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 Study of Pembrolizumab (MK-3475) vs Standard Therapy in Participants With Microsatellite Instability-High (MSI-H) or Mismatch Repair Deficient (dMMR) Stage IV Colorectal Carcinoma (MK-3475-177/KEYNOTE-177) (NCT02563002), a randomized phase 3 study. The primary outcome is Progression-Free Survival (PFS) Per RECIST1.1 As Assessed by Central Imaging Vendor.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT02563002 |
| Phase | Phase 3 |
| Condition | Colorectal Carcinoma |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | None (open label) |
| Enrollment | 307 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Merck Sharp & Dohme LLC |
| Results posted | Yes |
2. Clinical Question
The clinical question concerns participants with stage IV colorectal carcinoma whose tumours were MSI-H or dMMR. The study compared pembrolizumab with standard chemotherapy selected by the investigator. Its primary hypothesis addressed whether pembrolizumab would prolong progression-free survival or overall survival relative to standard chemotherapy; the primary outcome reported in the registry record is progression-free survival.
Population
Participants with stage IV MSI-H or dMMR colorectal carcinoma. The primary outcome population is all randomized participants.
Intervention
Pembrolizumab, described as 200 mg intravenously on Day 1 of each 21-day cycle for up to 35 treatments. The record also describes the possibility of a second course for eligible participants after stopping the initial course.
Comparator
Investigator’s choice of 1 of 6 standard chemotherapy regimens. The listed drug names include mFOLFOX6, FOLFIRI, bevacizumab and cetuximab, including combinations.
Primary question
How did progression-free survival compare between the randomized treatment groups, using progression or death as the endpoint event?
The registry reports 307 enrolled participants. The primary result lists 153 participants in the pembrolizumab group and 154 in the standard-of-care group. This is a comparison of treatment strategies in the specified tumour and disease population; it does not directly answer questions about other colorectal cancer populations or other treatment settings.
The registry’s brief summary also names overall survival as part of the study hypothesis, but an overall-survival result is not reported in the registry record. The quantitative interpretation therefore focuses on the reported progression-free survival result, while treating other outcomes as supporting context rather than substituting them for the primary endpoint.
3. Trial Design
This was a Phase III, randomized, parallel-group study with no masking reported. Participants were assigned to pembrolizumab or standard of care. The registry lists 307 enrolled participants and identifies all randomized participants as the population for the primary outcome. The result entries list 153 participants for pembrolizumab and 154 for standard of care.
The pembrolizumab arm received 200 mg intravenously on Day 1 of each 21-day cycle for up to 35 treatments. The registry describes a potential second course for participants who stopped the initial course with stable disease and then progressed after discontinuation. The standard-of-care arm allowed the investigator to choose 1 of 6 chemotherapy regimens. The named drugs include mFOLFOX6, FOLFIRI, bevacizumab and cetuximab. The registry’s description of the possible regimens is not complete enough to reconstruct all six options in detail.
The study began on 2015-11-30, reached primary completion on 2021-02-19, and has a completed status in the registry. The primary endpoint timeframe is listed as up to approximately 59 months. These dates describe the registry record and do not, by themselves, establish when every participant was followed or when each endpoint event occurred.
Randomization supports a comparison of the assigned groups, while the parallel design means participants were assigned to a treatment group rather than crossing over as part of the initial comparison. The record separately lists groups who switched from standard of care to pembrolizumab and groups receiving a second course for safety reporting. Those later-treatment groups should not be treated as additional randomized arms in the primary efficacy comparison.
The registry record does not report the original sample-size justification, planned interim analyses, or the detailed statistical analysis plan. Those items should not be inferred from the number enrolled, the observed results, or the planning illustrations based on the observed effect.
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: Of the 307 participants randomized in the study, 296 participants received study medication and were evaluable for safety analyses.
Overall Study
| Stage | Pembrolizumab | Standard of Care (SOC) |
|---|---|---|
| STARTED | 153 | 154 |
| Treated | 153 | 143 |
| Received Second Course of Pembrolizumab | 12 | 5 |
| Switched Over to Pembrolizumab | 0 | 7 |
| COMPLETED | 0 | 0 |
| NOT COMPLETED | 153 | 154 |
Reasons for not completing this period:
| Reason | Pembrolizumab | Standard of Care (SOC) |
|---|---|---|
| Death | 72 | 87 |
| Lost to Follow-up | 5 | 0 |
| Physician Decision | 0 | 2 |
| Withdrawal by Subject | 2 | 10 |
| Sponsor decision | 74 | 55 |
Analysis population for the primary outcome, as defined in the registry: All randomized participants
5. Baseline Characteristics
The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.
