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 Pemetrexed + Platinum Chemotherapy With or Without Pembrolizumab (MK-3475) in Adults With Tyrosine Kinase Inhibitor- (TKI)-Resistant Epidermal Growth Factor Receptor- (EGFR)-Mutated Metastatic Non-squamous Non-small Cell Lung Cancer (NSCLC) (MK-3475-789/KEYNOTE-789) (NCT03515837), 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).
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT03515837 |
| Phase | Phase 3 |
| Condition | Non-small Cell Lung Cancer |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Quadruple |
| Enrollment | 492 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Merck Sharp & Dohme LLC |
| Results posted | Yes |
2. Clinical Question
Population
Adults with metastatic non-squamous non-small cell lung cancer whose tumors had EGFR mutations and were resistant to tyrosine kinase inhibitor treatment. The registry summary describes TKI failures with T790M-negative tumors, T790M-positive tumors after prior osimertinib exposure, and first-line osimertinib failures regardless of T790M status. The primary outcome population is all randomized participants.
Intervention
Pembrolizumab combined with pemetrexed and platinum chemotherapy. The platinum agent could be carboplatin or cisplatin. The registry describes pembrolizumab 200 mg by intravenous infusion on Day 1 of each 3-week cycle for up to 35 cycles and pemetrexed 500 mg/m^2 by intravenous infusion every 3 weeks, with no restriction on the number of cycles.
Comparator
Saline placebo combined with pemetrexed and platinum chemotherapy, using carboplatin or cisplatin. The registry describes placebo by intravenous infusion on Day 1 of each 3-week cycle for up to 35 cycles. This comparison is intended to isolate the contribution of adding pembrolizumab to the chemotherapy regimen.
Primary question
Does adding pembrolizumab to pemetrexed plus platinum chemotherapy improve progression-free survival compared with saline placebo plus the same chemotherapy? The registry’s primary hypothesis also concerned overall survival. The stated success criterion allowed superiority on either progression-free survival or overall survival; the posted primary result is progression-free survival.
3. Trial Design
KEYNOTE-789 (NCT03515837) is a completed, randomized, parallel-group Phase 3 study sponsored by Merck Sharp & Dohme LLC. The official title describes a double-blind study; the registry lists quadruple masking. The record reports enrollment of 492. It gives a study start date of 2018-06-29 and a primary completion date of 2023-01-17.
The comparison was pembrolizumab plus pemetrexed and platinum chemotherapy versus saline placebo plus pemetrexed and platinum chemotherapy. The registry identifies carboplatin or cisplatin as the platinum options. It describes pembrolizumab at 200 mg by intravenous infusion on Day 1 of each 3-week cycle, for up to 35 cycles, and pemetrexed at 500 mg/m^2 every 3 weeks without restriction on the number of cycles. The placebo arm received saline on Day 1 of each 3-week cycle for up to 35 cycles. The complete platinum dosing descriptions are not reported in the registry record.
The primary outcome was progression-free survival assessed by blinded independent central review using RECIST 1.1. The stated primary hypotheses covered both progression-free survival and overall survival, with success defined as superiority on either outcome. The posted results include the progression-free survival analysis. The registry record describes other outcomes involving objective response, duration of response, quality of life, symptom deterioration and adverse events. On study completion, participants were discontinued and could enroll in a pembrolizumab extension study if available.
4. Participant Flow and Accounting
The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.
Overall Study
| Stage | Pembro + Pemetrexed + Chemo | Placebo + Pemetrexed + Chemo |
|---|---|---|
| STARTED | 245 | 247 |
| Treated | 245 | 246 |
| Switched Over to Pembro Monotherapy | 0 | 50 |
| COMPLETED | 0 | 0 |
| NOT COMPLETED | 245 | 247 |
Reasons for not completing this period:
| Reason | Pembro + Pemetrexed + Chemo | Placebo + Pemetrexed + Chemo |
|---|---|---|
| Death | 219 | 227 |
| Lost to Follow-up | 0 | 1 |
| Withdrawal by Subject | 0 | 4 |
| Participation Was Terminated By Sponsor | 26 | 15 |
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.
