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) For the Treatment of Metastatic Renal Cell Cancer (NCT00920816), a randomized phase 3 study. The primary outcome is Progression Free Survival (PFS): First-Line Participants.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT00920816 |
| Phase | Phase 3 |
| Condition | Kidney Neoplasms |
| Allocation | Randomized |
| Design model | Not Stated |
| Masking | None (open label) |
| Enrollment | 492 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Pfizer |
| Results posted | Yes |
2. Clinical Question
Population
Participants with metastatic renal cell cancer were enrolled. The primary endpoint concerns the treatment-naive participants who were randomized; the registry describes this analysis population as the full analysis set, or FAS, and says participants remained classified by initial randomization even if they did not receive the assigned study drug or received a different drug. The primary result is specifically for first-line participants.
Intervention
The intervention was axitinib (AG-013736), a drug intervention. The registry describes a randomized study and identifies the first-line axitinib group in the primary endpoint results.
Comparator
The comparator was sorafenib, also identified as a drug intervention. The primary comparison is between axitinib and sorafenib among first-line participants. The registry lists second-line groups and outcomes separately; those are not the population used for the primary endpoint result.
Primary question
The study was designed to test whether axitinib was superior to sorafenib in delaying tumor progression in metastatic renal cell cancer. The primary outcome was median progression-free survival, measured from randomization until objective tumor progression or death from any cause. The posted comparison is a hazard ratio of 0.767, with a 95% confidence interval from 0.559 to 1.053. The interval includes 1, so the estimate is not precise enough to rule out no difference in the relative event rate at the conventional confidence level. The registry does not report a p-value for this comparison.
3. Trial Design
This was a randomized phase 3 study comparing axitinib with sorafenib in metastatic renal cell cancer. The registry lists an enrollment of 492 and describes the allocation as randomized. Masking is listed as none, so the record describes the study as unmasked. The sponsor was Pfizer. The listed status is completed.
The registry’s study summary states that the study was designed to demonstrate superiority of axitinib over sorafenib in delaying tumor progression. The primary endpoint analyzed first-line participants. Its stated analysis population was the FAS: treatment-naive participants who were randomized, classified according to their initial randomization regardless of whether they took the assigned drug or received a different drug. That description is important because it defines who contributes to the primary comparison and how treatment assignment is handled.
The primary endpoint was assessed from baseline until progression or death, with tumor assessments scheduled at Week 6, Week 12, and thereafter every 8 weeks up to Week 107. The registry also lists second-line participants and secondary outcomes concerning objective response, duration of response, and overall survival. The objective-response results are posted for first-line and second-line participants. Detailed results for duration of response and overall survival are not reported in the registry record.
The registry lists 16 outcome measures and 2 analyses. It does not report the original sample-size justification, the planned allocation ratio, or the study’s complete statistical analysis plan in the information described. The record therefore establishes the randomized, unmasked, phase 3 comparison and the reported analysis population, but does not establish all details of how the original trial was designed statistically.
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: All China participants were excluded from safety analysis due to inability to obtain timely approval to use data in accordance with Human Genetic Resources Administration of China (HGRAC) regulation.
Overall Study
| Stage | Axitinib (First-line Participants) | Sorafenib (First-line Participants) | Axitinib (Second-line Participants) | Sorafenib (Second-line Participants) |
|---|---|---|---|---|
| STARTED | 192 | 96 | 135 | 69 |
| Treated | 189 | 96 | 135 | 69 |
| Participants From China (Excluded From Safety Analysis) | 16 | 8 | 124 | 64 |
| COMPLETED | 0 | 0 | 0 | 0 |
| NOT COMPLETED | 192 | 96 | 135 | 69 |
Reasons for not completing this period:
| Reason | Axitinib (First-line Participants) | Sorafenib (First-line Participants) | Axitinib (Second-line Participants) | Sorafenib (Second-line Participants) |
|---|---|---|---|---|
| Death | 116 | 63 | 8 | 3 |
| Participant refused continued treatment for reason other than adverse events | 11 | 5 | 1 | 0 |
| Global deterioration of health status | 2 | 0 | 0 | 0 |
| Objective progression or relapse | 6 | 2 | 0 | 0 |
| Other | 26 | 15 | 1 | 2 |
| Lost to Follow-up | 11 | 2 | 0 | 0 |
| Adverse Event | 1 | 1 | 1 | 0 |
| Data not disclosed due to lack of HGRAC filings | 16 | 8 | 124 | 64 |
| Randomized but not treated | 3 | 0 | 0 | 0 |
Analysis population for the primary outcome, as defined in the registry: FAS included all treatment-naive 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 treatment-naive 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.
