p < 0.001. The registry does not report whether these p-values were adjusted for multiplicity. The posted values should therefore be read as the reported analyses, not as evidence that all potential testing considerations have been resolved.
What information is unavailable?
The registry does not report the full statistical analysis plan, the original sample-size justification, assumptions behind the trial's design, interim-analysis procedures, or the stratification factors. It also does not provide individual participant data from which to independently reproduce the time-to-event analyses. The trial's primary analysis population is identified as intent to treat, but detailed handling of missing observations and additional sensitivity analyses are not reported. These omissions limit how fully an outside reader can audit the analysis decisions.
11. Confidence Intervals and Precision
The overall-survival median for the combination group is 8.5 months, with a 95% confidence interval from 7.89 to 9.53 months. For gemcitabine, the median is 6.7 months, with a 95% confidence interval from 6.01 to 7.23 months. The sponsor-reported hazard ratio is 0.72, with a 95% confidence interval from 0.617 to 0.835. The interval for the hazard ratio describes uncertainty in the relative time-to-event comparison; it is not a range containing the outcomes of 95% of participants.
General statistical explanation: confidence intervals quantify statistical uncertainty under the methods and assumptions used. A narrower interval indicates greater precision for the particular estimate, while a wider interval indicates greater uncertainty. An interval is not a guarantee that the true value lies within its endpoints, and a 95% confidence interval is not a statement that 95% of individual outcomes fall inside it.
The secondary time-to-event estimate also has a reported interval: the progression-free-survival hazard ratio is 0.69, with a 95% confidence interval from 0.581 to 0.821. The response percentages have separate confidence intervals: 19.1 to 27.2 for the combination group and 5.0 to 10.1 for gemcitabine. Those intervals describe uncertainty in the response percentages, not in survival time.
Confidence intervals should be read alongside the endpoint definition, analysis method, and population. The primary analysis uses all randomized participants under the intent-to-treat definition, while the registry lists different numbers at risk for the adverse-event summaries. Follow-up ends at specified data cutoffs, and censoring means that not every participant's event time was observed. Those features affect the information available for the estimates. The registry does not report enough detail to assess precision under alternative analysis assumptions or to reconstruct confidence intervals from individual-level records.
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 | 0.72 | 291 | 390 |
| 75% of the observed effect | 0.78 | 518 | 693 |
| 50% of the observed effect | 0.85 | 1,164 | 1,558 |
The planning figures are illustrations based on the observed effect, not the trial's original design justification. For the time-to-event outcomes, the entries are total numbers of events required. For the response outcome, the entries are participants per arm. The two kinds of figures therefore have different units and should not be read as interchangeable sample-size targets.
The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each planning scenario uses a stated fraction of the observed effect: 100%, 75%, or 50%. The time-to-event planning figures use the Schoenfeld approach. The registry does not report the original trial's sample-size assumptions or justification, so these illustrations should not be mistaken for the design assumptions actually used to plan the trial.
The 80% power column describes the event total or per-arm participant count estimated to give an 80% chance of detecting the specified effect under those planning assumptions, if that effect were the true one. The 90% power column gives the corresponding planning quantity for a 90% chance. These are prospective design calculations under assumptions, not estimates of the chance that the completed trial detected a true effect.
Smaller effects require more information to detect reliably, so the planning figures increase as the assumed effect moves from 100% to 75% to 50% of the observed effect. For time-to-event outcomes, information is tied to the number of events rather than only to the number enrolled. For the response outcome, the entries are participants per arm. This is not observed power: it does not summarize the probability that the completed study's result is true or that it will be reproduced.
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 = 0.720, so ln(HR) = -0.3285.
- d = 4 × (1.96 + 0.842)2 / [ln(0.720)]2 = 290.9, rounded up to 291 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 <- 0.72 # 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(844649)
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 = 291 (80% power), 390 (90% power)
75% of observed effect: events = 518 (80% power), 693 (90% power)
50% of observed effect: events = 1,164 (80% power), 1,558 (90% power)
Simulated power with 291 events: 0.788 (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 445 participants in total, with the boundaries below.
