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
OPTIMIZE was a randomized, parallel-group, quadruple-masked phase 3 trial evaluating roflumilast dosing strategies as add-on treatment to standard COPD treatment. The registered primary endpoint was premature discontinuation of study treatment for any reason during the 12-week Main Period.
| Feature | OPTIMIZE |
|---|---|
| Phase | Phase 3 |
| Condition | Chronic Obstructive Pulmonary Disease (COPD) |
| Therapeutic area | Respiratory |
| Design | Randomized, parallel-group, quadruple-masked |
| Allocation | Randomized |
| Primary purpose | Treatment |
| Enrollment | 1,323 |
| Interventions | Roflumilast; roflumilast placebo; standard of care COPD treatment |
| Primary endpoint | Percentage of participants prematurely discontinuing study treatment due to any reason |
| Primary endpoint time frame | Baseline to Week 12 (Main Period) |
| Lead sponsor | AstraZeneca |
| Trial status | Completed |
2. Clinical Question
The primary statistical question was whether roflumilast dosing strategies could reduce premature discontinuation of study treatment during the 12-week Main Period compared with roflumilast 500 μg once daily.
Population
Participants with chronic obstructive pulmonary disease, in a phase 3 treatment study of severe COPD.
Intervention strategies
Roflumilast 250 μg once daily followed by 500 μg once daily, or roflumilast 500 μg every other day followed by 500 μg once daily.
Comparator
Roflumilast 500 μg once daily.
Primary question
Does either dosing strategy reduce the likelihood or hazard of premature treatment discontinuation during the Main Period?
3. Trial Design
250 μg OD Then 500 μg OD
- Roflumilast 250 μg once daily initially
- Then roflumilast 500 μg once daily
- Compared directly with roflumilast 500 μg once daily in the posted primary analyses
500 μg EOD Then 500 μg OD
- Roflumilast 500 μg every other day initially
- Then roflumilast 500 μg once daily
- Compared directly with roflumilast 500 μg once daily in the posted primary analyses
4. Primary Endpoint
The registered primary endpoint was the percentage of participants prematurely discontinuing study treatment due to any reason during the Main Period from Visit 1 (V1) to the Last Visit (Vend).
| Endpoint component | Registry definition |
|---|---|
| Endpoint | Percentage of participants prematurely discontinuing study treatment due to any reason |
| Time frame | Baseline to Week 12 (Main Period) |
| Discontinuation definition | Permanently stopping randomized treatment |
| Resumption of treatment | Participants who resume randomized treatment after an interval are not counted as having discontinued |
| Period considered | Discontinuations occurring during the Main Period, irrespective of whether a participant subsequently entered the Down-Titration Period |
This endpoint is naturally suited to two complementary statistical perspectives. A binary analysis asks whether discontinuation occurred during the specified period, whereas a time-to-event analysis additionally uses the timing of discontinuation and censoring.
5. Analysis Population and Statistical Framework
The posted analyses used the Safety Analysis Set (SAS), defined as all randomized participants who took at least one dose of study medication.
The combination of logistic regression and Cox regression is statistically informative. The logistic model reduces the endpoint to whether premature discontinuation occurred during the Main Period, while the Cox model retains information about when discontinuation occurred.
6. Statistical Methodology
Logistic regression
For the binary version of the primary endpoint, logistic regression models the probability of premature discontinuation as a function of treatment and other model terms specified for the analysis. The reported effect measure is an odds ratio.
The odds ratio compares the odds of premature discontinuation between treatment groups. An odds ratio below 1 indicates lower estimated odds in the first group relative to the comparator.
Cox proportional-hazards model
The time-to-event primary analyses used a Cox proportional-hazards model. The registry specifies study treatment and country as class effects, with baseline FEV1 entered as a continuous variable.
The hazard ratio summarizes the relative instantaneous rate of discontinuation between treatment groups under the proportional-hazards model.
