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 Pembrolizumab (MK-3475) Versus Paclitaxel, Docetaxel, or Vinflunine for Participants With Advanced Urothelial Cancer (MK-3475-045/KEYNOTE-045) (NCT02256436), a randomized phase 3 study. The primary outcome is Progression-Free Survival (PFS) Per Response Evaluation Criteria in Solid Tumors Version 1.1 (RECIST 1.1) - All Participants.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT02256436 |
| Phase | Phase 3 |
| Condition | Urothelial Cancer |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | None (open label) |
| Enrollment | 542 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Merck Sharp & Dohme LLC |
| Results posted | Yes |
2. Clinical Question
Population
Participants had recurrent or progressive metastatic, or locally advanced and unresectable, urothelial cancer following platinum-based chemotherapy. The primary analysis included all randomized participants, whether or not they received study treatment, and kept them in their assigned treatment group. The registry reports 542 participants enrolled.
Intervention
Participants assigned to pembrolizumab received 200 mg intravenously on Day 1 of each 3-week cycle. The registry describes the possibility of a second course for eligible participants who stopped treatment with stable disease or better and later progressed.
Comparator
The control group received the investigator’s choice of paclitaxel, docetaxel, or vinflunine. These drugs were scheduled intravenously on Day 1 of each 3-week cycle. Eligible participants who progressed could be able to switch to pembrolizumab.
Primary question
The primary endpoint was progression-free survival (PFS), assessed by blinded independent central review using RECIST 1.1. The study description states hypotheses about both overall survival and PFS, but the primary outcome posted in this record is PFS. The statistical comparison reported for this endpoint is a Cox-model hazard ratio; its confidence interval includes 1, so the posted estimate is not precise enough to distinguish clearly between the groups’ event rates.
3. Trial Design
This was a randomized, open-label, parallel-group phase III trial. The registry lists 542 participants and a completed status. The study began on 2014-10-22, and its primary completion date was 2016-09-07. The primary endpoint was assessed through the database cutoff of 07-Sep-2016, described as up to approximately 20 months.
Participants were assigned to pembrolizumab or to a control group in which the investigator chose paclitaxel, docetaxel, or vinflunine. The posted primary analysis includes 270 participants in the pembrolizumab arm and 272 in the control arm. Its population definition includes all randomized participants regardless of whether they received treatment, analyzed according to assigned group. This preserves the randomized comparison in the endpoint analysis.
The trial was not masked. However, PFS under RECIST 1.1 was assessed by blinded independent central review. This distinction matters: participants and treating investigators knew the assigned treatment, while the central review of progression was described as blinded. The record does not report further details of how that blinding was maintained.
The control-arm description permits a switch to pembrolizumab for eligible participants experiencing progression. The pembrolizumab-arm description also permits an eligible second course after stopping with stable disease or better and subsequently progressing. These options are part of the treatment descriptions, but the registry record does not report how many participants used the second-course option. It reports 13 participants in the control-switched-over safety group; that group should not be confused with the randomized control group in the primary PFS analysis.
The record does not report the original sample-size justification, the trial’s planned power, or the detailed statistical analysis plan. Planning illustrations based on observed effects are not evidence of the assumptions used to design this trial.
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: Per protocol, 13 participants randomized to receive Control were switched over to receive Pembrolizumab. Per protocol, response/progression or adverse events that occurred during a non-randomized switch-over or second course of pembrolizumab were not counted towards efficacy or safety outcome measures, respectively. These results are for randomized treatment only.
Overall Study
| Stage | Control | Pembrolizumab |
|---|---|---|
| STARTED | 272 | 270 |
| Treated | 255 | 266 |
| Switched Over to Pembrolizumab | 13 | 0 |
| COMPLETED | 0 | 0 |
| NOT COMPLETED | 272 | 270 |
Reasons for not completing this period:
| Reason | Control | Pembrolizumab |
|---|---|---|
| Adverse Event | 9 | 14 |
| Death | 216 | 208 |
| Lost to Follow-up | 1 | 2 |
| Physician Decision | 1 | 0 |
| Protocol Violation | 0 | 1 |
| Withdrawal by Subject | 26 | 10 |
| Transferred to Extension Study | 11 | 23 |
| Did Not Continue on Extension Study | 8 | 12 |
Analysis population for the primary outcome, as defined in the registry: The analysis population consisted of all randomized participants, regardless of whether or not they received study treatment. Participants were included in the treatment group 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.
