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
BRAVO was a randomized, parallel-group, phase 3 study in participants with relapsing-remitting multiple sclerosis. The study compared laquinimod and placebo and included Avonex® as a rater-blinded reference arm.
| Feature | BRAVO |
|---|---|
| Phase | Phase 3 |
| Condition | Multiple Sclerosis |
| Study population | Participants with relapsing-remitting multiple sclerosis |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Quadruple |
| Primary purpose | Treatment |
| Enrollment | 1,331 |
| Interventions | Laquinimod; Placebo; Avonex® |
| Primary endpoint type | Count / rate |
| Primary endpoint | Annualized Rate of Confirmed Relapses |
| Primary analysis | Baseline-adjusted negative binomial regression |
| Primary effect measure | Risk Ratio (RR) |
| ClinicalTrials.gov | NCT00605215 |
2. Clinical Question
The central statistical question was whether the annualized rate of confirmed relapses differed between participants randomized to placebo and those randomized to laquinimod, and between participants randomized to placebo and those randomized to Avonex®, during the period from baseline up to Month 24.
Population
Participants with relapsing-remitting multiple sclerosis enrolled in the BRAVO phase 3 study.
Intervention
Laquinimod.
Comparator
Placebo for the primary treatment comparison, with Avonex® serving as a reference arm.
Primary question
How did the annualized rate of confirmed relapses compare between placebo and each active study arm over the 24-month treatment period?
3. Trial Design
Laquinimod
- Laquinimod was one of the three study interventions.
- The primary statistical comparison was placebo versus laquinimod.
- The analysis used the ITT analysis set.
Placebo
- Placebo was the comparator for both posted primary analyses.
- The placebo group was compared with laquinimod and with Avonex®.
- The analysis used the ITT analysis set.
Avonex®
- Avonex® was included as a rater-blinded reference arm.
- The posted analysis compared placebo with Avonex®.
- The study was quadruple-masked overall.
4. Study Timeline
| Milestone | Date |
|---|---|
| Study start | April 24, 2008 |
| Primary completion | June 10, 2011 |
| Status | Completed |
The registry identifies Teva Branded Pharmaceutical Products R&D, Inc. as the lead sponsor and classifies the sponsor type as industry.
5. Primary Endpoint
| Endpoint | Registry definition | Time frame |
|---|---|---|
| Annualized Rate of Confirmed Relapses | A relapse was defined as the appearance of new neurological abnormalities or the reappearance of previously observed neurological abnormalities; lasting at least 48 hours and immediately preceded by an improved neurological state of ≥30 days from onset of previous relapse, accompanied by observed objective neurological changes: an increase of ≥0.5 in Expanded Disability Status Scale [EDSS] score, or an increase of 1 grade in the score of 2 or more of the 7 Functional Systems [FS], or an increase of 2 grades in the score of 1 FS as compared to the previous evaluation. Total number of confirmed relapses during the treatment period was divided by the sum of number of days on study in the treatment period and then multiplied by the number of days in the year to calculate the annualized relapse rate. Annualized relapse rate was derived from a baseline-adjusted negative binomial regression. | Baseline up to Month 24 |
This endpoint is a count/rate outcome. Each participant can contribute more than one confirmed relapse, and participants can contribute different amounts of observation time. The statistical analysis therefore models the number of events while accounting for exposure time rather than treating each participant as having only a single binary outcome.
6. Analysis Population
The posted analyses used the ITT analysis set, which included all randomized participants. This is important because the comparison remains anchored to the randomized treatment assignment rather than being restricted to participants who completed treatment or contributed a particular amount of follow-up.
The ITT framework preserves the treatment groups created by randomization. For a randomized comparison, this helps maintain the interpretive advantage of random allocation even when participants have different amounts of observation or treatment exposure.
7. Statistical Methodology
Negative binomial regression
The registry reports negative binomial regression as the primary analytical method. This is a regression model for count data that is useful when the observed variability in event counts is greater than would be adequately represented by a simple Poisson model.
Here, the response variable was each participant's number of relapses during the double-blind, placebo-controlled phase. The model incorporated an offset based on the log of participant exposure in years. The offset accounts for variability in the amount of time participants were observed and places the model on a rate scale.
The exposure offset allows participants with different observation times to contribute information on an annualized rate rather than treating their raw relapse counts as directly comparable.
Baseline covariate adjustment
The negative binomial model was baseline-adjusted. The registry identifies three covariates: baseline EDSS score, log of (prior 2-year number of relapses + 1), and CGR.
