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 A Study of Atezolizumab Compared With Chemotherapy in Participants With Locally Advanced or Metastatic Urothelial Bladder Cancer [IMvigor211] (NCT02302807), a randomized phase 3 study. The primary outcome is Overall Survival (OS).
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT02302807 |
| Phase | Phase 3 |
| Condition | Bladder Cancer |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | None (open label) |
| Enrollment | 931 |
| Arms in the primary outcome | 6 |
| Lead sponsor | Hoffmann-La Roche |
| Results posted | Yes |
2. Clinical Question
Population
Participants with locally advanced or metastatic urothelial bladder cancer whose disease had progressed during or after a platinum-containing regimen. The primary analysis population was the intent-to-treat population: all randomized participants, regardless of whether they received their assigned treatment.
Intervention
Atezolizumab, an anti-PD-L1 antibody, administered intravenously. The registry describes treatment continuing while clinical benefit was considered to continue, until unacceptable toxicity or another stopping condition.
Comparator
Investigator-selected chemotherapy with vinflunine, paclitaxel, or docetaxel. The registry describes these drugs being administered intravenously on Day 1 of each 21-day cycle.
Primary question
How did overall survival from randomization to death from any cause compare between the randomized treatment groups? The registry also reports comparisons within immune-cell subgroups, alongside the overall comparison.
The trial addressed a treatment comparison after participants had experienced progression during or following platinum-containing chemotherapy. Its primary outcome, overall survival, captures time to death from any cause rather than a tumor measurement alone. That makes it a direct measure of survival experience, but it does not by itself explain why survival may differ between groups or characterize other aspects of disease control and treatment burden.
The registry describes the study as global, multicenter, randomized, controlled, open-label, and Phase III. The chemotherapy arm was not a single fixed drug: the investigator selected vinflunine, paclitaxel, or docetaxel. As a result, the comparison is between atezolizumab and a chemotherapy strategy whose specific drug could vary, rather than between atezolizumab and one uniform chemotherapy agent.
The posted primary comparisons include the full analysis population and two immune-cell-defined groups. Those subgroup results address estimates in the named groups, but the registry record does not report enough information to establish how subgroup comparisons were positioned in the original testing strategy. Interpretation therefore needs to keep the overall endpoint and the subgroup estimates distinct.
3. Trial Design
This was a Phase III randomized parallel-group study with an open-label design. The registry lists enrollment of 931 and describes the study as global and multicenter. It is marked completed. The recorded study start is 2015-01-13, and primary completion is recorded as 2017-03-13.
Participants were assigned to atezolizumab or chemotherapy. The chemotherapy choice was vinflunine, paclitaxel, or docetaxel, selected by the investigator. Atezolizumab was described as an intravenous fixed dose of 1200 mg on Day 1 of each 21-day cycle. The chemotherapy drugs were also described as intravenous Day 1 treatments on 21-day cycles, with the dose varying by drug. The registry describes study treatment as continuing while clinical benefit persisted, subject to stopping conditions.
Open-label means that treatment assignment was not masked, as the registry explicitly records no masking. That can matter for outcomes involving subjective assessment or decisions made during care. Overall survival is based on death from any cause, an outcome less dependent on an assessor's judgment than some tumor-response or symptom outcomes, although the registry record does not describe its procedures for determining or recording deaths.
The primary analysis population was intent to treat: all randomized participants, irrespective of whether assigned treatment was actually received. This preserves the comparison according to randomized assignment. The registry record does not report the actual treatment exposure, adherence, treatment crossover, or handling of treatment changes in the primary analysis. It also does not report the original statistical analysis plan, the sample-size justification, or whether interim analyses were planned or conducted. Those design details should not be inferred from the posted outcome results or planning illustrations.
The registry record gives a target sample size of 931 as part of the study description and also records enrollment of 931. That information describes the planned and recorded enrollment, but does not establish the trial's original assumptions about expected survival, target effect, power, or significance threshold. Those original design assumptions are not reported in the registry record.
4. Participant Flow and Accounting
The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.
Overall Study
| Stage | Chemotherapy (Vinflunine, Paclitaxel, or Docetaxel) | Atezolizumab |
|---|---|---|
| STARTED | 464 | 467 |
| Received Treatment | 443 | 459 |
| COMPLETED | 0 | 0 |
| NOT COMPLETED | 464 | 467 |
Reasons for not completing this period:
| Reason | Chemotherapy (Vinflunine, Paclitaxel, or Docetaxel) | Atezolizumab |
|---|---|---|
| Withdrawal by Subject | 28 | 11 |
| Lost to Follow-up | 4 | 6 |
| Death | 397 | 385 |
| Study Terminated By Sponsor | 35 | 64 |
| Physician Decision | 0 | 1 |
Analysis population for the primary outcome, as defined in the registry: Intent To Treat (ITT) was defined as all randomized participants, irrespective of whether the assigned treatment was actually received.