| Characteristic | Unit | Control | Pembrolizumab | Total |
|---|---|---|---|---|
| Participants analysed | 272 | 270 | 542 | |
| Age, Continuous | Years | 65.1 (SD 9.2) | 66.0 (SD 10.2) | 65.5 (SD 9.7) |
| Sex: Female, Male: Female | Participants | 70 | 70 | 140 |
| Sex: Female, Male: Male | Participants | 202 | 200 | 402 |
6. Primary Endpoint
The registry lists the primary outcome as Progression-Free Survival (PFS) Per Response Evaluation Criteria in Solid Tumors Version 1.1 (RECIST 1.1) - All Participants, measured over Through primary analysis database cut-off date of 07-Sep-2016 (Up to approximately 20 months).
| Element | Registry entry |
|---|---|
| Result type | Median |
| Measure of spread | 95% Confidence Interval |
| Unit | Months |
| Endpoint classification | Time-to-Event Analysis |
PFS measures the time from randomization until the first documented disease progression or death from any cause, whichever occurs first. It is a time-to-event endpoint: each participant’s follow-up contributes information about how long they remain alive without documented progression, while participants without an event by the analysis cutoff may have censored follow-up.
Progression was assessed under RECIST 1.1 by blinded independent central review. The registry defines progressive disease as at least a 20% increase in the sum of target-lesion diameters, together with an absolute increase of at least 5 mm; appearance of one or more new lesions also qualifies. Central review applies a defined assessment process and, in this trial, was blinded despite the open-label treatment assignment.
The median PFS is the time by which half of the analyzed group has experienced progression or death, under the endpoint definition and analysis. It provides an interpretable summary of event timing, but it does not describe every participant’s experience or the full shape of the event-time distributions. The hazard ratio is a separate summary comparing event rates over follow-up under the Cox model. It is not a ratio of the two medians.
PFS is used in trials because it captures disease progression or death within a defined follow-up period. It does not, by itself, establish an effect on overall survival or describe all aspects of benefit and harm. The registry’s posted primary result concerns PFS, not the overall-survival hypothesis described in the study summary.
7. Results Posted in the Registry
- Control vs Pembrolizumab: hazard ratio 0.98 (95% CI 0.81–1.19), reported p = 0.416 (as reported in the registry).
Hazard ratio: Control vs Pembrolizumab
95% CI: 0.81 to 1.19
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 |
|---|---|---|---|---|
| Objective Response Rate (ORR) Per RECIST 1.1 - Participants With Strongly PD-L1 Positive Tumors | Binary Endpoint | Risk difference | +13.6 pts (3.1 to 24.1) | 98 per arm |
| ORR Per RECIST 1.1 - Participants With PD-L1 Positive Tumors | Binary Endpoint | Risk difference | +14.4 pts (5.1 to 23.7) | 99 per arm |
| ORR Per RECIST 1.1 - All Participants | Binary Endpoint | Risk difference | +10.1 pts (4.0 to 16.2) | 208 per arm |
Objective Response Rate (ORR) Per RECIST 1.1 - Participants With Strongly PD-L1 Positive Tumors
- 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:
- Pembrolizumab: 20.3% (15/74) versus 6.7% (6/90) on control; risk difference 13.6 percentage points (95% CI 3.1 to 24.1), risk ratio 3.04 (1.24–7.44); unadjusted two-proportion z-test p = 0.009.
- Interpretation:
- The 95% confidence interval excludes no difference, so the proportion with the event is statistically higher for Pembrolizumab than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
ORR Per RECIST 1.1 - Participants With PD-L1 Positive Tumors
- 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:
- Pembrolizumab: 22.7% (25/110) versus 8.3% (10/120) on control; risk difference 14.4 percentage points (95% CI 5.1 to 23.7), risk ratio 2.73 (1.37–5.42); unadjusted two-proportion z-test p = 0.002.
