Rheos® Pivotal Trial: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Rheos® Pivotal Trial (NCT00442286), a randomized na study. The primary outcome is Percent of Patients With a 10mmHg or Greater Reduction in Office Cuff Systolic Blood Pressure.

2. Clinical Question

The primary outcome is a binary response: each participant either achieved the specified reduction from Month 0 to Month 6 or did not. The registry describes a double-blind, randomized, parallel-group comparison. It also lists quadruple masking for the trial, so the masking information is not expressed identically in every registry field.

The posted results report a response of 54.1% in the Device On group and 46.4% in the Device Off group. The reported comparison is a risk difference of -0.077, with a confidence interval from -0.206 to 0.052 and an unadjusted p value of 0.242. The comparison is recorded as Device Off relative to Device On, so the negative estimate is in the direction of a lower response proportion in the Off group. The interval includes no difference and also extends across effects in either direction. These estimates describe the posted outcome; they do not by themselves establish what the treatment would do for an individual or in a different population.

3. Trial Design

The registry identifies the Rheos® Pivotal Trial as a completed, randomized, parallel-group device trial sponsored by CVRx, Inc. The phase is listed as NA. Enrollment is recorded as 591. The trial began in 2006-10, and primary completion is listed as 2016-01. These are registry-level characteristics and do not explain the timing of every analysis or follow-up.

The intervention was the Rheos® Baroreflex Hypertension System. Participants were allocated to Device On or Device Off at the time of system activation. The arm descriptions state that randomization used a 2:1 allocation. The posted primary-outcome groups include 181 participants in the Device On arm and 84 in the Device Off arm; these outcome denominators should not be assumed to represent every enrolled participant or every safety population.

The primary endpoint timeframe is six months post-activation. The arm descriptions say that after the six-month follow-up evaluation, therapy would be activated for all subjects and that subjects and treating physicians would not be informed of randomized treatment assignment. The wording of the registry arm descriptions is incomplete, so further details about this transition are not reported in the registry record.

Masking is listed as quadruple in the trial-design field. The primary-outcome description calls the comparison double-blind. The record does not clarify the relationship between those labels or identify all masked roles in the posted material. It describes a parallel-group design and a superiority margin of 20% for the primary proportion comparison. The original sample-size justification, operational details of randomization, and full protocol are not reported in the registry record. The record lists five outcome measures, but it does not post secondary outcome results in the summary.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Before assignment: Of the 591 patients enrolled, 78 withdrew prior to implant and 187 screen-failed. 4 implants were unsuccessful, and 2 randomized patients were terminated prior to the randomization visit. 55 patients were roll-in patients that were not randomized. A total of 265 patients were both randomized and implanted.

Overall Study

Reasons for not completing this period:

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

6. Primary Endpoint

The registry lists the primary outcome as Percent of Patients With a 10mmHg or Greater Reduction in Office Cuff Systolic Blood Pressure, measured over 6 months post-activation.

The primary endpoint is the percentage of participants who had at least a 10 mm Hg reduction in office cuff systolic blood pressure at Month 6 compared with Month 0. It is measured as a binary response: the threshold is met or it is not. The endpoint timeframe is six months after device activation.

A threshold-based endpoint makes the comparison straightforward to describe as the proportion of participants meeting a prespecified response criterion in each randomized group. It retains a clinically interpretable threshold while reducing each participant’s blood-pressure change to a response status. That simplification also means the endpoint does not show the full distribution of blood-pressure changes: participants just below the threshold and participants with little change are both counted as not meeting it, while the magnitude of response among those who meet the threshold is not represented by the binary outcome.

The registry describes the primary comparison as Group A, Rheos Device On, versus Group B, Rheos Device Off, for the proportion achieving the threshold. It also describes a superiority margin of 20%. The posted summary does not provide enough information to reconstruct the formal testing procedure or determine how the margin was incorporated into the sponsor’s analysis. The result should therefore be read as the posted group proportions and comparison estimate, rather than as a complete account of the endpoint’s prespecified statistical test.