Covariate adjustment can improve precision by accounting for prespecified baseline characteristics related to the outcome. Importantly, the adjusted effect estimate is still interpreted as the comparison between the randomized treatment groups under the fitted model.
Risk ratio / relative risk as the reported effect measure
The registry reports Risk Ratio (RR) as the effect measure for both primary analyses. In the context of this count/rate analysis, the numerical estimate compares the modeled annualized relapse rates between the two groups.
An estimate below 1 indicates a lower estimated rate in the numerator group relative to the reference group. The precise interpretation should remain tied to the registry's reported comparison and model.
Exposure offset
The offset was based on the log of participant exposure in years. This is an important feature of the analysis because annualized relapse rate depends not only on the number of observed relapses but also on how long each participant was observed.
8. Primary Results: Placebo vs Laquinimod
The first posted primary analysis compared placebo with laquinimod for the annualized rate of confirmed relapses from baseline up to Month 24.
Annualized Rate of Confirmed Relapses
95% CI: 0.664–1.020 · P = 0.0746
Analysis population: ITT analysis set, including all randomized participants.
| Feature | Placebo vs Laquinimod |
|---|---|
| Endpoint | Annualized Rate of Confirmed Relapses |
| Time frame | Baseline up to Month 24 |
| Method | Baseline-adjusted negative binomial regression |
| Analysis population | ITT analysis set |
| Effect measure | Risk Ratio (RR) |
| Estimate | 0.823 |
| 95% CI | 0.664–1.020 |
| P-value | 0.0746 |
An RR of 0.823 corresponds to an estimated rate about 17.7% lower for the numerator group relative to the reference group, using the reciprocal comparison implied by the reported placebo-versus-laquinimod estimate. The estimate therefore describes a relative difference in modeled annualized relapse rates, not a statement that 17.7% of participants avoided a relapse.
The 95% confidence interval of 0.664–1.020 spans 1.00. Thus, the interval includes values corresponding to no relative difference as well as values corresponding to lower or higher rates. The interval is therefore important for understanding the precision of the estimate rather than focusing only on the point estimate.
The P-value of 0.0746 describes the compatibility of the observed result with the statistical hypothesis framework used for the comparison; it is not a measure of the size or clinical importance of the effect. A P-value should not be interpreted as the probability that the treatment works or as the probability that the null hypothesis is true.
The analysis was model-based and adjusted for baseline EDSS score, log of prior 2-year relapses plus 1, and CGR, with an exposure offset. The estimate therefore reflects the fitted negative binomial model rather than a simple unadjusted division of total relapses by total follow-up.
9. Primary Results: Placebo vs Avonex®
The second posted primary analysis used the same endpoint, time frame, analysis population, and negative binomial modeling framework, but compared placebo with Avonex®.
Annualized Rate of Confirmed Relapses
95% CI: 0.596–0.920 · P = 0.0067
Analysis population: ITT analysis set, including all randomized participants.
| Feature | Placebo vs Avonex® |
|---|---|
| Endpoint | Annualized Rate of Confirmed Relapses |
| Time frame | Baseline up to Month 24 |
| Method | Baseline-adjusted negative binomial regression |
| Analysis population | ITT analysis set |
| Effect measure | Risk Ratio (RR) |
| Estimate | 0.741 |
| 95% CI | 0.596–0.920 |
| P-value | 0.0067 |
An RR of 0.741 corresponds to an estimated rate about 25.9% lower for the numerator group relative to the reference group. Again, this is a relative rate interpretation and does not mean that 25.9% of participants experienced a particular individual-level outcome.
The 95% confidence interval of 0.596–0.920 does not include 1.00. The interval nevertheless provides more information than the P-value alone: it describes the range of effect estimates that are compatible with the model and sampling uncertainty represented by the confidence-interval procedure.
The P-value of 0.0067 is evidence against the corresponding null hypothesis under the analysis framework. It does not quantify the magnitude of the effect, the probability that an individual participant will benefit, or the clinical importance of the observed rate difference.
As with the placebo-versus-laquinimod comparison, the estimate came from a baseline-adjusted negative binomial regression with an exposure offset and the same listed covariates. The Avonex® arm was described as a rater-blinded reference arm, which provides a distinct design role from the primary placebo comparison.