| Characteristic | Unit | Axitinib (First-line Participants) | Sorafenib (First-line Participants) | Axitinib (Second-line Participants) | Sorafenib (Second-line Participants) | Total |
|---|---|---|---|---|---|---|
| Participants analysed | 192 | 96 | 135 | 69 | 492 | |
| Age, Customized: Less than (<) 65 years | Participants | 142 | 77 | 110 | 56 | 385 |
| Age, Customized: Greater than or equal to (>=) 65 years | Participants | 50 | 19 | 25 | 13 | 107 |
| Sex: Female, Male: Female | Participants | 58 | 22 | 41 | 20 | 141 |
| Sex: Female, Male: Male | Participants | 134 | 74 | 94 | 49 | 351 |
6. Primary Endpoint
The registry lists the primary outcome as Progression Free Survival (PFS): First-Line Participants, measured over Baseline until disease progression or death (assessed on Week 6, Week 12 and thereafter every 8 weeks up to Week 107).
| Element | Registry entry |
|---|---|
| Result type | Median |
| Measure of spread | 95% Confidence Interval |
| Unit | months |
| Endpoint classification | Time-to-Event Analysis |
Progression-free survival (PFS) is the time from randomization to the first documentation of objective tumor progression or death from any cause. It is a time-to-event endpoint: each participant contributes information about how long they remain without either event, rather than only whether an event occurred by a single fixed visit. The registry says PFS was calculated in months using the event date and randomization date, with a stated conversion factor of 30.4 days per month.
Tumor progression was determined from oncologic assessment data when criteria for progressive disease were met, or from adverse-event data when the outcome was death. The record describes progression using RECIST criteria, including an increase in the summed longest diameters of target lesions, a measurable increase in a non-target lesion, or appearance of new lesions.
PFS is used in trials of cancer treatments because it captures the timing of progression or death, events that can occur before overall survival is known. It can therefore provide an earlier measure of disease control. That general rationale does not make PFS interchangeable with overall survival, nor does it establish the clinical meaning of a particular result. The posted endpoint is specifically median PFS among first-line participants; it should not be interpreted as the experience of every enrolled participant or as an overall-survival result.
7. Results Posted in the Registry
- Axitinib (First-line Participants) vs Sorafenib (First-line Participants): hazard ratio 0.77 (95% CI 0.56–1.05) (as reported in the registry).
Hazard ratio: Axitinib (First-line Participants) vs Sorafenib (First-line Participants)
95% CI: 0.56 to 1.05
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 |
|---|---|---|---|---|
| Percentage of Participants With Objective Response (OR): First-Line Participants | Binary Endpoint | Risk difference | -17.7 pts (-27.4 to -8.0) | 89 per arm |
| Percentage of Participants With Objective Response (OR): Second-Line Participants | Binary Endpoint | Risk difference | -13.6 pts (-23.7 to -3.4) | 119 per arm |
Percentage of Participants With Objective Response (OR): First-Line Participants
- 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:
- Sorafenib (First-line Participants): 14.6% (14/96) versus 32.3% (62/192) on control; risk difference -17.7 percentage points (95% CI -27.4 to -8.0), risk ratio 0.45 (0.27–0.76); 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 Sorafenib (First-line Participants) than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Percentage of Participants With Objective Response (OR): Second-Line Participants
- 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:
- Sorafenib (Second-line Participants): 10.1% (7/69) versus 23.7% (32/135) on control; risk difference -13.6 percentage points (95% CI -23.7 to -3.4), risk ratio 0.43 (0.20–0.92); unadjusted two-proportion z-test p = 0.020.
- Interpretation:
- The 95% confidence interval excludes no difference, so the proportion with the event is statistically lower for Sorafenib (Second-line Participants) than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The secondary outcome pattern includes posted objective-response results for both first-line and second-line participants. In both populations, the reported response percentages are higher in the axitinib group than in the sorafenib group. This directional pattern is consistent with the direction of the primary PFS point estimate, but consistency in direction is not independent proof of the primary result. These outcomes measure different features of treatment response and have their own uncertainty and analysis considerations.