| Characteristic | Unit | Pembro + Pemetrexed + Chemo | Placebo + Pemetrexed + Chemo | Total |
|---|---|---|---|---|
| Participants analysed | 245 | 247 | 492 | |
| Age, Continuous | Years | 61.7 (SD 10.9) | 63.1 (SD 10.0) | 62.4 (SD 10.4) |
| Sex: Female, Male: Female | Participants | 152 | 151 | 303 |
| Sex: Female, Male: Male | Participants | 93 | 96 | 189 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 16 | 19 | 35 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 222 | 221 | 443 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 7 | 7 | 14 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 3 | 3 | 6 |
| Race (NIH/OMB): Asian | Participants | 165 | 163 | 328 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 0 | 0 | 0 |
| Race (NIH/OMB): Black or African American | Participants | 2 | 5 | 7 |
| Race (NIH/OMB): White | Participants | 67 | 72 | 139 |
| Race (NIH/OMB): More than one race | Participants | 1 | 0 | 1 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 7 | 4 | 11 |
| Geographic Region: East Asia | Count of Participants | 150 | 150 | 300 |
| Geographic Region: Non-East Asia | Count of Participants | 95 | 97 | 192 |
| Geographic Region: EU | Count of Participants | 53 | 47 | 100 |
| Geographic Region: Non-EU | Count of Participants | 192 | 200 | 392 |
| Geographic Region: US | Count of Participants | 3 | 6 | 9 |
| Geographic Region: Non-US | Count of Participants | 242 | 241 | 483 |
| Programmed Death Ligand 1 (PD-L1) Status: TPS ≥ 50% | Count of Participants | 52 | 51 | 103 |
| Programmed Death Ligand 1 (PD-L1) Status: TPS <50% | Count of Participants | 181 | 185 | 366 |
| Programmed Death Ligand 1 (PD-L1) Status: TPS ≥1% AND ≤49% | Count of Participants | 54 | 72 | 126 |
| Programmed Death Ligand 1 (PD-L1) Status: TPS <1% | Count of Participants | 127 | 113 | 240 |
| Programmed Death Ligand 1 (PD-L1) Status: Not evaluable | Count of Participants | 12 | 11 | 23 |
| Previous use of Tyrosine Kinase Inhibitor (TKI) Treatment History with Osimertinib: Treated with TKI except for Osimertinib | Count of Participants | 128 | 126 | 254 |
| Previous use of Tyrosine Kinase Inhibitor (TKI) Treatment History with Osimertinib: Treated with first line Osimertinib | Count of Participants | 28 | 33 | 61 |
| Previous use of Tyrosine Kinase Inhibitor (TKI) Treatment History with Osimertinib: Treated with second line Osimertinib | Count of Participants | 88 | 88 | 176 |
| Previous use of Tyrosine Kinase Inhibitor (TKI) Treatment History with Osimertinib: Other | Count of Participants | 1 | 0 | 1 |
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), measured over Up to ~40 months.
| Element | Registry entry |
|---|---|
| Result type | Median |
| Measure of spread | 95% Confidence Interval |
| Unit | Months |
| Endpoint classification | Time-to-Event Analysis |
Progression-free survival measures the time from randomization until the first documented progressive disease or death from any cause, whichever occurs first. In this study, progression was assessed by blinded independent central review using RECIST 1.1. The registry definition describes progression as at least a 20% increase in the sum of diameters of target lesions, together with an absolute increase of at least 5 mm; a new lesion also qualifies as progression.
This endpoint combines tumor progression and death into a time-to-event outcome. It can therefore reflect how long participants remain alive without documented progression, rather than counting only whether progression occurred by one selected visit. The registry reports that the analysis used the Kaplan-Meier product-limit method, which accommodates censored observations. Censoring occurs when the event time is not observed during the available follow-up; the method estimates the event-time distribution from the observed follow-up while accounting for such incomplete observation.
Progression-free survival is useful in a randomized cancer study because it directly addresses the timing of progression or death under the assigned treatment strategies. It does not, by itself, establish an effect on overall survival, symptom burden, quality of life or safety. Those questions require their own outcomes and analyses. The registry lists overall survival as a primary hypothesis, but the result discussed in this analysis is progression-free survival.
7. Results Posted in the Registry
- Pembro + Pemetrexed + Chemo vs Placebo + Pemetrexed + Chemo: hazard ratio 0.80 (95% CI 0.65–0.97), reported p = 0.012 (as reported in the registry).
Hazard ratio: Pembro + Pemetrexed + Chemo vs Placebo + Pemetrexed + Chemo
95% CI: 0.65 to 0.97
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 | Binary Endpoint | Risk difference | +1.9 pts (-6.1 to 9.8) | 9,216 per arm |
| Time to True Deterioration (TTD) in the EORTC Questionnaire Composite Endpoint of Cough, Chest Pain or Dyspnea | Time-to-Event Analysis | Hazard ratio | 0.93 (0.68 to 1.27) | 5,962 events |
Objective Response Rate (ORR) Per RECIST 1.1
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Pembro + Pemetrexed + Chemo: 29.0% (71/245) versus 27.1% (67/247) on control; risk difference 1.9 percentage points (95% CI -6.1 to 9.8), risk ratio 1.07 (0.80–1.42); unadjusted two-proportion z-test p = 0.647.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Pembro + Pemetrexed + Chemo and the control. The interval gives the range of effects that remain compatible with the data.
