This page separates reported trial results from statistical interpretation. Numerical results are restricted to the information provided in the ClinicalTrials.gov record.
1. Trial at a Glance
KEYNOTE-240 was a randomized, parallel, triple-masked phase 3 trial evaluating pembrolizumab plus best supportive care versus placebo plus best supportive care in participants with previously systemically treated advanced hepatocellular carcinoma.
| Feature | KEYNOTE-240 |
|---|---|
| Phase | Phase 3 |
| Condition | Hepatocellular carcinoma |
| Population | Participants with previously systemically treated advanced hepatocellular carcinoma |
| Design | Randomized, parallel, triple-masked |
| Primary purpose | Treatment |
| Enrollment | 413 |
| Interventions | Pembrolizumab; placebo; best supportive care |
| Primary endpoints | Progression-Free Survival (PFS) and Overall Survival (OS) |
| Primary endpoint type | Time-to-event |
| Status | Completed |
| Lead sponsor | Merck Sharp & Dohme LLC |
| Sponsor type | Industry |
| ClinicalTrials.gov | NCT02702401 |
2. Clinical Question
The central statistical question was whether pembrolizumab plus best supportive care produced a different time-to-event outcome from placebo plus best supportive care in participants with previously systemically treated advanced hepatocellular carcinoma.
Population
Participants with previously systemically treated advanced hepatocellular carcinoma.
Intervention
Pembrolizumab plus best supportive care.
Comparator
Placebo plus best supportive care.
Primary question
How does the randomized comparison affect progression-free survival and overall survival?
3. Trial Design
Pembrolizumab + Best Supportive Care
- Pembrolizumab
- Best supportive care
- Serious adverse events: 106/279
Placebo + Best Supportive Care
- Placebo
- Best supportive care
- Serious adverse events: 37/134
The registry also reports a pembrolizumab second-course group with serious adverse events in 3 of 7 participants. This is a distinct reported safety group and should not be combined with the randomized treatment-arm denominators when describing the primary comparison.
4. Randomization, Stratification, and Analysis Populations
The primary efficacy analyses included all randomized participants, with participants analyzed in the treatment group to which they were randomized. This is the key intention-to-treat principle represented in the posted statistical analyses.
| Feature | Registry-supported description |
|---|---|
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Triple |
| Primary efficacy population | All randomized participants |
| Treatment assignment for analysis | Participants remained in the group to which they were randomized |
| Stratification variables in primary analyses | Geographic region, macrovascular invasion, and alfa-fetoprotein level |
The stratification variables are important because the reported time-to-event analyses were not simple unstratified comparisons. The log-rank analyses and Cox regression models accounted for geographic region, macrovascular invasion, and alfa-fetoprotein level.
5. Primary Endpoints
| Endpoint | Registry definition / time frame | Analysis |
|---|---|---|
| Progression-Free Survival (PFS) Per RECIST 1.1 | Time from randomization to the first documented progressive disease or death due to any cause, whichever occurred first, per RECIST 1.1 as assessed by Blinded Independent Central Review (BICR). Time frame: through database cutoff date of 26-Mar-2018, up to approximately 21 months. | Stratified log-rank test; stratified Cox regression |
| Overall Survival (OS) | Time from randomization to death due to any cause. Participants were censored at the date of their last follow-up. Time frame: through database cutoff date of 02-Jan-2019, up to approximately 30 months. | Kaplan-Meier; stratified log-rank test; stratified Cox regression |
PFS definition in statistical terms
PFS is a composite time-to-event endpoint. The event is whichever occurs first: documented progressive disease or death from any cause. The registry definition specifies RECIST 1.1 assessment by Blinded Independent Central Review and defines progressive disease using an increase of at least 20% in the sum of diameters of target lesions together with an absolute increase of at least 5 mm; the appearance of at least 1 new lesion was also considered progressive disease.
OS definition in statistical terms
OS is simpler conceptually: the event is death from any cause. Participants who remained alive without a documented death contributed follow-up until their last follow-up date and were censored there.
6. Statistical Methodology
Kaplan-Meier estimation
The registry specifies the product-limit, or Kaplan-Meier, method for OS. Kaplan-Meier estimation is designed for time-to-event data with right censoring. It estimates the probability of remaining event-free as follow-up accumulates without requiring every participant to experience the event during the observation period.