The registry lists duration of response and overall survival among the secondary outcomes for first-line and second-line participants, but their results are not reported in the registry record. They therefore cannot be used to establish whether the response pattern persisted over time or was accompanied by an overall-survival difference. The record also does not report sponsor analyses for the objective-response comparisons in the analysis fields described.
The posted recalculated response comparisons include unadjusted p-values. In general, when multiple outcomes and comparisons are examined, the chance of at least one apparently notable result can increase unless the analysis plan accounts for multiplicity. A prespecified hierarchy or adjustment method can help control that issue, but the registry record does not report whether one was used. For that reason, the unadjusted secondary findings carry less evidential weight than a properly interpreted primary analysis and should be regarded as supportive context, not as separate confirmatory evidence.
The secondary findings also should not be pooled into a single overall conclusion. First-line and second-line participants are distinct analysis groups, and the response results do not answer the same question as PFS. The primary PFS comparison remains the central result for the study’s stated superiority question; the secondary results add context but do not resolve its uncertainty.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Percentage of Participants With Objective Response (OR): First-Line Participants
- Percentage of Participants With Objective Response (OR): Second-Line Participants
- Duration of Response (DR): First-Line Participants
- Duration of Response (DR): Second-Line Participants
- Overall Survival (OS): First-Line Participants
- Overall Survival (OS): Second-Line Participants
9. Statistical Interpretation
For first-line participants, median PFS was 10.1 months in the axitinib group, with a 95% confidence interval from 7.2 to 12.1 months. In the sorafenib group, median PFS was 6.5 months, with a 95% confidence interval from 4.7 to 8.3 months. The sponsor-reported hazard ratio was 0.767, with a 95% confidence interval from 0.559 to 1.053. The registry record does not report a p-value for this comparison.
A hazard ratio compares the event rates over follow-up under the proportional-hazards interpretation. An estimate below 1 points toward a lower instantaneous rate of progression or death in the axitinib group relative to the sorafenib group, under that interpretation. It is not a ratio of the two median times, and it does not directly say how many months an individual might gain. The confidence interval extends to 1.053, crossing the null value of 1. Thus, although the point estimate favors axitinib in direction, the interval remains compatible with no relative difference as well as with effects in either direction within its range. The result is not a definitive statistical demonstration of superiority based on the confidence interval alone.
The medians describe the time by which half of each group’s observed survival distribution has experienced progression or death, subject to the methods and follow-up used. They do not describe every participant’s time to event, and they do not capture the full shape of the event-time distributions. The confidence intervals around the medians also overlap. These separate intervals are not a formal test of the treatment contrast; the hazard ratio is the registry’s reported comparative estimate.
The objective-response results are secondary and should be read as supportive context, not as a substitute for the primary time-to-event result. The registry reports response percentages for both first-line and second-line participants, but the interpretation of those comparisons depends on analysis details and multiplicity handling that are not reported in the registry record. Results for duration of response and overall survival are listed as secondary outcomes but are not reported in the record. Those outcomes therefore cannot be used to confirm or qualify the primary result.
The study is randomized, which supports a causal comparison in principle when the analysis follows the randomized assignment and the assumptions for the endpoint are suitable. However, randomization alone does not resolve uncertainty from the confidence interval, missing outcome information, endpoint assessment, or unreported analysis choices. The study was unmasked, and the registry record does not give details about blinded endpoint review or other safeguards against assessment bias. The result should be interpreted as the reported first-line PFS comparison, with these limits in view, rather than as a broad conclusion about every outcome or population in the trial.
10. Statistical Methods Explained
What does a time-to-event endpoint represent?
In general, a time-to-event analysis studies both whether an event occurs and when it occurs. For this endpoint, the event is the first objective tumor progression or death from any cause. Participants without a recorded event by their last available assessment may contribute follow-up information up to that point; standard time-to-event methods can retain that partial information rather than treating every participant as if they had completed the same follow-up. The registry record does not report the censoring rules or the detailed handling of missing assessments, so the exact implementation cannot be reconstructed from the reported information.
The median is a summary of the event-time distribution: it marks the time at which the estimated proportion remaining free of the event reaches one half. It is not an average of all observed follow-up times and should not be read as the time at which every participant experiences progression or death. Medians are easy to communicate, but they compress a distribution into a single point and do not show whether relative effects change over time.