Time to True Deterioration (TTD) in the EORTC Questionnaire Composite Endpoint of Cough, Chest Pain or Dyspnea
- Endpoint type: Time to event: compared as a hazard ratio.
- Test: Hazard ratio as reported by the sponsor; it was not recalculated.
- Result:
- Pembro + Pemetrexed + Chemo vs Placebo + Pemetrexed + Chemo: hazard ratio 0.93 (95% CI 0.68–1.27) (as reported in the registry).
- Interpretation:
- The 95% confidence interval includes no difference (a ratio of 1), so these data do not show a statistically significant difference between Pembro + Pemetrexed + Chemo vs Placebo + Pemetrexed + Chemo and the control. The interval gives the range of effects that remain compatible with the data.
The secondary outcomes extend the assessment beyond progression-free survival. They include objective response and duration of response, patient-reported quality-of-life measures, time to true deterioration in cough, chest pain or dyspnea, and adverse-event outcomes. The registry lists six secondary outcomes, but the registry entries analyzed include numerical estimates for objective response and the symptom deterioration endpoint; numerical findings for the other listed outcomes are not reported in the registry record.
These outcomes address different aspects of the treatment comparison. Response concerns tumor shrinkage under RECIST 1.1, while symptom deterioration and quality-of-life measures concern participant-reported experience. Safety outcomes concern harms. They can add context to the primary progression-free survival result, but none is a replacement for it. In particular, a result on tumor progression does not automatically establish a corresponding change in symptoms, quality of life, overall survival or adverse events.
The response estimates are close in the posted group summaries, and the simple unadjusted risk-difference interval includes zero. The reported symptom deterioration hazard-ratio interval also includes 1. These patterns do not provide the same clear statistical signal as the reported primary analysis. The sponsor’s response analysis is presented as a mean difference in final values, which is not the same estimand as the unadjusted binary risk difference.
Secondary endpoints generally carry less inferential weight when many outcomes are assessed, because the chance of at least one apparently unusual result can increase across multiple tests. Adjustments, a prespecified testing hierarchy, or other multiplicity controls can help address this issue. The multiplicity procedure and the inferential status of each secondary result are not reported in the registry record. The secondary findings should therefore be read as additional descriptive evidence, with caution about confirmatory claims.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Objective Response Rate (ORR) Per RECIST 1.1
- Duration of Response (DOR) Per RECIST 1.1
- Change From Baseline in European Organization for Research and Treatment of Cancer (EORTC) Quality of Life Questionnaire-Core 30 (QLQ-C30) Global Health Status (Item 29) and Quality of Life (Item 30) Combined Score
- Time to True Deterioration (TTD) in the EORTC Questionnaire Composite Endpoint of Cough, Chest Pain or Dyspnea
- Percentage of Participants Who Experienced an Adverse Event (AE)
- Percentage of Participants Who Discontinued Study Treatment Due to AEs
9. Statistical Interpretation
The registry reports median progression-free survival of 5.6 months for pembrolizumab plus pemetrexed and chemotherapy, with a 95% confidence interval of 5.5 to 5.8 months. For placebo plus pemetrexed and chemotherapy, the median was 5.5 months, with a 95% confidence interval of 5.4 to 5.6 months. These medians describe the estimated time by which half of the analyzed group had experienced progression or death; they do not describe every participant’s individual course.
The reported hazard ratio was 0.80, with a 95% confidence interval from 0.65 to 0.97 and p = 0.012. In general, a hazard ratio compares event rates over follow-up between groups; a value below 1 indicates a lower estimated event hazard in the first named group relative to the comparator, under the analysis model. The interval does not include 1, and the reported p-value is below 0.05. The registry lists this as a superiority analysis. These statistics support a between-group difference in the progression-free survival analysis, but do not establish that every participant benefited or quantify an individual’s likely outcome.
The medians are close, while the hazard ratio summarizes the comparison across the event-time follow-up rather than simply comparing the two medians. These measures answer related but distinct questions, so they should not be treated as interchangeable. The confidence interval expresses uncertainty in the estimated hazard ratio; it remains compatible with a range of relative hazard values rather than one exact effect.
Interpretation is limited to the posted outcome and analysis. Overall survival was part of the primary hypotheses, but its results are not reported in the registry record for this analysis. The primary timeframe is described as up to ~40 months. The registry lists all randomized participants as the primary outcome population. Details of censoring rules, missing outcome handling and the statistical plan beyond the reported method are not reported in the registry record.
