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Kidney Neoplasms Phase 3 Time-to-Event Analysis NCT00678392

Axitinib (AG 013736) As Second Line Therapy For Metastatic Renal Cell Cancer: Complete Statistical Analysis

The AXIS trial compared axitinib with sorafenib as second-line therapy for metastatic renal cell cancer. The primary endpoint was progression-free survival, with overall survival and objective response rate among the secondary outcomes.

Trial start: 2008-09-03  ·  Enrollment: 723  ·  Sponsor: Pfizer
Scope of this record

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

1. Trial at a Glance

This page covers the registry results for Axitinib (AG 013736) As Second Line Therapy For Metastatic Renal Cell Cancer (NCT00678392), a randomized phase 3 study. The primary outcome is Progression-Free Survival (PFS).

723
Enrollment
Phase 3
2
Arms
In the primary outcome
0.67
Hazard ratio
Axitinib 5 mg vs Sorafenib 400 mg
0.54–0.81
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT00678392
PhasePhase 3
ConditionKidney Neoplasms
AllocationRandomized
Design modelParallel
MaskingNone (open label)
Enrollment723
Arms in the primary outcome2
Lead sponsorPfizer
Results postedYes

2. Clinical Question

Population

Participants with metastatic renal cell cancer after failure of one first-line regimen. The primary endpoint population was the full analysis set: randomized participants, classified according to their initial assignment regardless of whether they received study drug or a different drug.

Intervention

Axitinib (AG-013736), listed in the treatment arm as axitinib 5 mg.

Comparator

Sorafenib, listed in the comparison arm as sorafenib 400 mg.

Primary question

Did the time from starting study treatment to objective tumor progression or death differ between the axitinib and sorafenib groups? The trial’s stated aim was to demonstrate that axitinib was superior to sorafenib in delaying tumor progression after failure of one first-line regimen. The endpoint also counted death from any cause, so it captured more than tumor progression alone.

This was a randomized, phase 3 comparison with parallel treatment groups and no masking. The registry lists 723 participants enrolled. The primary endpoint was progression-free survival, measured in months and reported as a median with a 95% confidence interval. The sponsor’s comparison used a hazard ratio estimated with a log-rank method.

The clinical question is therefore about the relative timing of progression or death under the two assigned strategies in this study population. It is not a question about every possible treatment outcome: overall survival, response rate, adverse events, and laboratory abnormalities were listed separately as secondary outcomes. Those outcomes can add context, but they address different questions and do not replace the primary endpoint.

3. Trial Design

The registry identifies AXIS as a phase 3 randomized parallel-group study of axitinib (AG-013736) and sorafenib for metastatic renal cell cancer. It lists Pfizer as the sponsor and records the study as completed. The study start date was 2008-09-03, and the primary completion date was 2010-08-31. The registry lists 723 participants enrolled.

The two treatment groups were axitinib 5 mg and sorafenib 400 mg. The posted primary endpoint results include 361 participants in the axitinib group and 362 in the sorafenib group. The registry describes the study as unmasked; masking was none. Arm descriptions beyond the treatment names and doses are not reported in the registry record.

The stated study purpose was to test whether axitinib was superior to sorafenib in delaying tumor progression among patients with metastatic renal cell cancer after failure of one first-line regimen. The primary endpoint was progression-free survival. Overall survival, objective response rate, duration of response, and safety and laboratory outcomes were among the listed secondary outcomes.

For the primary endpoint, the full analysis set included all randomized participants. The record says participants were analyzed according to their initial randomization, whether or not they received study drug or received a different drug from the one to which they were randomized. This preserves assignment as the basis for the primary group comparison, rather than reclassifying participants according to treatment received.

Further details about the original sample-size justification, allocation procedure, stratification, treatment schedules, follow-up rules beyond the endpoint timeframe, and any interim analyses are not reported in the registry record. The posted record describes a follow-up period of up to 3 years for the primary endpoint, but does not give more detail about the conduct of follow-up.