How should the hazard ratio be read?
In general, a hazard is the rate at which an event occurs at a particular time among participants who have not yet experienced it. A hazard ratio compares these rates between groups over the follow-up period, under the model or summary assumptions used. A ratio of 1 represents equal hazards; a value below 1 points toward a lower event hazard in the numerator group, while a value above 1 points toward a higher one. The reported hazard ratio of 0.767 is therefore directional evidence favoring axitinib for the PFS event, but its uncertainty must be considered alongside the point estimate.
A hazard ratio is not a probability, an absolute risk difference, or a direct comparison of median months. Its interpretation as a single summary is most straightforward when the relative hazard is reasonably stable over time. The registry record does not report a test of the proportional-hazards assumption or the model details used to estimate the hazard ratio. It is therefore not possible to assess that assumption from the posted information alone.
What does a confidence interval add?
In general, a confidence interval describes the statistical uncertainty around an estimate under the method used to construct it. A narrower interval indicates greater precision on that scale; a wider interval indicates that the data are compatible with a broader range of values. A 95% confidence interval is not a statement that there is a 95% probability that the fixed true value lies inside this particular interval. Rather, under repeated use of the procedure and its assumptions, intervals constructed in this way would cover the true value at the stated frequency.
For a hazard ratio, the null value is 1. The reported interval, 0.559 to 1.053, includes 1. This means the data do not exclude equal hazards at the conventional interval level. It also means the point estimate alone should not be treated as a conclusive result. The interval includes estimates that favor axitinib and estimates slightly above the null, so the direction and magnitude remain uncertain.
What can be said about the secondary response analyses?
Objective response is a binary outcome: participants are classified according to whether they met response criteria. The posted percentages are accompanied by confidence intervals. A risk difference expresses the contrast between two response probabilities on an absolute scale; a confidence interval for that difference indicates the range of contrasts compatible with the data and method. The posted recalculated response comparisons also include unadjusted p-values. In general, an unadjusted p-value tests a specified null hypothesis without accounting for the fact that multiple outcomes or comparisons may have been examined.
The registry does not report sponsor analyses for the objective-response comparisons in the listed analysis fields. The response results can describe the observed group proportions, but their statistical weight depends on the trial’s prespecified testing hierarchy and multiplicity approach. Those details are not reported in the registry record. The unadjusted results should therefore be treated as exploratory or supportive rather than as standalone confirmation of the primary PFS finding.
Why does over-dispersion matter?
In general, over-dispersion occurs when observed variability exceeds what a statistical model assumes. It can make standard errors too small and confidence intervals too narrow if the model does not account for that extra variability. Its relevance depends on the endpoint and model. The registry record does not identify an over-dispersion assessment or a method requiring such an adjustment for the reported PFS comparison. It would be inappropriate to assume that over-dispersion was present or to infer how it was handled.
For time-to-event outcomes, other model considerations may be more directly relevant, including the proportional-hazards assumption, event-time definitions, censoring, and the completeness and timing of assessments. The record gives the endpoint definition and assessment schedule but not enough analysis detail to evaluate these modeling choices.
What do the planning illustrations represent?
The sample-size illustrations are based on the observed effect and use a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. They consider detecting stated fractions of the observed effect. For time-to-event planning, the displayed quantities are total events, using the Schoenfeld approach; for other outcomes, they are participants per arm. These are planning scenarios, not a reconstruction of the trial’s original design or a report of its prespecified assumptions. The original sample-size justification is not reported in the registry record.
11. Confidence Intervals and Precision
The PFS medians have 95% confidence intervals of 7.2 to 12.1 months for axitinib and 4.7 to 8.3 months for sorafenib. These intervals describe uncertainty in each group’s median estimate. Their width reflects that the medians are estimates rather than exact population values. The intervals should not be treated as a direct confidence interval for the difference between medians.
The more direct comparative summary is the sponsor-reported hazard ratio of 0.767, with a 95% confidence interval from 0.559 to 1.053. This interval spans the null hazard ratio of 1. It therefore does not rule out equal hazards, and the point estimate should not be read without its uncertainty. The interval permits a range of relative effects, including a lower hazard in the axitinib group and a value slightly above the null. The registry record does not report a p-value for this primary comparison.