- Interpretation:
- The 95% confidence interval excludes no difference, so the proportion with the event is statistically higher for Pembrolizumab than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
ORR Per RECIST 1.1 - All 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:
- Pembrolizumab: 21.1% (57/270) versus 11.0% (30/272) on control; risk difference 10.1 percentage points (95% CI 4.0 to 16.2), risk ratio 1.91 (1.27–2.88); unadjusted two-proportion z-test p = 0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the proportion with the event is statistically higher for Pembrolizumab than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Across the posted secondary objective response rate analyses, the response percentage is higher in the pembrolizumab arm than in the control arm, both in the overall analysis and in the reported PD-L1-positive tumor groups. These outcomes provide a response-focused view that differs from the primary PFS endpoint. They do not overturn or replace the primary PFS result, because response and time to progression or death measure different aspects of the clinical course.
The subgroup analyses concern fewer participants than the all-participant analysis, and their estimates are consequently based on smaller analysis groups. Subgroup findings can be less stable than results from the full randomized population. The registry record does not report whether these groups or their comparisons were designated in a hierarchy for confirmatory testing.
These outcomes are secondary, and multiple endpoints and subgroup analyses create multiplicity: the more comparisons considered, the greater the chance that one appears compelling by chance alone. The registry does not report an adjustment for multiplicity across the posted secondary analyses. Their unadjusted results therefore carry less confirmatory weight than a prespecified primary result with an appropriate analysis plan.
The secondary response pattern can be described alongside the PFS finding, but it should not be treated as a combined test or as proof that the primary endpoint had the same pattern. The record also lists secondary safety outcomes, including adverse events and discontinuations due to adverse events, but the posted information in this analysis is not a complete account of every secondary result.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Number of Participants Who Experienced an Adverse Event (AE)
- Number of Participants Who Discontinued Study Treatment Due to an AE
- Objective Response Rate (ORR) Per RECIST 1.1 - Participants With Strongly PD-L1 Positive Tumors
- ORR Per RECIST 1.1 - Participants With PD-L1 Positive Tumors
- ORR Per RECIST 1.1 - All Participants
- PFS Per Modified RECIST (mRECIST) - Participants With Strongly PD-L1 Positive Tumors
- PFS Per mRECIST - Participants With PD-L1 Positive Tumors
- PFS Per mRECIST - All Participants
9. Statistical Interpretation
The primary PFS medians were 3.3 months in the control arm and 2.1 months in the pembrolizumab arm. The corresponding 95% confidence intervals were 2.3 to 3.5 months and 2.0 to 2.2 months. The sponsor-reported Cox hazard ratio for Control vs Pembrolizumab was 0.98, with a 95% confidence interval from 0.81 to 1.19. The interval spans 1, so the posted estimate is compatible with event rates favoring either group under the reported comparison. It does not provide a clear distinction between the groups on this endpoint.
The median values and hazard ratio summarize different features of follow-up. The median is the point at which half the group has had an event, while the hazard ratio compares event rates across the observed time. Neither number should be interpreted alone as a complete account of the PFS experience. The confidence intervals express uncertainty in the estimates; they are not ranges containing a known treatment effect with certainty.
The secondary response outcomes have a different pattern from the primary PFS result. In the reported overall response analysis and the PD-L1-positive subgroups, the posted response percentages were higher in the pembrolizumab arm than in the control arm. These response analyses use different endpoints and, for subgroup results, different participant subsets from the all-randomized primary PFS analysis. They therefore provide complementary information rather than replacing the primary result.
The response comparisons are secondary analyses, and the registry record does not report a multiplicity adjustment for interpreting them. Their unadjusted results should be treated as less conclusive than a prespecified primary analysis because assessing several outcomes and subgroups increases the opportunity for apparently strong findings by chance. They should not be combined with the PFS estimate as if they were one test or one endpoint.
The record also posts serious and other adverse-event counts, but those are descriptive safety data rather than a randomized efficacy estimate. The safety groups and denominators differ from the primary PFS analysis population, including a separate group of control participants who switched to pembrolizumab. The posted counts do not on their own establish comparative safety across treatment strategies.