Population: All randomized participants
| Characteristic | Unit | Pembrolizumab | Standard of Care (SOC) | Total |
|---|---|---|---|---|
| Participants analysed | 153 | 154 | 307 | |
| Age, Continuous | Years | 61.9 (SD 14.9) | 60.6 (SD 14.8) | 61.2 (SD 14.8) |
| Sex: Female, Male: Female | Participants | 82 | 72 | 154 |
| Sex: Female, Male: Male | Participants | 71 | 82 | 153 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 11 | 10 | 21 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 128 | 131 | 259 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 14 | 13 | 27 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 0 | 0 | 0 |
| Race (NIH/OMB): Asian | Participants | 24 | 26 | 50 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 0 | 0 | 0 |
| Race (NIH/OMB): Black or African American | Participants | 9 | 5 | 14 |
| Race (NIH/OMB): White | Participants | 113 | 116 | 229 |
| Race (NIH/OMB): More than one race | Participants | 0 | 0 | 0 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 7 | 7 | 14 |
6. Primary Endpoint
The registry lists the primary outcome as Progression-Free Survival (PFS) Per RECIST1.1 As Assessed by Central Imaging Vendor, measured over Up to approximately 59 months.
| Element | Registry entry |
|---|---|
| Result type | Median |
| Measure of spread | 95% Confidence Interval |
| Unit | Months |
| Endpoint classification | Time-to-Event Analysis |
The primary endpoint is progression-free survival (PFS), measured in months. It is defined as the time from randomization to the first documented disease progression or death from any cause, whichever occurs first. Progression was assessed under RECIST 1.1 by a blinded central imaging vendor. The registry defines progression as an increase of at least 20% in the sum of target-lesion diameters, with an absolute increase of at least 5 mm also required; the appearance of one or more new lesions also qualifies.
PFS is a time-to-event endpoint: it uses both whether an event occurred and how long participants remained without an event. Combining progression and death gives a measure of time until the disease worsens by the stated imaging criteria or death occurs. Central imaging review provides a common assessment process across the groups. The registry describes that central review as blinded, although the study itself is listed as having no masking.
The reported summaries include a median PFS for each group and a hazard ratio for the comparison. A median describes the time by which the estimated event-free proportion has reached the midpoint; it does not describe every participant’s experience. The hazard ratio summarizes the relative event rate over follow-up under the model used. These measures answer related but different questions, so the medians and hazard ratio should be interpreted together rather than treated as interchangeable.
The endpoint does not measure overall survival alone, tumour response alone, or quality of life. Overall survival results are not reported in the registry record.
7. Results Posted in the Registry
- Pembrolizumab vs Standard of Care (SOC): hazard ratio 0.59 (95% CI 0.45–0.79), reported p < 0.001 (as reported in the registry).
Hazard ratio: Pembrolizumab vs Standard of Care (SOC)
95% CI: 0.45 to 0.79
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 |
|---|---|---|---|---|
| Overall Response Rate (ORR) Per RECIST1.1 as Assessed by Central Imaging Vendor | Binary Endpoint | Risk difference | +12.0 pts (1.1 to 22.8) | 260 per arm |
Overall Response Rate (ORR) Per RECIST1.1 as Assessed by Central Imaging Vendor
- 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: 45.1% (69/153) versus 33.1% (51/154) on control; risk difference 12.0 percentage points (95% CI 1.1 to 22.8), risk ratio 1.36 (1.02–1.81); unadjusted two-proportion z-test p = 0.031.
- 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.
The secondary outcomes span tumour response and treatment-related safety reporting. Overall response rate provides a binary response summary that is related to tumour activity but differs from PFS, which incorporates time to progression or death. The registry also lists the number of participants experiencing an adverse event and the number discontinuing study treatment due to an adverse event. These outcomes address different aspects of the trial and should not be treated as substitutes for the primary endpoint.
The response result is directionally consistent with the PFS comparison in the sense that the reported response percentage is higher in the pembrolizumab group. That descriptive alignment does not make response and PFS the same outcome, nor does it independently confirm a time-to-event effect. Response is assessed as a classification; PFS records the time to progression or death. The estimands, assessment processes and uncertainty measures differ.
Secondary outcomes are often evaluated alongside a primary endpoint, creating multiple opportunities to observe a result that appears notable by chance. Whether and how that multiplicity was controlled is not reported in the registry record. The response p-value from the unadjusted recalculation is therefore not a multiplicity-adjusted confirmatory result. The sponsor’s reported response analysis is also secondary to the primary PFS analysis, and the registry does not report an overall testing strategy for interpreting the full set of endpoints.