Precision is not the same as importance. A confidence interval indicates statistical uncertainty under the analysis method; it does not decide whether a result is clinically meaningful. Nor does a confidence interval account for every possible source of uncertainty, such as unreported analysis choices, incomplete outcome assessment, or departures from model assumptions.
The posted response percentages also have confidence intervals, which are wider for some groups than others. In general, binary-outcome estimates can be imprecise when the available group size or number of responses is limited. The second-line groups have fewer participants than the first-line groups, so their estimates warrant particular caution; this observation does not determine the reason for the group sizes. The record does not report the original precision targets or a formal plan for interpreting secondary confidence intervals.
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 | 0.77 | 447 | 598 |
| 75% of the observed effect | 0.82 | 794 | 1,062 |
| 50% of the observed effect | 0.88 | 1,785 | 2,390 |
The planning illustrations translate observed effects into hypothetical sample-size or event-count requirements under stated assumptions. For time-to-event outcomes, the figures are total events, not participants per arm. The planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set to a stated fraction of the observed effect. The time-to-event calculations use the Schoenfeld approach. For non-time-to-event outcomes, the figures are participants per arm.
The 80% power column represents the number of events or participants that the calculation estimates would be needed for an 80% chance of rejecting the null hypothesis, if the assumed effect and other assumptions were correct. The 90% power column uses a higher target chance of detecting that assumed effect, and consequently requires more information. These percentages describe design targets in a hypothetical planning calculation; they do not describe the probability that the trial’s observed result is true.
Each planning row changes the assumed effect size. Planning for 75% of the observed effect requires more information than planning for 100% of the observed effect; planning for 50% requires still more. This is a general consequence of trying to distinguish a smaller signal from random variation. It does not show what effect the trial was originally designed to detect, because the original design assumptions and sample-size justification are not reported in the registry record.
These calculations are planning illustrations, not observed power. They should not be used to judge the trial’s success by comparing a post hoc calculation with the result. The observed effect itself is uncertain, and using it as a planning input does not establish that the same effect would be expected in another study.
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 = 0.767, so ln(HR) = -0.2653.
- d = 4 × (1.96 + 0.842)2 / [ln(0.767)]2 = 446.2, rounded up to 447 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 <- 0.767 # 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(920816)
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 = 447 (80% power), 598 (90% power)
75% of observed effect: events = 794 (80% power), 1,062 (90% power)
50% of observed effect: events = 1,785 (80% power), 2,390 (90% power)
Simulated power with 447 events: 0.787 (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 676 participants in total, with the boundaries below.
| Analysis | Calendar time (months) | Events | Efficacy boundary (z) | Nominal one-sided p | Cumulative alpha spent |
|---|---|---|---|---|---|
| Look 1 | 15.7 | 201 | 3.710 | 0.0001 | 0.0001 |
| Look 2 | 24.8 | 402 | 2.511 | 0.0060 | 0.0060 |
| Look 3 | 60.0 | 603 | 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% | 445 | 499 | 60.0 |
| Two looks, O'Brien-Fleming | 80% | 447 | 501 | 60.0 |
| Three looks, O'Brien-Fleming | 80% | 451 | 505 | 60.0 |
| Three looks, Pocock | 80% | 521 | 584 | 60.0 |
| Fixed design, one analysis | 90% | 596 | 668 | 60.0 |
| Two looks, O'Brien-Fleming | 90% | 598 | 670 | 60.0 |
| Three looks, O'Brien-Fleming | 90% | 603 | 676 | 60.0 |
| Three looks, Pocock | 90% | 688 | 771 | 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 | 0.767 | 603 | 676 |
| 75% of the observed effect | 0.820 | 1,073 | 1,196 |
| 50% of the observed effect | 0.876 | 2,416 | 2,678 |
For context, this trial enrolled 492 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 <- 6.5 # control-arm median, months (converted from the posted unit)
hr <- 0.767 # 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: 442 p (1-sided) 0.0001
Events: 202 ~HR at bound 0.5926
Month: 16 P(Cross) if HR=1 0.0001
P(Cross) if HR=0.77 0.0338
IA 2: 67% Z 2.5114
N: 676 p (1-sided) 0.0060
Events: 403 ~HR at bound 0.7785
Month: 25 P(Cross) if HR=1 0.0060
P(Cross) if HR=0.77 0.5603
Final Z 1.9930
N: 676 p (1-sided) 0.0231
Events: 604 ~HR at bound 0.8502
Month: 60 P(Cross) if HR=1 0.0250
P(Cross) if HR=0.77 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 |
|---|---|---|---|
| not stated | Hazard Ratio (HR) 0.767 | 0.559 to 1.053 | not reported |
The sponsor-reported primary comparison is a hazard ratio of 0.767, with a 95% confidence interval from 0.559 to 1.053. The registry does not report a p-value or the method used for that analysis. The principal interpretation therefore rests on the hazard-ratio estimate and its confidence interval: the point estimate favors axitinib in direction, but the interval includes the null value of 1.