7. Results Posted in the Registry

• Rheos® Device Off: 46.4% (39/84) versus 54.1% (98/181) on control; risk difference -7.7 percentage points (95% CI -20.6 to 5.2), risk ratio 0.86 (0.66–1.12); unadjusted two-proportion z-test p = 0.242.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary endpoint is a proportion: the number of participants meeting a binary response definition divided by the relevant group denominator. Here, the response definition is a reduction of at least 10 mm Hg in office cuff systolic blood pressure between Month 0 and Month 6. This type of endpoint is often summarized with a percentage and a confidence interval because the observed proportion is an estimate of the response rate in a broader population, not a value known without uncertainty.

What does the risk difference mean?

The risk difference compares two proportions by subtracting one from the other. In the posted comparison, the contrast is Device Off relative to Device On. Its estimate is -0.077, with a 95% confidence interval from -0.206 to 0.052. A value of zero on this scale corresponds to equal response proportions. A negative value indicates a lower estimated response proportion in the first group of this contrast, Device Off; a positive value would indicate a higher estimated proportion in that group. The interval crosses zero, so it includes equal proportions as one possibility.

Risk differences are expressed on an absolute scale, making them useful for describing the size and direction of a contrast in proportions. They should not be confused with relative measures such as a risk ratio or odds ratio. The record also contains relative estimates, but the risk difference is the comparison most directly aligned with the percentage-point outcome. No adjustment for covariates is described in the posted comparison.

What does a confidence interval convey?

In general, a confidence interval is a range generated by a statistical procedure that reflects uncertainty in an estimate. Under repeated use of the same procedure and its assumptions, intervals constructed in this way have a stated coverage property. The interval is not a range containing a fixed proportion of individual participants, and it is not a guarantee that the true value lies inside the particular interval. Its width depends on the amount of information in the data and on the variability of the outcome.

The arm-specific 95% confidence intervals are 46.9% to 61.4% for Device On and 35.8% to 57.1% for Device Off. The risk-difference interval is more directly informative about uncertainty in the contrast. Looking only at whether two separate arm intervals overlap is not a substitute for examining the confidence interval or test for the difference itself.

How should the p value be read?

The registry reports an unadjusted p value of 0.242. In general, a p value summarizes how incompatible the observed data are with a specified null model, assuming the model and analysis procedure are appropriate. It is not an effect-size measure and does not express the probability that the null hypothesis is true. “Unadjusted” indicates that the reported value is not described as adjusted for other comparisons or covariates. The record does not report enough detail to identify the exact test, its assumptions, or how it relates to the stated superiority margin.

There is an important distinction between testing for any difference and testing whether a specified superiority margin has been exceeded. A margin changes the statistical question: the relevant benchmark is no longer necessarily equality alone. The primary outcome description states a superiority margin of 20%, but the posted registry summary does not give the full hypothesis formulation, test statistic, or sponsor analysis. It is therefore not appropriate to infer the formal margin-based conclusion from the unadjusted p value alone.

Why does a binary endpoint have limits?

Turning a continuous blood-pressure change into a yes-or-no response can make a result easier to communicate against a defined threshold. However, it discards information about the size of changes within each response category. Participants with very different changes can receive the same binary status, and small changes around the cutoff can place otherwise similar measurements in different categories. This is a general property of dichotomizing continuous outcomes, not a claim about any individual participant in this trial.

Proportions can also have uncertainty that depends on the group denominator and on the observed response rate. When proportions are compared, a confidence interval for the difference helps show how much uncertainty remains in the contrast. In this trial the interval spans negative and positive values, so the estimate does not pin down the direction of the underlying difference with precision.

What analysis details are not available?

The registry record lists zero posted analyses. It does not report the sponsor’s full statistical analysis plan, the exact method used for the primary p value and confidence interval, covariate adjustment, handling of missing outcome values, or the primary analysis population. The specific procedures for testing the 20% superiority margin are also not reported in the registry record. Without those details, the posted summary supports description of the estimates and their reported uncertainty, but not reconstruction of the complete prespecified analysis.

General statistical interpretation also depends on design and conduct. Randomization supports a comparison of assigned groups when the analysis preserves that assignment and outcome data are appropriately handled. Masking may reduce some forms of bias, but the registry’s different labels—quadruple masking in the design field and double-blind in the endpoint description—are not reconciled in the posted record. These limitations do not change the reported estimates, but they constrain what can be inferred from the summary alone.