Safety outcomes contribute descriptive evidence about events observed during treatment, but comparisons across safety groups require attention to exposure, follow-up, and group definition. Some safety groups represent participants after switching treatment or receiving a second course. They do not have the same status as the original randomized groups. The registry record does not report enough detail to reconstruct exposure-adjusted comparisons or to establish that all secondary analyses were prespecified.
Accordingly, the secondary outcomes add context about response and safety but should be interpreted in light of their distinct definitions, uncertainty and multiplicity. They do not establish the unreported overall-survival result or replace the primary PFS comparison.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Overall Response Rate (ORR) Per RECIST1.1 as Assessed by Central Imaging Vendor
- Number of Participants Who Experienced an Adverse Event (AE)
- Number of Participants Who Discontinued Study Treatment Due to an AE
9. Statistical Interpretation
The registry reports median PFS of 16.5 months for pembrolizumab, with a 95% confidence interval from 5.4 to 38.1 months, and 8.2 months for standard of care, with a 95% confidence interval from 6.1 to 10.2 months. The reported hazard ratio for pembrolizumab versus standard of care is 0.59, with a 95% confidence interval from 0.45 to 0.79. The registry reports p < 0.001 for the comparison.
In general, a hazard ratio compares event rates over follow-up under the fitted time-to-event model. A value below 1 indicates that the estimated event hazard in the pembrolizumab group was lower than in the standard-of-care group under that model. It is not a ratio of median survival times, and it should not be converted into a percentage change without a separate calculation. The result is an estimate for the randomized groups and the endpoint definition in this record.
The median estimates are not equally precise. The confidence interval for pembrolizumab spans from 5.4 to 38.1 months, while the interval for standard of care spans from 6.1 to 10.2 months. The hazard-ratio interval lies from 0.45 to 0.79. Confidence intervals represent uncertainty in estimated quantities, not the range of outcomes that every participant experienced. Their width is relevant when judging how precisely the registry estimates the typical event time and relative hazard.
The reported p-value is evidence against the null hypothesis used for the comparison, conditional on the analysis and its assumptions. It is not the probability that the null hypothesis is true, nor does it quantify the size or clinical importance of the difference. The estimated hazard ratio and its confidence interval provide information about the magnitude and precision of the comparison; the p-value addresses a different question.
The secondary overall response result reports 45.1% for pembrolizumab, with a 95% confidence interval from 37.1% to 53.3%, and 33.1% for standard of care, with a 95% confidence interval from 25.8% to 41.1%. This outcome concerns response under RECIST 1.1 and is not the same as time to progression or death. Its interpretation is secondary to the primary PFS result, particularly because the registry record does not report a multiplicity adjustment for secondary testing.
These data describe the registry’s reported analyses; they do not establish effects in people outside the trial’s specified population. The registry lists the primary population as all randomized participants, but details such as missing-data handling and the treatment of every analysis population are not reported in the registry record. No conclusion about overall survival can be drawn from the absent overall-survival results.
10. Statistical Methods Explained
The primary outcome is time to an event, where the event is progression by RECIST 1.1 or death from any cause. Time-to-event methods are useful when participants can have different follow-up durations and when some participants have not had an event by the end of their observed follow-up. In general, methods for this type of data use the timing of events and account for participants who are event-free at their last known follow-up, rather than treating those participants as if an event occurred at that time. The exact censoring rules and missing-data procedures are not reported in the registry record.
What does a median PFS estimate describe?
A median time-to-event estimate is the point at which the estimated event-free proportion reaches its midpoint. It is a summary of the event-time distribution, not an average and not a prediction for an individual participant. The registry gives median PFS values for both groups with 95% confidence intervals. Because the confidence interval for the pembrolizumab median is broad, that median estimate has substantial uncertainty. The interval is an uncertainty statement about the estimated median, not a statement that all individual event times fall within its limits.
What does the hazard ratio describe?
A hazard ratio compares the event hazards in the two groups over follow-up under a time-to-event model. The registry reports a hazard ratio of 0.59 for pembrolizumab versus standard of care, with a 95% confidence interval from 0.45 to 0.79. A hazard ratio below 1 indicates a lower estimated event hazard in the first-named group under the comparison as reported. The hazard ratio is not a difference in months and does not mean that each participant’s event time changes by the same amount.
The registry describes a Cox proportional hazards model with Efron’s method for handling tied event times and a single treatment covariate for the first-course study treatment. The proportional-hazards model summarizes the treatment comparison through a hazard ratio and assumes that the relative hazards are proportional over time. Whether that assumption was assessed, and what diagnostic results were obtained, are not reported in the registry record. Efron’s method is a way to handle tied event times in the model; it does not change the endpoint definition.
