This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record.
1. Trial at a Glance
AREDS2 was a randomized, double-blind, phase 3 trial evaluating lutein/zeaxanthin and DHA/EPA dietary supplements in people at moderate to high risk for progression of age-related macular degeneration. The trial enrolled 4203 participants and used four parallel treatment arms.
| Feature | AREDS2 |
|---|---|
| Phase | Phase 3 |
| Status | Completed |
| Condition | Age-related Macular Degeneration; Cataract |
| Design | Randomized, double-blind, parallel |
| Primary purpose | Treatment |
| Enrollment | 4203 |
| Interventions | Lutein/zeaxanthin; DHA/EPA; lutein/zeaxanthin and DHA/EPA |
| Primary endpoint | Development of Advanced AMD in People at Moderate to High Risk for Progression |
| Primary endpoint time frame | 5 years of follow-up |
| Lead sponsor | National Eye Institute (NEI) |
| Sponsor type | NIH |
| ClinicalTrials.gov | NCT00345176 |
2. Clinical Question
The primary statistical question was whether assignment to lutein/zeaxanthin, DHA/EPA, or their combination changed the time to development of advanced AMD compared with the placebo/control arm over 5 years of follow-up.
Population
People at moderate to high risk for progression of age-related macular degeneration, within a trial addressing age-related macular degeneration and cataract.
Interventions
Lutein/zeaxanthin, DHA/EPA, and lutein/zeaxanthin plus DHA/EPA were evaluated as dietary-supplement interventions.
Comparator
The placebo/control arm served as the reference group for the three primary treatment comparisons.
Primary question
Does assignment to an active supplement strategy alter the hazard of developing advanced AMD during 5 years of follow-up?
3. Trial Design
Placebo / Control
- Reference group for the three primary treatment comparisons.
- Used as the reference category in the reported hazard-ratio analyses.
Lutein / Zeaxanthin
- Dietary-supplement intervention.
- Compared directly with placebo/control for advanced AMD, moderate vision loss, and mortality analyses.
DHA / EPA
- Dietary-supplement intervention.
- Compared directly with placebo/control for advanced AMD, moderate vision loss, and mortality analyses.
Lutein / Zeaxanthin + DHA / EPA
- Combined dietary-supplement intervention.
- Compared directly with placebo/control for advanced AMD, moderate vision loss, and mortality analyses.
4. Endpoints
| Endpoint | Registry definition | Time frame | Type |
|---|---|---|---|
| Development of Advanced AMD in People at Moderate to High Risk for Progression | Defined as central geographic atrophy or retinal features of choroidal neovascularization detected on central grading of the stereoscopic fundus photographs or a history of treatment for advanced AMD after study enrollment. | 5 years of follow-up | Time-to-event |
| Progression to Moderate Vision Loss | Progression to moderate vision loss. | 5 years of follow-up | Time-to-event |
| Adverse Events | Number of deaths in 5 years. | 5 years of follow-up | Time-to-event |
| Progression to Cataract Surgery | Progression to cataract surgery among participants who were phakic in at least 1 eye at baseline. | 5 years of follow-up | Time-to-event |
The registry identifies one registered primary endpoint: development of advanced AMD in people at moderate to high risk for progression. The posted analyses also include secondary time-to-event outcomes involving moderate vision loss, mortality, and cataract surgery.
5. Statistical Methodology
Primary analysis: Cox proportional-hazards model
The primary endpoint was analyzed as a time-to-event outcome using a Cox proportional-hazards model. The analysis population was intention-to-treat. Participants lost to follow-up during the course of the study were censored at the time of last contact.
The reported hazard ratio is obtained by exponentiating the treatment coefficient: HR = exp(β). A hazard ratio below 1 indicates a lower estimated instantaneous event rate in the compared active group relative to the reference group, under the model.
Hazard ratio as the effect measure
All ten posted statistical analyses use hazard ratios. This is appropriate for outcomes in which the timing of the event matters and participants can be censored before experiencing the event.
This is a relative statement about the estimated event hazard. It is not a statement that 10% of participants benefited, that the absolute probability was reduced by 10 percentage points, or that every participant experienced the same effect.
Intention-to-treat analysis
The primary analyses were conducted under an intention-to-treat framework. This means that participants were analyzed according to their randomized treatment assignment rather than being reclassified according to subsequent exposure. Participants lost to follow-up were censored at their last contact.