The result is a statistical comparison of assigned treatment strategies in the trial population. It should not be recast as proof of a biological mechanism, a guarantee of benefit for an individual, or a conclusion about every clinical outcome. The registry result is most directly read as evidence favoring the pembrolizumab-containing group on the specified progression-free survival analysis, with uncertainty reflected in the confidence interval.
10. Statistical Methods Explained
The primary analysis concerns a time-to-event endpoint: progression-free survival from randomization to progressive disease or death, whichever came first. Time-to-event methods retain information about when an event occurred, rather than reducing follow-up to a simple event/no-event count at a single time point. The registry states that progression-free survival was analyzed with the product-limit, or Kaplan-Meier, method for censored data and assessed by blinded independent central review under RECIST 1.1.
What does Kaplan-Meier estimation do?
General statistical explanation: Kaplan-Meier estimation uses the sequence of event times and the numbers still under observation at those times to estimate the probability of remaining event-free over follow-up. Participants whose event time is not observed during their available follow-up contribute information until their censoring time. Censoring does not mean that an event did not occur; it means that the event was not observed within the period available for that participant. Valid interpretation depends on appropriate censoring and follow-up assumptions. The detailed censoring rules are not reported in the registry record.
A median from a Kaplan-Meier curve is the estimated time at which the probability of remaining free of the event reaches one half. The registry reports medians of 5.6 months and 5.5 months for the pembrolizumab and placebo groups, respectively. These are estimates from the event-time distributions, not arithmetic averages of each participant’s observed follow-up. Their confidence intervals describe uncertainty in each median estimate.
How should the hazard ratio be read?
General statistical explanation: A hazard is an event rate at a particular time among participants who remain event-free and under observation. A hazard ratio compares these rates between groups across follow-up under the fitted analysis. It is not a ratio of median survival times, and it does not directly state the absolute probability that a participant will experience an event. The registry reports a hazard ratio of 0.80 for pembrolizumab plus chemotherapy versus placebo plus chemotherapy, with a 95% confidence interval of 0.65 to 0.97. The reported method is Log Rank. The detailed model specification and any additional assumptions are not reported in the registry record.
The log-rank procedure is a standard method for comparing time-to-event experience between randomized groups. In general, it evaluates whether observed events occur differently across the groups over follow-up, taking account of the risk sets at event times. The registry lists the analysis as a superiority analysis. The p-value of 0.012 is the reported test result; it is not the probability that the null hypothesis is true, nor is it a measure of effect size.
Why do the median and hazard ratio differ in meaning?
General statistical explanation: A median reduces a whole event-time distribution to one location summary. A hazard ratio uses information across event times. The two groups can have medians that are close while the estimated relative hazard over follow-up is not exactly 1. Neither summary alone shows the full shape of the event-time curves. The registry record’s numerical information for this endpoint includes the medians and hazard ratio, but does not provide curve-specific estimates at selected times in the registry record analyzed.
What do the secondary analyses add?
The registry reports objective response rate as a percentage outcome, and time to true deterioration as another time-to-event outcome. For response, the posted group estimates are 29.0% and 27.1%, with 95% confidence intervals of 23.4% to 35.1% and 21.7% to 33.1%. A simple unadjusted re-calculation based on the posted response counts estimates a risk difference of 0.018, with a 95% confidence interval from -0.061 to 0.098 and p = 0.647. This is distinct from the sponsor’s reported analysis, which is described as a mean difference in final values. It should not be substituted for that analysis.
For time to true deterioration in cough, chest pain or dyspnea, the reported hazard ratio is 0.93, with a 95% confidence interval of 0.68 to 1.27. In general, a confidence interval spanning 1 for a hazard ratio indicates that the estimated data are compatible with no relative hazard difference as well as effects in either direction. The registry lists no p-value for this comparison. Secondary outcomes provide additional context, but they do not replace the prespecified primary comparison.
Why can over-dispersion matter?
General statistical explanation: Over-dispersion arises when variation in observed data exceeds what a statistical model assumes. If it is ignored in a setting where it matters, estimated standard errors may be too small and confidence intervals too narrow, making evidence appear more precise than it is. The registry does not report an over-dispersion adjustment for the primary time-to-event analysis, and the record does not establish that such an adjustment was needed. This is a general consideration, not a claim about the analysis used in KEYNOTE-789.
11. Confidence Intervals and Precision
The primary hazard ratio estimate is 0.80, with a 95% confidence interval from 0.65 to 0.97. A confidence interval is an uncertainty range produced by a statistical procedure: under its assumptions, repeated use of that procedure would yield intervals that cover the underlying parameter at the stated rate. It is not a range containing 95% of individual participants’ outcomes, and it does not mean there is a 95% probability that the true value lies in this particular interval.