10. Confidence Intervals and Precision

The primary comparison estimate is -0.077 for Device Off relative to Device On, with a 95% confidence interval from -0.206 to 0.052. The interval includes zero and extends to values on both sides of it. This indicates that the posted estimate has substantial uncertainty about the direction and size of the between-group difference. The interval is not evidence that all values within it are equally plausible, nor does it identify the true value with certainty.

The arm-specific response estimates are 54.1% for Device On, with a 95% confidence interval from 46.9% to 61.4%, and 46.4% for Device Off, with a 95% confidence interval from 35.8% to 57.1%. These ranges describe uncertainty around each arm’s proportion. The interval for the between-group contrast should be used to assess uncertainty in that contrast, rather than treating overlap between arm-specific intervals as a significance test.

In general, confidence intervals tend to be wider when data provide less information and narrower when estimates are more precise. The relevant endpoint denominators are 181 for Device On and 84 for Device Off. The registry does not explain why the endpoint denominators differ from one another or from overall enrollment, nor does it report how missing outcome data affected the estimates. These are important qualifications when assessing precision.

The confidence intervals are informative but do not resolve every question. The registry record does not provide the full analysis plan, a detailed account of the margin-based test, or additional uncertainty summaries for secondary outcomes. The interval should be read as uncertainty under the reported statistical procedure, not as a guarantee about the result in another population or setting.

11. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

The planning figures are participants per arm, not total events. They are illustrations based on the observed effect, not a report of the original trial’s design justification. The assumptions stated for these calculations are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set to the stated fraction of the observed effect.

The entries for 100% of the observed effect use the observed effect as the planning target. The entries for 75% and 50% of the observed effect use smaller target effects. For each target, the 80% power column means the number of participants per arm in a hypothetical design intended to have an 80% chance of detecting that target effect under the stated assumptions if the effect were present. The 90% power column describes a corresponding hypothetical design with a 90% chance under those assumptions.

The figures increase as the target effect becomes smaller: detecting a smaller difference generally requires more participants, because it is harder to distinguish a small effect from random variation. The listed planning values are 659 and 881 participants per arm for 100% of the observed effect; 1,171 and 1,567 for 75% of the observed effect; and 2,631 and 3,522 for 50% of the observed effect. Within each pair, the first figure is for 80% power and the second is for 90% power.

This is not observed power. It is a planning illustration calculated from the observed effect and the stated assumptions; it does not describe the probability that the completed trial’s result was correct. The trial’s own original sample-size assumptions are not reported in the registry record.

12. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n is the number of participants in each arm, p₀ and p₁ are the control and treatment proportions, and p̄ is their average.

Worked calculation for this trial

1. Control proportion p₀ = 0.541; treatment proportion p₁ = 0.464; average p̄ = 0.503.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.7071 = 1.3859.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.7050 = 0.5933.
4. n = (1.3859 + 0.5933)² / (-0.0772)² = 658.1, rounded up to 659 participants per arm for 80% power.

The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
p0 <- 0.541436464088398                          # control proportion
p1 <- 0.464285714285714                          # treatment proportion
n_per_arm <- function(power, frac = 1) {
  q1 <- p0 + (p1 - p0) * frac               # smaller effect = fraction of the observed difference
  pbar <- (p0 + q1) / 2
  z_b <- qnorm(power)
  ceiling(round((z_a * sqrt(2 * pbar * (1 - pbar)) + z_b * sqrt(p0 * (1 - p0) + q1 * (1 - q1)))^2 / (q1 - p0)^2, 6))
}
for (f in c(1, 0.75, 0.5))
  cat(sprintf("%3.0f%% of observed effect: n per arm = %s (80%% power), %s (90%% power)\n", 100 * f,
              format(n_per_arm(0.80, f), big.mark = ","), format(n_per_arm(0.90, f), big.mark = ",")))

# Check against R's built-in function (unrounded n per arm)
cat("power.prop.test:", round(power.prop.test(p1 = p0, p2 = p1, power = 0.80)$n, 1), "\n")

# Simulation: how often does the z-test reject at the 80%-power sample size?
set.seed(442286)
n    <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z  <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))