Overall, the registry’s primary PFS estimate is near 1 with a confidence interval that includes 1. The secondary response outcomes point in a different direction, but they answer distinct questions and carry the limitations of secondary, multiple analyses. The results describe the posted analyses; they do not establish conclusions about outcomes not reported in the record.
10. Statistical Methods Explained
How to read the median
The primary endpoint is time-to-event data, not a simple yes-or-no outcome measured at one fixed time. The median PFS is the time by which half of the analyzed participants have had progression or death. It is a compact description of event timing. It does not mean that every participant had an event at the median, and it does not show how event rates varied throughout follow-up.
Time-to-event methods can use partial follow-up from participants who have not yet had an event by the cutoff. Such observations are generally treated as censored at their last relevant follow-up rather than counted as events. The record’s primary endpoint definition and cutoff are stated, but its detailed censoring rules are not reported in the registry record.
What the Cox hazard ratio summarizes
The sponsor reported a Cox regression hazard ratio for Control vs Pembrolizumab. In general, a hazard ratio compares the instantaneous event rates between groups over follow-up, conditional on remaining event-free up to that time. A value of 1 represents equal event rates under the comparison’s direction; values on either side indicate different relative rates. The reported value is 0.98, with a 95% confidence interval from 0.81 to 1.19.
A hazard ratio is not the same as a risk ratio, an odds ratio, or the ratio of median PFS times. Its interpretation depends on the group ordering used for the comparison. The registry labels the comparison Control vs Pembrolizumab and reports the hazard ratio as given; the record does not provide additional detail on model covariates. The hazard ratio compresses information across follow-up, so it should be read alongside the medians and their intervals.
In general, a Cox model is commonly used for time-to-event comparisons. Its usual interpretation assumes that the relative hazards are sufficiently stable over time for a single hazard ratio to be meaningful. Whether that assumption was assessed, and what diagnostics were used, are not reported in the registry record.
How the response analyses differ
The secondary objective response rate analyses count participants meeting response criteria and express the result as a percentage. Unlike PFS, this is a binary outcome for the analysis period: a participant is classified as having or not having an objective response under RECIST 1.1. The registry posts results for all participants and for strongly PD-L1-positive and PD-L1-positive tumor groups. Those subgroup analyses involve fewer participants than the full randomized groups.
For a binary endpoint, an unadjusted risk difference compares the two observed proportions by subtraction. The simple recalculations use posted summary counts and are not adjusted for other variables. The sponsor’s reported response comparisons use the Miettinen & Nurminen method. Differences between a simple recalculation and a sponsor analysis can arise because the methods and estimation procedures differ; the sponsor’s analysis is the relevant reported analysis when interpreting its own inferential result.
Unadjusted comparisons do not account for testing multiple endpoints or subgroups. A p-value from one such comparison does not measure the probability that the null hypothesis is true, nor does it convey the size or precision of an effect. Effect estimates and confidence intervals are needed to understand magnitude and uncertainty.
What confidence intervals contribute
A confidence interval gives a range of values compatible with the observed data under the method’s assumptions. In general, a 95% confidence interval is produced by a procedure that would cover the true parameter in 95% of repeated samples under those assumptions. It is not a guarantee that the particular interval contains the true value.
For the primary hazard ratio, the interval includes 1. This indicates that the estimate is not sufficiently precise to rule out equal event rates under the model at the interval’s stated confidence level. The interval also allows values on either side of 1, so the direction and size of a difference remain uncertain. The PFS median intervals describe uncertainty in each group’s median separately; they are not a direct confidence interval for the difference between medians.
Why event counts and over-dispersion matter generally
In general, time-to-event analyses gain information from observed events and their timing, not just from the number enrolled. Participants with shorter follow-up or no event by the cutoff contribute differently from those with an event. In binary-outcome analyses, the number of participants and the outcome frequency both affect precision.
In general, over-dispersion occurs when observed variability is greater than a model’s assumed variability. If it is ignored, standard errors and confidence intervals can be too narrow. The registry record does not report an over-dispersion assessment for these outcomes, and the posted summaries are not enough to infer one.
The record identifies the primary PFS analysis population as all randomized participants analyzed according to assigned group, and identifies blinded independent central review for the RECIST assessment. Further details about missing-data handling, covariate adjustment, interim analyses, and the original statistical plan are not reported in the registry record.