Here, di represents events at an event time and ni represents the number at risk immediately before that time.
Stratified log-rank test
The primary PFS and OS analyses used a log-rank method with stratification by geographic region, macrovascular invasion, and alfa-fetoprotein level. Stratification allows the comparison to account for the prespecified factors rather than treating all participants as though these characteristics had no role in the analysis structure.
Cox proportional-hazards regression
The reported analyses used a Cox regression model with treatment as a covariate and stratification by geographic region, macrovascular invasion, and alfa-fetoprotein level. Efron's method was used for tied event times.
Equivalently, 1 − 0.775 = 0.225, so the estimate corresponds to an approximately 22.5% lower estimated hazard in the pembrolizumab group under the fitted model. This is a relative hazard measure, not an absolute probability difference.
Score-based confidence intervals for response
The secondary Objective Response Rate analysis used a score-based confidence-interval approach, specifically the Miettinen & Nurminen method, stratified by geographic region, macrovascular invasion, and alfa-fetoprotein level. The reported effect measure was a difference in percentage, or risk difference.
7. Primary Results: Progression-Free Survival
The registry reports a formal primary analysis of PFS through the database cutoff date of 26-Mar-2018, corresponding to up to approximately 21 months. The analysis included all randomized participants in their randomized treatment groups.
Hazard ratio for progression or death
95% CI: 0.609–0.987 · One-sided P = 0.0186
Stratified by geographic region, macrovascular invasion, and alfa-fetoprotein level.
| Feature | PFS analysis |
|---|---|
| Comparison | Pembrolizumab + Best Supportive Care vs Placebo + Best Supportive Care |
| Analysis population | All randomized participants |
| Method | Log-rank test |
| Effect measure | Hazard ratio |
| Estimate | 0.775 |
| 95% CI | 0.609–0.987 |
| P-value | 0.0186, one-sided |
| Time frame | Through 26-Mar-2018, up to approximately 21 months |
The estimated PFS hazard ratio of 0.775 means that, under the reported stratified time-to-event model, the estimated instantaneous rate of progression or death in the pembrolizumab group was approximately 77.5% of the corresponding rate in the placebo group. Expressed as a relative hazard reduction, this is approximately 22.5%.
The HR does not mean that 22.5% of participants avoided progression, that PFS increased by 22.5%, or that each participant experienced the same reduction in risk. It is a model-based relative measure of the event rate over the analyzed follow-up.
The two-sided 95% confidence interval of 0.609–0.987 describes statistical uncertainty around the estimated hazard ratio. It does not describe the range of individual patient outcomes. The interval is relatively close to 1 at its upper boundary, so the numerical precision of the treatment-effect estimate matters when interpreting the size of the effect.
The reported one-sided P-value of 0.0186 addresses the prespecified superiority-testing framework; it does not measure the size or clinical importance of the treatment effect. The hazard ratio and its confidence interval provide that effect-size information.
Because the analysis is based on time-to-event methods and a Cox model, interpretation also depends on the way censoring was handled and on the model's proportional-hazards framework. A single HR should not automatically be interpreted as a constant relative risk at every time point.
8. Primary Results: Overall Survival
The registry reports the final OS analysis for the first pembrolizumab course through the database cutoff date of 02-Jan-2019, corresponding to up to approximately 30 months.
Hazard ratio for death
95% CI: 0.611–0.998 · One-sided P = 0.0238
Stratified by geographic region, macrovascular invasion, and alfa-fetoprotein level.
| Feature | OS analysis |
|---|---|
| Comparison | Pembrolizumab + Best Supportive Care vs Placebo + Best Supportive Care |
| Analysis population | All randomized participants |
| Method | Log-rank test |
| Effect measure | Hazard ratio |
| Estimate | 0.781 |
| 95% CI | 0.611–0.998 |
| P-value | 0.0238, one-sided |
| Time frame | Through 02-Jan-2019, up to approximately 30 months |
The estimated OS hazard ratio of 0.781 means that, under the reported stratified Cox model, the estimated instantaneous rate of death in the pembrolizumab group was approximately 78.1% of the corresponding rate in the placebo group. In relative terms, this corresponds to an approximately 21.9% lower estimated hazard.
The HR does not mean that 21.9% fewer participants died, nor does it represent a 21.9% increase in survival time. It is a relative time-to-event measure based on the observed follow-up and fitted model.