The posted primary estimate is the sponsor’s own reported analysis, and no discrepancy is flagged between that result and the registry’s analysis record. The recalculated material does not replace the sponsor’s analysis. Any simple recalculation from posted summary statistics would be unadjusted and could not reproduce details of the original time-to-event model, its assumptions, or its handling of individual participant data. For the primary result, the sponsor’s reported estimate is the relevant analysis to quote.
The registry does not provide enough detail to independently verify the sponsor’s model specification, assessment of assumptions, or treatment of missing and censored observations. The absence of those details does not invalidate the reported estimate, but it limits how fully its analytic basis can be assessed from the registry record.
16. Multiplicity, Missing Data and Analysis Populations
Multiplicity arises when a study evaluates more than one outcome, comparison, subgroup, or analysis. In general, each additional statistical test creates another opportunity for a result to appear notable by chance. Trial analysis plans may address this through a prespecified testing sequence, adjustment of significance thresholds, or other methods. The registry lists 16 outcome measures and 2 analyses, but it does not report a complete multiplicity strategy, testing hierarchy, or whether the secondary outcomes were intended to be confirmatory. The unadjusted response p-values therefore need cautious interpretation.
The primary analysis population is described as treatment-naive randomized participants, analyzed according to initial assignment regardless of whether they received the assigned drug or another drug. This resembles an intention-to-treat principle in its use of randomized assignment, but the exact label and implementation should follow the registry’s stated FAS definition rather than assumptions about a protocol. The record does not report a full account of exclusions from that population or the disposition of all randomized participants.
Missingness matters because participants without complete follow-up may contribute less information, and the reason for missing data can influence interpretation. In time-to-event analyses, participants may be censored at their last known assessment, but the registry record does not state the detailed censoring rules or explain how missed tumor assessments were handled. It also does not report sensitivity analyses for missing outcomes. No particular missing-data procedure should be inferred.
The record describes an unmasked study. It does not report whether tumor assessments were reviewed independently or blinded to treatment assignment, nor does it provide enough information to assess potential effects of knowledge of treatment on assessment or follow-up. These are questions for the full protocol and analysis documentation; the registry record alone does not answer them.
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 |
|---|---|---|---|
| Axitinib (First-line Participants) | 77 | 173 | 44.5% |
| Sorafenib (First-line Participants) | 26 | 88 | 29.5% |
| Axitinib (Second-line Participants) | 6 | 11 | 54.5% |
| Sorafenib (Second-line Participants) | 3 | 5 | 60.0% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Axitinib (First-line Participants) | 117 of 173 |
| Sorafenib (First-line Participants) | 63 of 88 |
| Axitinib (Second-line Participants) | 9 of 11 |
| Sorafenib (Second-line Participants) | 3 of 5 |
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 |
|---|---|
| Axitinib (First-line Participants) | 161 of 173 |
| Sorafenib (First-line Participants) | 83 of 88 |
| Axitinib (Second-line Participants) | 11 of 11 |
| Sorafenib (Second-line Participants) | 5 of 5 |
Most frequent serious adverse event terms
| Event term | Organ system | Axitinib (First-line Participants) | Sorafenib (First-line Participants) | Axitinib (Second-line Participants) | Sorafenib (Second-line Participants) |