Output from running the code

100% of observed effect: n per arm = 659 (80% power), 881 (90% power)
 75% of observed effect: n per arm = 1,171 (80% power), 1,567 (90% power)
 50% of observed effect: n per arm = 2,631 (80% power), 3,522 (90% power)
power.prop.test: 658.1 
Simulated power at n = 659 per arm: 0.798 (20000 replicates)

The simulation draws many pairs of event counts at the planned sample size and counts how often the two-proportion z-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

13. Multiplicity, Missing Data and Analysis Populations

The registry record lists five outcome measures, but the summary does not post secondary outcome results. It lists zero posted analyses. The record does not explain whether the primary endpoint was the only confirmatory outcome, whether secondary outcomes were tested, or whether any procedure was used to control the chance of false-positive findings across multiple outcomes or analyses. Multiplicity handling is therefore not reported in the registry record.

In general, testing multiple outcomes or performing many analyses can increase the chance that at least one result appears statistically notable by chance. Prespecified testing strategies and multiplicity adjustments can address that concern, but the appropriate approach depends on the research questions and analysis plan. No such plan is described in the posted registry summary, so it is not possible to determine how the reported primary result fits into a wider testing strategy.

Missing-data handling is also not reported in the registry record. The primary outcome has group denominators of 181 for Device On and 84 for Device Off, while overall enrollment is recorded as 591. The registry does not state whether every randomized participant had an endpoint measurement, how participants without a measurement were treated, or whether imputation or sensitivity analyses were used. The denominator difference should not be attributed to a particular reason without that information.

The analysis population is not specified in the posted summary. It is not reported whether the primary estimate follows an intention-to-treat approach, a per-protocol approach, or another population definition. In general, an intention-to-treat analysis retains participants in their randomized groups, while other analysis populations may exclude participants according to defined criteria. The record does not provide the criteria or tell readers which approach generated the posted endpoint estimates.

The primary description includes a superiority margin of 20%, but details of the formal test are not reported. That omission matters because the interpretation of a result depends on the null hypothesis and decision rule, not only on an unadjusted p value. No additional analysis details should be inferred from the registry summary.

14. Safety Results

The registry reports serious adverse events as affected participants divided by participants at risk.

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 5% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: hypertensive crisis (9.5%), chest pain (6.1%), nerve injury (3.6%), cerebrovascular accident (3.6%), syncope (3.6%).

The registry reports serious adverse events affecting 102 of 181 participants in the Rheos Device On group and 45 of 84 in the Device Off group. Other adverse events are reported for 75 of 181 participants in the On group and 39 of 84 in the Off group. These are participant counts and denominators as recorded; they are not comparisons adjusted for follow-up duration or other factors.

The listed serious adverse-event terms and percentages are hypertensive crisis, 9.5%; chest pain, 6.1%; nerve injury, 3.6%; cerebrovascular accident, 3.6%; syncope, 3.6%; and hypotension, 3.3%. The registry summary does not specify enough detail to determine whether these terms represent people, events, or another reporting unit, or how the percentages were calculated. They should be read as reported terms rather than as a complete accounting of all safety outcomes.

Death counts are not reported in the registry record. The available information does not describe event timing, severity grading beyond the serious classification, relatedness assessment, or arm-specific follow-up completeness. Counts alone do not establish whether an event was caused by the device or whether safety differed between randomized groups.

15. What the Result Does, and Does Not, Mean

The posted outcome shows that the response proportion was 54.1% in the Rheos Device On group and 46.4% in the Device Off group. The risk-difference estimate, recorded as Device Off relative to Device On, is -0.077. Its 95% confidence interval extends from -0.206 to 0.052, and the unadjusted p value is 0.242. Together, these summaries indicate uncertainty around the size and direction of the difference. The interval includes no difference and values on either side of zero.

The result does not, on its own, establish whether the trial met its stated superiority margin. Although the endpoint description mentions a 20% margin, the registry record does not provide the full testing procedure or sponsor analysis. A p value for an unspecified or differently framed comparison cannot be assumed to answer the margin-based question. The posted estimates can be described, but a definitive account of the prespecified test is not available in the registry summary.