The two-sided 95% confidence interval of 0.611–0.998 quantifies uncertainty around the estimated hazard ratio. Its upper limit is close to 1, making the distinction between the point estimate and its uncertainty especially important. The interval does not represent the range of effects across individual participants.
The reported one-sided P-value of 0.0238 describes the evidence under the trial's stated superiority framework. A P-value is not a measure of effect magnitude, clinical relevance, or probability that the treatment hypothesis is true.
As with PFS, OS is subject to censoring and is summarized with a time-to-event model. The Cox model provides a compact HR, but the HR should not be treated as an absolute survival probability or automatically assumed to describe an identical relative effect at every point in time.
9. Secondary Endpoint: Objective Response Rate
Objective Response Rate (ORR) was a secondary endpoint evaluated through the database cutoff date of 02-Jan-2019, up to approximately 30 months. The analysis population included all randomized participants.
Difference in objective response rate
95% CI: 7.7–19.5 percentage points
Miettinen & Nurminen method, stratified by geographic region, macrovascular invasion, and alfa-fetoprotein level.
| Feature | ORR analysis |
|---|---|
| Comparison | Pembrolizumab + Best Supportive Care vs Placebo + Best Supportive Care |
| Analysis population | All randomized participants |
| Endpoint type | Binary |
| Effect measure | Difference in Percent / Risk difference |
| Estimate | 13.8 |
| 95% CI | 7.7–19.5 |
| Analysis method | Score-based CI for proportions; Miettinen & Nurminen method |
| Time frame | Through 02-Jan-2019, up to approximately 30 months |
The reported effect estimate of 13.8 percentage points is a risk difference: it describes the difference between the proportions of participants achieving the defined objective-response outcome in the two randomized groups.
This is different from a hazard ratio. ORR does not incorporate the timing of response in the same way that PFS and OS incorporate time to progression, death, or censoring. A response-rate difference therefore answers a different question from the primary time-to-event endpoints.
The 95% confidence interval of 7.7–19.5 percentage points describes uncertainty around the estimated difference in response proportions. It does not describe the range of response probabilities for individual patients.
The Miettinen & Nurminen method is a score-based approach for confidence intervals for a difference in proportions. The reported stratification means that the analysis was structured around geographic region, macrovascular invasion, and alfa-fetoprotein level rather than treating the randomized population as a completely unstratified sample.
10. Secondary Endpoint: Time to Progression
Time to Progression (TTP) was a secondary time-to-event endpoint evaluated through the database cutoff date of 02-Jan-2019, up to approximately 30 months.
Hazard ratio for time to progression
95% CI: 0.540–0.877 · P = 0.0011
Stratified Cox regression by geographic region, macrovascular invasion, and alfa-fetoprotein level.
| Feature | TTP analysis |
|---|---|
| Comparison | Pembrolizumab + Best Supportive Care vs Placebo + Best Supportive Care |
| Analysis population | All randomized participants |
| Method | Log-rank test |
| Effect measure | Hazard ratio |
| Estimate | 0.688 |
| 95% CI | 0.540–0.877 |
| P-value | 0.0011 |
| Time frame | Through 02-Jan-2019, up to approximately 30 months |
The TTP HR of 0.688 corresponds to an estimated hazard approximately 68.8% as large in the pembrolizumab group as in the placebo group under the reported model. In relative terms, that corresponds to an approximately 31.2% lower estimated hazard of progression.
TTP differs conceptually from PFS because the registered PFS endpoint includes both documented progression and death as events, whereas TTP is specifically time to progression. Therefore, the two endpoints should not be treated as interchangeable measures.
The 95% confidence interval of 0.540–0.877 describes uncertainty around the estimated relative hazard. It is narrower than the corresponding PFS interval in this dataset, but that does not by itself establish that the TTP estimate is more clinically important.
The reported P-value of 0.0011 quantifies evidence under the specified statistical comparison; it does not quantify the size of the effect. The HR and its confidence interval are the appropriate quantities for describing magnitude and precision.