11. Confidence Intervals and Precision
The primary PFS medians are 3.3 months for control, with a 95% confidence interval of 2.3 to 3.5 months, and 2.1 months for pembrolizumab, with a 95% confidence interval of 2.0 to 2.2 months. These intervals describe uncertainty around each group’s median. They do not directly estimate a difference between medians.
The sponsor-reported hazard ratio is 0.98, and its 95% confidence interval is 0.81 to 1.19. The interval includes 1 and spans values on both sides of that reference. Thus, the point estimate alone should not be treated as a precise indication of the comparative event rate. The interval permits materially different interpretations of the relative rate, including little difference.
A confidence interval is not a prediction interval for individual participants, and it does not account automatically for every potential source of bias or uncertainty. Its meaning depends on the statistical method and assumptions. The registry reports the Cox regression method for the hazard ratio and blinded independent central review for PFS assessment, but detailed model diagnostics and other analysis choices are not reported.
The response estimates also have confidence intervals, and their widths reflect uncertainty in those secondary analyses, particularly in the smaller biomarker subgroups. Those intervals should be interpreted in the context of the analyses’ secondary status and the absence of a reported multiplicity adjustment. Precision in an estimate is distinct from whether an outcome is clinically important; the registry record does not establish clinical importance by statistical precision alone.
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 | 0.98 | 76,922 | 102,977 |
| 75% of the observed effect | 0.98 | 136,750 | 183,069 |
| 50% of the observed effect | 0.99 | 307,687 | 411,905 |
The planning illustrations are based on observed effects and are not the original trial’s design calculations. For the time-to-event endpoint, the figures are total event counts, not participants per arm. For the other planning illustrations, the figures are participants per arm.
The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. Each scenario uses the stated fraction of the observed effect as the effect to detect. The time-to-event planning figures use the Schoenfeld approach. The trial’s own original sample-size assumptions and justification are not reported in the registry record.
The 80% power column gives the planning count that, under those assumptions and the selected effect size, would yield an 80% chance of detecting an effect at the specified significance level if that effect were real. The 90% power column uses a higher chance of detection and therefore generally requires more information. These are design illustrations, not a measure of how much power the completed trial had after results were observed.
Each row changes the assumed effect relative to the observed effect. Planning for 75% of the observed effect requires more information than planning for 100%; planning for 50% requires still more. Smaller effects are harder to distinguish from random variation, so they require more participants or more events under otherwise unchanged assumptions. These 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 = 0.980, so ln(HR) = -0.0202.
- d = 4 × (1.96 + 0.842)2 / [ln(0.980)]2 = 76,921.6, rounded up to 76,922 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 <- 0.98 # 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(2256436)
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 = 76,922 (80% power), 102,977 (90% power)
75% of observed effect: events = 136,750 (80% power), 183,069 (90% power)
50% of observed effect: events = 307,687 (80% power), 411,905 (90% power)
Simulated power with 76,922 events: 0.797 (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 107,381 participants in total, with the boundaries below.