Covariate adjustment
The posted analysis comparing placebo/control with lutein/zeaxanthin states that the Cox model was adjusted for baseline AMD status. The analysis comparing placebo/control with the combined lutein/zeaxanthin plus DHA/EPA arm also reports adjustment for multiple comparisons.
Two-sided confidence intervals
The primary analyses report 98.7% two-sided confidence intervals. The secondary analyses report 95% two-sided confidence intervals. The confidence level therefore differs between the primary and secondary analyses, which is important when interpreting the numerical boundaries.
Multiple comparisons
Three active treatment arms were compared with the placebo/control arm for the primary endpoint. The registry specifically notes adjustment for multiple comparisons for the combined lutein/zeaxanthin plus DHA/EPA comparison and reports the same 98.7% confidence level across the three primary analyses.
6. Statistical Methods Explained
Why was a Cox model used?
Advanced AMD, moderate vision loss, mortality, and cataract surgery are recorded as events occurring over follow-up rather than simply as binary outcomes at one fixed time. A Cox model uses both whether an event occurred and the amount of follow-up available before an event or censoring. This makes it well suited to the registry's reported time-to-event analyses.
What does a hazard ratio of 0.90 mean?
A hazard ratio of 0.90 means that the estimated instantaneous event rate in the lutein/zeaxanthin group was approximately 90% of that in the placebo/control group under the fitted model. Equivalently, it corresponds to an estimated 10% lower hazard. It does not mean that the probability of advanced AMD was exactly 10% lower over the entire 5-year period.
Why does censoring matter?
Participants who leave follow-up before experiencing the endpoint do not simply become events or non-events. In the primary analysis, participants lost to follow-up were censored at the time of last contact. The Cox analysis therefore uses the information available up to that censoring time.
Why use intention-to-treat analysis?
Analyzing participants according to randomized assignment preserves the treatment comparison created by randomization. It avoids redefining the treatment groups based on later events or exposure and is therefore a natural framework for estimating the effect associated with treatment assignment.
What does a confidence interval add beyond the hazard ratio?
The hazard ratio is a point estimate. The confidence interval describes the statistical uncertainty surrounding that estimate under the model and sampling framework. For example, the primary lutein/zeaxanthin comparison has an HR of 0.90 with a 98.7% confidence interval of 0.76 to 1.07. The interval is therefore substantially more informative about precision than the point estimate alone.
Why should the p-value not be treated as an effect-size measure?
A p-value addresses evidence against a specified null hypothesis under the statistical testing framework. It does not quantify the magnitude of the treatment effect. The hazard ratio describes relative effect magnitude, while the confidence interval describes uncertainty around that magnitude. These quantities answer different statistical questions.
Why is the proportional-hazards assumption relevant?
The Cox model is built around proportional hazards: the treatment-to-control hazard ratio is interpreted as a relative hazard over the analyzed time scale. If the relative hazard changes substantially over time, a single hazard ratio can become a less complete description of the treatment-effect pattern. The registry reports Cox analyses but does not provide a separate assessment of the proportional-hazards assumption.
7. Primary Results: Development of Advanced AMD
The registered primary endpoint was development of advanced AMD in people at moderate to high risk for progression over 5 years of follow-up. The endpoint included central geographic atrophy, retinal features of choroidal neovascularization detected on central grading of stereoscopic fundus photographs, or a history of treatment for advanced AMD after study enrollment.
Lutein / Zeaxanthin vs Placebo / Control
Hazard ratio for development of advanced AMD
98.7% two-sided CI: 0.76–1.07 · P < 0.013
Adjusted for baseline AMD status; placebo/control was the reference group.
An HR of 0.90 corresponds to an estimated 10% lower hazard of the primary event for lutein/zeaxanthin relative to placebo/control under the reported Cox model. This is a relative hazard interpretation, not a 10-percentage-point reduction in the probability of developing advanced AMD.
The 98.7% confidence interval of 0.76 to 1.07 indicates uncertainty around the point estimate. Because the interval includes 1, the reported interval is compatible with a range extending from an estimated lower hazard to a possible modestly higher hazard. The width of the interval also shows that the point estimate should not be interpreted as a highly precise estimate of a single underlying effect.
The reported P < 0.013 should not be interpreted as an effect-size measure. The p-value concerns the statistical testing framework, whereas the HR and confidence interval describe magnitude and precision. The primary analysis also involves three active-arm comparisons and a reported 98.7% confidence level, so the multiplicity structure is important to interpretation.