What is the role of the log-rank method?
The registry lists Log Rank as the method for the reported hazard-ratio comparison and gives p < 0.001. The log-rank test compares event-time patterns between groups while accounting for the timing of events and censoring. It tests a null hypothesis of no group difference under the test’s framework. A p-value does not measure the probability that the null is true, and it does not describe the magnitude or precision of the effect. The hazard ratio and confidence interval complement the test by giving an estimated direction, magnitude and uncertainty.
The record also identifies a Cox model for the hazard ratio presentation. The registry does not give enough detail to resolve every implementation choice or to describe all diagnostics, stratification factors, or sensitivity analyses. Those details are not reported in the registry record and should not be inferred from the method labels alone.
How should the response outcome be understood?
Overall response rate is a binary outcome: participants are classified according to whether they meet the response criteria during the assessment period. The registry reports percentages and 95% confidence intervals for each randomized group. It also reports a sponsor analysis using the Miettinen & Nurminen method for the difference in percentage. The unadjusted recalculation from the posted summary statistics uses a risk difference and gives a separate confidence interval and p-value. These calculations use different stated methods, so small differences in estimates or inferential results need not indicate an error.
For binary outcomes, the risk difference expresses the difference between the groups’ response proportions. A confidence interval around that difference describes uncertainty in the estimated contrast. The recalculated p-value is unadjusted and should not be treated as a replacement for the sponsor’s reported analysis. The sponsor’s analysis is the registry’s own inferential result for that endpoint.
Why does over-dispersion matter in general?
Over-dispersion is a general issue for count data when the observed variability exceeds what a simple model assumes. It can make standard errors too small if the model does not allow for the extra variability. The primary endpoint is time-to-event, and the response endpoint is binary; the registry does not identify an over-dispersion adjustment for these analyses. This general concept should not be mistaken for a reported feature of this trial.
What are the limits of the analysis descriptions?
The primary population is stated as all randomized participants. The record does not report full analysis-set definitions, handling of missing endpoint assessments, censoring details, sensitivity analyses, or the original statistical plan. It also does not report whether interim analyses were conducted. A method description identifies some tools used for the reported comparison, but it does not supply a complete account of design assumptions and analytic decisions.
11. Confidence Intervals and Precision
Precision concerns how narrowly a result is estimated, not whether the result is important or whether it should guide care. A confidence interval gives a range of values compatible with the data and the method used, under the confidence-interval procedure’s assumptions. It is not a guarantee that the true value is within the interval, nor does it describe the range of individual outcomes.
For median PFS, the pembrolizumab estimate is 16.5 months with a 95% confidence interval from 5.4 to 38.1 months. The standard-of-care estimate is 8.2 months with a 95% confidence interval from 6.1 to 10.2 months. The interval around the pembrolizumab estimate is broad, which signals considerable uncertainty in the location of that median. The standard-of-care interval is narrower, though it too remains an estimate rather than a fixed value.
The hazard ratio is 0.59, with a 95% confidence interval from 0.45 to 0.79. The interval lies below 1, and its range indicates uncertainty about the size of the relative hazard estimate. It does not describe the absolute change in PFS months, and it should not be read as an individual-level prediction. The reported p-value of < 0.001 addresses the test’s compatibility with a null comparison; it does not make the confidence interval narrower or eliminate uncertainty.
For overall response rate, the registry reports 45.1% with a 95% confidence interval from 37.1% to 53.3% for pembrolizumab, and 33.1% with a 95% confidence interval from 25.8% to 41.1% for standard of care. The reported sponsor confidence interval for the difference in percentage is from 1.0 to 22.6. These intervals are tied to their respective estimands and methods. A confidence interval for a group percentage is not interchangeable with an interval for the difference between groups.
Precision depends on the amount and distribution of outcome information, not simply the number enrolled. For PFS, event timing and follow-up contribute to the estimate. Event counts and detailed follow-up distributions are not reported in the registry record in the outcome information, so precision should be judged from the reported intervals rather than guessed from enrollment 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 | 0.59 | 113 | 151 |
| 75% of the observed effect | 0.67 | 201 | 269 |
| 50% of the observed effect | 0.77 | 452 | 604 |
The sample-size illustrations are planning calculations based on the observed effects, not the trial’s original design calculation. For the PFS comparison, the figures are total events, not participants per arm. For the response comparison, the figures are participants per arm. Each row considers planning for 100%, 75%, or 50% of the observed effect, and the columns describe the number of events or participants associated with 80% or 90% power under the stated assumptions.