11. Secondary Results Summary
| Endpoint | Effect measure | Estimate | 95% CI | P-value |
|---|---|---|---|---|
| Progression-Free Survival | Hazard ratio | 0.775 | 0.609–0.987 | 0.0186, one-sided |
| Overall Survival | Hazard ratio | 0.781 | 0.611–0.998 | 0.0238, one-sided |
| Objective Response Rate | Risk difference | 13.8 | 7.7–19.5 | Not reported |
| Time to Progression | Hazard ratio | 0.688 | 0.540–0.877 | 0.0011 |
The registry therefore provides formal analyses for both primary endpoints and for two secondary endpoints. The four posted statistical analyses use two different effect-measure families: hazard ratios for time-to-event outcomes and a risk difference for the binary response outcome.
12. Safety Results
The ClinicalTrials.gov record reports serious adverse events by arm. These counts should be kept separate from the efficacy analysis because safety is exposure-related and answers a different statistical question.
| Reported safety group | Affected / at risk |
|---|---|
| Pembrolizumab + Best Supportive Care | 106 / 279 |
| Placebo + Best Supportive Care | 37 / 134 |
| Pembrolizumab Second Course | 3 / 7 |
The reported serious-adverse-event data indicate the number affected and the corresponding number at risk for each listed group. The second-course group is reported separately and should not be treated as another randomized arm in the primary efficacy comparison.
13. How the Primary Analysis Fits Together
Step 1: Preserve randomization
Primary efficacy analyses included all randomized participants and retained their randomized treatment assignment.
Step 2: Respect time-to-event structure
PFS and OS were analyzed as times from randomization to defined events, with censoring incorporated into the survival analysis.
Step 3: Stratify the comparison
Geographic region, macrovascular invasion, and alfa-fetoprotein level were incorporated into the reported stratified analyses.
Step 4: Report relative effect
The Cox model produces hazard ratios that summarize the relative event rate between treatment groups.
This structure matters because the reported HR is not simply the ratio of two proportions. It comes from a model that uses the ordering and timing of events, accommodates censoring, and incorporates the specified stratification structure.
14. Statistical Methods Explained
Why was a log-rank test used?
PFS, OS, and TTP are time-to-event endpoints. Participants can have different lengths of follow-up, and some participants may be censored before an event occurs. The log-rank test is designed for comparing survival distributions between randomized groups while using information accumulated over follow-up rather than reducing each participant to a simple event/no-event indicator.
What does a hazard ratio of 0.775 mean?
A hazard ratio of 0.775 means that the estimated instantaneous event rate in the pembrolizumab group was 77.5% of the corresponding rate in the comparator group under the fitted time-to-event model. The complementary quantity, 1 − 0.775, is approximately 22.5%, which provides a convenient way to describe the estimated relative reduction in hazard.
Why does the PFS confidence interval matter?
The point estimate alone gives only one estimate of the treatment effect. The 95% confidence interval of 0.609–0.987 shows the uncertainty surrounding that estimate under the statistical framework used for the analysis. It does not tell us that individual patients' effects must lie between those two numbers.
Why is the OS P-value not the effect size?
The OS P-value of 0.0238 is a measure of evidence under the stated superiority-testing framework. It is not a measure of how large the treatment effect is. The HR of 0.781 describes the estimated relative effect, while the 95% CI of 0.611–0.998 describes its uncertainty.
Why were the analyses stratified?
The registry reports stratification by geographic region, macrovascular invasion, and alfa-fetoprotein level. Stratification allows the primary comparison to respect these specified factors in the time-to-event analysis. It does not mean that the treatment effect was separately estimated as an independent primary trial within each subgroup.
Why is ORR analyzed differently from PFS and OS?
ORR is a binary endpoint: a participant either meets the defined response criterion or does not. PFS and OS contain information about when an event occurs and whether observations are censored. The statistical structure therefore differs, with ORR summarized using a difference in percentages and a score-based confidence-interval method rather than a hazard ratio.
What does censoring mean for OS?
For OS, the registry defines death from any cause as the event and states that participants are censored at their last follow-up. Censoring means that the analysis knows a participant remained alive through a particular observation time but does not treat the participant as having experienced an event after that point.
15. Confidence Intervals, One-Sided Testing, and Effect Size
An important feature of the two primary analyses is that the registry reports one-sided P-values alongside two-sided 95% confidence intervals. These are related but distinct statistical summaries.
| Endpoint | Estimate | Two-sided 95% CI | Reported P-value |
|---|---|---|---|
| PFS | HR 0.775 | 0.609–0.987 | 0.0186, one-sided |
| OS | HR 0.781 | 0.611–0.998 | 0.0238, one-sided |
The distinction is worth preserving when teaching clinical-trial statistics. A P-value is tied to a hypothesis-testing framework, whereas a confidence interval gives a range of values describing uncertainty around an estimated effect. Neither quantity alone provides the complete clinical interpretation.