DHA / EPA vs Placebo / Control
Hazard ratio for development of advanced AMD
98.7% two-sided CI: 0.82–1.16 · P < 0.013
Placebo/control was the reference group.
An HR of 0.97 corresponds to an estimated hazard approximately 3% lower in the DHA/EPA group than in the placebo/control group under the reported Cox model. The estimate is close to 1, so the point estimate represents only a small relative difference in estimated hazard.
The 98.7% confidence interval of 0.82 to 1.16 spans 1 and includes both a possible lower hazard and a possible higher hazard. The interval therefore communicates substantial uncertainty about the direction and magnitude of the underlying relative hazard.
The reported P < 0.013 is a statistical-testing result rather than a measure of treatment benefit. It should be considered together with the hazard ratio, confidence interval, and the multiple-comparison structure rather than read as a statement about clinical magnitude.
Lutein / Zeaxanthin + DHA / EPA vs Placebo / Control
Hazard ratio for development of advanced AMD
98.7% two-sided CI: 0.75–1.06 · P < 0.013
Adjusted for multiple comparisons; placebo/control was the reference group.
An HR of 0.89 corresponds to an estimated 11% lower hazard of the primary event for the combined lutein/zeaxanthin plus DHA/EPA group relative to placebo/control. Again, this is not equivalent to an 11-percentage-point reduction in cumulative risk.
The 98.7% confidence interval of 0.75 to 1.06 crosses 1. The point estimate therefore should not be separated from its uncertainty interval: the reported data are compatible with a range of relative effects around the null value.
The registry specifically notes adjustment for multiple comparisons for this comparison. The reported p-value is therefore part of a prespecified testing context rather than a standalone measure of effect magnitude.
8. Comparing the Three Primary Hazard Ratios
| Comparison | HR | 98.7% two-sided CI | P-value | Adjustment noted |
|---|---|---|---|---|
| Lutein/zeaxanthin vs placebo/control | 0.90 | 0.76–1.07 | <0.013 | Adjusted for baseline AMD status |
| DHA/EPA vs placebo/control | 0.97 | 0.82–1.16 | <0.013 | Not specified in posted analysis text |
| Lutein/zeaxanthin + DHA/EPA vs placebo/control | 0.89 | 0.75–1.06 | <0.013 | Adjusted for multiple comparisons |
The three point estimates are all below 1, with estimates ranging from 0.89 to 0.97. However, the confidence intervals for all three comparisons cross 1. The appropriate statistical reading is therefore not to treat the point estimates alone as definitive evidence of a particular treatment effect, but to consider each estimate together with its uncertainty interval and the trial's multiplicity structure.
9. Secondary Results: Progression to Moderate Vision Loss
Progression to moderate vision loss was analyzed as a time-to-event endpoint over 5 years of follow-up using Cox regression. All three reported comparisons used two-sided 95% confidence intervals and a reported P < 0.05.
| Comparison | HR | 95% two-sided CI | P-value |
|---|---|---|---|
| Lutein/zeaxanthin vs placebo/control | 0.95 | 0.84–1.08 | <0.05 |
| DHA/EPA vs placebo/control | 0.96 | 0.84–1.09 | <0.05 |
| Lutein/zeaxanthin + DHA/EPA vs placebo/control | 0.94 | 0.83–1.07 | <0.05 |
The hazard-ratio estimates range from 0.94 to 0.96, corresponding to relatively small estimated differences in hazard. Each 95% confidence interval crosses 1, so the intervals encompass the possibility of no relative difference as well as modest effects in either direction.
The registry reports P < 0.05 for each analysis. Because the corresponding confidence intervals cross 1, these fields should be interpreted exactly as posted rather than assuming that a conventional two-sided p-value/confidence-interval relationship was used. The p-value does not quantify the size of the estimated effect.