Power is the probability, under a particular assumed effect and analysis framework, of rejecting the null hypothesis when that effect is true. The 80% power column therefore describes a planning target with an 80% chance of detecting the specified effect under the assumptions; the 90% column uses a higher chance target. These are design illustrations, not guarantees about a future study’s result.
The stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. For the time-to-event illustrations, the calculation uses the Schoenfeld approach and reports total events. For the other illustrations, it reports participants per arm. The effect to detect is the stated fraction of the observed effect. The original trial’s own sample-size assumptions and justification are not reported in the registry record.
Smaller effects are harder to distinguish from random variation and therefore require more events or participants under these planning assumptions. The illustrations use the observed effect as their reference, so they should not be read as independent evidence about what effect a future trial will find. This is not observed power; it is a planning illustration based on the estimated effect and stated assumptions.
The figures do not account for unreported design features such as the trial’s original interim-analysis plan or any original allowance for missing observations. Those features should not be assumed from the planning calculations.
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 = 0.590, so ln(HR) = -0.5276.
- d = 4 × (1.96 + 0.842)2 / [ln(0.590)]2 = 112.8, rounded up to 113 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 <- 0.59 # 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(2563002)
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 = 113 (80% power), 151 (90% power)
75% of observed effect: events = 201 (80% power), 269 (90% power)
50% of observed effect: events = 452 (80% power), 604 (90% power)
Simulated power with 113 events: 0.818 (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 183 participants in total, with the boundaries below.
| Analysis | Calendar time (months) | Events | Efficacy boundary (z) | Nominal one-sided p | Cumulative alpha spent |
|---|---|---|---|---|---|
| Look 1 | 17.3 | 50 | 3.710 | 0.0001 | 0.0001 |
| Look 2 | 27.4 | 101 | 2.511 | 0.0060 | 0.0060 |
| Look 3 | 60.0 | 151 | 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% | 112 | 135 | 60.0 |
| Two looks, O'Brien-Fleming | 80% | 112 | 135 | 60.0 |
| Three looks, O'Brien-Fleming | 80% | 113 | 136 | 60.0 |
| Three looks, Pocock | 80% | 131 | 157 | 60.0 |
| Fixed design, one analysis | 90% | 150 | 180 | 60.0 |
| Two looks, O'Brien-Fleming | 90% | 150 | 181 | 60.0 |
| Three looks, O'Brien-Fleming | 90% | 151 | 183 | 60.0 |
| Three looks, Pocock | 90% | 173 | 208 | 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 | 0.590 | 151 | 183 |
| 75% of the observed effect | 0.673 | 270 | 319 |
| 50% of the observed effect | 0.768 | 610 | 709 |
For context, this trial enrolled 307 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 <- 8.2 # control-arm median, months (converted from the posted unit)
hr <- 0.59 # 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: 132 p (1-sided) 0.0001
Events: 51 ~HR at bound 0.3519
Month: 17 P(Cross) if HR=1 0.0001
P(Cross) if HR=0.59 0.0338
IA 2: 67% Z 2.5114
N: 184 p (1-sided) 0.0060
Events: 101 ~HR at bound 0.6066
Month: 27 P(Cross) if HR=1 0.0060
P(Cross) if HR=0.59 0.5603
Final Z 1.9930
N: 184 p (1-sided) 0.0231
Events: 152 ~HR at bound 0.7233
Month: 60 P(Cross) if HR=1 0.0250
P(Cross) if HR=0.59 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) 0.59 | 0.45 to 0.79 | < 0.001 |
For PFS, the registry reports the sponsor’s comparison as a hazard ratio of 0.59, with a 95% confidence interval from 0.45 to 0.79 and p < 0.001. The registry labels the comparison method Log Rank and describes a Cox proportional hazards model with Efron’s method for tied times and a single treatment covariate. These are the reported inferential results for the primary endpoint; no separate recalculated PFS comparison is listed.
For overall response rate, the sponsor’s reported analysis uses the Miettinen & Nurminen method and reports a difference in percentage of 12.0, with a 95% confidence interval from 1.0 to 22.6 and p = 0.016. The unadjusted recalculation from the posted summary statistics gives a risk difference of 0.120, with a 95% confidence interval from 0.011 to 0.228 and p = 0.031. The recalculation uses a different stated approach from the sponsor analysis, so the estimates and p-values are not expected to be identical in every detail.
The registry record does not flag a discrepancy. The recalculation is a simple, unadjusted check based on summary statistics; it does not replace the sponsor’s analysis, its chosen method, or any adjustment that may be part of a fuller analysis. The sponsor’s reported result remains the appropriate reference for what the registry says the trial analysis found. The methods and the estimands should be considered before interpreting differences between the two presentations.