The interval lies below 1, which is the value representing equal hazards in the general interpretation of a hazard ratio. It therefore supports a lower estimated hazard in the pembrolizumab group under the reported comparison. At the same time, the interval extends from 0.65 to 0.97, so the point estimate should not be treated as exact. The reported p-value is 0.012, consistent with the registry’s superiority classification for this analysis.
The group median estimates also have confidence intervals: 5.6 months with 5.5 to 5.8 months for the pembrolizumab group, and 5.5 months with 5.4 to 5.6 months for the placebo group. These intervals describe uncertainty in the group median estimates. Their overlap or proximity is not a substitute for the reported between-group time-to-event analysis, because separate median intervals do not directly test the hazard ratio.
For the response outcome, the unadjusted risk-difference interval runs from -0.061 to 0.098, and its p-value is 0.647. That interval includes zero, the value corresponding to no absolute difference on this scale. The time-to-deterioration hazard-ratio interval of 0.68 to 1.27 includes 1. These secondary estimates are less precise about direction than the primary result. In general, precision depends on the amount and distribution of information, event counts, follow-up, and analysis assumptions. The detailed event counts for the primary analysis and the corresponding precision calculations are not reported in the registry record.
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 | 0.80 | 631 | 845 |
| 75% of the observed effect | 0.85 | 1,121 | 1,501 |
| 50% of the observed effect | 0.89 | 2,523 | 3,377 |
The planning illustrations are based on the observed effect and are not the trial’s original design calculations; the original design assumptions are not reported in the registry record. Their stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, a normal approximation, and an effect to detect set to the stated fraction of the observed effect. For time-to-event outcomes, the figures are total events using the Schoenfeld method. For other outcomes, the figures are participants per arm.
For the primary progression-free survival comparison, the planning figures are total events. Planning for 100% of the observed effect gives 631 total events for 80% power and 845 total events for 90% power. Planning for 75% of the observed effect gives 1,121 total events for 80% power and 1,501 total events for 90% power. Planning for 50% of the observed effect gives 2,523 total events for 80% power and 3,377 total events for 90% power.
In plain language, the 80% power column gives the event count estimated to provide an 80% chance of detecting the specified effect under the listed assumptions if that effect is present. The 90% power column uses a higher chance of detection and therefore has a larger required event count for each listed effect. A smaller effect is harder to distinguish from random variation, so the planning figures require more events as the effect being targeted becomes smaller.
These are planning illustrations, not observed power. They do not describe the study’s actual design rationale or establish that the trial achieved a particular power. The response outcome has separate planning figures expressed as participants per arm, not total events.
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 = 0.800, so ln(HR) = -0.2231.
- d = 4 × (1.96 + 0.842)2 / [ln(0.800)]2 = 630.5, rounded up to 631 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 <- 0.8 # 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(3515837)
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 = 631 (80% power), 845 (90% power)
75% of observed effect: events = 1,121 (80% power), 1,501 (90% power)
50% of observed effect: events = 2,523 (80% power), 3,377 (90% power)
Simulated power with 631 events: 0.792 (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 934 participants in total, with the boundaries below.
| Analysis | Calendar time (months) | Events | Efficacy boundary (z) | Nominal one-sided p | Cumulative alpha spent |
|---|---|---|---|---|---|
| Look 1 | 14.8 | 284 | 3.710 | 0.0001 | 0.0001 |
| Look 2 | 23.6 | 569 | 2.511 | 0.0060 | 0.0060 |
| Look 3 | 60.0 | 853 | 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% | 630 | 690 | 60.0 |
| Two looks, O'Brien-Fleming | 80% | 632 | 692 | 60.0 |
| Three looks, O'Brien-Fleming | 80% | 638 | 698 | 60.0 |
| Three looks, Pocock | 80% | 737 | 807 | 60.0 |
| Fixed design, one analysis | 90% | 843 | 923 | 60.0 |
| Two looks, O'Brien-Fleming | 90% | 846 | 926 | 60.0 |
| Three looks, O'Brien-Fleming | 90% | 853 | 934 | 60.0 |
| Three looks, Pocock | 90% | 973 | 1,065 | 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 | 0.800 | 853 | 934 |
| 75% of the observed effect | 0.846 | 1,518 | 1,655 |
| 50% of the observed effect | 0.894 | 3,416 | 3,714 |
For context, this trial enrolled 492 participants.
Cross-check, upper boundaries: gsDesign 3.71, 2.511, 1.993 | rpact 3.71, 2.511, 1.993. Agreement between the two packages confirms the boundary calculation.