Hierarchical testing
The registry states that the posted analyses were performed using a hierarchical testing procedure. Hierarchical testing provides an ordered framework for evaluating multiple hypotheses so that later hypotheses are interpreted according to the prespecified sequence rather than as unrelated tests.
This matters because the nominal P-value for an individual comparison is not, by itself, the complete description of multiplicity control. The order and rules governing the hierarchy determine how statistical evidence propagates through the testing sequence.
Two complementary effect measures
The odds ratio and hazard ratio are related but not interchangeable. The odds ratio summarizes the relative odds of experiencing the binary endpoint during the defined period. The hazard ratio incorporates the timing of the event and therefore answers a somewhat different question.
Odds ratio
Best understood as a comparison of discontinuation odds during the Main Period. It does not directly describe a relative probability or risk ratio.
Hazard ratio
Describes the relative instantaneous discontinuation rate under the Cox model. It is not the same quantity as an odds ratio or a risk ratio.
7. Primary Results: 250 μg OD Then 500 μg OD vs 500 μg OD
Binary analysis
Odds ratio for premature discontinuation
95% CI: 0.47–0.93 · P = 0.017
Logistic regression; Safety Analysis Set; superiority hypothesis.
The estimated odds of premature treatment discontinuation were lower for the roflumilast 250 μg once-daily-then-500 μg once-daily strategy than for roflumilast 500 μg once daily. The odds ratio of 0.66 corresponds to approximately 34% lower estimated odds because 1 − 0.66 = 0.34.
The 0.66 odds ratio describes relative odds, not a 34-percentage-point reduction in discontinuation and not necessarily a 34% reduction in the probability of discontinuation. The confidence interval of 0.47–0.93 describes statistical precision around the estimated odds ratio; because the interval remains below 1, the posted two-sided analysis provides evidence favoring lower discontinuation odds under the stated superiority framework.
The P = 0.017 value addresses compatibility with the null hypothesis used for this comparison under the statistical testing framework. It does not measure the magnitude or clinical importance of the treatment effect. The hierarchical testing procedure is also relevant when interpreting the evidentiary status of the P-value.
Time-to-event analysis
Hazard ratio for premature discontinuation
95% CI: 0.51–0.92
Cox proportional-hazards model; Safety Analysis Set; superiority hypothesis.
The Cox model estimated a lower hazard of premature discontinuation with the 250 μg once-daily-then-500 μg once-daily strategy. An HR of 0.68 corresponds to approximately a 32% lower estimated instantaneous discontinuation hazard because 1 − 0.68 = 0.32.
The 0.68 hazard ratio is a model-based relative comparison of the instantaneous rate of discontinuation. It does not mean that 32% fewer participants discontinued, nor does it mean that every participant experienced exactly a 32% reduction in probability of discontinuation.
The 95% CI of 0.51–0.92 indicates uncertainty around the hazard-ratio estimate and remains below 1. The Cox interpretation depends on the proportional-hazards framework: if the relative hazards change materially over time, a single HR may compress a more complicated time-dependent pattern into one summary measure.
No P-value is reported in the posted Cox analysis. The absence of a displayed P-value should not be treated as evidence for either significance or non-significance; the confidence interval supplies the principal inferential information reported for this analysis.
8. Primary Results: 500 μg EOD Then 500 μg OD vs 500 μg OD
Binary analysis
Odds ratio for premature discontinuation
95% CI: 0.55–1.07 · P = 0.114
Logistic regression; Safety Analysis Set; superiority hypothesis.
The estimated odds of premature discontinuation were lower with the 500 μg every-other-day-then-500 μg once-daily strategy than with 500 μg once daily, with an estimated odds ratio of 0.76.
The 0.76 odds ratio corresponds to approximately 24% lower estimated odds of premature discontinuation relative to the comparator because 1 − 0.76 = 0.24. This is an odds comparison, not a direct estimate of a 24% lower probability.