10. Secondary Results: Mortality
The registry records mortality under the outcome measure "Adverse Events," with the analysis population described as the number of deaths in 5 years. Each comparison was analyzed with a Cox proportional-hazards model using a two-sided 95% confidence interval.
| Comparison | HR | 95% two-sided CI | P-value | Registry analysis note |
|---|---|---|---|---|
| Lutein/zeaxanthin vs placebo/control | 1.04 | 0.77–1.40 | <0.05 | Comparison of lutein/zeaxanthin versus control for mortality |
| DHA/EPA vs placebo/control | 1.13 | 0.84–1.52 | <0.05 | Comparison of DHA/EPA versus placebo for mortality |
| Lutein/zeaxanthin + DHA/EPA vs placebo/control | 1.23 | 0.92–1.65 | <0.05 | Comparison of combination versus placebo for mortality |
The mortality estimates are above 1 for all three active-arm comparisons, ranging from 1.04 to 1.23. A hazard ratio above 1 represents a higher estimated instantaneous event rate in the active group relative to control under the model; it does not establish a causal increase by itself.
The confidence intervals are relatively wide and include 1 for all three comparisons. The uncertainty intervals therefore include the possibility of no relative difference in mortality as well as effects in either direction.
As with the other secondary analyses, the registry reports P < 0.05. The p-value should not be treated as an estimate of the magnitude of the mortality difference, and the confidence interval is essential for understanding the precision of each estimate.
11. Secondary Result: Progression to Cataract Surgery
Progression to cataract surgery was analyzed among participants who were phakic in at least 1 eye at baseline. The posted comparison was no lutein/zeaxanthin versus lutein/zeaxanthin, rather than the placebo/control comparison used for the primary AMD analyses.
Hazard ratio for progression to cataract surgery
95% two-sided CI: 0.84–1.10 · P < 0.05
Analysis population: participants who were phakic in at least 1 eye at baseline.
The estimated hazard ratio of 0.96 corresponds to an estimated 4% lower hazard of cataract surgery in the lutein/zeaxanthin group relative to the no-lutein/zeaxanthin group under the Cox model.
The 95% confidence interval of 0.84 to 1.10 includes 1, so the interval is compatible with no difference as well as modest differences in either direction. The p-value is reported as <0.05, but it does not measure the size of the effect.
This analysis also uses a different comparison framework from the three primary AMD analyses. The reference group is defined as no lutein/zeaxanthin rather than simply the placebo/control arm.
12. Safety Results
The registry reports serious adverse events by randomized arm as affected participants divided by participants at risk. These values provide the arm-level serious-adverse-event counts available in the record.
| Arm | Serious adverse events affected / at risk |
|---|---|
| Placebo / Control | 479 / 1012 |
| Lutein / Zeaxanthin | 484 / 1044 |
| DHA / EPA | 505 / 1068 |
| Lutein / Zeaxanthin + DHA / EPA | 519 / 1079 |
The serious-adverse-event figures should be distinguished from the mortality analyses above. Mortality is analyzed in the posted statistical analyses as a time-to-event outcome, whereas the serious-adverse-event information here is presented as affected participants and participants at risk by arm.
Numerator
The first number in each arm is the number of participants affected by serious adverse events.
Denominator
The second number is the number of participants at risk reported for that arm.
13. Missing Follow-Up and Censoring
For the primary advanced-AMD analyses, participants lost to follow-up during the course of the study were censored at the time of last contact. This is a standard feature of time-to-event analysis: a participant can contribute information for the period during which their event status is known without being treated as having experienced the event after contact ends.
A censored participant contributes information up to the censoring time. The validity of the resulting survival comparison depends on assumptions concerning the censoring process and the adequacy of follow-up.
The registry specifically documents censoring at last contact for the primary endpoint. It does not provide additional missing-data or imputation procedures in the posted primary-analysis descriptions.
14. Randomization and Blinding
Randomization and blinding are design features rather than statistical tests. Their importance is that they help establish a cleaner framework for causal treatment comparisons, while the Cox analysis provides the model-based estimation of relative event hazards during follow-up.
15. Understanding the Primary Endpoint Statistically
The advanced-AMD endpoint is more informative than a simple yes/no assessment at 5 years because it records the timing of the event. Two participants can both develop advanced AMD, but if one develops it substantially earlier, a time-to-event analysis preserves that distinction.
Event occurrence
The endpoint records whether advanced AMD develops according to the registry definition.
Event timing
The Cox analysis uses when the event occurs during the 5-year follow-up rather than reducing every participant to a single binary status.
Censoring
Participants lost to follow-up are censored at their last contact for the primary analysis.
Relative effect
The hazard ratio summarizes the modeled relative event hazard between each active arm and the reference group.