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.
| Characteristic | Unit | Chemotherapy (Vinflunine, Paclitaxel, or Docetaxel) | Atezolizumab | Total |
|---|---|---|---|---|
| Participants analysed | 464 | 467 | 931 | |
| Age, Continuous | Years | 66.1 (SD 9.3) | 65.9 (SD 9.6) | 66.0 (SD 9.4) |
| Sex: Female, Male: Female | Participants | 103 | 110 | 213 |
| Sex: Female, Male: Male | Participants | 361 | 357 | 718 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 16 | 13 | 29 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 368 | 363 | 731 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 80 | 91 | 171 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 0 | 0 | 0 |
| Race (NIH/OMB): Asian | Participants | 55 | 63 | 118 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 0 | 0 | 0 |
| Race (NIH/OMB): Black or African American | Participants | 2 | 1 | 3 |
| Race (NIH/OMB): White | Participants | 336 | 335 | 671 |
| Race (NIH/OMB): More than one race | Participants | 1 | 0 | 1 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 70 | 68 | 138 |
6. Primary Endpoint
The registry lists the primary outcome as Overall Survival (OS), measured over Between randomization and death due to any cause, up to approximately 25 months after first participant enrolled.
| Element | Registry entry |
|---|---|
| Result type | Median |
| Measure of spread | 95% Confidence Interval |
| Unit | Months |
| Endpoint classification | Time-to-Event Analysis |
Overall survival is defined in the registry as the time from randomization to death from any cause. The posted measure is the median time to that event, expressed in months, with a 95% confidence interval. The timeframe is described as extending between randomization and death, up to approximately 25 months after the first participant enrolled.
The median is the point in the observed survival distribution at which the estimated proportion still alive has reached the halfway point. It describes the middle of the survival-time distribution, not the survival time of every participant and not the difference in survival time for a typical individual. A median also does not describe the entire shape of the survival experience. A hazard ratio is a separate time-to-event summary used for the reported comparisons; it summarizes relative event rates over follow-up under the assumptions of the analysis, rather than directly expressing a difference in median months.
Overall survival is used because death from any cause is clinically direct and does not require deciding whether a change in a tumor measurement qualifies as progression or response. It can nonetheless be influenced by events and care after randomization, and a summary estimate does not identify those pathways. The registry record does not report the survival-curve details, censoring procedures, or follow-up distribution needed to examine those features in depth.
The ITT definition is important: the primary population includes all randomized participants whether or not assigned treatment was received. Thus the posted endpoint is a comparison by randomized assignment in that population, not a comparison restricted to participants who completed treatment.
7. Results Posted in the Registry
- IC2/3 Chemotherapy vs IC2/3 Atezolizumab: hazard ratio 0.87 (95% CI 0.63–1.21), reported p = 0.413 (as reported in the registry).
- IC1/2/3 Chemotherapy vs IC1/2/3 Atezolizumab: hazard ratio 0.87 (95% CI 0.71–1.05) (as reported in the registry).
- Chemotherapy (Vinflunine, Paclitaxel, or Docetaxel) vs Atezolizumab: hazard ratio 0.85 (95% CI 0.73–0.99) (as reported in the registry).
Hazard ratio: IC2/3 Chemotherapy vs IC2/3 Atezolizumab
95% CI: 0.63 to 1.21
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 Post-Baseline Anti-therapeutic Antibodies (ATA) to Atezolizumab | Binary Endpoint | Risk difference | +1.7 pts (-5.4 to 8.8) | 12,309 per arm |
| Percentage of Participants With Unconfirmed Objective Response Rate (ORR) as Determined by the Investigator With Use of Response Evaluation Criteria In Solid Tumors Version 1.1 (RECIST v1.1) | Binary Endpoint | Risk difference | -5.5 pts (-10.4 to -0.5) | 781 per arm |
Percentage of Participants With Post-Baseline Anti-therapeutic Antibodies (ATA) to Atezolizumab
- 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:
- IC1/2/3 Atezolizumab: 34.9% (101/289) versus 33.3% (142/427) on control; risk difference 1.7 percentage points (95% CI -5.4 to 8.8), risk ratio 1.05 (0.85–1.29); unadjusted two-proportion z-test p = 0.639.
- IC2/3 Atezolizumab: 33.0% (35/106) versus 33.3% (142/427) on control; risk difference -0.2 percentage points (95% CI -10.2 to 9.8), risk ratio 0.99 (0.73–1.34); unadjusted two-proportion z-test p = 0.963.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between IC1/2/3 Atezolizumab and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between IC2/3 Atezolizumab and the control. The interval gives the range of effects that remain compatible with the data.