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

StageAxitinib 5 mgSorafenib 400 mg
STARTED361362
Treated359355
COMPLETED00
NOT COMPLETED361362

Reasons for not completing this period:

ReasonAxitinib 5 mgSorafenib 400 mg
Adverse Event06
Death280269
Lost to Follow-up1513
Objective Progression or Relapse38
Sponsor's Decision12
Withdrawal by Subject44
Randomized But Not Treated27
Other5653

Analysis population for the primary outcome, as defined in the registry: FAS included all participants who were randomized, with study drug assignment designated according to initial randomization, regardless of whether participants received study drug or received a different drug from that to which they were randomized.

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: Full analysis set (FAS) included all participants who were randomized, with study drug assignment designated according to initial randomization, regardless of whether participants received study drug or receive a different drug from that to which they were randomized.

CharacteristicUnitAxitinib 5 mgSorafenib 400 mgTotal
Participants analysed361362723
Age, Customized: Less than (<) 65 yearsParticipants238238476
Age, Customized: Greater than or equal to (>=) 65 yearsParticipants123124247
Sex: Female, Male: FemaleParticipants96104200
Sex: Female, Male: MaleParticipants265258523

6. Primary Endpoint

The registry lists the primary outcome as Progression-Free Survival (PFS), measured over From initiation of treatment up to follow-up period (up to 3 years).

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

Progression-free survival (PFS) was defined as the time in months from the start of study treatment to the first documented objective tumor progression or death from any cause, whichever occurred first. Counting death as an event means that PFS includes a clinically important outcome even when progression has not been documented before death. The endpoint therefore reflects the time until either of two events, rather than the time to tumor progression alone.

Tumor progression was assessed using RECIST version 1.0. The registry definition includes an increase of at least 20% in the sum of the longest dimensions of target lesions, using the smallest recorded sum since treatment began as the reference. It also includes unequivocal progression in non-target lesions or the appearance of one or more new lesions. Pleural effusion or ascites could count as progression when confirmed by cytological investigation and not previously documented; new bone lesions could count when confirmed by computed tomography, magnetic resonance imaging, or X-ray.

A time-to-event endpoint is useful when the question concerns how long participants remain alive without the event of interest, while allowing follow-up times to differ. The median describes the point by which half of the relevant event-time distribution has been reached; it does not describe every participant’s experience. A hazard ratio compares event rates over follow-up under the model and analysis used, rather than comparing the medians directly.

The registry reports median PFS with a 95% confidence interval and gives the timeframe as treatment initiation through follow-up of up to 3 years. The full analysis set included all randomized participants, assigned to their original group regardless of treatment received.

7. Results Posted in the Registry

Hazard ratio: Axitinib 5 mg vs Sorafenib 400 mg

0.67

95% CI: 0.54 to 0.81

As reported in the registry

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Axitinib 5 mg vs Sorafenib 40…0.520.600.690.790.911.05hazard ratio (as reported) vs control (95% CI)

8. Secondary Efficacy Endpoints

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

Secondary outcomeTypeEffect measureEstimate (95% CI)Planning size, 80% power
Overall Survival (OS)Time-to-Event AnalysisHazard ratio0.97 (0.80 to 1.17)31,660 events
Objective Response Rate (ORR)Binary EndpointRisk difference-10.0 pts (-15.1 to -4.9)193 per arm

Overall Survival (OS)

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Axitinib 5 mg vs Sorafenib 40…0.780.850.931.011.111.21hazard ratio (as reported) vs control (95% CI)

Objective Response Rate (ORR)

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Sorafenib 400 mg-16-13-9.28-5.78-2.291.21risk difference (percentage points) vs control (95% CI)

The secondary outcomes broaden the picture beyond progression-free survival. They include overall survival, objective response rate, duration of response, treatment-emergent adverse events and serious adverse events, adverse events by severity, treatment-related adverse events, and clinically significant hematology and biochemistry abnormalities. Together, these outcomes concern survival, tumor response, and safety; they are not interchangeable measures of the primary endpoint.

The posted overall survival comparison has a different pattern from the primary PFS comparison: its confidence interval includes the null hazard ratio of 1, and its reported p-value is 0.374. This means the registry does not report a statistically significant overall-survival comparison by the stated analysis. The result does not establish that the groups are identical; the interval also expresses uncertainty about the relative hazard.