16. Why the Hazard Ratio Is Not a Risk Ratio
A hazard ratio and a risk ratio answer related but different questions. A risk ratio compares cumulative probabilities over a specified period. A hazard ratio compares the instantaneous event rates represented by a time-to-event model.
| Measure | Question answered | AREDS2 use |
|---|---|---|
| Hazard ratio | How does the estimated instantaneous event rate compare between treatment groups under the Cox model? | Primary and secondary time-to-event analyses |
| Confidence interval | How uncertain is the estimated relative effect under the model and sampling framework? | 98.7% for primary analyses; 95% for secondary analyses |
| P-value | How compatible are the data with the null hypothesis under the specified testing framework? | Reported for each posted analysis |
| Event count | How many participants experienced the specified event? | Reported directly for serious adverse events by arm |
This distinction matters because an HR of 0.90 should not be rewritten as "10% lower 5-year risk." The direct statistical statement supported by the reported analysis is an estimated 10% lower hazard under the Cox model.
17. Confidence Intervals and Precision
The primary analyses use 98.7% two-sided confidence intervals, while the secondary analyses use 95% two-sided confidence intervals. A confidence interval is therefore part of the result itself, not an optional supplement to the hazard ratio.
| Analysis | Estimate | Confidence interval | What the interval shows |
|---|---|---|---|
| Primary: lutein/zeaxanthin | 0.90 | 0.76–1.07 | Includes 1; range spans lower and higher estimated hazards |
| Primary: DHA/EPA | 0.97 | 0.82–1.16 | Includes 1; range spans lower and higher estimated hazards |
| Primary: combination | 0.89 | 0.75–1.06 | Includes 1; range spans lower and higher estimated hazards |
| Secondary: moderate vision loss, lutein/zeaxanthin | 0.95 | 0.84–1.08 | Includes 1 |
| Secondary: moderate vision loss, DHA/EPA | 0.96 | 0.84–1.09 | Includes 1 |
| Secondary: moderate vision loss, combination | 0.94 | 0.83–1.07 | Includes 1 |
The interval does not describe the range of treatment effects that individual participants experience. It describes uncertainty around the estimated population-level relative effect under the statistical framework.
18. Multiplicity in a Four-Arm Trial
AREDS2 has three active treatment comparisons against a common placebo/control reference for the primary endpoint. Testing several treatment comparisons creates a multiplicity issue because the probability of observing an apparently unusual result can increase when multiple hypotheses are considered.
Three primary comparisons
The registry reports separate primary analyses for lutein/zeaxanthin, DHA/EPA, and the combined intervention versus placebo/control.
98.7% confidence level
The primary analyses use two-sided 98.7% confidence intervals rather than the 95% intervals used for the secondary analyses.
Adjusted analysis
The registry explicitly notes adjustment for multiple comparisons for the combined-intervention primary analysis.
Interpretation
Primary p-values should be interpreted within the trial's multiple-comparison framework rather than as isolated numerical quantities.
19. A Closer Look at the Secondary Analyses
The secondary analyses illustrate why the same Cox methodology can produce quite different scientific questions. The event can be vision loss, death, or cataract surgery; the population and reference group can also change.
| Outcome | Reference comparison | Population detail | Effect measure |
|---|---|---|---|
| Moderate vision loss | Each active arm vs placebo/control | 5 years of follow-up | HR |
| Mortality | Each active arm vs placebo/control | Number of deaths in 5 years | HR |
| Cataract surgery | No lutein/zeaxanthin vs lutein/zeaxanthin | Participants phakic in at least 1 eye at baseline | HR |
The difference in comparison structure is especially important for cataract surgery. That analysis is not simply another copy of the primary placebo/control comparison: the registry explicitly defines the groups as no lutein/zeaxanthin versus lutein/zeaxanthin.
20. Interpreting the Trial Without Overreading the Point Estimates
The three primary HR estimates for advanced AMD are 0.90, 0.97, and 0.89. Each is below 1, which corresponds to a lower estimated hazard in the active arm under the Cox model.
The corresponding 98.7% confidence intervals are 0.76–1.07, 0.82–1.16, and 0.75–1.06. Each interval includes 1, so the point estimates should not be interpreted without their uncertainty intervals.
The moderate-vision-loss HRs are close to 1, while the mortality HRs are above 1. These are different endpoints with different clinical meanings, and they should not be collapsed into a single overall treatment-effect statistic.