| Analysis | Calendar time (months) | Events | Efficacy boundary (z) | Nominal one-sided p | Cumulative alpha spent |
|---|---|---|---|---|---|
| Look 1 | 10.9 | 34,731 | 3.710 | 0.0001 | 0.0001 |
| Look 2 | 19.0 | 69,461 | 2.511 | 0.0060 | 0.0060 |
| Look 3 | 60.0 | 104,192 | 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% | 76,921 | 79,276 | 60.0 |
| Two looks, O'Brien-Fleming | 80% | 77,208 | 79,572 | 60.0 |
| Three looks, O'Brien-Fleming | 80% | 77,902 | 80,286 | 60.0 |
| Three looks, Pocock | 80% | 90,030 | 92,786 | 60.0 |
| Fixed design, one analysis | 90% | 102,976 | 106,128 | 60.0 |
| Two looks, O'Brien-Fleming | 90% | 103,328 | 106,491 | 60.0 |
| Three looks, O'Brien-Fleming | 90% | 104,192 | 107,381 | 60.0 |
| Three looks, Pocock | 90% | 118,857 | 122,495 | 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 | 0.980 | 104,192 | 107,381 |
| 75% of the observed effect | 0.985 | 185,230 | 190,885 |
| 50% of the observed effect | 0.990 | 416,768 | 429,459 |
For context, this trial enrolled 542 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 <- 2.1 # control-arm median, months (converted from the posted unit)
hr <- 0.98 # 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: 48742 p (1-sided) 0.0001
Events: 34731 ~HR at bound 0.9610
Month: 11 P(Cross) if HR=1 0.0001
P(Cross) if HR=0.98 0.0338
IA 2: 67% Z 2.5114
N: 84852 p (1-sided) 0.0060
Events: 69462 ~HR at bound 0.9811
Month: 19 P(Cross) if HR=1 0.0060
P(Cross) if HR=0.98 0.5603
Final Z 1.9930
N: 107382 p (1-sided) 0.0231
Events: 104192 ~HR at bound 0.9877
Month: 60 P(Cross) if HR=1 0.0250
P(Cross) if HR=0.98 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 |
|---|---|---|---|
| Regression, Cox | Hazard Ratio (HR) 0.98 | 0.81 to 1.19 | 0.416 |
For primary PFS, the registry reports the sponsor’s Cox regression hazard ratio directly: 0.98 for Control vs Pembrolizumab, with a 95% confidence interval from 0.81 to 1.19. The posted interpretation uses this reported hazard ratio rather than a simple recalculation from the arm-level medians. A hazard ratio cannot be reconstructed from the medians alone.
The response outcomes include sponsor-reported comparisons using the Miettinen & Nurminen method as well as simple, unadjusted recalculations from posted summary counts. These are different analyses and need not produce identical estimates or intervals. The sponsor’s analysis is the primary reference for the sponsor-reported inferential result; the simple recalculations are descriptive checks based on aggregate figures.
The registry’s discrepancy indicator is false. No discrepancy between a sponsor result and a recalculation is flagged in the record. The response calculations remain unadjusted and do not incorporate a multiplicity adjustment. The record does not report the full model specifications or additional analysis details needed to reproduce every sponsor estimate from participant-level data.
16. Multiplicity, Missing Data and Analysis Populations
Multiplicity arises when a study evaluates more than one endpoint, subgroup, or comparison. Even when each test is conducted using a conventional significance threshold, repeated testing increases the chance of at least one apparently notable result arising by chance. General approaches include prespecifying a testing sequence or adjusting the threshold across comparisons. Which approach is appropriate depends on the trial’s aims and analysis plan.
The registry lists 20 outcome measures and 15 analyses, including a primary PFS endpoint and secondary response and safety outcomes. It does not report a multiplicity adjustment or testing hierarchy for the secondary analyses. Consequently, the secondary results should be treated as exploratory or supportive rather than as independent confirmatory evidence. That description does not alter the values posted; it qualifies how much evidential weight to assign them.
The primary analysis population is stated clearly: all randomized participants, analyzed in the groups to which they were assigned, whether or not they received study treatment. This is an intention-to-treat-style population definition. The record does not report detailed rules for missing endpoint assessments, censoring, or other missing-data handling. Those details can affect time-to-event estimates and cannot be inferred from the arm summaries.
The record also does not report whether interim analyses were planned or conducted, whether any statistical adjustments were made for interim looks, or the original statistical analysis plan. These omissions limit assessment of the complete inferential framework. They do not change the reported endpoint estimates, but they leave uncertainty about how the reported analyses fit into the full prespecified testing strategy.