The objective response outcome has a reported group percentage of 19.4% for axitinib and 9.4% for sorafenib. The sponsor’s reported risk ratio is 2.056, with a 95% confidence interval from 1.408 to 3.003 and p < 0.001. Response is a measure of tumor shrinkage meeting the study’s response criteria, not the time until progression or death. It therefore complements but does not duplicate PFS.

Secondary outcomes usually carry less inferential weight than a prespecified primary outcome, particularly when many outcomes are examined. Testing multiple outcomes can increase the chance of apparently notable results arising by chance. The registry lists multiple secondary outcomes, but a multiplicity adjustment or hierarchy governing their interpretation is not reported in the registry record. Secondary results can inform context and generate questions, but should be interpreted with that limitation in mind.

The safety and laboratory outcomes address additional questions and have their own denominators and definitions. Their presence is relevant to a balanced reading of the study, but the registry record does not provide a single summary measure that combines these outcomes with the efficacy endpoints. The overall secondary pattern therefore adds distinct evidence rather than a single unified confirmation of the primary result.

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

9. Statistical Interpretation

Clinical Biostats interpretation

The posted median PFS was 6.7 months for axitinib and 4.7 months for sorafenib. The corresponding 95% confidence intervals were 6.3 to 8.6 months and 4.6 to 5.6 months. These summaries describe the observed event-time distributions in the two randomized groups; they do not mean that every participant had a PFS equal to the group median.

The sponsor-reported hazard ratio for axitinib versus sorafenib was 0.665, with a 95% confidence interval from 0.544 to 0.812 and p < 0.001 using a log-rank method. In general, a hazard ratio below 1 indicates a lower estimated event hazard in the first named group relative to the second under the analysis. The confidence interval lies below 1, and the reported p-value is small under the usual null comparison. These statistical features are consistent with the registry’s stated superiority question for PFS. They do not establish the size or importance of an effect for an individual participant, and they do not mean that progression or death was prevented for every participant.

The hazard ratio and median values answer related but different questions. The medians identify the midpoint of each group’s event-time distribution. The hazard ratio summarizes a relative comparison across the observed follow-up under the log-rank analysis. It should not be interpreted as a ratio of the two medians or as a direct measure of months gained. No such derived comparison is needed to describe the posted results.

The endpoint combines tumor progression and death. Consequently, its result cannot by itself identify how much of the comparison reflects progression rather than death. The registry provides overall survival as a separate secondary outcome, which addresses death directly, but that outcome should not be conflated with PFS.

There are limits to what can be concluded from the registry record. It does not report details of the analysis plan, missing-data handling, or interim analyses. The primary analysis population is defined, but the record does not give participant-level event times or enough detail to evaluate all analytic assumptions. The stated follow-up was up to 3 years; the posted summaries do not provide a fuller account of follow-up patterns.

The PFS result is one part of a broader study record. Secondary outcomes include overall survival, response, duration of response, adverse events, and laboratory abnormalities. These outcomes differ in definition and statistical role. They should be interpreted alongside the primary endpoint rather than treated as interchangeable evidence about the same outcome. The posted results describe group-level observations and statistical uncertainty, not an individualized prediction or a treatment recommendation.

10. Statistical Methods Explained

The primary endpoint is a time-to-event outcome. For each participant, the event was the first objective tumor progression or death from any cause after treatment began. Time-to-event methods are designed for outcomes where the timing of an event matters and where participants may have different lengths of observation. A participant who has not had a recorded event by the end of their available follow-up may contribute information up to that point, although the registry record does not describe the detailed handling of censoring.

What does a median time-to-event result mean?

The median PFS is the time at which the estimated event-time distribution reaches its midpoint. It is a group summary, not a promise about the experience of any particular participant. The record gives median values for each treatment group and confidence intervals around those estimates. The median alone does not describe the full shape of the event-time distribution or establish how the groups compare across every point in follow-up.

What does the hazard ratio describe?

The sponsor reported a hazard ratio of 0.665 for axitinib versus sorafenib, using a log-rank method. In general, a hazard ratio compares the event hazard between groups over the follow-up represented by the analysis. A value below 1 points toward a lower estimated hazard in the first named group, under the stated comparison. It is not an absolute risk difference, a ratio of median times, or a statement that the same relative comparison applies to every participant or every time point.