Percentage of Participants With Unconfirmed Objective Response Rate (ORR) as Determined by the Investigator With Use of Response Evaluation Criteria In Solid Tumors Version 1.1 (RECIST v1.1)
- 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:
- Atezolizumab: 15.4% (71/462) versus 20.8% (96/461) on control; risk difference -5.5 percentage points (95% CI -10.4 to -0.5), risk ratio 0.74 (0.56–0.97); unadjusted two-proportion z-test p = 0.031.
- IC2/3 Chemotherapy: 29.3% (34/116) versus 20.8% (96/461) on control; risk difference 8.5 percentage points (95% CI -0.6 to 17.6), risk ratio 1.41 (1.01–1.97); unadjusted two-proportion z-test p = 0.051.
- Interpretation:
- The 95% confidence interval excludes no difference, so the proportion with the event is statistically lower for Atezolizumab than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between IC2/3 Chemotherapy and the control. The interval gives the range of effects that remain compatible with the data.
The secondary outcomes cover distinct aspects of treatment and disease: progression-free survival, duration of response, adverse events, anti-therapeutic antibodies, serum concentrations, objective response, and quality of life. The registry lists these outcomes, but numerical results are posted for only some of them in the record. Results for progression-free survival, duration of response, adverse events as a secondary endpoint, serum concentration measures, and quality of life are not reported in the registry record.
For the available objective-response results, the posted overall response proportions are lower in the atezolizumab group than in the chemotherapy group. The immune-cell subgroup estimates do not show a uniform pattern across the listed comparisons. The available anti-therapeutic-antibody proportions across the atezolizumab groups are broadly similar in the posted summaries. These observations concern secondary endpoints and do not establish that the primary survival effect differs across subgroups or explain the primary survival estimates.
Secondary outcomes can help describe response, treatment exposure, safety, or patient-reported experience, but they do not replace the primary endpoint. Their measures differ in definition, timing, population, and interpretation. A response proportion is not a survival-time comparison, and antibody status is not a measure of clinical benefit by itself.
Some recalculated secondary comparisons are unadjusted. An unadjusted result does not account for the fact that multiple outcomes and subgroup comparisons may be examined. When many comparisons are made, chance findings become more likely unless the testing strategy addresses multiplicity. The registry record does not report a multiplicity adjustment or the original hierarchy governing secondary tests. Accordingly, secondary signals deserve less inferential weight than a prespecified primary analysis with a clearly reported testing plan. The posted results can describe patterns, but they cannot establish which secondary findings were confirmatory.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Progression-free Survival (PFS) as Determined by the Investigator With Use of RECIST v1.1
- Unconfirmed Duration of Response (DOR) as Determined by the Investigator With Use of RECIST v1.1
- Percentage of Participants With Adverse Events (AEs)
- Percentage of Participants With Post-Baseline Anti-therapeutic Antibodies (ATA) to Atezolizumab
- Minimum Observed Serum Atezolizumab Concentration (Cmin)
- Percentage of Participants With Unconfirmed Objective Response Rate (ORR) as Determined by the Investigator With Use of Response Evaluation Criteria In Solid Tumors Version 1.1 (RECIST v1.1)
- Maximum Observed Serum Atezolizumab Concentration (Cmax)
- Change From Baseline in European Organisation for Research and Treatment of Cancer (EORTC) Quality-of-Life Questionnaire Core 30 (QLQ-C30) Score: Global Health Status Scale
9. Statistical Interpretation
The registry reports median overall survival for the full groups and for two immune-cell-defined groups. In the overall groups, median survival is 8.0 months for chemotherapy and 8.6 months for atezolizumab. The corresponding 95% confidence intervals are 7.2 to 8.6 months and 7.8 to 9.6 months. These are separate group estimates; their medians alone do not provide a complete comparison of the survival distributions.
For the IC2/3 groups, the reported medians are 10.6 months for chemotherapy and 11.1 months for atezolizumab, with confidence intervals of 8.4 to 12.2 months and 8.6 to 15.5 months. For the IC1/2/3 groups, the corresponding medians are 8.2 and 8.9 months, with confidence intervals of 7.4 to 9.5 months and 8.2 to 10.9 months. These subgroup summaries should not be read as proof that treatment effects differ by subgroup. The registry record does not report a treatment-by-subgroup interaction analysis or the original subgroup-testing strategy.
The sponsor-reported hazard ratio for IC2/3 chemotherapy versus IC2/3 atezolizumab is 0.87, with a 95% confidence interval from 0.63 to 1.21 and a reported p-value of 0.413. For IC1/2/3 chemotherapy versus IC1/2/3 atezolizumab, the reported hazard ratio is 0.87, with a 95% confidence interval from 0.71 to 1.05. For the overall chemotherapy-versus-atezolizumab comparison, it is 0.85, with a 95% confidence interval from 0.73 to 0.99. The registry does not report p-values for the latter two comparisons.