The 95% CI of 0.55–1.07 crosses 1, so the posted interval includes the possibility of no difference in odds. The interval is therefore important for understanding uncertainty rather than focusing only on the point estimate of 0.76.
The P = 0.114 value is not a measure of effect size. It reflects the statistical evidence under the specified hypothesis-testing framework. Because the confidence interval includes 1, the estimate does not establish superiority in this posted analysis.
Time-to-event analysis
Hazard ratio for premature discontinuation
95% CI: 0.58–1.02
Cox proportional-hazards model; Safety Analysis Set; superiority hypothesis.
The estimated hazard of premature discontinuation was lower with the 500 μg every-other-day-then-500 μg once-daily strategy, with an HR of 0.77. This corresponds to approximately a 23% lower estimated instantaneous hazard because 1 − 0.77 = 0.23.
The 0.77 HR summarizes the relative discontinuation hazard under the Cox model. It does not establish that the cumulative probability of discontinuation was exactly 23% lower and does not describe individual treatment experiences.
The 95% CI of 0.58–1.02 is relatively close to 1 at its upper boundary and includes 1. Thus, the reported estimate is compatible with a modest reduction in hazard as well as with little or no difference under the model.
No P-value is reported in the posted Cox analysis. As with the other Cox result, interpretation should also recognize the proportional-hazards assumption and the fact that timing and censoring are incorporated into the analysis.
9. Primary Endpoint Results at a Glance
| Comparison | Method | Estimate | 95% CI | P-value |
|---|---|---|---|---|
| 250 μg OD Then 500 μg OD vs 500 μg OD | Logistic regression | OR 0.66 | 0.47–0.93 | 0.017 |
| 250 μg OD Then 500 μg OD vs 500 μg OD | Cox proportional-hazards model | HR 0.68 | 0.51–0.92 | Not reported |
| 500 μg EOD Then 500 μg OD vs 500 μg OD | Logistic regression | OR 0.76 | 0.55–1.07 | 0.114 |
| 500 μg EOD Then 500 μg OD vs 500 μg OD | Cox proportional-hazards model | HR 0.77 | 0.58–1.02 | Not reported |
The two statistical approaches point in the same directional direction for both comparisons: the point estimates are below 1. However, the strength of the evidence differs between dosing strategies. The 250 μg once-daily-then-500 μg once-daily strategy has confidence intervals below 1 for both reported effect measures, whereas the 500 μg every-other-day-then-500 μg once-daily strategy has intervals that extend across 1.
10. Secondary Endpoint: Adverse Events of Interest
The registry also posted analyses of the secondary endpoint percentage of participants with adverse events of interest during the Main Period from baseline to Week 12. These analyses used logistic regression in the Safety Analysis Set.
250 μg OD Then 500 μg OD vs 500 μg OD
Odds ratio for adverse events of interest
95% CI: 0.47–0.83 · P = 0.001
Logistic regression; superiority hypothesis.
The estimated odds of adverse events of interest were lower for the 250 μg once-daily-then-500 μg once-daily strategy, with an odds ratio of 0.63. This corresponds to approximately 37% lower estimated odds because 1 − 0.63 = 0.37.
The 0.63 odds ratio is a relative odds measure and should not be translated directly into a 37-percentage-point reduction in adverse-event probability. The 95% CI of 0.47–0.83 lies below 1, indicating that the posted analysis estimated lower odds under the stated superiority framework.
The P = 0.001 value describes statistical evidence against the relevant null hypothesis; it does not quantify clinical importance or tell us how large the absolute difference in adverse-event frequency was.
500 μg EOD Then 500 μg OD vs 500 μg OD
Odds ratio for adverse events of interest
95% CI: 0.59–1.04 · P = 0.091
Logistic regression; superiority hypothesis.
The estimated odds of adverse events of interest were lower with the 500 μg every-other-day-then-500 μg once-daily strategy, with an odds ratio of 0.78.