The log-rank method is a standard approach for comparing time-to-event experience between groups. It uses event timing and follow-up information, rather than reducing all data to a single endpoint status at one fixed time. The registry reports the method and the hazard ratio, but does not provide enough information to reconstruct the complete analysis or check the assumptions from participant-level data.

How should a confidence interval be read?

A confidence interval expresses uncertainty in an estimated quantity. In general, it describes a range of values compatible with the data and the method used, rather than a range that contains a fixed proportion of individual participant outcomes. The PFS hazard ratio confidence interval is 0.544 to 0.812. The intervals around the group medians are reported separately in months. The distinct intervals correspond to distinct summaries and should not be compared as if they were the same statistic.

The reported p-value, p < 0.001, is a measure of how inconsistent the observed comparison is with the null hypothesis under the analysis assumptions. It is not the probability that the null hypothesis is true, and it does not quantify the probability that the result will be reproduced. The registry labels the analysis as a superiority-or-other analysis and identifies the reported comparison as a log-rank hazard ratio.

Why define an analysis population?

The primary endpoint population was the full analysis set. It included all randomized participants and retained their initial group assignment, regardless of whether they received study drug or a different drug. In general, analyzing participants according to randomized assignment preserves the original comparison created by randomization. The record does not describe other analysis populations or provide details about exclusions, protocol deviations, or the extent of treatment switching.

Other outcomes use other statistical forms. Overall survival is also a time-to-event outcome, and its posted comparison is expressed as a hazard ratio. Objective response rate is a binary outcome: participants either met the response definition or did not, as defined by the study. The posted sponsor analysis for response uses a risk ratio and a Cochran-Mantel-Haenszel method. A risk ratio compares the probability of the outcome between groups; it is not the same quantity as a hazard ratio. The record’s secondary outcomes also include duration of response, adverse-event measures, and laboratory abnormalities.

For binary outcomes, a confidence interval around a group percentage or comparative effect describes uncertainty in the estimate. General methods for binary outcomes depend on the chosen effect measure and analysis. For time-to-event outcomes, the timing and censoring structure matter. Because these outcome types differ, estimates and p-values across them should not be ranked as if they were all measuring the same thing.

Statistical methods can support a comparison without answering every clinical or design question. The registry record identifies some methods and outcome definitions, but the full statistical analysis plan, missing-data procedures, assumptions about the hazard ratio, and any multiplicity strategy are not reported in the registry record. Those missing details limit independent assessment of the complete analytic process.

11. Confidence Intervals and Precision

Precision concerns how much uncertainty surrounds an estimate. For the primary PFS comparison, the sponsor-reported hazard ratio was 0.665, with a 95% confidence interval from 0.544 to 0.812. The interval is entirely below 1, the value that represents equal hazards in the usual relative comparison. This is consistent with the reported p < 0.001, but the interval remains important: it conveys a range of relative hazard values compatible with the analysis, not a single known effect.

The median PFS estimate was 6.7 months for axitinib, with a 95% confidence interval of 6.3 to 8.6 months. For sorafenib, the median was 4.7 months, with a 95% confidence interval of 4.6 to 5.6 months. These intervals describe uncertainty around each group’s median estimate. They are not confidence intervals for the difference between medians, and their overlap or separation should not be used as a substitute for the reported comparative test.

In general, a confidence interval is affected by both the observed data and the statistical method. It does not capture every source of uncertainty, such as bias from missing information or limitations in outcome assessment. The registry does not report the detailed missing-data procedures or full assumptions underlying the time-to-event analysis. Confidence intervals should therefore be read as statistical precision conditional on the analysis, not as a complete account of uncertainty about the study.

The estimate is more informative than a p-value alone because it gives both the direction and a range of plausible values under the analysis. Even so, statistical precision is not the same as clinical importance. The registry record does not specify a threshold for a clinically important PFS difference, so the results should not be judged against an unreported threshold.

12. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

Effect to detect (log scale)Hazard ratioEvents, 80% powerEvents, 90% power
100% of the observed effect0.67189253
75% of the observed effect0.74336449
50% of the observed effect0.827551,011
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect2005001,0002,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: events required (total))
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, Schoenfeld approximation for the log-rank test or Cox model. The answer is the total number of events, not participants; the number of participants depends on how quickly events accrue. Calculated for the comparison: Axitinib 5 mg vs Sorafenib 400 mg.