A hazard ratio's direction depends on which group is in the numerator and how the comparison was coded. The registry gives the comparison order and the estimate, but the posted information does not spell out the coding convention in enough detail to assign a treatment-favoring direction from the ratio alone. The interval for the IC2/3 and IC1/2/3 estimates includes 1; the overall interval does not. An interval's position relative to 1 is a feature of that estimate, not a substitute for the full analysis plan or evidence about multiple comparisons.
The results therefore describe median survival and sponsor-reported relative hazard estimates in the recorded populations. They do not establish a causal explanation for the pattern, demonstrate that subgroup effects differ, or settle how the overall comparison should be interpreted under any unreported testing hierarchy. The sponsor's reported analysis is the relevant inferential analysis for these time-to-event comparisons; recalculated planning illustrations are not a replacement for it.
10. Statistical Methods Explained
Time-to-event methods are designed for outcomes whose timing matters and where some participants may not experience the event during observed follow-up. For overall survival, the event is death from any cause. The registry reports medians and hazard ratios, and identifies a Log Rank method for the IC2/3 comparison. It does not report a method for the other two hazard-ratio analyses in the posted record.
What does a median survival estimate describe?
General explanation: a median is a location summary for the estimated survival distribution. It indicates the time by which the estimated survival probability has reached the halfway point. It is not an average, does not describe the full distribution, and does not tell how many months an individual participant would live. The posted medians should therefore be considered alongside the confidence intervals and comparative analyses rather than treated as a stand-alone treatment effect.
What does a hazard ratio describe?
General explanation: a hazard is the instantaneous rate of an event among participants who have not yet experienced it, as follow-up proceeds. A hazard ratio compares those rates between groups under the analysis. It is not a ratio of median survival times and should not be translated into a fixed difference in months. Its direction is interpretable only with the numerator and reference-group coding clear. The registry gives comparisons in a chemotherapy-versus-atezolizumab order but does not explicitly describe the coding convention in the posted analysis details.
The proportional-hazards interpretation typically relies on the relative hazard being sufficiently stable over time. Whether that assumption was assessed, and what results any assessment produced, is not reported in the registry record. If relative hazards vary over time, one hazard ratio can be a limited summary of a more complex pattern. The registry record does not provide the survival curves or time-specific estimates needed to examine that possibility.
How should the confidence intervals be read?
General explanation: a confidence interval describes uncertainty in an estimate under the statistical method used. It is not a range containing the individual survival times, and it does not mean that every value inside it is equally plausible. A wider interval indicates less precision than a narrower interval, all else being comparable. The reported 95% intervals for medians and hazard ratios reflect uncertainty in different quantities, so they should not be treated as interchangeable.
For a hazard ratio, 1 represents equal hazards under the ratio definition. An interval that includes 1 is compatible with equal hazards as well as with values on either side of 1 under the interval procedure. An interval that does not include 1 indicates that the interval's range excludes that reference value, but interpretation still depends on the analysis, comparison coding, and any multiplicity plan. The registry record reports a p-value only for the IC2/3 comparison and does not provide a p-value for the other hazard-ratio comparisons.
What does the Log Rank method contribute?
General explanation: the Log Rank test compares the observed event experience between groups across follow-up, taking account of when events occur and participants' time at risk. It is commonly used for time-to-event comparisons. Its result depends on the observed event-time information and censoring. The registry names this method for the IC2/3 comparison; it does not report a method name for the other two comparisons, so the method should not be assumed to have been identical.
The trial's primary population is ITT, defined as all randomized participants regardless of whether assigned treatment was received. This keeps participants in the group to which they were randomized for the primary comparison. The posted record does not describe censoring rules, missing survival status, or any sensitivity analysis for missing outcome information. Nor does it state whether the proportional-hazards assumption was part of the sponsor's analysis plan or how it was evaluated.
The registry also includes secondary measures such as response and anti-therapeutic antibodies. Those are not time-to-event summaries of overall survival and use different denominators and statistical interpretations. A response proportion, for example, summarizes the participants meeting a response definition in the reported assessment, whereas overall survival follows time to death from randomization. Differences in endpoint type mean that results across these measures cannot be combined as though they were repeated measurements of the same outcome.
11. Confidence Intervals and Precision
Precision concerns how much uncertainty surrounds an estimate. The registry reports 95% confidence intervals for the primary medians and hazard ratios. The medians for the overall treatment groups have intervals of 7.2 to 8.6 months for chemotherapy and 7.8 to 9.6 months for atezolizumab. For the overall hazard ratio, the interval is 0.73 to 0.99. These intervals convey uncertainty in the separate medians and the relative hazard estimate; they are not interchangeable measures.