R code and output
suppressWarnings(suppressMessages({ library(gsDesign); library(rpact) }))
med_control <- 5.5 # control-arm median, months (converted from the posted unit)
hr <- 0.8 # 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: 576 p (1-sided) 0.0001
Events: 285 ~HR at bound 0.6440
Month: 15 P(Cross) if HR=1 0.0001
P(Cross) if HR=0.8 0.0338
IA 2: 67% Z 2.5114
N: 920 p (1-sided) 0.0060
Events: 569 ~HR at bound 0.8101
Month: 24 P(Cross) if HR=1 0.0060
P(Cross) if HR=0.8 0.5603
Final Z 1.9930
N: 934 p (1-sided) 0.0231
Events: 854 ~HR at bound 0.8725
Month: 60 P(Cross) if HR=1 0.0250
P(Cross) if HR=0.8 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) 0.80 | 0.65 to 0.97 | 0.012 |
The registry reports the sponsor’s primary progression-free survival comparison as a Log Rank analysis with a hazard ratio of 0.80, 95% confidence interval of 0.65 to 0.97, and p = 0.012. The posted group medians are 5.6 months and 5.5 months. The time-to-event interpretation in this analysis uses that sponsor-reported hazard ratio rather than constructing a new hazard-ratio estimate from the group medians. Median summaries alone do not contain enough information to reproduce the event-time comparison.
For objective response, the registry’s reported analysis is labeled Mean Difference (Final Values), with an estimate of 1.9 and a 95% confidence interval from -6.0 to 9.9. A separate simple unadjusted re-calculation from the posted response counts gives a risk difference of 0.018, with a 95% confidence interval from -0.061 to 0.098 and p = 0.647. These statistics are based on different analysis descriptions and should not be treated as interchangeable. The sponsor’s own analysis takes precedence for the registry’s reported inferential result.
Re-calculated statistics are useful as transparent checks of posted summary data, but they do not recreate a sponsor analysis that may use methods or data details not present in the registry record. The posted information does not describe all analysis specifications for the response comparison.
16. Multiplicity, Missing Data and Analysis Populations
The registry summary describes two primary hypotheses: superiority on progression-free survival and superiority on overall survival. It states that success would be achieved if the pembrolizumab combination were superior on either outcome. This statement identifies the trial’s broad success criterion, but the detailed procedure for controlling the chance of a false-positive conclusion across the two primary outcomes is not reported in the registry record. The order of testing, any allocation of significance levels, and any formal gatekeeping process are also not reported.
The registry lists multiple secondary outcomes, including response, duration of response, quality-of-life measures, symptom deterioration and adverse events. The multiplicity strategy for those outcomes is not reported in the registry record. Without that information, secondary p-values or confidence intervals should not automatically be read as confirmatory evidence, especially when results are considered across several outcomes. A nominal result and a result adjusted for multiple testing answer different inferential questions.
The primary analysis population is described as all randomized participants. The registry states the primary endpoint timeframe as up to ~40 months, and the secondary time-to-deterioration timeframe as baseline and up to ~51 months. The specific rules for censoring, missing endpoint assessments, withdrawal, treatment discontinuation and protocol deviations are not reported in the registry record. Those details matter because time-to-event analyses depend on follow-up and censoring, while response and questionnaire outcomes depend on how missing assessments are handled.
Interim analyses and any associated stopping rules are not reported in the registry record. The record also does not provide the full statistical analysis plan, detailed model diagnostics, or the exact handling of all analysis populations for the secondary outcomes. These omissions do not invalidate the reported estimates, but they limit independent assessment of how design choices, missing data and multiplicity were managed.