The sample-size material is a planning illustration based on the observed effect, not the original design calculation for AXIS. The original trial’s own design assumptions and sample-size justification are not reported in the registry record. The assumptions for the illustration are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. For time-to-event outcomes, the entries are total events required, calculated using the Schoenfeld approach. For other outcomes, entries are participants per arm.

The 80% power column gives the planning number associated with an 80% chance of detecting the stated effect under those assumptions, if that effect were the true effect and the planned analysis were carried out. The 90% power column gives the corresponding planning number for a 90% chance. These are conventional planning probabilities, not guarantees about what a future study will find. For the PFS illustration, the event totals are 189 for planning at 80% power and 253 at 90% power when using 100% of the observed effect. Planning for 75% of the observed effect uses 336 total events for 80% power and 449 for 90% power. Planning for 50% uses 755 total events for 80% power and 1,011 for 90% power.

The effect fractions refer to smaller target effects relative to the observed effect. Smaller effects are harder to distinguish from random variation, so they require more participants or events to attain the same planned power, all else equal. In the time-to-event setting, the table expresses the requirement as events rather than participants, because the number of observed events drives information for the comparison. In the non-time-to-event setting, the figures are participants per arm, not total participants.

These planning calculations are not observed power. They do not describe the probability that the completed trial was successful after seeing its results, and they are not evidence that the trial was designed using these assumptions.

13. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z1−α/2 = 1.960) and the desired power (z1−β = 0.842 for 80% and 1.282 for 90%).

Formula

d = 4 (z1−α/2 + z1−β)2 / [ln(HR)]2

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

Worked calculation for this trial

  1. Hazard ratio HR = 0.665, so ln(HR) = -0.4080.
  2. d = 4 × (1.96 + 0.842)2 / [ln(0.665)]2 = 188.6, rounded up to 189 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 <- 0.665                              # 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(678392)
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 = 189 (80% power), 253 (90% power)
 75% of observed effect: events = 336 (80% power), 449 (90% power)
 50% of observed effect: events = 755 (80% power), 1,011 (90% power)
Simulated power with 189 events: 0.814 (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 278 participants in total, with the boundaries below.

AnalysisCalendar time (months)EventsEfficacy boundary (z)Nominal one-sided pCumulative alpha spent
Look 114.5853.7100.00010.0001
Look 223.31702.5110.00600.0060
Look 360.02551.9930.02310.0250
01234z = 3.7114 mo85 eventsz = 2.5123 mo170 eventsz = 1.9960 mo255 eventsUpper efficacy boundary (z)

Fixed design versus group-sequential alternatives

DesignPowerEvents at final analysisParticipantsStudy length (months)
Fixed design, one analysis80%18820560.0
Two looks, O'Brien-Fleming80%18920660.0
Three looks, O'Brien-Fleming80%19020860.0
Three looks, Pocock80%22024060.0
Fixed design, one analysis90%25227560.0
Two looks, O'Brien-Fleming90%25327660.0
Three looks, O'Brien-Fleming90%25527860.0
Three looks, Pocock90%29131760.0

Group-sequential designs cost a small increase in maximum sample size and events compared with the fixed design, in exchange for the chance to stop early for overwhelming efficacy. O'Brien-Fleming spending keeps early boundaries very conservative and the final boundary close to the fixed-design value, whereas Pocock spending spends more alpha early.

Sensitivity to a smaller true effect

Planning for exactly the observed effect is optimistic, because observed effects in published trials tend to be somewhat larger than the true effect. The table repeats the main design (three looks, O'Brien-Fleming spending, 90% power) for smaller true hazard ratios.