| Analysis | Calendar time (months) | Events | Efficacy boundary (z) | Nominal one-sided p | Cumulative alpha spent |
|---|---|---|---|---|---|
| Look 1 | 16.0 | 131 | 3.710 | 0.0001 | 0.0001 |
| Look 2 | 25.2 | 262 | 2.511 | 0.0060 | 0.0060 |
| Look 3 | 60.0 | 393 | 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% | 290 | 328 | 60.0 |
| Two looks, O'Brien-Fleming | 80% | 291 | 329 | 60.0 |
| Three looks, O'Brien-Fleming | 80% | 294 | 332 | 60.0 |
| Three looks, Pocock | 80% | 339 | 384 | 60.0 |
| Fixed design, one analysis | 90% | 388 | 439 | 60.0 |
| Two looks, O'Brien-Fleming | 90% | 390 | 441 | 60.0 |
| Three looks, O'Brien-Fleming | 90% | 393 | 445 | 60.0 |
| Three looks, Pocock | 90% | 448 | 507 | 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 | 0.720 | 393 | 445 |
| 75% of the observed effect | 0.782 | 700 | 785 |
| 50% of the observed effect | 0.849 | 1,575 | 1,757 |
For context, this trial enrolled 861 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 <- 6.7 # control-arm median, months (converted from the posted unit)
hr <- 0.72 # 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: 296 p (1-sided) 0.0001
Events: 132 ~HR at bound 0.5229
Month: 16 P(Cross) if HR=1 0.0001
P(Cross) if HR=0.72 0.0338
IA 2: 67% Z 2.5114
N: 446 p (1-sided) 0.0060
Events: 263 ~HR at bound 0.7332
Month: 25 P(Cross) if HR=1 0.0060
P(Cross) if HR=0.72 0.5603
Final Z 1.9930
N: 446 p (1-sided) 0.0231
Events: 394 ~HR at bound 0.8179
Month: 60 P(Cross) if HR=1 0.0250
P(Cross) if HR=0.72 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 |
|---|---|---|---|
| Stratified Log-rank Test | Hazard Ratio (HR) 0.72 | 0.617 to 0.835 | < 0.001 |
The sponsor-reported primary comparison is a hazard ratio of 0.72 for albumin-bound paclitaxel plus gemcitabine compared with gemcitabine, with a 95% confidence interval of 0.617 to 0.835 and p < 0.001. The reported method is the stratified log-rank test. For the secondary time-to-event analysis, the reported hazard ratio is 0.69, with a 95% confidence interval of 0.581 to 0.821 and p < 0.001. The response analysis reports a response rate ratio of 3.19, with a 95% confidence interval of 2.178 to 4.662 and p < 0.001.
The registry marks no discrepancy between the posted results and the sponsor's analyses. The sponsor's own analysis is therefore the reference for interpreting the reported hazard ratios. A summary-level re-calculation should not be treated as a replacement for the sponsor's stratified time-to-event analysis. General statistical context: medians and their confidence intervals alone do not contain the event-time information needed to reproduce a log-rank test or hazard-ratio analysis. Individual participant data and further analytic details are not reported in the registry record.
The registry does not report enough detail to independently verify the stratification factors or all model choices. The sponsor's reported values and methods should be distinguished from the planning illustrations, which are based on stated fractions of the observed effect and are not the trial's original design calculations.
16. Multiplicity, Missing Data and Analysis Populations
The registry identifies overall survival as the primary outcome and lists progression-free survival and confirmed objective response as secondary outcomes. It reports analyses for these endpoints, but it does not report whether the statistical testing plan adjusted for multiplicity, whether a hierarchy of hypotheses was prespecified, or whether secondary outcomes were intended as confirmatory or exploratory. The number of outcome measures in the record is 7, while 2 secondary outcomes are posted. Without the full analysis plan, the status and handling of other outcomes are not clear.
Interim analyses and stopping rules are not reported in the registry record. The original sample-size justification and the assumptions used for the trial's design are also not reported. The planning illustrations available for interpretation are based on the observed effect and stated assumptions; they do not establish what the investigators used when designing the trial.
The primary analysis population is the intent-to-treat population, defined as all randomized participants. This preserves the randomized group comparison as described in the record. For overall survival, participants who did not die were censored at their last known time alive. The registry does not report detailed missing-data procedures, sensitivity analyses, or the extent of missing outcome information. It does not provide the analysis population and missing-data handling details for every secondary endpoint.
General statistical context: censoring and missingness are not identical. Censoring is part of the time-to-event outcome definition when event time is not observed beyond the last known follow-up; missing data can arise in other ways, including unavailable measurements. The validity of time-to-event methods depends on assumptions about the relationship between censoring and the event process. The registry's summary does not provide enough detail to assess those assumptions or their sensitivity.
The study is described as randomized and unmasked, but the registry does not report allocation-concealment procedures, stratification factors, a full protocol, or the complete statistical analysis plan. These omissions limit assessment of the prespecified nature of analyses and the possible influence of design or analysis choices. They do not alter the reported values, but they constrain how comprehensively the posted results can be audited.