The statistical evidence consists of the prespecified randomized comparisons, time-to-event models, effect estimates, confidence intervals, and reported p-values. Whether an estimated difference is clinically important is a separate question that requires consideration of the magnitude, endpoint, precision, and clinical context.
21. Important Limitations and Interpretation Issues
- Confidence intervals crossing 1: all three primary hazard-ratio confidence intervals include 1, so the point estimates should not be treated as precise estimates of a single non-null effect.
- Multiplicity: three active treatment arms were compared with a common placebo/control arm for the primary endpoint, making the multiple-comparison framework important.
- Censoring: participants lost to follow-up were censored at the time of last contact for the primary analyses. Interpretation therefore depends in part on the assumptions underlying the censoring mechanism.
- Proportional hazards: the Cox model provides a single hazard-ratio summary, but the registry does not report a separate assessment of the proportional-hazards assumption.
- Different confidence levels: the primary analyses use 98.7% confidence intervals, whereas the secondary analyses use 95% confidence intervals.
- Different comparison for cataract surgery: the cataract-surgery analysis compares no lutein/zeaxanthin with lutein/zeaxanthin rather than using the placebo/control comparison.
- Secondary endpoint interpretation: the registry reports p-values and confidence intervals for secondary outcomes, but these analyses should be distinguished from the registered primary endpoint.
- Serious adverse events: the registry provides affected/at-risk counts by arm, while the posted statistical analyses separately model mortality as a time-to-event outcome.
22. Why This Trial Matters Statistically
AREDS2 is a useful statistical teaching case because it combines randomized treatment assignment with a four-arm design and several clinically distinct time-to-event endpoints. The primary endpoint requires survival-analysis methods because both event occurrence and event timing are relevant.
| Concept | How it appears in AREDS2 |
|---|---|
| Randomization | Participants were randomized across four parallel arms. |
| Blinding | The registry identifies the study as double-blind. |
| Intention-to-treat analysis | The primary analyses used an intention-to-treat population. |
| Time-to-event endpoints | Advanced AMD, moderate vision loss, mortality, and cataract surgery were analyzed as time-to-event outcomes. |
| Cox proportional-hazards model | Used for all ten posted statistical analyses. |
| Hazard ratio | Used as the reported effect measure across the statistical analyses. |
| Confidence intervals | 98.7% for primary analyses and 95% for secondary analyses. |
| Censoring | Primary analyses censored participants lost to follow-up at last contact. |
| Covariate adjustment | The lutein/zeaxanthin primary analysis was adjusted for baseline AMD status. |
| Multiplicity | Three active-arm comparisons were made against placebo/control for the primary endpoint. |
23. Related Tutorials
Learn more about the statistical methods used in this trial:
24. Related Calculators
25. Sources
- ClinicalTrials.gov: NCT00345176 — Age-Related Eye Disease Study 2 (AREDS2).
- Linked publication: PubMed record for PMID 37702300.
- Linked publication: PubMed record for PMID 34793832.
- Linked publication: PubMed record for PMID 32285590.
- Linked publication: PubMed record for PMID 26305649.
- Linked publication: PubMed record for PMID 24638908.
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26. Record Summary
AREDS2 provides a clear example of randomized clinical-trial analysis centered on time-to-event methodology. The primary endpoint, development of advanced AMD over 5 years, was analyzed using intention-to-treat Cox proportional-hazards models with censoring at last contact for participants lost to follow-up. The three primary treatment comparisons produced hazard-ratio estimates of 0.90, 0.97, and 0.89, with 98.7% two-sided confidence intervals of 0.76–1.07, 0.82–1.16, and 0.75–1.06, respectively.
The secondary analyses demonstrate how the same survival-analysis framework can be applied to different endpoints. Moderate vision loss produced HR estimates from 0.94 to 0.96, mortality produced estimates from 1.04 to 1.23, and cataract surgery produced an HR of 0.96 for lutein/zeaxanthin versus no lutein/zeaxanthin. The interpretation of each estimate depends on the endpoint, comparison group, analysis population, confidence interval, and testing framework.
The statistical lesson is broader than any individual hazard ratio. A complete interpretation combines randomization, blinding, intention-to-treat analysis, censoring, Cox regression, hazard ratios, confidence intervals, and multiplicity. Presenting these elements together makes the statistical structure of the trial more transparent than reporting isolated p-values or point estimates.