True effect assumedHazard ratioEvents at final analysisParticipants
100% of the observed effect0.665255278
75% of the observed effect0.736454492
50% of the observed effect0.8151,0211,101

For context, this trial enrolled 723 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 <- 4.7          # control-arm median, months (converted from the posted unit)
hr          <- 0.665          # 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: 168         p (1-sided)   0.0001
  Events: 85        ~HR at bound   0.4470
   Month: 14    P(Cross) if HR=1   0.0001
             P(Cross) if HR=0.66   0.0338
   IA 2: 67%                   Z   2.5114
      N: 270         p (1-sided)   0.0060
 Events: 170        ~HR at bound   0.6802
   Month: 23    P(Cross) if HR=1   0.0060
             P(Cross) if HR=0.66   0.5603
       Final                   Z   1.9930
      N: 278         p (1-sided)   0.0231
 Events: 255        ~HR at bound   0.7791
   Month: 60    P(Cross) if HR=1   0.0250
             P(Cross) if HR=0.66   0.9000



Cross-check, upper boundaries: gsDesign 3.71, 2.511, 1.993 | rpact 3.71, 2.511, 1.993

15. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
Log RankHazard Ratio (HR) 0.6650.544 to 0.812< 0.001

The primary PFS comparison is reported as the sponsor’s analysis: a log-rank hazard ratio of 0.665, with a 95% confidence interval from 0.544 to 0.812 and p < 0.001. The registry’s primary time-to-event presentation uses the sponsor-reported hazard ratio; it does not give a separate recalculated hazard ratio. The group medians and their confidence intervals provide additional descriptive summaries, but are not recalculations of that comparative hazard ratio.

For overall survival, the sponsor-reported log-rank hazard ratio was 0.969, with a 95% confidence interval from 0.800 to 1.174 and p = 0.374. For objective response rate, the sponsor reported a Cochran-Mantel-Haenszel risk ratio of 2.056, with a 95% confidence interval from 1.408 to 3.003 and p < 0.001. These methods and effect measures differ by endpoint, so a recalculation from group summaries, when available, is not automatically identical to the sponsor’s analysis.

The record does not flag a discrepancy between posted and sponsor-reported results. Where the sponsor’s analysis is the reported analysis, it is the principal inferential result to use. Any simple unadjusted recalculation based on posted summary statistics is a supplementary check, not a replacement for the sponsor’s stated analysis. Such a recalculation may not reproduce adjustments or analytic details that are not represented in the summary data.

16. Multiplicity, Missing Data and Analysis Populations

The primary analysis population is described as the full analysis set. It includes all randomized participants and assigns them according to their initial randomization, irrespective of whether they received study drug or a different drug. This is useful information for interpreting the primary comparison because it indicates that treatment assignment, rather than treatment received, defined the groups.

The registry record does not report the details of missing-data handling for the primary or secondary outcomes. It does not explain how participants with incomplete follow-up were treated, how incomplete outcome assessments were addressed, or whether any imputation methods were used. For a time-to-event endpoint, follow-up that ends before an event is often handled through censoring, but the specific rules and checks used in this trial are not reported in the registry record. Those details matter because incomplete follow-up can affect the information available for estimating event times.

The record lists multiple secondary outcomes, including overall survival, response, duration of response, and several safety and laboratory measures. A multiplicity procedure, testing hierarchy, or other strategy for controlling the interpretation of multiple comparisons is not reported in the registry record. Without such information, secondary p-values should not automatically be treated as if each were the sole prespecified test. This is especially relevant when many outcomes are examined, since repeated testing can make isolated small p-values more likely by chance.

The record does not report whether interim analyses were planned or conducted. It also does not provide the complete statistical analysis plan, details of stratification or covariate adjustment, or a comprehensive account of protocol deviations. These omissions do not establish that such procedures were absent; they mean that their use cannot be assessed from the registry record.

The endpoint definitions and the full analysis set definition provide important interpretive information, but they do not answer every question about analysis conduct. In particular, there is not enough information to independently evaluate the handling of missing observations, the multiplicity strategy, or all assumptions behind the reported time-to-event comparisons.

17. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Axitinib 5 mg14635940.7%
Sorafenib 400 mg12735535.8%
Participants with at least one serious adverse event
Serious adverse events by armAxitinib 5 mg40.7%Sorafenib 400 mg35.8%% of participants with at least one serious adverse event

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 5% reporting threshold.