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 |
|---|---|---|---|
| Control | 104 | 255 | 40.8% |
| Pembrolizumab | 107 | 266 | 40.2% |
| Control Switched Over to Pembrolizumab | 8 | 13 | 61.5% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Control | 230 of 272 |
| Pembrolizumab | 224 of 270 |
| Control Switched Over to Pembrolizumab | 9 of 13 |
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 |
|---|---|
| Control | 237 of 255 |
| Pembrolizumab | 236 of 266 |
| Control Switched Over to Pembrolizumab | 11 of 13 |
Most frequent serious adverse event terms
| Event term | Organ system | Control | Pembrolizumab | Control Switched Over to Pembrolizumab |
|---|---|---|---|---|
| Urinary tract infection | Infections and infestations | 12 of 255 | 12 of 266 | 0 of 13 |
| Pneumonia | Infections and infestations | 8 of 255 | 11 of 266 | 1 of 13 |
| Febrile neutropenia | Blood and lymphatic system disorders | 16 of 255 | 0 of 266 | 0 of 13 |
| Anaemia | Blood and lymphatic system disorders | 7 of 255 | 6 of 266 | 0 of 13 |
| Pyrexia | General disorders | 5 of 255 | 5 of 266 | 2 of 13 |
| Acute kidney injury | Renal and urinary disorders | 6 of 255 | 5 of 266 | 0 of 13 |
| Intestinal obstruction | Gastrointestinal disorders | 8 of 255 | 0 of 266 | 2 of 13 |
| Haematuria | Renal and urinary disorders | 4 of 255 | 6 of 266 | 0 of 13 |
| Constipation | Gastrointestinal disorders | 7 of 255 | 0 of 266 | 0 of 13 |
| Pneumonitis | Respiratory, thoracic and mediastinal disorders | 0 of 255 | 6 of 266 | 1 of 13 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Control | Pembrolizumab | Control Switched Over to Pembrolizumab |
|---|---|---|---|---|
| Fatigue | General disorders | 85 of 255 | 66 of 266 | 3 of 13 |
| Constipation | Gastrointestinal disorders | 79 of 255 | 54 of 266 | 2 of 13 |
| Anaemia | Blood and lymphatic system disorders | 86 of 255 | 45 of 266 | 1 of 13 |
| Nausea | Gastrointestinal disorders | 73 of 255 | 56 of 266 | 2 of 13 |
| Decreased appetite | Metabolism and nutrition disorders | 53 of 255 | 57 of 266 | 4 of 13 |
| Alopecia | Skin and subcutaneous tissue disorders | 100 of 255 | 2 of 266 | 0 of 13 |
| Diarrhoea | Gastrointestinal disorders | 47 of 255 | 43 of 266 | 1 of 13 |
| Asthenia | General disorders | 52 of 255 | 33 of 266 | 0 of 13 |
| Pruritus | Skin and subcutaneous tissue disorders | 15 of 255 | 66 of 266 | 0 of 13 |
| Vomiting | Gastrointestinal disorders | 34 of 255 | 38 of 266 | 0 of 13 |
Serious events with the highest arm-level rate: intestinal obstruction (15.4%), pyrexia (15.4%), colitis (7.7%), nausea (7.7%), vomiting (7.7%).
The safety record separates three groups. In the randomized control safety group, 104 of 255 participants at risk are listed as having a serious adverse event; 237 of 255 are listed for other adverse events, and 230 deaths are reported. In the pembrolizumab safety group, the corresponding figures are 107 of 266 for serious adverse events, 236 of 266 for other adverse events, and 224 deaths.
A separate control-switched-over-to-pembrolizumab group lists 8 of 13 participants with a serious adverse event, 11 of 13 with other adverse events, and 9 deaths. This small, post-switch group is distinct from either randomized treatment group and should not be treated as a randomized comparison.
The listed serious-event terms include intestinal obstruction and pyrexia, each reported at 15.4%, and colitis, nausea, vomiting, and diverticulitis, each at 7.7%. These figures describe reported event terms; the registry summary does not provide enough detail to establish comparative risks for individual events. Differences in denominators and treatment exposure also limit direct comparison of raw counts.
18. What the Result Does, and Does Not, Mean
The primary result describes PFS in the randomized population under the registry’s endpoint definition and analysis cutoff. The reported medians were 3.3 months for control and 2.1 months for pembrolizumab, while the reported Cox hazard ratio was 0.98 with a 95% confidence interval from 0.81 to 1.19. The interval includes 1, so the estimate does not clearly distinguish the groups’ event rates.
This does not mean that the groups are proven equivalent. A confidence interval spanning 1 can reflect uncertainty about the size and direction of a difference. Nor does the result establish that no participant benefited or experienced harm; group summaries cannot describe each individual outcome.