10. Comparing the Two Posted Primary Analyses
| Feature | Placebo vs Laquinimod | Placebo vs Avonex® |
|---|---|---|
| Endpoint | Annualized Rate of Confirmed Relapses | Annualized Rate of Confirmed Relapses |
| Time frame | Baseline up to Month 24 | Baseline up to Month 24 |
| Analysis population | ITT | ITT |
| Method | Negative binomial regression | Negative binomial regression |
| Effect measure | Risk Ratio | Risk Ratio |
| Estimate | 0.823 | 0.741 |
| 95% CI | 0.664–1.020 | 0.596–0.920 |
| P-value | 0.0746 | 0.0067 |
The two analyses address different randomized comparisons even though they share the same primary endpoint and statistical model. They should therefore be interpreted as separate treatment contrasts rather than as two estimates of a single laquinimod-versus-Avonex® effect.
11. Statistical Methods Explained
Why was negative binomial regression used?
The primary endpoint is based on a count of confirmed relapses over a period of observation. Negative binomial regression is designed for count outcomes and provides a way to model the expected event rate while accommodating variability in counts. In BRAVO, the model also incorporated an exposure offset because participants could contribute different amounts of observation time.
What does the exposure offset do?
The offset based on the log of exposure in years converts a raw event-count analysis into a rate analysis. Conceptually, a participant observed for more time has more opportunity to experience a relapse than a participant observed for less time. The offset allows the model to account for that difference rather than treating equal counts as equivalent regardless of exposure.
What does an RR of 0.823 mean?
The reported RR of 0.823 represents the modeled relative annualized relapse-rate comparison for placebo versus laquinimod under the registry's analysis. Because the reported estimate is below 1, the numerator rate is estimated to be lower than the reference rate under that comparison. The estimate does not describe the proportion of participants who relapsed, nor does it describe an individual participant's probability of relapse.
What does the 95% confidence interval tell us?
The confidence interval describes statistical uncertainty around the estimated relative rate under the model. For the placebo-versus-laquinimod analysis, the interval is 0.664–1.020 and therefore includes 1.00. For placebo versus Avonex®, the interval is 0.596–0.920 and does not include 1.00. The width of each interval also conveys the precision of the estimate.
Why was baseline covariate adjustment used?
The model included baseline EDSS score, log of the prior 2-year number of relapses plus 1, and CGR. Adjustment incorporates these baseline variables directly into the regression model. In a randomized trial, the primary causal comparison remains based on randomized assignment, while adjustment can account for baseline information in estimation.
Why is the ITT analysis important?
The ITT analysis set included all randomized participants. An ITT analysis preserves the original randomized groups, which helps maintain the balance created by randomization. It also means the primary comparison is not restricted to participants who remained on treatment for the entire study period.
What does the P-value not tell us?
A P-value is not an effect-size measure. A smaller P-value does not mean a larger treatment effect, and a P-value does not give the probability that a treatment is effective. Effect size, confidence interval, exposure, endpoint definition, and clinical context all provide information that a P-value alone cannot provide.
12. Serious Adverse Events
The registry reports serious adverse events by study arm using affected participants over participants at risk.
| Study arm | Participants with serious adverse events / participants at risk |
|---|---|
| Placebo | 36 / 449 |
| Laquinimod | 31 / 433 |
| Avonex® | 25 / 442 |
These counts are presented separately from the primary efficacy analysis because serious adverse events and relapse rates are different outcome constructs. The registry does not provide a posted inferential comparison of these serious adverse-event counts in the information summarized here.
The annualized confirmed relapse rate measures disease-related events under a defined neurological relapse criterion. Serious adverse events summarize safety events. They require different definitions, denominators, and statistical interpretations.
13. Statistical Interpretation of Count / Rate Outcomes
BRAVO illustrates an important distinction between counts, rates, and risks. A raw relapse count is simply the number of confirmed relapses. An annualized relapse rate additionally accounts for the amount of observation time. The registry reports the resulting treatment effect as a Risk Ratio.
Count
The number of confirmed relapse events observed during the treatment period.
Rate
The relapse count standardized using participant exposure time, expressed on an annualized basis.
Relative effect
The reported RR summarizes the modeled comparison between the randomized groups.
Uncertainty
The 95% confidence interval shows the statistical uncertainty around the estimated relative effect.
This distinction matters because two groups can have different numbers of observed relapses simply because they contributed different amounts of follow-up. The exposure offset is therefore a central component of the BRAVO analysis rather than a technical detail that can be ignored.