ArmParticipants affected of at risk
Axitinib 5 mg337 of 359
Sorafenib 400 mg346 of 355

Most frequent serious adverse event terms

Event termOrgan systemAxitinib 5 mgSorafenib 400 mg
Disease progressionGeneral disorders32 of 35918 of 355
DiarrhoeaGastrointestinal disorders8 of 3595 of 355
PyrexiaGeneral disorders7 of 3595 of 355
DehydrationMetabolism and nutrition disorders10 of 3591 of 355
Myocardial infarctionCardiac disorders6 of 3594 of 355
DyspnoeaRespiratory, thoracic and mediastinal disorders7 of 3593 of 355
DeathGeneral disorders3 of 3596 of 355
PneumoniaInfections and infestations5 of 3594 of 355
AnaemiaBlood and lymphatic system disorders0 of 3598 of 355
General physical health deteriorationGeneral disorders3 of 3595 of 355

Most frequent non-serious adverse event terms

Event termOrgan systemAxitinib 5 mgSorafenib 400 mg
DiarrhoeaGastrointestinal disorders208 of 359195 of 355
Palmar-plantar erythrodysaesthesia syndromeSkin and subcutaneous tissue disorders100 of 359183 of 355
FatigueGeneral disorders151 of 359122 of 355
HypertensionVascular disorders156 of 359107 of 355
Decreased appetiteMetabolism and nutrition disorders140 of 359112 of 355
NauseaGastrointestinal disorders128 of 35984 of 355
Weight decreasedInvestigations111 of 35983 of 355
DysphoniaRespiratory, thoracic and mediastinal disorders116 of 35949 of 355
VomitingGastrointestinal disorders95 of 35969 of 355
RashSkin and subcutaneous tissue disorders53 of 359109 of 355

Serious events with the highest arm-level rate: disease progression (8.9%), dehydration (2.8%), anaemia (2.3%), diarrhoea (2.2%), pyrexia (1.9%).

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

The registry reports serious adverse events and other adverse events by treatment group. For serious adverse events, 146 participants were affected among 359 at risk in the axitinib group, and 127 were affected among 355 at risk in the sorafenib group. For other adverse events, 337 were affected among 359 at risk in the axitinib group, and 346 among 355 at risk in the sorafenib group. These are counts with the listed at-risk denominators; they should not be read as a causal comparison without considering the study’s definitions and analysis.

The registry also lists serious adverse-event terms, including disease progression at 8.9%, dehydration at 2.8%, anaemia at 2.3%, diarrhoea at 2.2%, pyrexia at 1.9%, and dyspnoea at 1.9%. These entries describe reported terms and do not, on their own, establish that a treatment caused an event or show how the terms were distributed between groups. Death counts are not reported in the registry record.

Safety outcomes require attention to definitions, follow-up, severity, relatedness, and the number of participants assessed. The record lists additional safety and laboratory outcomes, but the figures above should not be treated as a complete account of every safety measure or as individualized risk estimates.

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

The registry’s primary result is a group-level comparison of progression-free survival in randomized participants with metastatic renal cell cancer after failure of one first-line regimen. The reported medians were 6.7 months for axitinib and 4.7 months for sorafenib, and the sponsor-reported hazard ratio was 0.665 with a 95% confidence interval from 0.544 to 0.812. The reported p-value was p < 0.001. Together, these results support a difference between the groups in the time-to-event comparison under the analysis reported in the registry.

That statistical conclusion does not mean that every participant experienced a delay in progression, that all participants benefited to the same degree, or that the result predicts an individual’s outcome. A group median is not an individual forecast. The hazard ratio is a relative time-to-event measure, not a direct count of additional months for each participant and not an absolute probability of avoiding progression.

PFS includes either objective progression or death, whichever occurred first. The result therefore does not isolate tumor progression from death. Overall survival is a separate outcome, and its reported analysis does not show a statistically significant difference by the stated comparison. Response rate is another distinct outcome and should not be substituted for either PFS or overall survival.

The registry record gives a study-specific result, not a universal conclusion for every patient group or clinical setting. It describes participants with metastatic renal cell cancer after failure of one first-line regimen, and the trial compared the listed axitinib and sorafenib regimens. The record does not establish how the result applies beyond that population or to different treatment strategies.