The 0.78 odds ratio corresponds to approximately 22% lower estimated odds because 1 − 0.78 = 0.22. The 95% CI of 0.59–1.04 includes 1, so the interval does not exclude no difference in odds.
The P = 0.091 value should not be interpreted as a probability that the treatment is ineffective. P-values measure statistical evidence relative to a null hypothesis under the specified model and testing framework; they do not measure effect magnitude, clinical relevance, or the probability that a hypothesis is true.
11. Safety: Serious Adverse Events by Arm
The registry reports serious adverse events by the listed treatment periods and arms as affected participants over participants at risk.
| Arm / treatment period | Affected / at risk |
|---|---|
| Roflumilast 250 μg OD Then 500 μg OD — Main | 19/441 |
| Roflumilast 500 μg EOD Then 500 μg OD — Main | 22/437 |
| Roflumilast 500 μg OD — Main Treatment Period | 20/443 |
| Roflumilast 250 μg OD Then 500 μg OD — Down-Titration | 1/27 |
| Roflumilast 500 μg EOD — Down-Titration Period | 0/39 |
| Roflumilast 500 μg OD — Down-Titration Period | 0/38 |
These counts are descriptive safety summaries. They should not be interpreted as causal comparisons merely by comparing the numerators. The denominators differ across the listed treatment periods, and the registry's posted inferential analyses concern the specified adverse-events-of-interest endpoint rather than these serious-adverse-event counts.
12. Statistical Methods Explained
Why use both logistic regression and a Cox model?
The primary endpoint can be viewed in two ways. Logistic regression asks whether a participant discontinued during the Main Period. Cox regression additionally uses the timing of discontinuation, so a participant who discontinues earlier contributes different information from one who discontinues later, subject to the model's censoring framework.
What does an odds ratio of 0.66 mean?
An OR of 0.66 means that the estimated odds of premature discontinuation were 0.66 times the comparator odds. Equivalently, the estimated odds were approximately 34% lower. This is not the same as saying that the probability of discontinuation was 34% lower, because odds and probabilities are different quantities.
What does a hazard ratio of 0.68 mean?
Under the Cox proportional-hazards model, an HR of 0.68 means that the estimated instantaneous hazard of premature discontinuation was approximately 32% lower in the first treatment group relative to the comparator. It is a relative rate measure over time, not an absolute probability.
Why can the odds ratio and hazard ratio be different?
The two models use different information. Logistic regression treats the endpoint as a binary outcome over the defined period. The Cox model uses event timing and censoring. Consequently, an OR of 0.66 and an HR of 0.68 can both describe the same randomized comparison without being numerically identical.
Why is the confidence interval important?
A point estimate is only one summary of the observed data. The confidence interval describes the statistical uncertainty around that estimate under the model and sampling framework. For the 250 μg once-daily-then-500 μg once-daily comparison, the OR interval of 0.47–0.93 and HR interval of 0.51–0.92 remain below 1. For the 500 μg every-other-day-then-500 μg once-daily comparison, both intervals include 1.
Why does the P-value not measure treatment effect size?
A P-value addresses statistical evidence relative to a null hypothesis. It is influenced by effect magnitude, variability, and information in the analysis, but it is not itself a measure of clinical benefit. Effect size is better conveyed by the OR or HR together with its confidence interval and, when available, absolute event probabilities.
Why does hierarchical testing matter?
The registry states that the analyses were performed using a hierarchical testing procedure. When multiple hypotheses are evaluated, the order of testing can determine how evidence is carried forward and how type I error is controlled. A reported P-value therefore needs to be interpreted in the context of the prespecified testing sequence rather than as an isolated number.
13. Understanding the Cox Model in OPTIMIZE
The Cox model used in the posted primary analyses included study treatment and country as class effects and baseline FEV1 as a continuous variable.
| Model component | Role in the posted analysis |
|---|---|
| Study treatment | Primary exposure defining the randomized comparison |
| Country | Class effect included in the Cox model |
| Baseline FEV1 | Continuous covariate included in the Cox model |
| Effect measure | Hazard ratio |
| Endpoint timing | Premature discontinuation during the Main Period |
Including baseline FEV1 as a continuous variable allows the model to account for variation in baseline lung function without converting the measurement into arbitrary categories. Country as a class effect accounts for the categorical country structure specified by the registry analysis.