14. Covariate Adjustment in the BRAVO Model
| Covariate | How the registry describes its role |
|---|---|
| Baseline EDSS score | Included as a baseline covariate in the negative binomial regression. |
| Log of (prior 2-year number of relapses + 1) | Included as a baseline covariate in the negative binomial regression. |
| CGR | Included as a baseline covariate in the negative binomial regression. |
| Exposure in years | Entered through an offset based on the log of participant exposure in years. |
The model therefore combines three types of information: the observed relapse count, baseline characteristics, and the amount of participant exposure. This is more informative than a simple comparison of unadjusted total relapse counts.
Adjustment does not turn an observational comparison into a randomized one; BRAVO was already randomized. Instead, the regression uses baseline information to estimate the treatment contrast more efficiently within the specified model. The validity of the adjusted estimate depends on the model being appropriately specified for the data.
15. Confidence Intervals and Precision
The two primary analyses demonstrate why the confidence interval should be considered alongside the point estimate.
| Comparison | RR | 95% CI | What the interval shows |
|---|---|---|---|
| Placebo vs Laquinimod | 0.823 | 0.664–1.020 | Includes 1.00 and therefore includes a value corresponding to no relative rate difference. |
| Placebo vs Avonex® | 0.741 | 0.596–0.920 | Does not include 1.00 and is centered below the null value. |
A confidence interval is not a range containing the true effect with a fixed probability for this particular dataset. Rather, it is produced by a statistical procedure that has a stated long-run coverage property under its assumptions. For readers interpreting a clinical trial, the practical value is that the interval communicates both the estimated effect and the uncertainty surrounding it.
16. P-values and Effect Sizes
The primary analyses have P-values of 0.0746 and 0.0067, respectively. These numbers should not be used as substitutes for the reported effect estimates and confidence intervals.
P-value
Addresses compatibility of the observed data with the statistical hypothesis framework used for the comparison.
Effect estimate
Describes the magnitude and direction of the modeled relative rate comparison.
Confidence interval
Describes statistical uncertainty around the estimated effect under the specified procedure.
Clinical meaning
Requires consideration of the endpoint definition, magnitude of the rate difference, uncertainty, and the clinical context.
For the placebo-versus-laquinimod analysis, the point estimate is below 1, but its 95% confidence interval extends slightly above 1. For placebo versus Avonex®, the estimate is also below 1 and the reported confidence interval remains below 1.
17. What the Primary Estimates Do — and Do Not — Mean
The reported RR of 0.823 indicates a lower estimated annualized relapse rate for the numerator group under the reported comparison. It does not mean that 82.3% of participants avoided relapse, that every participant experienced an 17.7% reduction, or that the treatment effect is identical for every participant.
The reported RR of 0.741 indicates a lower estimated annualized relapse rate for the numerator group under the reported comparison. It does not mean that 74.1% of participants avoided relapse, nor does it describe an individual participant's probability of remaining relapse-free.
Because the endpoint is an annualized rate, the analysis accounts for participant exposure time. The interpretation therefore concerns a modeled rate of events rather than a simple proportion of participants experiencing at least one event.
18. Limitations
- Rate-model dependence: the primary effect estimates depend on the specified negative binomial regression model and its covariate structure.
- Exposure adjustment: the analysis uses an exposure offset, so interpretation depends on the modeled relationship between event counts and participant exposure time.
- Covariate adjustment: the reported estimates are baseline-adjusted rather than simple unadjusted rate comparisons.
- Interpretation of RR: the registry reports Risk Ratio as the effect measure, although the underlying outcome is a modeled annualized count/rate endpoint. The numerical estimate should therefore be interpreted in the context of the negative binomial rate model.
- Multiple posted comparisons: two primary endpoint analyses were posted, one comparing placebo with laquinimod and one comparing placebo with Avonex®. The registry summary does not provide additional multiplicity details for these comparisons.
- Safety detail: serious adverse events are reported as affected participants over participants at risk by arm, but the summarized registry information does not provide a formal inferential comparison for these counts.
- Additional statistical detail: the registry information summarized here does not report additional details on missing-data imputation, interim analysis, Bayesian methods, non-inferiority margins, or crossover.
These limitations are primarily about interpretation and statistical specification. They do not change the fact that the registry identifies the study as randomized, parallel, and quadruple-masked, with the primary efficacy analyses performed in the ITT analysis set.