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 |
|---|---|---|---|
| Albumin-bound Paclitaxel (ABI-007)/Gemcitabine | 212 | 421 | 50.4% |
| Gemcitabine | 172 | 402 | 42.8% |
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 |
|---|---|
| Albumin-bound Paclitaxel (ABI-007)/Gemcitabine | 412 of 421 |
| Gemcitabine | 392 of 402 |
Most frequent serious adverse event terms
| Event term | Organ system | Albumin-bound Paclitaxel (ABI-007)/Gemcitabine | Gemcitabine |
|---|---|---|---|
| Pyrexia | General disorders | 27 of 421 | 9 of 402 |
| Pulmonary embolism | Respiratory, thoracic and mediastinal disorders | 13 of 421 | 20 of 402 |
| Dehyration | Metabolism and nutrition disorders | 20 of 421 | 12 of 402 |
| Vomiting | Gastrointestinal disorders | 18 of 421 | 12 of 402 |
| Pneumonia | Infections and infestations | 17 of 421 | 11 of 402 |
| Abdominal Pain | Gastrointestinal disorders | 11 of 421 | 10 of 402 |
| Deep vein thrombosis | Vascular disorders | 9 of 421 | 12 of 402 |
| Nausea | Gastrointestinal disorders | 11 of 421 | 8 of 402 |
| Cholangitis | Hepatobiliary disorders | 10 of 421 | 5 of 402 |
| Cellulitis | Infections and infestations | 8 of 421 | 5 of 402 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Albumin-bound Paclitaxel (ABI-007)/Gemcitabine | Gemcitabine |
|---|---|---|---|
| Fatigue | General disorders | 247 of 421 | 183 of 402 |
| Nausea | Gastrointestinal disorders | 223 of 421 | 189 of 402 |
| Oedema peripheral | General disorders | 194 of 421 | 123 of 402 |
| Anaemia | Blood and lymphatic system disorders | 175 of 421 | 131 of 402 |
| Neutropenia | Blood and lymphatic system disorders | 172 of 421 | 122 of 402 |
| Diarrhoea | Gastrointestinal disorders | 182 of 421 | 94 of 402 |
| Pyrexia | General disorders | 160 of 421 | 111 of 402 |
| Decreased appetite | Metabolism and nutrition disorders | 149 of 421 | 104 of 402 |
| Vomiting | Gastrointestinal disorders | 145 of 421 | 107 of 402 |
| Thrombocytopenia | Blood and lymphatic system disorders | 127 of 421 | 115 of 402 |
Serious events with the highest arm-level rate: pyrexia (6.4%), pulmonary embolism (5.0%), dehyration (4.8%), vomiting (4.3%), pneumonia (4.0%).
The serious-adverse-event summaries list 421 participants at risk in the combination group, of whom 212 were reported with a serious adverse event, and 402 at risk in the gemcitabine group, of whom 172 were reported with a serious adverse event. The summaries also list 412 and 392 participants, respectively, with other adverse events among those at risk. These are counts as recorded, not a comparison adjusted for follow-up, exposure, or participant characteristics.
The registry lists serious adverse-event terms and percentages including Pyrexia at 6.4%, Pulmonary embolism at 5.0%, Dehyration at 4.8%, Vomiting at 4.3%, Pneumonia at 4.0%, and Deep vein thrombosis at 3.0%. The record does not specify an arm-specific denominator for these listed percentages, so they should not be interpreted as group-specific rates. The registry's spelling of Dehyration is retained.
Deaths in the adverse-event summary are not reported in the registry record. General statistical context: adverse-event counts depend on how events were defined, collected, and attributed, and raw counts do not by themselves establish comparative risk. The posted figures do not provide enough detail to make a complete safety comparison or to account for differences in exposure and observation.
18. What the Result Does, and Does Not, Mean
The posted results describe group-level outcomes in a randomized Phase III study of participants with metastatic adenocarcinoma of the pancreas. The primary endpoint was overall survival, measured from randomization to death from any cause. The reported medians, confidence intervals, hazard ratio, and p-value summarize the observed outcomes under the registry's stated analysis. They do not predict the outcome for an individual participant.
General statistical context: a hazard ratio is a relative time-to-event measure under the analysis model; it is not a direct statement about the number of months gained by each participant. A median is a point in an estimated group survival distribution, not a guarantee that an individual will experience that duration. Confidence intervals express uncertainty about estimates under the method's assumptions, not a range of likely individual outcomes.