The direction of the hazard ratio is straightforward, but the magnitude still requires the confidence interval and consideration of the proportional-hazards assumption.
14. Odds Ratios and the Probability Scale
Because the primary endpoint is binary, it is important to distinguish odds from probability. If the probability of discontinuation is p, the odds are p/(1−p). Logistic regression models the logarithm of those odds.
An odds ratio of 0.66 therefore cannot automatically be described as a 34% reduction in probability. The corresponding probability difference depends on the baseline probability in the comparator group.
This distinction becomes especially important when communicating results to clinical audiences. Relative odds can appear large or small depending on baseline event frequency, while absolute risk differences depend directly on that baseline frequency.
15. Multiplicity and Hierarchical Testing
The registry explicitly states that the posted analyses were performed using a hierarchical testing procedure. This is an important part of the inferential structure because the trial has more than one posted hypothesis and more than one treatment comparison.
Why hierarchy matters
Multiple statistical tests can increase the chance of false-positive findings if treated as independent confirmatory tests. A hierarchy specifies an ordered sequence for evaluating hypotheses.
Why P-values need context
A P-value such as 0.017 should be interpreted within the prespecified testing strategy rather than treated as a standalone statement about the entire trial.
The posted analyses identify multiplicity adjustment as an analysis concept. The registry does not provide further numerical detail about the full hierarchy in the information summarized here, so the principal interpretive point is the existence of the hierarchical testing framework.
16. Endpoint Interpretation: Discontinuation as a Clinical-Trial Outcome
Treatment discontinuation is different from a traditional efficacy endpoint. A participant may stop treatment for tolerability, safety, preference, logistical reasons, or another reason, and the registered endpoint intentionally combines these possibilities under "due to any reason."
| Statistical question | What it captures |
|---|---|
| Binary discontinuation endpoint | Whether permanent discontinuation occurred during the Main Period |
| Time-to-discontinuation endpoint | Whether and when permanent discontinuation occurred, subject to the analysis framework |
| Adverse events of interest | Whether participants experienced the registered adverse-event endpoint during the Main Period |
| Serious adverse events | Descriptive affected/at-risk counts by listed treatment period |
This distinction is important because a lower discontinuation rate can reflect improved tolerability or other treatment-exposure differences, but the discontinuation endpoint alone does not identify the mechanism of the difference.
17. Results Summary
| Endpoint | Comparison | Estimate | 95% CI | P-value |
|---|---|---|---|---|
| Premature discontinuation | 250 μg OD Then 500 μg OD vs 500 μg OD | OR 0.66 | 0.47–0.93 | 0.017 |
| Premature discontinuation | 250 μg OD Then 500 μg OD vs 500 μg OD | HR 0.68 | 0.51–0.92 | Not reported |
| Premature discontinuation | 500 μg EOD Then 500 μg OD vs 500 μg OD | OR 0.76 | 0.55–1.07 | 0.114 |
| Premature discontinuation | 500 μg EOD Then 500 μg OD vs 500 μg OD | HR 0.77 | 0.58–1.02 | Not reported |
| Adverse events of interest | 250 μg OD Then 500 μg OD vs 500 μg OD | OR 0.63 | 0.47–0.83 | 0.001 |
| Adverse events of interest | 500 μg EOD Then 500 μg OD vs 500 μg OD | OR 0.78 | 0.59–1.04 | 0.091 |
The most consistent statistical signal in the posted analyses is associated with the 250 μg once-daily-then-500 μg once-daily strategy. Its primary discontinuation OR and HR both have confidence intervals below 1, while its adverse-events-of-interest OR is also below 1 with a confidence interval below 1. The corresponding 500 μg every-other-day-then-500 μg once-daily estimates are also below 1, but their reported confidence intervals extend across 1 for the primary endpoint and the adverse-events-of-interest endpoint.