The most informative reading of a trial result considers all three rather than treating a P-value as a substitute for the effect estimate.
16. Stratified Analysis and Covariate Adjustment
The registry's primary analyses identify three stratification variables: geographic region, macrovascular invasion, and alfa-fetoprotein level.
| Analysis component | Registry-supported role |
|---|---|
| Geographic region | Stratification factor |
| Macrovascular invasion | Stratification factor |
| Alfa-fetoprotein level | Stratification factor |
| Treatment | Covariate in the reported Cox regression model |
| Tied event times | Efron's method |
This is an important distinction between a simple two-group analysis and the reported model. The treatment comparison is still anchored to randomization, but the survival analysis incorporates the specified stratification structure.
For the ORR analysis, the Miettinen & Nurminen method was likewise stratified by the same three factors. Thus, the trial used a consistent stratified-analysis concept across both time-to-event and binary response analyses, although the statistical machinery differed by endpoint type.
17. What the Hazard Ratio Does — and Does Not — Mean
A hazard ratio below 1 indicates a lower estimated event hazard in the pembrolizumab group relative to the placebo group under the fitted model. For example, the PFS estimate of 0.775 corresponds to an approximately 22.5% lower estimated hazard.
A hazard ratio is not the probability that a participant will remain progression-free or alive. It is also not the percentage of participants who benefit and is not equivalent to a risk ratio or risk difference.
The Cox model produces a single summary measure, but the underlying hazard functions can change over time. A single HR should therefore not automatically be interpreted as though the same relative difference must hold at every time point.
An HR is a population-level comparative estimate. It does not imply that every participant experienced the same proportional change in event hazard.
18. PFS, OS, TTP, and ORR Answer Different Questions
| Endpoint | Statistical type | What it captures |
|---|---|---|
| PFS | Time-to-event | Time from randomization to first documented progression or death, whichever occurs first. |
| OS | Time-to-event | Time from randomization to death from any cause. |
| TTP | Time-to-event | Time to progression under the registered endpoint definition. |
| ORR | Binary | Whether a participant meets the objective-response criterion. |
The fact that these endpoints can all favor the same randomized group does not make them redundant. PFS incorporates both progression and death, OS focuses on death, TTP focuses on progression, and ORR focuses on response status. Their effect measures therefore describe different aspects of treatment outcome.
19. Multiplicity and Endpoint Interpretation
KEYNOTE-240 has 2 registered primary endpoints: PFS and OS. The ClinicalTrials.gov record identifies both as formal primary analyses with estimates, confidence intervals, and P-values.
| Endpoint / analysis | Role | Effect measure |
|---|---|---|
| PFS | Primary | Hazard ratio |
| OS | Primary | Hazard ratio |
| ORR | Secondary | Risk difference |
| TTP | Secondary | Hazard ratio |
Because the trial has more than one primary endpoint and multiple efficacy analyses, interpretation of individual P-values depends on the trial's prespecified testing framework. The ClinicalTrials.gov record identifies the primary analyses as superiority analyses and identify one-sided P-values for PFS and OS, but they do not provide a complete alpha-allocation or multiplicity procedure. The page therefore does not infer an additional multiplicity adjustment that is not contained in the ClinicalTrials.gov record.
20. Limitations and Interpretation Issues
- Limited numerical scope: the ClinicalTrials.gov record provides formal analyses for four endpoints but do not provide the complete set of possible descriptive efficacy summaries.
- No median survival estimates: median PFS, median OS, and median TTP are not provided in the ClinicalTrials.gov record and therefore are not reported here.
- No baseline table: baseline demographic and disease characteristics are not provided in the ClinicalTrials.gov record.
- No subgroup estimates: the registry identifies stratification variables but does not provide subgroup-specific treatment-effect estimates in the statistical analyses posted on ClinicalTrials.gov.
- Hazard-ratio interpretation: Cox HRs are model-based and should not be treated as absolute risk differences or as guarantees of a constant relative effect throughout follow-up.
- Censoring: survival analyses rely on censoring rules. OS explicitly states that participants were censored at their last follow-up.