The secondary endpoints provide additional information about progression and confirmed response, but they differ from overall survival in definition, assessment, and analysis. The registry does not report whether testing across multiple endpoints was adjusted, or whether interim analyses occurred. The reported secondary findings should be considered in that context rather than treated as independent confirmation free of statistical uncertainty.
The record also does not report the original sample-size justification, detailed missing-data procedures, stratification factors, or a complete analysis plan. Such information would help readers understand the design assumptions and assess analytic choices. Its absence does not change what the registry reports, but it limits independent evaluation of those choices.
These results should be understood as evidence about the randomized groups during the follow-up and data cutoffs recorded, not as a universal statement about all patients or settings. The statistics do not establish that every participant had the same response, survival time, or adverse events. They also do not, by themselves, support individualized treatment decisions.
19. Why This Trial Matters Statistically
This trial illustrates why time-to-event results are often presented with both a median and a hazard ratio. The median gives an interpretable point on the estimated survival distribution, while the hazard ratio summarizes a relative comparison across follow-up. They answer related but nonidentical questions. Reading them together, with their confidence intervals and the endpoint definition, gives a more complete statistical description than relying on a single number.
The study also shows the importance of distinguishing the primary outcome from secondary outcomes. Overall survival measures death from any cause. Progression-free survival includes progression or death, and objective response is a confirmed radiological outcome. Consistency in the direction of results across these endpoints can provide context, but differing definitions and multiplicity mean the endpoints cannot be treated as interchangeable tests of one claim.
The record demonstrates the role of censoring in survival analysis: participants who had not died were censored at the last time they were known to be alive. This allows available follow-up to contribute information without treating censoring as an event. At the same time, interpretation depends on assumptions and details that are not fully reported in the registry, including the stratification factors and detailed handling of missing information.
Finally, the planning illustrations emphasize that sample-size quantities depend on the effect assumed and on whether the endpoint is time-to-event or binary. They are not observed power and do not establish the trial's original design rationale. Separating these planning calculations from the reported trial results is essential for reading the statistics accurately.
20. Limitations
- The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
- Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.
The registry record leaves important design and analysis details unreported. It does not give the original sample-size justification, the trial's design assumptions, interim-analysis procedures, the full statistical analysis plan, or the factors used to stratify the log-rank tests. These omissions limit assessment of how analyses were prespecified and how fully the reported results can be independently reproduced.
The record marks the study as unmasked. It does not report further information about outcome-assessor masking or safeguards around radiological assessment, although progression-free survival and response are described as assessed by independent radiological review. The registry also does not explain the different data cutoffs used for survival and response outcomes.
For overall survival, the registry states that non-dying participants were censored at the last known time alive, but it does not report detailed follow-up completeness or sensitivity analyses. Missing-data procedures for the secondary outcomes are not reported. The posted adverse-event summary does not identify arm-specific denominators for the listed serious-event terms, and deaths in that summary are not reported.
The outcome summaries provide group-level statistics rather than individual participant data. Consequently, the time-to-event analyses cannot be independently reconstructed from the registry summary alone. The registry does not report whether multiplicity adjustments were made for secondary endpoints, or how all listed outcome measures were handled. These limitations affect the depth of statistical audit possible from the record; they do not justify adding assumptions about analyses or outcomes that are not documented.
21. Related Tutorials
22. Related Statistical Calculators
23. Sources
- ClinicalTrials.gov: Phase III Study of ABI-007(Albumin-bound Paclitaxel) Plus Gemcitabine Versus Gemcitabine in Metastatic Adenocarcinoma of the Pancreas — NCT00844649.
- Registry record last updated 2019-11-25; status last verified 2019-11.
- Results first posted 2013-12-11.
- 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
The registry describes a completed, randomized, parallel-group, unmasked Phase III study sponsored by Celgene, with 861 participants enrolled. It compared albumin-bound paclitaxel (ABI-007) plus gemcitabine with gemcitabine alone in metastatic adenocarcinoma of the pancreas.
Overall survival was the primary endpoint, defined as time from randomization to death from any cause and summarized with Kaplan-Meier methods in the intent-to-treat population. The sponsor reported a stratified log-rank hazard ratio of 0.72, with a 95% confidence interval of 0.617 to 0.835 and p < 0.001. Secondary outcomes were progression-free survival by independent radiological review and confirmed objective response by independent radiological review.
The registry does not report the original sample-size justification, interim-analysis procedures, a complete statistical analysis plan, or several details needed to assess missing data and multiplicity. The posted statistics therefore describe the reported analyses and their stated timeframes, while leaving some design and analysis decisions undocumented.