Statistical significance does not by itself establish clinical importance, and the registry record does not state a threshold for a clinically meaningful PFS difference. Nor does the efficacy comparison alone summarize safety. The secondary safety outcomes and their definitions should be considered separately. The findings describe what was observed in this trial and how precisely the reported comparisons were estimated; they are not medical advice or a recommendation for an individual.

19. Why This Trial Matters Statistically

This trial illustrates why a clinical comparison needs a clearly defined primary endpoint. PFS was not simply a tumor measurement at one visit: it combined the timing of objective progression with death from any cause. That definition determines what counts as an event and therefore shapes the meaning of the result. The registry’s RECIST-based progression criteria also show how operational rules translate a clinical concept into an assessable endpoint.

The comparison illustrates the distinction between descriptive group summaries and comparative estimates. Median PFS reports a central time for each group, while the hazard ratio uses time-to-event information to compare groups over follow-up. These quantities are related but answer different statistical questions. Reading both helps avoid treating medians as if they were a complete description of the comparative effect.

It also highlights the value of confidence intervals. The reported hazard ratio is an estimate rather than a known fixed effect, and its confidence interval communicates uncertainty around that estimate under the analysis. A p-value can indicate compatibility with a null comparison, but does not show the range of effect sizes as directly as an interval.

The trial record includes several secondary outcomes that broaden the clinical and statistical picture. Overall survival and response rate do not measure the same event as PFS, while safety outcomes address different potential consequences of treatment. Their interpretation depends on outcome definitions and on how multiple comparisons are handled. The registry does not report a multiplicity strategy, so the secondary analyses require more caution than an isolated primary test.

Finally, the record demonstrates that a useful summary should separate reported analysis from planning illustrations. Sample-size illustrations based on observed effects can help readers understand how study size relates to a target effect, but they are not the original trial design and not observed power. Keeping these distinctions clear supports a more accurate reading of both the statistical evidence and the boundaries of what the registry record establishes.

20. Limitations

The registry record does not provide the complete statistical analysis plan, the original sample-size justification, or the assumptions used to design the trial. Although the record reports a planning illustration based on the observed effect, that illustration is not evidence about the study’s original design. Details about allocation procedures beyond randomization, stratification, and any covariate adjustment are also not reported in the registry record.

Information about missing data and follow-up is limited. The primary endpoint timeframe is described as treatment initiation through follow-up of up to 3 years, but detailed follow-up patterns, censoring rules, and procedures for incomplete assessments are not reported. These details are relevant for evaluating a time-to-event analysis and cannot be reconstructed from the posted summary statistics.

The study was unmasked. That design characteristic is stated in the record, but the registry summary does not explain whether or how lack of masking affected outcome assessment, treatment decisions, or reporting. Progression was assessed using RECIST version 1.0, yet the record does not provide further information about independent review or other safeguards for assessment.

The registry lists many secondary outcomes, but does not report a multiplicity strategy or testing hierarchy. This limits how confidently multiple secondary p-values can be interpreted as confirmatory. The record also does not report whether interim analyses were planned or conducted, and it does not provide enough information to evaluate all statistical assumptions for the hazard-ratio analysis.

Finally, summary results cannot show individual trajectories or the full distribution of event times. They also do not establish causation for individual adverse events. The posted figures are useful for understanding the reported comparisons, but the limitations in analytic detail and the absence of participant-level data constrain independent reassessment.

21. Related Tutorials

22. Related Statistical Calculators

23. Sources

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24. Record Summary

AXIS was a completed, randomized, unmasked, parallel-group phase 3 trial of axitinib (AG-013736) and sorafenib in metastatic renal cell cancer. The stated aim was to compare treatment after failure of one first-line regimen. The registry lists 723 participants enrolled and a follow-up period of up to 3 years for the primary endpoint.

The primary outcome was progression-free survival, defined as time from treatment initiation to objective progression or death from any cause. The posted medians were 6.7 months for axitinib and 4.7 months for sorafenib. The sponsor-reported log-rank hazard ratio was 0.665, with a 95% confidence interval from 0.544 to 0.812 and p < 0.001.

Overall survival, objective response, duration of response, and safety and laboratory outcomes were listed as secondary measures. The registry record does not report the complete statistical analysis plan, missing-data procedures, or multiplicity strategy.

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