|---|---|---|---|---|---|
| Disease progression | General disorders | 20 of 173 | 6 of 88 | 0 of 11 | 0 of 5 |
| Diarrhoea | Gastrointestinal disorders | 8 of 173 | 2 of 88 | 1 of 11 | 0 of 5 |
| Abdominal pain | Gastrointestinal disorders | 1 of 173 | 3 of 88 | 2 of 11 | 1 of 5 |
| Pneumonia | Infections and infestations | 4 of 173 | 1 of 88 | 1 of 11 | 1 of 5 |
| Anaemia | Blood and lymphatic system disorders | 0 of 173 | 1 of 88 | 3 of 11 | 1 of 5 |
| Myocardial infarction | Cardiac disorders | 3 of 173 | 2 of 88 | 0 of 11 | 0 of 5 |
| Pleural effusion | Respiratory, thoracic and mediastinal disorders | 2 of 173 | 3 of 88 | 0 of 11 | 0 of 5 |
| Acute myocardial infarction | Cardiac disorders | 1 of 173 | 2 of 88 | 1 of 11 | 0 of 5 |
| Cardiac arrest | Cardiac disorders | 3 of 173 | 0 of 88 | 0 of 11 | 0 of 5 |
| Cardio-respiratory arrest | Cardiac disorders | 2 of 173 | 0 of 88 | 0 of 11 | 1 of 5 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Axitinib (First-line Participants) | Sorafenib (First-line Participants) | Axitinib (Second-line Participants) | Sorafenib (Second-line Participants) |
|---|---|---|---|---|---|
| Diarrhoea | Gastrointestinal disorders | 88 of 173 | 34 of 88 | 6 of 11 | 2 of 5 |
| Hypertension | Vascular disorders | 83 of 173 | 28 of 88 | 4 of 11 | 1 of 5 |
| Weight decreased | Investigations | 70 of 173 | 24 of 88 | 4 of 11 | 1 of 5 |
| Fatigue | General disorders | 55 of 173 | 25 of 88 | 4 of 11 | 2 of 5 |
| Palmar-plantar erythrodysaesthesia syndrome | Skin and subcutaneous tissue disorders | 41 of 173 | 31 of 88 | 4 of 11 | 4 of 5 |
| Decreased appetite | Metabolism and nutrition disorders | 48 of 173 | 16 of 88 | 5 of 11 | 0 of 5 |
| Asthenia | General disorders | 41 of 173 | 15 of 88 | 5 of 11 | 0 of 5 |
| Nausea | Gastrointestinal disorders | 38 of 173 | 15 of 88 | 1 of 11 | 0 of 5 |
| Cough | Respiratory, thoracic and mediastinal disorders | 33 of 173 | 14 of 88 | 2 of 11 | 1 of 5 |
| Vomiting | Gastrointestinal disorders | 38 of 173 | 11 of 88 | 0 of 11 | 0 of 5 |
Serious events with the highest arm-level rate: anaemia (27.3%), abdominal pain (20.0%), anal fistula (20.0%), multiple organ dysfunction syndrome (20.0%), anal abscess (20.0%).
The registry reports serious adverse-event counts with group-specific numbers at risk. Among first-line participants, serious adverse events were reported for 77 of 173 participants in the axitinib group and 26 of 88 in the sorafenib group. For second-line participants, the corresponding counts were 6 of 11 and 3 of 5. The registry also lists other adverse events for these groups: 161 of 173, 83 of 88, 11 of 11, and 5 of 5, respectively. These are descriptive counts; they do not by themselves establish that treatment caused an event or permit a complete comparative safety assessment.
The listed serious-event terms include anaemia at 27.3%, abdominal pain at 20.0%, anal fistula at 20.0%, multiple organ dysfunction syndrome at 20.0%, anal abscess at 20.0%, and axonal and demyelinating polyneuropathy at 20.0%. The registry information described does not clarify the denominator behind these term percentages, so they should not be interpreted as participant-level risks without that context. Death counts are also listed, but the record does not establish that these deaths were caused by treatment. The small second-line groups make those descriptive counts especially difficult to compare.
18. What the Result Does, and Does Not, Mean
The posted data show a first-line PFS point estimate favoring axitinib: median PFS was 10.1 months with axitinib and 6.5 months with sorafenib, and the reported hazard ratio was 0.767. The 95% confidence interval for that hazard ratio, 0.559 to 1.053, includes 1. The result therefore leaves uncertainty about the relative event rate and does not, by itself, establish a statistically clear difference at the conventional confidence-interval level. No primary p-value is reported in the registry record.