The subgroup intervals are also informative. In the IC2/3 groups, the median intervals extend from 8.4 to 12.2 months for chemotherapy and from 8.6 to 15.5 months for atezolizumab. In the IC1/2/3 groups, they extend from 7.4 to 9.5 months and from 8.2 to 10.9 months, respectively. The IC2/3 hazard-ratio interval ranges from 0.63 to 1.21; the IC1/2/3 interval ranges from 0.71 to 1.05. These ranges show uncertainty around the estimates, not certainty about which value is the true effect.
General explanation: confidence intervals are affected by the amount of information available and by the variability in the data. A confidence interval for a group median does not test the difference between two medians. Likewise, the intervals around two separate group estimates cannot be used as a replacement for the reported comparative analysis. The hazard-ratio intervals directly concern the comparative measure, but their interpretation still depends on its coding and statistical assumptions.
The registry record does not include the complete survival curves, event counts for each primary comparison, follow-up summaries, or detailed missing-data and censoring information. Without those details, precision can be described from the posted intervals, but not fully diagnosed. The estimates should be read as bounded but uncertain summaries rather than as exact values.
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 | 0.87 | 1,619 | 2,168 |
| 75% of the observed effect | 0.90 | 2,878 | 3,853 |
| 50% of the observed effect | 0.93 | 6,476 | 8,669 |
The planning figures are illustrations calculated from the observed effects, not the trial's original design assumptions. For the time-to-event comparisons, the figures are total events required, not participants per arm. For the other planning illustrations, the figures are participants per arm. This distinction matters: event requirements describe how many outcome events an analysis would need, while per-arm participant requirements describe an illustrative enrollment scale.
The stated 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 the stated fraction of the observed effect. The time-to-event illustrations use the Schoenfeld approach. The original sample-size justification and assumptions are not reported in the registry record.
The 80% power column represents an illustrative design with an 80% chance of detecting the specified effect under the stated assumptions if that effect is real. The 90% power column represents a design with a 90% chance under those same assumptions. Power is a property of a planned design and a specified effect, not a measure of whether the observed trial result is true. Smaller effects require more participants or events to detect with the same planned power. That is why planning for 75% or 50% of the observed effect requires larger figures than planning for 100% of it.
For example, the overall time-to-event illustration lists 1,189 total events for 80% power and 1,592 for 90% power when planning for 100% of the observed effect. These are event targets under the illustration, not observed events and not a reconstruction of the trial's actual design. The planning figures are not observed power.
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 = 0.870, so ln(HR) = -0.1393.
- d = 4 × (1.96 + 0.842)2 / [ln(0.870)]2 = 1,618.8, rounded up to 1,619 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 <- 0.87 # 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(2302807)
d <- events_needed(0.80)
reps <- 20000
D1 <- rbinom(reps, d, hr / (1 + hr))
z <- (D1 - d / 2) / sqrt(d / 4)
cat(sprintf("Simulated power with %s events: %.3f (%d replicates)\n", format(d, big.mark = ","), mean(abs(z) > z_a), reps))
Output from running the code
100% of observed effect: events = 1,619 (80% power), 2,168 (90% power)
75% of observed effect: events = 2,878 (80% power), 3,853 (90% power)
50% of observed effect: events = 6,476 (80% power), 8,669 (90% power)
Simulated power with 1,619 events: 0.803 (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 2,652 participants in total, with the boundaries below.