The higher response percentages posted for pembrolizumab in the secondary analyses address a different outcome from PFS. They do not demonstrate that the primary endpoint has the same comparative result, and their interpretation is limited by their secondary status, subgroup sizes, and the lack of a reported multiplicity adjustment.
The results do not establish an effect on overall survival from the primary PFS analysis. Although overall survival appears in the study hypotheses, the primary outcome posted in this record is PFS. The registry information also does not establish the full balance of benefits and harms, the effect in populations outside the enrolled trial population, or the implications for an individual’s care.
Statistically, the most defensible reading is limited to the estimates, uncertainty intervals, populations, and methods recorded. The primary estimate is imprecise for distinguishing the groups, while secondary response analyses show a different descriptive pattern. These findings should be considered separately rather than collapsed into a single claim.
19. Why This Trial Matters Statistically
This trial illustrates why the endpoint, analysis method, and uncertainty measure need to be read together. The medians describe the timing of events at a particular point in each group’s distribution; the Cox hazard ratio summarizes relative event rates over follow-up. They answer related but not identical questions, so one cannot be substituted for the other.
It also shows the importance of distinguishing an open-label treatment assignment from a blinded outcome assessment. Participants and investigators were not masked, while PFS was assessed by blinded independent central review. That separation is relevant when evaluating an endpoint based on recorded disease progression.
The primary estimate and the secondary response results do not have the same evidential status. A trial can post several outcomes that appear to point in different directions because they measure different things, involve different analysis populations, or have different precision. The absence of reported multiplicity procedures makes restraint particularly important when interpreting multiple secondary comparisons.
Finally, planning illustrations based on observed effects should not be confused with the original design or with power calculated after results are known. The registry record does not report the original sample-size rationale. Keeping planning assumptions distinct from observed findings is essential for sound statistical interpretation.
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 primary result is a registry summary rather than a full account of participant-level data and the complete analysis plan. The record reports the Cox method and hazard ratio, but does not report model covariates, proportional-hazards diagnostics, detailed censoring rules, or sensitivity analyses. These omissions limit independent assessment of the time-to-event analysis.
The trial was open-label, although central PFS review was blinded. The record does not describe further procedures for maintaining the central reviewers’ blinding. Treatment switching was permitted for eligible control participants who progressed, and the record reports a separate switched-over safety group. The information posted does not quantify the effect of switching on the primary comparison.
The response analyses include biomarker-defined subgroups with smaller populations than the full randomized groups. The record does not report whether all subgroup analyses were prespecified, how multiplicity was handled, or whether a hierarchy governed interpretation. The response results should therefore be read as secondary evidence with uncertainty.
The registry does not report detailed missing-data methods, interim-analysis procedures, or the original sample-size justification. Nor do the posted adverse-event counts alone provide a complete comparative safety analysis, particularly because treatment exposure and analysis denominators may differ. These limitations concern what can be established from the registry record; they do not negate the reported values.
21. Related Tutorials
22. Related Statistical Calculators
23. Sources
- ClinicalTrials.gov: A Study of Pembrolizumab (MK-3475) Versus Paclitaxel, Docetaxel, or Vinflunine for Participants With Advanced Urothelial Cancer (MK-3475-045/KEYNOTE-045) — NCT02256436.
- Registry record last updated 2021-09-20; status last verified 2021-08.
- Results first posted 2017-08-31.
- 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
NCT02256436 is a completed randomized, open-label, parallel-group phase III trial of pembrolizumab versus investigator’s choice of paclitaxel, docetaxel, or vinflunine in advanced urothelial cancer following platinum-based chemotherapy. The registry reports 542 participants enrolled.
The primary endpoint was PFS by RECIST 1.1, assessed by blinded independent central review. The reported medians were 3.3 months for control and 2.1 months for pembrolizumab. The sponsor-reported Cox hazard ratio for Control vs Pembrolizumab was 0.98, with a 95% confidence interval of 0.81 to 1.19.
Secondary response analyses show higher posted response percentages in the pembrolizumab arm, but are distinct from the primary endpoint and lack a reported multiplicity adjustment. The record does not report the original sample-size justification, detailed missing-data procedures, interim analyses, or the full statistical analysis plan.