16. Multiplicity, Missing Data and Analysis Populations
Multiplicity arises when several outcomes, comparisons, or analyses are examined. Even when each individual test uses a conventional significance threshold, conducting multiple tests can increase the chance that at least one result appears statistically notable by chance. A prespecified testing hierarchy or adjustment procedure can address this issue, but the approach must be known to interpret secondary p-values as part of a confirmatory strategy.
The registry lists PFS as the primary outcome and overall response rate and adverse-event outcomes among the secondary outcomes. It reports a primary PFS comparison and a sponsor analysis for response, but a multiplicity adjustment or gatekeeping procedure is not reported in the registry record. It is also not reported whether all secondary outcomes were prespecified in the same analysis plan or whether additional analyses were conducted. Consequently, the response result can be described as a secondary finding, but its p-value should not be treated as establishing a multiplicity-controlled claim.
Missing data can affect both time-to-event and binary outcomes. In general, time-to-event analyses require rules for censoring participants whose event status is not observed through the end of follow-up, while binary analyses need a rule for participants whose response assessment is unavailable. The registry record does not report detailed censoring rules, missing-data methods, or sensitivity analyses for these endpoints. No assumptions about those procedures should be inferred from the outcome estimates alone.
The primary outcome population is stated as all randomized participants. That identifies the stated population but does not fully describe the analysis set, treatment of protocol deviations, or handling of post-randomization events. The registry record does not report those details. It also does not report whether interim analyses occurred, whether any statistical stopping boundaries were used, or how an interim plan would have affected the final analysis.
These omissions limit assessment of the full inferential framework, especially for secondary outcomes and missing observations. They do not change the values reported for the primary comparison, but they mean the registry record alone cannot establish how multiplicity, missingness, or all analysis-population decisions were handled.
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 |
|---|---|---|---|
| Pembrolizumab First Course | 62 | 153 | 40.5% |
| Standard of Care (SOC) First Course | 76 | 143 | 53.1% |
| SOC Switched Over to Pembrolizumab | 27 | 57 | 47.4% |
| Pembrolizumab Second Course | 3 | 12 | 25.0% |
| SOC Switched Over to Pembrolizumab-Second Course | 1 | 5 | 20.0% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Pembrolizumab First Course | 68 of 153 |
| Standard of Care (SOC) First Course | 58 of 154 |
| SOC Switched Over to Pembrolizumab | 30 of 57 |
| Pembrolizumab Second Course | 4 of 12 |
| SOC Switched Over to Pembrolizumab-Second Course | 2 of 5 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 5% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Pembrolizumab First Course | 145 of 153 |
| Standard of Care (SOC) First Course | 142 of 143 |
| SOC Switched Over to Pembrolizumab | 53 of 57 |
| Pembrolizumab Second Course | 11 of 12 |
| SOC Switched Over to Pembrolizumab-Second Course | 4 of 5 |
Most frequent serious adverse event terms
| Event term | Organ system | Pembrolizumab First Course | Standard of Care (SOC) First Course | SOC Switched Over to Pembrolizumab | Pembrolizumab Second Course | SOC Switched Over to Pembrolizumab-Second Course |
|---|---|---|---|---|---|---|
| Diarrhoea | Gastrointestinal disorders | 4 of 153 | 9 of 143 | 1 of 57 | 0 of 12 | 0 of 5 |
| Abdominal pain | Gastrointestinal disorders | 7 of 153 | 2 of 143 | 2 of 57 | 0 of 12 | 0 of 5 |
| Small intestinal obstruction | Gastrointestinal disorders | 2 of 153 | 5 of 143 | 3 of 57 | 0 of 12 | 0 of 5 |
| Acute kidney injury | Renal and urinary disorders | 3 of 153 | 2 of 143 | 3 of 57 | 0 of 12 | 1 of 5 |
| Febrile neutropenia | Blood and lymphatic system disorders | 1 of 153 | 6 of 143 | 0 of 57 | 0 of 12 | 0 of 5 |
| Pneumonia | Infections and infestations | 3 of 153 | 2 of 143 | 2 of 57 | 0 of 12 | 0 of 5 |
| Pulmonary embolism | Respiratory, thoracic and mediastinal disorders | 1 of 153 | 4 of 143 | 1 of 57 | 0 of 12 | 0 of 5 |
| Ileus | Gastrointestinal disorders | 1 of 153 | 3 of 143 | 1 of 57 | 0 of 12 | 0 of 5 |
| Vomiting | Gastrointestinal disorders | 1 of 153 | 4 of 143 | 0 of 57 | 0 of 12 | 0 of 5 |