| Analysis | Calendar time (months) | Events | Efficacy boundary (z) | Nominal one-sided p | Cumulative alpha spent |
|---|---|---|---|---|---|
| Look 1 | 17.8 | 730 | 3.710 | 0.0001 | 0.0001 |
| Look 2 | 28.1 | 1,461 | 2.511 | 0.0060 | 0.0060 |
| Look 3 | 60.0 | 2,191 | 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% | 1,618 | 1,957 | 60.0 |
| Two looks, O'Brien-Fleming | 80% | 1,624 | 1,965 | 60.0 |
| Three looks, O'Brien-Fleming | 80% | 1,638 | 1,982 | 60.0 |
| Three looks, Pocock | 80% | 1,893 | 2,291 | 60.0 |
| Fixed design, one analysis | 90% | 2,166 | 2,621 | 60.0 |
| Two looks, O'Brien-Fleming | 90% | 2,173 | 2,630 | 60.0 |
| Three looks, O'Brien-Fleming | 90% | 2,191 | 2,652 | 60.0 |
| Three looks, Pocock | 90% | 2,500 | 3,025 | 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 | 0.870 | 2,191 | 2,652 |
| 75% of the observed effect | 0.901 | 3,897 | 4,694 |
| 50% of the observed effect | 0.933 | 8,770 | 10,516 |
For context, this trial enrolled 931 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 <- 10.6 # control-arm median, months (converted from the posted unit)
hr <- 0.87 # 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: 1966 p (1-sided) 0.0001
Events: 731 ~HR at bound 0.7599
Month: 18 P(Cross) if HR=1 0.0001
P(Cross) if HR=0.87 0.0338
IA 2: 67% Z 2.5114
N: 2652 p (1-sided) 0.0060
Events: 1461 ~HR at bound 0.8769
Month: 28 P(Cross) if HR=1 0.0060
P(Cross) if HR=0.87 0.5603
Final Z 1.9930
N: 2652 p (1-sided) 0.0231
Events: 2192 ~HR at bound 0.9184
Month: 60 P(Cross) if HR=1 0.0250
P(Cross) if HR=0.87 0.9000
Cross-check, upper boundaries: gsDesign 3.71, 2.511, 1.993 | rpact 3.71, 2.511, 1.993
15. Analyses Reported by the Sponsor
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| Log Rank | Hazard Ratio (HR) 0.87 | 0.63 to 1.21 | 0.413 |
| not stated | Hazard Ratio (HR) 0.87 | 0.71 to 1.05 | not reported |
| not stated | Hazard Ratio (HR) 0.85 | 0.73 to 0.99 | not reported |
The primary outcome is time to event, and the registry includes sponsor-reported hazard ratios for the IC2/3, IC1/2/3, and overall comparisons. The IC2/3 analysis is identified as a Log Rank analysis and includes a reported p-value of 0.413. The other two hazard-ratio records do not include reported p-values or method names. Those omissions should not be filled by assuming a method or deriving a sponsor p-value from the interval.
The statistical interpretation should follow the sponsor-reported analysis for these time-to-event comparisons. The record does not flag a discrepancy between sponsor results and recalculated results. The planning illustrations elsewhere are not alternative estimates of the trial's treatment effect: they translate an observed effect into hypothetical sample-size requirements under stated assumptions. They do not override or independently verify the sponsor's inferential analysis.
The reported hazard ratios are 0.87 for each of the subgroup comparisons and 0.85 for the overall comparison. Their confidence intervals are 0.63 to 1.21, 0.71 to 1.05, and 0.73 to 0.99, respectively. The registry comparison labels give chemotherapy versus atezolizumab, but the posted analysis does not spell out which group is the numerator. The ratio's direction should therefore not be translated into a treatment-favoring conclusion without that coding detail.
The registry record does not report the complete sponsor analysis plan, a multiplicity procedure, or the rationale for the subgroup comparisons. The sponsor estimates are the appropriate posted results to describe, while conclusions about confirmatory status and the broader testing strategy remain limited by the unreported information.
16. Multiplicity, Missing Data and Analysis Populations
Multiplicity arises when several hypotheses are tested, such as multiple outcomes, subgroup comparisons, or treatment contrasts. Repeated testing can increase the chance of at least one apparently notable result even when there is no underlying effect. A prespecified hierarchy or adjustment can control how results are interpreted, but the registry record does not report such a plan for the posted primary and secondary comparisons.
The primary outcome is overall survival, and the record also reports estimates in the IC2/3 and IC1/2/3 groups. It does not report whether those subgroup analyses were prespecified, whether they were part of a sequential testing hierarchy, or whether any adjustment was made for them. It also does not state whether secondary endpoints were formally tested or treated as descriptive. This limits the ability to distinguish confirmatory findings from exploratory patterns.
Missing-data handling is also not described in sufficient detail. The ITT population is defined as all randomized participants regardless of treatment received, but the record does not describe missing survival status, censoring rules, missing endpoint assessments, or sensitivity analyses. For secondary outcomes, the record shows endpoint-specific participant counts, but the posted information does not explain how missing observations or unevaluable participants were handled.
Interim analyses and stopping rules are not reported in the registry record. The statistical analysis plan, sample-size justification, and assumptions used in the original design are also not reported. These omissions do not invalidate the posted estimates, but they restrict assessment of the analysis pathway and of how much evidential weight to assign to multiple comparisons. No unreported design or analysis feature should be inferred from the numerical results alone.