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 |
|---|---|---|---|
| Pembro + Pemetrexed + Chemo | 86 | 245 | 35.1% |
| Placebo + Pemetrexed + Chemo | 70 | 246 | 28.5% |
| Placebo + Pemetrexed + Chemo Switched Over to Pembro Monotherapy | 8 | 50 | 16.0% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Pembro + Pemetrexed + Chemo | 219 of 245 |
| Placebo + Pemetrexed + Chemo | 186 of 247 |
| Placebo + Pemetrexed + Chemo Switched Over to Pembro Monotherapy | 44 of 50 |
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 |
|---|---|
| Pembro + Pemetrexed + Chemo | 233 of 245 |
| Placebo + Pemetrexed + Chemo | 225 of 246 |
| Placebo + Pemetrexed + Chemo Switched Over to Pembro Monotherapy | 31 of 50 |
Most frequent serious adverse event terms
| Event term | Organ system | Pembro + Pemetrexed + Chemo | Placebo + Pemetrexed + Chemo | Placebo + Pemetrexed + Chemo Switched Over to Pembro Monotherapy |
|---|---|---|---|---|
| Anaemia | Blood and lymphatic system disorders | 6 of 245 | 8 of 246 | 0 of 50 |
| Pneumonia | Infections and infestations | 8 of 245 | 5 of 246 | 1 of 50 |
| Pleural effusion | Respiratory, thoracic and mediastinal disorders | 7 of 245 | 4 of 246 | 0 of 50 |
| Pyrexia | General disorders | 5 of 245 | 4 of 246 | 1 of 50 |
| Platelet count decreased | Investigations | 8 of 245 | 1 of 246 | 0 of 50 |
| Vomiting | Gastrointestinal disorders | 2 of 245 | 5 of 246 | 0 of 50 |
| Neutrophil count decreased | Investigations | 5 of 245 | 2 of 246 | 0 of 50 |
| Febrile neutropenia | Blood and lymphatic system disorders | 4 of 245 | 2 of 246 | 0 of 50 |
| White blood cell count decreased | Investigations | 5 of 245 | 1 of 246 | 0 of 50 |
| Nausea | Gastrointestinal disorders | 2 of 245 | 3 of 246 | 0 of 50 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Pembro + Pemetrexed + Chemo | Placebo + Pemetrexed + Chemo | Placebo + Pemetrexed + Chemo Switched Over to Pembro Monotherapy |
|---|---|---|---|---|
| Anaemia | Blood and lymphatic system disorders | 99 of 245 | 110 of 246 | 4 of 50 |
| Nausea | Gastrointestinal disorders | 96 of 245 | 107 of 246 | 4 of 50 |
| Neutrophil count decreased | Investigations | 90 of 245 | 113 of 246 | 2 of 50 |
| White blood cell count decreased | Investigations | 71 of 245 | 87 of 246 | 2 of 50 |
| Constipation | Gastrointestinal disorders | 81 of 245 | 76 of 246 | 1 of 50 |
| Decreased appetite | Metabolism and nutrition disorders | 64 of 245 | 61 of 246 | 4 of 50 |
| Alanine aminotransferase increased | Investigations | 60 of 245 | 58 of 246 | 3 of 50 |
| Aspartate aminotransferase increased | Investigations | 55 of 245 | 55 of 246 | 3 of 50 |
| Fatigue | General disorders | 60 of 245 | 49 of 246 | 1 of 50 |
| Platelet count decreased | Investigations | 49 of 245 | 52 of 246 | 0 of 50 |
Serious events with the highest arm-level rate: pneumonia (3.3%), platelet count decreased (3.3%), anaemia (3.3%), pleural effusion (2.9%), pyrexia (2.0%).
The registry reports serious adverse event counts for the two randomized treatment groups and for a separate group described as placebo plus chemotherapy switched over to pembrolizumab monotherapy. In the pembrolizumab plus chemotherapy group, 86 of 245 participants at risk were recorded as affected by a serious adverse event. In the placebo plus chemotherapy group, 70 of 246 at risk were affected. In the switched-over group, 8 of 50 at risk were affected. The switched-over group is reported separately and should not be combined with the randomized comparison when interpreting the primary treatment contrast.
The registry also reports participants affected by other adverse events: 233 of 245 in the pembrolizumab group, 225 of 246 in the placebo group, and 31 of 50 in the switched-over group. The deaths counts are 219, 186 and 44, respectively. These are counts in the registry’s adverse-event record; the registry entries do not provide further definitions or breakdowns for those death counts. No percentages have been calculated from these counts.
The most frequently listed serious adverse event terms include pneumonia, platelet count decreased and anaemia, each reported at 3.3%; pleural effusion at 2.9%; pyrexia and neutrophil count decreased, each at 2.0%. These term-level percentages are posted values, not estimates of comparative risk from a randomized test. Serious adverse event counts and individual event terms do not by themselves establish causation or a between-group safety difference. The detailed exposure-adjusted analyses and formal comparisons are not reported in the registry record.
18. What the Result Does, and Does Not, Mean
The primary result is an estimate of how progression-free survival differed between the assigned strategies in this randomized study. The reported hazard ratio of 0.80, with a 95% confidence interval from 0.65 to 0.97 and p = 0.012, indicates a statistically detectable difference in the reported analysis, with the estimate favoring the pembrolizumab-containing group. The result pertains to the trial population and the endpoint definition used by blinded independent central review.
It does not mean that every participant had a longer progression-free interval, nor does it predict a particular person’s outcome. A group-level hazard ratio is not an individual probability and does not describe the full distribution of possible benefit or harm for each participant. The median estimates, 5.6 months and 5.5 months, are group summaries and should not be interpreted as a promise of duration for an individual.