19. Why This Trial Matters Statistically
BRAVO is a useful statistical teaching case because its primary outcome is neither a simple binary response nor a conventional continuous measurement. Participants can experience repeated confirmed relapses, and the amount of observation can vary. That structure naturally leads to a count/rate framework.
| Concept | How it appears in BRAVO |
|---|---|
| Randomization | The study used randomized allocation. |
| Blinding | The registry identifies quadruple masking; the brief title identifies the Avonex® arm as rater blinded. |
| ITT analysis | The primary analyses included all randomized participants. |
| Repeated events | The endpoint counts confirmed relapse events rather than reducing the outcome to a single event indicator. |
| Negative binomial regression | Used for the annualized confirmed relapse-rate endpoint. |
| Covariate adjustment | Baseline EDSS score, log of prior 2-year relapses plus 1, and CGR were included. |
| Exposure offset | The log of participant exposure in years was used as an offset. |
| Relative rate measure | The registry reports Risk Ratio as the effect measure. |
| Confidence intervals | Both primary analyses provide two-sided 95% confidence intervals. |
| P-values | Each posted primary analysis includes a P-value. |
20. Statistical Methods Explained: A Deeper View
Why not simply compare the mean number of relapses?
A simple comparison of mean counts would not by itself account for differences in exposure time. BRAVO's registered endpoint is an annualized rate, and the analysis explicitly uses an exposure offset. The negative binomial framework therefore matches the structure of a repeated-event count outcome more directly than an unadjusted comparison of raw counts.
What is the role of the prior two-year relapse history?
The registry specifies the covariate as log of (prior 2-year number of relapses + 1). This incorporates prior relapse experience into the baseline-adjusted model. The addition of 1 allows the logarithm to be defined when the prior relapse count is zero.
Why is baseline EDSS included?
Baseline EDSS score is a prespecified baseline characteristic included in the model. Including baseline disease-status information can account for prognostic variation when estimating the treatment contrast.
Why does the model need an offset?
Suppose two participants have the same observed number of relapses but one contributes substantially more time on study. Treating their raw counts as directly comparable would ignore their different opportunities to experience an event. The log-exposure offset puts the model on an annualized rate scale.
How should the confidence interval be read when it crosses 1?
For the placebo-versus-laquinimod analysis, the 95% CI is 0.664–1.020. Because 1.00 is inside that interval, the interval includes the null relative-rate value. This does not prove that the true effect is exactly zero; it indicates that the data and model leave values on both sides of the null compatible with the stated confidence-interval procedure.
Does a smaller P-value mean a larger effect?
No. P-values are influenced by effect size, variability, sample information, and the statistical model. Effect size should be assessed using the RR, while the confidence interval provides information about uncertainty. In BRAVO, the two P-values cannot be used as a ranking of the magnitudes of the two treatment effects.
21. Results in Context
The two posted analyses provide a consistent statistical structure: the same annualized confirmed relapse endpoint, the same baseline-adjusted negative binomial regression framework, the same ITT population, and two-sided 95% confidence intervals. What changes is the randomized comparison.
| Question | Placebo vs Laquinimod | Placebo vs Avonex® |
|---|---|---|
| Estimated RR | 0.823 | 0.741 |
| 95% CI | 0.664–1.020 | 0.596–0.920 |
| P-value | 0.0746 | 0.0067 |
| CI includes 1.00? | Yes | No |
| Primary endpoint | Annualized Rate of Confirmed Relapses | Annualized Rate of Confirmed Relapses |
| Time frame | Baseline up to Month 24 | Baseline up to Month 24 |
The table demonstrates why a complete statistical interpretation should retain all three core quantities: the point estimate, the confidence interval, and the P-value. Each answers a different question.
22. Related Tutorials
Learn more about the methods used in this trial:
23. Related Statistical Calculators
24. Sources
- ClinicalTrials.gov: BRAVO — NCT00605215.
- PubMed: PMID 36163349.
- PubMed: PMID 26000222.
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25. Record Summary
BRAVO provides a clear example of statistical analysis for a randomized clinical trial with a repeated-event count outcome. The primary endpoint was the annualized rate of confirmed relapses from baseline up to Month 24, analyzed using baseline-adjusted negative binomial regression in the ITT population. The model incorporated baseline EDSS score, log of the prior 2-year number of relapses plus 1, and CGR, together with an exposure offset based on the log of participant exposure in years.
The placebo-versus-laquinimod analysis reported an RR of 0.823 with a two-sided 95% CI of 0.664–1.020 and P = 0.0746. The placebo-versus-Avonex® analysis reported an RR of 0.741 with a two-sided 95% CI of 0.596–0.920 and P = 0.0067. These estimates should be interpreted as model-based relative comparisons of the annualized relapse-rate endpoint, with the confidence intervals providing the principal measure of statistical uncertainty around the point estimates.