- Primary-endpoint multiplicity: two primary endpoints are reported, but the ClinicalTrials.gov record does not specify a complete alpha-allocation or hierarchical testing scheme.
- Safety comparison: serious adverse-event counts are reported by arm, but the ClinicalTrials.gov record does not provide a formal comparative statistical analysis.
- Second-course group: the 7 participants in the reported pembrolizumab second-course group should not be combined with the randomized treatment arms for primary efficacy interpretation.
21. Why This Trial Matters Statistically
KEYNOTE-240 is a useful teaching case because it connects several fundamental clinical-trial methods within one randomized comparison: time-to-event endpoints, stratified log-rank testing, Cox regression, hazard ratios, confidence intervals, one-sided testing, Kaplan-Meier estimation, binary response analysis, and score-based confidence intervals.
| Concept | How it appears in KEYNOTE-240 |
|---|---|
| Randomization | Randomized parallel-group phase 3 design |
| Blinding | Triple masking |
| ITT principle | Primary efficacy population included all randomized participants in their randomized groups |
| Kaplan-Meier estimation | OS analyzed using the product-limit method |
| Hazard ratio | Primary PFS and OS effects and secondary TTP effect |
| Log-rank test | Formal comparison for the time-to-event endpoints |
| Cox regression | Treatment modeled with stratification by three specified factors |
| Efron's method | Handling tied event times in the Cox model |
| One-sided testing | Reported for the PFS and OS primary analyses |
| Confidence intervals | Two-sided 95% intervals for primary hazard ratios |
| Risk difference | ORR reported as a difference in percentages |
| Miettinen-Nurminen method | Score-based confidence interval for the stratified ORR comparison |
| Safety analysis | Serious adverse events reported as affected / at risk by group |
22. Record Timeline
Trial start
The registry lists 26-May-2016 as the study start date.
PFS database cutoff
The primary PFS analysis used the database cutoff of 26-Mar-2018, up to approximately 21 months.
Primary completion and OS cutoff
The registry lists 02-Jan-2019 as the primary completion date and uses the same date as the OS database cutoff, up to approximately 30 months.
Registry status
The trial is listed as completed, with 413 participants enrolled and 8 outcome measures posted.
23. Overall Statistical Reading of the Results
The two primary time-to-event analyses report hazard ratios below 1: 0.775 for PFS and 0.781 for OS. Both analyses use stratified log-rank testing and stratified Cox regression, with the same three stratification factors. The corresponding two-sided 95% confidence intervals are 0.609–0.987 for PFS and 0.611–0.998 for OS, while the registry reports one-sided P-values of 0.0186 and 0.0238, respectively.
The secondary analyses add two different pieces of statistical information. ORR is summarized using a risk difference of 13.8 percentage points, with a 95% confidence interval of 7.7–19.5 percentage points. TTP is summarized using a hazard ratio of 0.688, with a 95% confidence interval of 0.540–0.877 and a P-value of 0.0011.
These results should be read as a collection of endpoint-specific estimates rather than as one universal measure of treatment effect. PFS, OS, TTP, and ORR have different definitions, different statistical structures, and different interpretations.
24. Related Tutorials
Learn more about the methods used in this trial:
25. Related Statistical Calculators
26. Sources
- ClinicalTrials.gov: NCT02702401.
- PubMed: PMID 31790344.
- PubMed: PMID 41453647.
- PubMed: PMID 40486134.
- PubMed: PMID 34616489.
Continue through the Clinical Biostats statistical pathway
Explore the statistical methods behind randomized clinical trials, from survival analysis and hazard ratios to confidence intervals and categorical-data methods.
27. Record Summary
KEYNOTE-240 provides a compact example of how a randomized phase 3 oncology trial can use several complementary statistical approaches. The primary endpoints were both time-to-event outcomes, analyzed using stratified log-rank tests and Cox regression, with hazard ratios of 0.775 for PFS and 0.781 for OS. The secondary analyses extended the statistical picture to a binary response endpoint using a risk difference and a score-based confidence interval, and to TTP using another hazard ratio.
The most important statistical distinction is between effect magnitude, precision, and hypothesis-test evidence. Hazard ratios describe relative event hazards; confidence intervals describe uncertainty around estimates; and P-values describe evidence under the specified testing framework. None of these quantities should be interpreted in isolation.