The result also does not establish an effect on every other outcome. The primary hypothesis included overall survival, but overall survival results are not reported in the registry record used for this analysis. The secondary outcome estimates do not have the same inferential pattern as the primary result, and the multiplicity approach is not reported. Safety data provide counts and selected serious event terms, but do not alone establish a comparative safety profile.
Statistical evidence is not the same as a clinical recommendation. Whether the estimated difference is important in a specific clinical setting depends on the broader evidence, the full benefit-harm profile, patient circumstances and clinical judgment. Those matters cannot be resolved from the registry summary alone. The careful conclusion is limited: the posted primary analysis supports a difference in progression-free survival between the randomized groups, while uncertainty remains about its size and about outcomes not reported in the registry record.
19. Why This Trial Matters Statistically
KEYNOTE-789 is statistically informative because it compares the addition of pembrolizumab against placebo while both groups receive pemetrexed and platinum chemotherapy. Randomization is intended to make treatment groups comparable on average, supporting a fair comparison of assigned strategies. The registry describes the study as randomized, parallel-group and masked, with blinded independent central review for the primary progression assessment.
The primary endpoint is time-to-event rather than a single follow-up response. Its analysis uses event timing and accounts for censored follow-up through the Kaplan-Meier method, while the reported hazard ratio summarizes the relative event experience between groups. Reading the median, hazard ratio, confidence interval and p-value together demonstrates why no single statistic fully describes a trial result: they capture different aspects of the evidence.
The record also highlights the distinction between sponsor-reported analyses and simple recalculations from posted summary data. The primary result is available as a sponsor-reported hazard ratio and test. For response, a recalculation from counts produces a different measure from the sponsor’s reported mean difference in final values. Clear labeling of estimands and analysis methods is essential when interpreting such comparisons.
Finally, this trial illustrates the importance of evaluating multiple outcomes without allowing secondary findings to displace the primary question. The registry includes response, symptoms, quality of life and safety, but the multiplicity strategy and several detailed results are not reported in the record used. Statistical interpretation therefore depends not only on effect estimates, but also on the endpoint hierarchy, uncertainty, analysis population and transparency of methods.
20. Limitations
- The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
- Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.
The registry record reports the primary progression-free survival result but does not report the overall survival result, even though overall survival was part of the primary hypotheses. That leaves the stated two-outcome success framework only partly assessable from the information. The detailed multiplicity procedure is also not reported, so the degree of error control across primary and secondary testing cannot be evaluated.
The primary outcome is based on blinded independent central review, but detailed information on censoring rules, missing assessments, protocol deviations and the statistical model beyond the listed Log Rank method is not reported in the registry record. These details can affect time-to-event interpretation and reproducibility. The full statistical analysis plan and interim analysis arrangements are not reported.
Some secondary outcome results are not present in the registry record analyzed here, including numerical findings for duration of response and the quality-of-life measures. The symptom deterioration result has no reported p-value, and the response analysis has a sponsor-reported mean difference in final values alongside a separate unadjusted re-calculation based on binary response counts. These are different estimands and should not be conflated.
The registry’s intervention descriptions are incomplete in the available record: the platinum chemotherapy dosing detail is truncated. The safety record includes a switched-over group in addition to the randomized treatment groups, so those figures cannot be treated as part of the original randomized contrast. Detailed exposure-adjusted safety comparisons and causal assessments for individual adverse events are not reported.
21. Related Tutorials
22. Related Statistical Calculators
23. Sources
- ClinicalTrials.gov: Study of Pemetrexed + Platinum Chemotherapy With or Without Pembrolizumab (MK-3475) in Adults With Tyrosine Kinase Inhibitor- (TKI)-Resistant Epidermal Growth Factor Receptor- (EGFR)-Mutated Metastatic Non-squamous Non-small Cell Lung Cancer (NSCLC) (MK-3475-789/KEYNOTE-789) — NCT03515837.
- Registry record last updated 2024-11-22; status last verified 2024-11.
- Results first posted 2024-01-17.
- 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
NCT03515837, KEYNOTE-789, is a completed randomized, parallel-group Phase 3 study of pembrolizumab plus pemetrexed and platinum chemotherapy versus saline placebo plus pemetrexed and platinum chemotherapy in adults with TKI-resistant EGFR-mutated metastatic non-squamous NSCLC. The registry reports enrollment of 492 and identifies progression-free survival assessed by blinded independent central review using RECIST 1.1 as the primary outcome.
The reported median progression-free survival estimates are 5.6 months and 5.5 months. The reported hazard ratio is 0.80, with a 95% confidence interval of 0.65 to 0.97 and p = 0.012. The record also lists response, symptom, quality-of-life and safety outcomes. Overall survival findings, detailed multiplicity handling, and several analysis details are not reported in the registry record.