| Colitis | Gastrointestinal disorders | 3 of 153 | 0 of 143 | 1 of 57 | 0 of 12 | 0 of 5 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Pembrolizumab First Course | Standard of Care (SOC) First Course | SOC Switched Over to Pembrolizumab | Pembrolizumab Second Course | SOC Switched Over to Pembrolizumab-Second Course |
|---|---|---|---|---|---|---|
| Diarrhoea | Gastrointestinal disorders | 65 of 153 | 89 of 143 | 17 of 57 | 2 of 12 | 0 of 5 |
| Nausea | Gastrointestinal disorders | 47 of 153 | 85 of 143 | 16 of 57 | 1 of 12 | 0 of 5 |
| Fatigue | General disorders | 58 of 153 | 70 of 143 | 9 of 57 | 2 of 12 | 0 of 5 |
| Vomiting | Gastrointestinal disorders | 33 of 153 | 53 of 143 | 12 of 57 | 0 of 12 | 0 of 5 |
| Decreased appetite | Metabolism and nutrition disorders | 36 of 153 | 57 of 143 | 2 of 57 | 1 of 12 | 0 of 5 |
| Constipation | Gastrointestinal disorders | 26 of 153 | 45 of 143 | 13 of 57 | 0 of 12 | 0 of 5 |
| Abdominal pain | Gastrointestinal disorders | 34 of 153 | 41 of 143 | 8 of 57 | 0 of 12 | 0 of 5 |
| Anaemia | Blood and lymphatic system disorders | 26 of 153 | 33 of 143 | 9 of 57 | 1 of 12 | 0 of 5 |
| Back pain | Musculoskeletal and connective tissue disorders | 25 of 153 | 24 of 143 | 11 of 57 | 1 of 12 | 1 of 5 |
| Headache | Nervous system disorders | 21 of 153 | 22 of 143 | 17 of 57 | 0 of 12 | 0 of 5 |
Serious events with the highest arm-level rate: acute kidney injury (20.0%), adrenal insufficiency (8.3%), covid-19 (8.3%), hypoglycaemia (8.3%), tumour pain (8.3%).
The safety results are counts of participants with at least one serious adverse event and counts of participants with any adverse event, within the named safety groups. For the first-course groups, the serious-event count is 62 among 153 participants at risk for pembrolizumab and 76 among 143 at risk for standard of care. Any adverse event is listed for 145 of 153 and 142 of 143, respectively. The registry also lists safety groups for participants who switched treatment and for second courses; those groups have different numbers at risk and are not the original randomized comparison.
The listed serious-event terms include acute kidney injury at 20.0%, adrenal insufficiency at 8.3%, COVID-19 at 8.3%, hypoglycaemia at 8.3%, tumour pain at 8.3%, and diarrhoea at 6.3%. These are the registry’s listed terms and percentages; the record information does not establish that these terms account for all serious events or provide a causal assessment for an individual event.
Safety counts are descriptive. Differences in the number at risk, treatment exposure, follow-up, switching and second-course eligibility affect how the groups can be compared. The listed deaths should not be interpreted as deaths caused by adverse events or as an overall-survival treatment comparison. Detailed exposure-adjusted safety analyses and causal attribution are not reported in the registry record.
18. What the Result Does, and Does Not, Mean
The registry reports a primary PFS comparison in which the estimated median and hazard ratio favour the pembrolizumab group numerically relative to standard of care. The hazard-ratio confidence interval lies below 1, and the reported p-value is < 0.001. These statements describe the registry’s analysis of randomized groups and the defined endpoint; they are not medical advice and do not establish an individual participant’s likely outcome.
The estimates do not mean that every participant in one group experienced a longer PFS time than every participant in the other. The medians summarize the groups, and the hazard ratio summarizes a relative event hazard under the model. The broad interval around the pembrolizumab median indicates that the median estimate is uncertain. Neither a median nor a hazard ratio captures every dimension of benefit, burden or risk.
The registry’s hypothesis mentions PFS or overall survival, but an overall-survival result is not reported in the registry record. Thus the PFS result cannot be presented as an overall-survival finding. The secondary response outcome provides a separate measure and does not replace PFS. Safety counts also require cautious interpretation because the reported groups include treatment switches and second courses as well as first-course groups.
The study population is limited to participants with stage IV MSI-H or dMMR colorectal carcinoma. The results do not automatically extend to other tumour biomarker groups, disease stages, populations, or treatment settings. The standard-of-care group also represents investigator choice among 1 of 6 possible regimens, rather than a comparison with a single uniform chemotherapy regimen.