The outcome also does not describe the full range of systolic blood-pressure changes. It classifies participants according to whether they crossed the 10 mm Hg threshold, without indicating how far each participant’s change was above or below it. It therefore cannot answer every question about blood-pressure trajectories, durability, or outcomes beyond the six-month endpoint.

The registry summary does not report the handling of missing endpoint data, the primary analysis population, or details of the formal analysis plan. These gaps limit assessment of how the posted estimates were generated. Nor do the safety counts alone establish causation or provide a complete safety profile. The appropriate interpretation is restricted to the posted proportions, comparison estimate, uncertainty, and recorded adverse-event summaries. The result does not by itself provide medical advice or determine what should be done for any individual.

16. Why This Trial Matters Statistically

This trial illustrates why a point estimate and its uncertainty need to be read together. The observed response proportions are different, but the risk-difference interval crosses zero and is broad enough to include effects in either direction. Reporting only the arm percentages could make the comparison appear more definite than the interval supports. Reporting only the p value would also omit information about the range of effects compatible with the data.

The endpoint is a threshold-based binary response. Such endpoints can make a target easy to state, but they compress a continuous measurement into response or non-response. Statistical interpretation therefore depends not only on the observed proportions but also on the threshold definition, the handling of participants without measurements, and the analysis population. The registry record gives the threshold and timeframe, but it does not report several of those analysis details.

The stated superiority margin adds another statistical issue: a margin-based design asks a particular question that may differ from a generic test for any difference. The posted record reports the margin but not the full hypothesis or decision procedure. This makes it important not to treat the unadjusted p value as a complete answer to the stated design objective.

Finally, the planning illustrations show the relationship between target effect size and the information needed for a study under specified assumptions. Smaller target effects require more participants per arm in those calculations. They are not evidence about the trial’s original planning or its observed power. Together, these features make the record useful for discussing effect estimation, interval precision, binary endpoints, and the limits of registry-level reporting.

17. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.
• Participant counts were reconstructed from posted percentages and arm sizes, so small rounding differences are possible.

The registry record gives an incomplete account of the analysis. It does not report the original sample-size justification, the full statistical analysis plan, the formal procedure for evaluating the stated 20% superiority margin, or the exact method used to calculate the primary confidence interval and p value. It also lists zero posted analyses. The registry summary therefore does not allow a full audit of the prespecified analysis against the reported result.

Important population details are absent from the posted outcome summary. The group denominators for the primary endpoint are 181 and 84, compared with overall enrollment of 591. The record does not explain this difference, describe the analysis population, or report how missing endpoint measurements were handled. It is not possible to determine from the summary whether missingness or exclusions could affect the estimate.

The masking information is not fully reconciled: the design field lists quadruple masking, while the primary description calls the comparison double-blind. The record does not clarify which roles were masked or explain the difference in terminology. The arm descriptions also say that therapy would be activated for all subjects after the six-month evaluation, but further details are not reported in the registry record.

Only the primary outcome result is detailed in the posted summary, despite the record listing five outcome measures. Secondary results, multiplicity procedures, extended outcome summaries, and death counts are not reported in the registry record. The safety listing also lacks detail about event attribution, timing, and the basis for the percentages attached to specific terms. These gaps limit interpretation of both efficacy-related estimates and safety summaries.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Rheos® Pivotal Trial — NCT00442286.
• Registry record last updated 2017-03-20; status last verified 2017-01.
• Results first posted 2017-03-20.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

21. Record Summary

The Rheos® Pivotal Trial is recorded as a completed, randomized, parallel-group device trial sponsored by CVRx, Inc., with enrollment of 591. The registry lists hypertension as the condition and the Rheos® Baroreflex Hypertension System as the intervention. The primary endpoint is the proportion with at least a 10 mm Hg reduction in office cuff systolic blood pressure at six months after activation, compared with Month 0.

The posted response proportions are 54.1% for Rheos Device On and 46.4% for Rheos Device Off. The reported risk difference is -0.077, with a 95% confidence interval from -0.206 to 0.052 and an unadjusted p value of 0.242. The record describes a 20% superiority margin but does not report the complete formal analysis. It also does not report the original design assumptions, missing-data procedures, or analysis population. Serious adverse-event counts are posted for both groups, while death counts are not reported in the registry record.