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 |
|---|---|---|---|
| Chemotherapy (Vinflunine, Paclitaxel, or Docetaxel) | 189 | 443 | 42.7% |
| Atezolizumab | 192 | 459 | 41.8% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Chemotherapy (Vinflunine, Paclitaxel, or Docetaxel) | 393 of 443 |
| Atezolizumab | 379 of 459 |
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 |
|---|---|
| Chemotherapy (Vinflunine, Paclitaxel, or Docetaxel) | 417 of 443 |
| Atezolizumab | 413 of 459 |
Most frequent serious adverse event terms
| Event term | Organ system | Chemotherapy (Vinflunine, Paclitaxel, or Docetaxel) | Atezolizumab |
|---|---|---|---|
| Urinary Tract Infection | Infections and infestations | 14 of 443 | 21 of 459 |
| Febrile Neutropenia | Blood and lymphatic system disorders | 22 of 443 | 1 of 459 |
| Sepsis | Infections and infestations | 15 of 443 | 8 of 459 |
| Constipation | Gastrointestinal disorders | 20 of 443 | 2 of 459 |
| Pyrexia | General disorders | 5 of 443 | 17 of 459 |
| Acute Kidney Injury | Renal and urinary disorders | 6 of 443 | 11 of 459 |
| Haematuria | Renal and urinary disorders | 7 of 443 | 10 of 459 |
| Anemia | Blood and lymphatic system disorders | 5 of 443 | 9 of 459 |
| Neutropenia | Blood and lymphatic system disorders | 14 of 443 | 0 of 459 |
| Abdominal Pain | Gastrointestinal disorders | 9 of 443 | 5 of 459 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Chemotherapy (Vinflunine, Paclitaxel, or Docetaxel) | Atezolizumab |
|---|---|---|---|
| Constipation | Gastrointestinal disorders | 163 of 443 | 131 of 459 |
| Fatigue | General disorders | 136 of 443 | 129 of 459 |
| Decreased Appetite | Metabolism and nutrition disorders | 113 of 443 | 135 of 459 |
| Nausea | Gastrointestinal disorders | 137 of 443 | 106 of 459 |
| Anaemia | Blood and lymphatic system disorders | 124 of 443 | 90 of 459 |
| Asthenia | General disorders | 107 of 443 | 92 of 459 |
| Diarrhoea | Gastrointestinal disorders | 94 of 443 | 97 of 459 |
| Pyrexia | General disorders | 62 of 443 | 93 of 459 |
| Urinary Tract Infection | Infections and infestations | 58 of 443 | 84 of 459 |
| Vomiting | Gastrointestinal disorders | 81 of 443 | 55 of 459 |
Serious events with the highest arm-level rate: febrile neutropenia (5.0%), urinary tract infection (4.6%), constipation (4.5%), pyrexia (3.7%), sepsis (3.4%).
The registry reports serious adverse event counts for the chemotherapy and atezolizumab groups. Serious events affected 189 of 443 participants at risk in the chemotherapy group and 192 of 459 at risk in the atezolizumab group. The record also gives counts of participants with other adverse events: 417 of 443 for chemotherapy and 413 of 459 for atezolizumab. These are separate categories in the posted safety record; they should not be added together, since overlap and category definitions are not described in the summary.
The recorded deaths are 393 in the chemotherapy group and 379 in the atezolizumab group. The registry summary does not provide enough context to interpret these death counts as adverse-event-related deaths, nor does it state the relevant timing or attribution. They should not be treated as a comparison of treatment-caused deaths.
The registry lists febrile neutropenia at 5.0%, urinary tract infection at 4.6%, constipation at 4.5%, pyrexia at 3.7%, sepsis at 3.4%, and neutropenia at 3.2% among the most frequent serious terms. The denominator and whether these percentages are treatment-specific are not reported in the registry record. These terms describe reported serious events, not a complete safety profile or evidence about causation. The posted figures do not establish that one treatment is safer than the other.
18. What the Result Does, and Does Not, Mean
The posted results describe overall survival from randomization, along with sponsor-reported hazard ratios and median survival estimates for the full groups and the named immune-cell groups. They show the estimates and their uncertainty as recorded, but do not by themselves explain the biological or clinical reasons for the observed pattern. A median is a group summary, and a hazard ratio is a relative time-to-event summary; neither tells an individual participant what would happen to them.
The confidence intervals matter. The intervals for the two subgroup hazard ratios include 1, while the overall hazard-ratio interval does not. This is a statistical feature of the reported estimates, not a complete statement about the study's prespecified decision rule. The registry record does not describe the multiplicity strategy, subgroup-testing hierarchy, or the analysis details needed to establish confirmatory status for each comparison. The sponsor reports a p-value only for the IC2/3 comparison.
These results do not establish that treatment effects differ between the immune-cell groups. Such a claim would require a direct assessment of interaction, which is not reported in the registry record. Nor do the median estimates alone establish the shape of survival over time or how participants' experiences varied within each group.