The record does not report all design and analysis details needed to assess every assumption, including the original sample-size justification, missing-data procedures, multiplicity strategy, or interim analyses. These limitations do not erase the posted estimates, but they constrain what can be concluded from the registry record alone.
19. Why This Trial Matters Statistically
This trial is statistically informative because it compares randomized treatment groups in a defined biomarker-selected population and reports a time-to-event primary outcome. Random allocation is intended to support a fair comparison of assigned strategies, while central imaging review under RECIST 1.1 provides a specified basis for classifying progression. The primary endpoint also includes death from any cause, so the event definition is broader than imaging progression alone.
The result illustrates why multiple summaries are useful. Median PFS describes a point in the event-time distribution, while the hazard ratio compares event hazards under a model. Their confidence intervals communicate uncertainty, and the reported p-value addresses compatibility with a null comparison. None of these measures alone gives a complete account of treatment effects or participant experience.
The comparator is a strategy rather than one fixed regimen: investigators selected 1 of 6 standard chemotherapy options. That makes the result relevant to the registry’s comparison of pembrolizumab with the specified standard-of-care choice, but it does not isolate a contrast against each individual regimen. The record’s details on the complete set of regimens are limited.
The study also highlights the importance of separating primary and secondary findings. Response rate offers context, while safety outcomes describe events in groups with differing treatment histories. Without a reported multiplicity strategy, secondary results carry less confirmatory weight. The absence of a posted overall-survival result is another reason to keep endpoint-specific conclusions distinct.
Finally, the record demonstrates how registry results can support statistical interpretation while leaving important protocol details unresolved. Sample-size planning based on observed effects is not the same as the original design calculation, and method labels do not reveal every analytic decision. Clear interpretation depends on respecting both the estimates reported and the limits of what the registry documents.
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 standard-of-care arm allowed investigator selection among 1 of 6 possible chemotherapy regimens. The record names mFOLFOX6, FOLFIRI, bevacizumab and cetuximab, but the full regimen descriptions are not available in the registry information. The comparison therefore represents pembrolizumab against a choice of standard regimens, not a single uniform comparator, and the reported result does not identify the effect relative to each possible regimen separately.
The study is listed as having no masking, although central imaging review is described as blinded. These design features are distinct: the record supports noting blinded central imaging assessment, but does not establish masking of participants or investigators. The registry does not report further details about procedures intended to limit bias in other outcome assessments.
The primary median estimate for pembrolizumab has a broad 95% confidence interval, from 5.4 to 38.1 months. This makes the precise location of that median uncertain even though the registry also reports a hazard-ratio comparison. A single summary should not obscure the different precision of the median and relative-hazard estimates.
The registry record does not report overall-survival results, the original sample-size justification, interim-analysis details, missing-data procedures, a multiplicity strategy, or the full statistical analysis plan. It does not provide enough information to assess all model diagnostics, including whether proportional hazards were evaluated. These are specific limits on interpreting the posted results and should not be filled in by assumption.
Safety information includes first-course, switch-over and second-course groups. Those groups differ in treatment history and numbers at risk, so they should not be pooled or read as equivalent randomized comparisons. The listed deaths are not identified as adverse-event deaths or as the primary overall-survival outcome. The record does not report enough information in these summaries to make those interpretations.
21. Related Tutorials
22. Related Statistical Calculators
23. Sources
- ClinicalTrials.gov: Study of Pembrolizumab (MK-3475) vs Standard Therapy in Participants With Microsatellite Instability-High (MSI-H) or Mismatch Repair Deficient (dMMR) Stage IV Colorectal Carcinoma (MK-3475-177/KEYNOTE-177) — NCT02563002.
- Registry record last updated 2024-10-03; status last verified 2024-09.
- Results first posted 2022-03-16.
- Data retrieved from ClinicalTrials.gov on 2026-11-09.
- Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.
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24. Record Summary
The registry describes NCT02563002, a completed Phase III randomized parallel-group study of pembrolizumab versus investigator-selected standard chemotherapy in participants with stage IV MSI-H or dMMR colorectal carcinoma. The record lists 307 enrolled participants and identifies all randomized participants as the primary outcome population.
The primary endpoint is PFS by RECIST 1.1 based on blinded central imaging review, or death from any cause. The reported median PFS is 16.5 months for pembrolizumab and 8.2 months for standard of care. The reported hazard ratio is 0.59, with a 95% confidence interval from 0.45 to 0.79 and p < 0.001.
Overall response rate is reported as a secondary outcome. The registry also lists adverse-event outcomes and safety information for first courses, treatment switches and second courses. Overall-survival results and several design and analysis details are not reported in the registry record.