This finding is about progression-free survival among the first-line analysis population. It is not an overall-survival result, and it does not describe the experience of every participant enrolled. The registry’s response percentages provide additional information, but they are secondary outcomes whose multiplicity handling is not reported. Duration-of-response and overall-survival results are not reported in the registry record, so conclusions about those outcomes cannot be drawn from the information available.
Statistical uncertainty is distinct from clinical importance. The reported interval does not decide whether a possible difference would matter to patients, and the registry record does not provide a threshold for clinical relevance. The median values and hazard ratio also do not predict an individual participant’s outcome. They summarize group-level data under the endpoint definition and analysis method.
The trial’s randomized design supports a comparative question, while its unmasked status and the absence of detailed analysis documentation limit assessment of some potential biases and assumptions. The appropriate conclusion is confined to the reported estimates and their uncertainty: the point estimates favor axitinib, but the primary hazard-ratio interval does not exclude the null, and the record does not supply enough detail to settle every interpretive question.
19. Why This Trial Matters Statistically
This study illustrates why a point estimate and its uncertainty need to be read together. The primary hazard ratio is below 1, and the group medians point in the same direction, but the hazard-ratio confidence interval includes 1. Reporting only the point estimate would conceal that uncertainty; reporting only whether a conventional threshold was crossed would conceal the size and direction of the estimated effect.
It also illustrates the distinction between a median and a comparative time-to-event measure. The medians give accessible summaries of each group’s event-time distribution, while the hazard ratio compares event rates across follow-up under its assumptions. They answer related but different questions. Treating the hazard ratio as a ratio of median times, or reading the median difference as a complete description of the survival curves, would misstate what these summaries mean.
Finally, the registry record contains multiple outcome domains: PFS, objective response, duration of response, overall survival, and safety. Their presence does not make all findings equally confirmatory. A clearly identified primary endpoint is central to the stated study question; secondary endpoints require attention to multiplicity, analysis populations, and missing results. The absence of some secondary results and of a detailed statistical plan is itself relevant to how broadly the evidence can be interpreted.
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 gives the reported primary hazard ratio and confidence interval but does not report a p-value, the model details, or a test of the proportional-hazards assumption. It also does not provide the original sample-size justification or enough information to reconstruct the trial’s prespecified statistical plan. The posted planning illustrations are based on the observed effect and are not evidence of the original design choices.
The study is listed as unmasked. The record does not say whether endpoint review was blinded or independently adjudicated, or how assessment-related concerns were addressed. It states the tumor-assessment schedule and progression criteria, but not the detailed procedures for missed assessments, censoring, or sensitivity analyses. These gaps limit independent evaluation of the time-to-event analysis.
The registry lists secondary outcomes for objective response, duration of response, and overall survival. Results are posted for objective response in first-line and second-line participants, but duration-of-response and overall-survival results are not reported in the registry record. The multiplicity strategy is also not reported, which matters when interpreting unadjusted secondary comparisons. The second-line groups are small, so their estimates and adverse-event counts are particularly limited in precision and comparative usefulness.
The serious adverse-event term percentages are listed without a clearly described denominator in the information discussed. Counts of events and deaths alone do not establish causality or provide a complete benefit-risk assessment. These limitations concern what can be concluded from the registry record; they do not establish that the underlying study documents lack further detail.
21. Related Tutorials
22. Related Statistical Calculators
23. Sources
- ClinicalTrials.gov: Axitinib (AG-013736) For the Treatment of Metastatic Renal Cell Cancer — NCT00920816.
- Registry record last updated 2022-05-06; status last verified 2022-04.
- Results first posted 2014-02-04.
- Data retrieved from ClinicalTrials.gov on 2026-11-09.
- Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.
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24. Record Summary
The registry describes a completed randomized phase 3 study of axitinib versus sorafenib in metastatic renal cell cancer, with enrollment of 492 and no masking. The primary outcome was median PFS among treatment-naive first-line participants analyzed according to initial randomized assignment. The sponsor-reported hazard ratio was 0.767, with a 95% confidence interval from 0.559 to 1.053; the interval includes 1, and no p-value is reported for this comparison.
Objective-response results are posted for first-line and second-line participants, while duration-of-response and overall-survival results are not reported in the registry record. The record also lists serious adverse events and deaths, but the posted counts are descriptive and do not establish treatment causation. The original sample-size justification, detailed multiplicity strategy, and several analysis procedures are not reported in the registry record.