The results also do not provide individualized treatment guidance. They are group-level findings from a randomized trial in participants with locally advanced or metastatic urothelial bladder cancer after platinum-containing chemotherapy. The registry record does not provide enough information to assess all aspects of representativeness, later treatment, or the full safety and quality-of-life profile. The appropriate interpretation is therefore bounded: the posted estimates characterize the recorded trial comparisons, but they do not settle every clinical or statistical question about them.
19. Why This Trial Matters Statistically
This trial is statistically informative because it uses random assignment to compare an immunotherapy strategy with investigator-selected chemotherapy in a defined post-platinum setting. Randomization supports a comparison by assigned group, and the ITT definition keeps that comparison tied to assignment even when treatment received may differ. The open-label design is also explicit, which helps readers consider where knowledge of treatment could matter for assessment and care decisions.
The primary endpoint is overall survival, a time-to-event outcome with a clear event definition. The record reports both median survival summaries and hazard ratios, allowing readers to distinguish a typical-location summary from a relative event-rate comparison. The confidence intervals show that these estimates have uncertainty; they should not be reduced to a binary reading of whether a result is notable.
The record also illustrates why subgroup estimates and secondary outcomes require care. The immune-cell subgroup results are not a substitute for a direct interaction analysis, and multiple endpoints raise questions about multiplicity. The registry record does not report the analysis plan needed to resolve those questions. The secondary outcome list spans response, safety, antibody status, pharmacokinetics, and quality of life, but numerical results for several listed outcomes are not reported in the registry record.
Finally, the trial's posted planning illustrations should not be mistaken for its original sample-size justification. They show how hypothetical requirements change with the effect targeted under stated assumptions, while the design assumptions used by the sponsor are not reported. Keeping the randomized comparison, sponsor analysis, secondary signals, and planning illustrations conceptually separate is essential to a sound statistical reading.
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 is incomplete for several details that would help evaluate the primary survival analysis. It does not provide the full statistical analysis plan, the original sample-size justification, the method names for two of the three reported hazard-ratio comparisons, or the proportional-hazards assessment. The Log Rank method is identified only for the IC2/3 comparison. The analysis coding for the hazard ratios is also not explicitly described, limiting a treatment-direction interpretation based on the ratios alone.
The posted record does not report a multiplicity plan or clarify whether the immune-cell subgroup comparisons were prespecified and confirmatory. It does not report an interaction analysis to test whether the treatment association differed across these subgroups. Consequently, the subgroup estimates should be treated as separate summaries rather than evidence of subgroup-specific treatment effects.
The primary outcome timeframe is described as up to approximately 25 months after the first participant enrolled, but detailed follow-up distributions, survival curves, event counts for the comparisons, and censoring rules are not included in the posted information. Missing survival and secondary-outcome data handling is not reported. The registry also does not provide enough detail to evaluate treatment exposure, crossover, adherence, or post-progression care.
The comparator includes three chemotherapy options chosen by the investigator. That makes the comparator a treatment strategy with variable drug selection, and the record does not report the distribution of choices or comparative results by chemotherapy drug. The open-label design may be relevant to assessments and decisions for some outcomes, though overall survival is defined by death from any cause. Finally, numerical results for several listed secondary outcomes are not reported in the registry record, limiting assessment of the broader benefit, safety, and quality-of-life profile.
21. Related Tutorials
22. Related Statistical Calculators
23. Sources
- ClinicalTrials.gov: A Study of Atezolizumab Compared With Chemotherapy in Participants With Locally Advanced or Metastatic Urothelial Bladder Cancer [IMvigor211] — NCT02302807.
- Registry record last updated 2019-08-01; status last verified 2019-07.
- Results first posted 2018-04-11.
- Data retrieved from ClinicalTrials.gov on 2026-11-09.
- Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.
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Use this trial's endpoint as a starting point for deeper study of effect measures, confidence intervals, and sample-size planning.
24. Record Summary
The registry record describes NCT02302807, a completed Phase III, randomized, open-label, multicenter study sponsored by Hoffmann-La Roche. It enrolled 931 participants with locally advanced or metastatic urothelial bladder cancer after progression during or following platinum-containing chemotherapy. Participants were assigned to atezolizumab or investigator-selected vinflunine, paclitaxel, or docetaxel.
The primary outcome was overall survival, defined as time from randomization to death from any cause in the ITT population. The record posts median survival estimates and sponsor-reported hazard ratios for the overall groups and two immune-cell-defined groups. The IC2/3 comparison includes a reported Log Rank method and p-value; p-values and method names for the other hazard-ratio comparisons are not reported.
The record also lists secondary outcomes, with numerical results available for objective response and anti-therapeutic antibodies in the posted information. Results for several other listed secondary outcomes are not reported in the registry record. The original statistical analysis plan, multiplicity approach, missing-data procedures, and original sample-size assumptions are not reported.