18. Limitations
- Endpoint interpretation: premature discontinuation due to any reason is a composite behavioral and treatment-exposure outcome rather than a direct measure of disease control.
- Analysis population: the posted analyses used the Safety Analysis Set, consisting of randomized participants who took at least one dose of study medication.
- Odds versus risk: odds ratios should not be described as risk ratios or direct probability reductions.
- Proportional hazards: Cox hazard ratios rely on the proportional-hazards framework. A single HR may not fully characterize an effect if the relative hazard changes substantially over time.
- Multiplicity: the registry identifies a hierarchical testing procedure, so individual P-values should be interpreted within the testing structure.
- Missing timing information: the posted summary results do not provide a full event-and-censoring dataset, so the numerical HR cannot be decomposed into a complete survival curve from the registry summary alone.
- Safety interpretation: serious-adverse-event counts are descriptive affected/at-risk summaries and should not be treated as equivalent to the posted logistic-regression analysis of adverse events of interest.
- Generalizability: the registry describes a phase 3 study of severe COPD, so applicability depends on how closely other populations resemble the enrolled study population.
19. Why This Trial Matters Statistically
OPTIMIZE is a useful teaching example because the same clinical endpoint is analyzed through two different statistical lenses. The trial demonstrates how a binary endpoint and a time-to-event endpoint can provide complementary evidence about treatment discontinuation.
| Concept | How it appears in OPTIMIZE |
|---|---|
| Randomization | Participants were randomized in a phase 3 parallel-group trial. |
| Blinding | The trial used quadruple masking. |
| Binary endpoint | Premature discontinuation was registered as a binary primary endpoint. |
| Logistic regression | Used to estimate odds ratios for discontinuation and adverse events of interest. |
| Odds ratio | Primary binary effect measure for the posted logistic analyses. |
| Time-to-event endpoint | Premature discontinuation was also analyzed according to timing. |
| Cox model | Used to estimate hazard ratios for premature discontinuation. |
| Hazard ratio | Provided a time-to-event measure complementary to the odds ratio. |
| Confidence intervals | Reported as two-sided 95% intervals for all posted primary analyses. |
| Multiplicity adjustment | The registry states that analyses used hierarchical testing. |
| Covariate adjustment | The Cox model included country and baseline FEV1 in addition to study treatment. |
20. Related Tutorials
Learn more about the methods used in this trial:
21. Related Calculators
22. Sources
- ClinicalTrials.gov: NCT02165826.
- Linked publication: PubMed record for PMID 29797235.
Continue through Clinical Biostats
Explore statistical tutorials, calculators, and additional clinical-trial analyses covering the methods used across randomized clinical research.
23. Record Summary
OPTIMIZE provides a clear example of how treatment discontinuation can be evaluated as both a binary outcome and a time-to-event outcome. The posted primary analyses used logistic regression to estimate odds ratios and Cox proportional-hazards models to estimate hazard ratios. For the 250 μg once-daily-then-500 μg once-daily strategy, the posted OR of 0.66 and HR of 0.68 both favored the dosing strategy relative to 500 μg once daily, with two-sided 95% confidence intervals below 1. For the 500 μg every-other-day-then-500 μg once-daily strategy, the corresponding estimates were 0.76 and 0.77, with confidence intervals that included 1. The secondary adverse-events-of-interest analyses followed the same general directional pattern, with ORs of 0.63 and 0.78, respectively.
The statistical lesson is broader than any single estimate. Logistic regression and Cox regression answer related but distinct questions; odds ratios and hazard ratios require different interpretations; confidence intervals provide essential information about precision; and hierarchical testing determines how multiple statistical comparisons should be interpreted. Together, these principles provide a rigorous framework for understanding the OPTIMIZE results.