← Clinical Trials
Hypertension Phase 4 Continuous Endpoint NCT00949884

Olmesartan Comparison to Losartan in Hypertensive Subjects: Complete Statistical Analysis

This randomized, double-blind, active-comparator trial compared olmesartan regimens with losartan in people with hypertension. The primary endpoint was change in trough seated diastolic blood pressure from baseline to Week 8; the registry also reports three secondary blood-pressure endpoints.

Trial start: 2009-08  ·  Enrollment: 941  ·  Sponsor: Daiichi Sankyo
Scope of this record

This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.

1. Trial at a Glance

This page covers the registry results for Olmesartan Comparison to Losartan in Hypertensive Subjects (NCT00949884), a randomized phase 4 study. The primary outcome is Change From Baseline to Week 8 in Trough, Cuff, Seated Diastolic Blood Pressure (SDBP).

941
Enrollment
Phase 4
3
Arms
In the primary outcome
0.10
Mean difference
Combined Olmesartan
-1.22–1.42
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT00949884
PhasePhase 4
ConditionHypertension
AllocationRandomized
Design modelParallel
MaskingDouble
Enrollment941
Arms in the primary outcome3
Lead sponsorDaiichi Sankyo
Results postedYes

2. Clinical Question

Population

Participants were people with hypertension enrolled in a Phase 4 randomized trial. The registry reports total enrollment of 941. The efficacy population included participants who received at least 1 dose of double-blind randomized study medication and had a baseline and at least 1 post-baseline blood pressure measurement.

Intervention

The registry lists olmesartan medoxomil regimens. One arm received olmesartan 20 mg once daily for four weeks, followed by 40mg once daily for four weeks. Another arm received a placebo capsule of olmesartan once daily for 2 weeks, then olmesartan 20 mg once daily for two weeks, followed by olmesartan 40 mg for 4 weeks.

Comparator

The active comparator was losartan potassium: 50 mg once daily for four weeks, followed by 100 mg once daily for four weeks. The registry lists a separate olmesartan arm, a placebo-followed-by-olmesartan arm, and a losartan arm. The posted analysis also reports a combined olmesartan group.

Primary question

How did trough, cuff, seated diastolic blood pressure change from baseline to Week 8 in the combined olmesartan group compared with losartan? The endpoint uses the blood pressure measurement taken when medication levels were at their lowest on study visit days. The registry reports least-squares means for the groups and an ANCOVA comparison of combined olmesartan with losartan.

3. Trial Design

This was a randomized, double-blind, parallel-group, Phase 4 study with an active comparator. The official title describes an 8-week forced-titration study of olmesartan medoxomil versus losartan potassium in hypertensive subjects. The study status is completed, and the registry lists Daiichi Sankyo as the sponsor. The registry dates the start to 2009-08 and primary completion to 2010-01.

The listed treatment schedules involved dose changes during the study. The olmesartan arm received 20 mg once daily for four weeks, then 40mg once daily for four weeks. A second olmesartan regimen began with placebo for 2 weeks, then olmesartan 20 mg once daily for two weeks and olmesartan 40 mg for 4 weeks. The losartan arm received 50 mg once daily for four weeks, then 100 mg once daily for four weeks. The registry calls the study double-blind and randomized; further details about concealment, the mechanics of blinding, or the allocation ratio are not reported in the registry record.

Total enrollment was 941. The posted primary endpoint analyses include Olmesartan, Combined Olmesartan, and Losartan groups, with group sizes that differ by endpoint and analysis population. The registry does not explain in detail how the combined olmesartan analysis group was formed. The primary endpoint analysis population was defined as participants who received at least 1 dose of randomized double-blind study medication and had a baseline and at least 1 post-baseline blood pressure measurement. Missing endpoint observations were handled using last observation carried forward.

The posted record includes 16 outcome measures and 100 analyses overall, but only three secondary blood-pressure outcomes are identified in the information reported for this trial. The original sample-size justification, target difference, design assumptions, allocation ratio, and any interim analysis plan are not reported in the registry record. The planning illustrations are based on observed effects and are not evidence of the study's original design choices.

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: Prior to group assignment was a 2-9 day screening period and a 3-4 week single-blind (participant was blinded) placebo run-in period. Participants were randomized in an 8:1:9 ratio to treatment arms as listed.

Overall Study

StageOlmesartanPlacebo Followed by OlmesartanLosartan
STARTED42052469
COMPLETED37037411
NOT COMPLETED501558

Reasons for not completing this period:

ReasonOlmesartanPlacebo Followed by OlmesartanLosartan
Adverse Event14312
Did not meet inclusion/exclusion213
Lost to Follow-up755
Physician Decision506
Treatment non-compliance508
Withdrawal by Subject13416
Lack of Efficacy427
Study terminated by sponsor001

Analysis population for the primary outcome, as defined in the registry: The Efficacy Population included participants who received at least 1 dose of double-blind randomized study medication and had a baseline and at least 1 post-baseline blood pressure measurement. Last observation carried forward.

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.

CharacteristicUnitOlmesartanPlacebo Followed by OlmesartanLosartanTotal
Participants analysed42052469941
Age, Categorical: <=18 yearsParticipants0000
Age, Categorical: Between 18 and 65 yearsParticipants38551423859
Age, Categorical: >=65 yearsParticipants3514682
Age Continuousyears52.0 (SD 9.84)49.9 (SD 8.67)52.1 (SD 9.76)51.9 (SD 9.74)
Sex: Female, Male: FemaleParticipants19027211428
Sex: Female, Male: MaleParticipants23025258513
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants52761120
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants36845408821
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants0000
Race (NIH/OMB): American Indian or Alaska NativeParticipants4026
Race (NIH/OMB): AsianParticipants2522653
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants0022
Race (NIH/OMB): Black or African AmericanParticipants11816133267
Race (NIH/OMB): WhiteParticipants27333304610
Race (NIH/OMB): More than one raceParticipants0000
Race (NIH/OMB): Unknown or Not ReportedParticipants0123
Hypertension stage: Stage Iparticipants12023134277
Hypertension stage: Stage IIparticipants30029335664
Heightcentimeter169.92 (SD 9.635)169.46 (SD 9.652)170.47 (SD 9.906)170.17 (SD 9.767)
Weightkilogram93.73 (SD 19.627)96.14 (SD 22.611)94.02 (SD 21.647)94.01 (SD 20.810)
Body Mass Indexkilogram/meter^232.41 (SD 6.089)33.62 (SD 8.103)32.28 (SD 6.619)32.41 (SD 6.480)
Systolic Blood PressuremmHg158.3 (SD 10.41)157.9 (SD 10.05)158.3 (SD 10.24)158.3 (SD 10.29)
Diastolic Blood PressuremmHg101.1 (SD 4.07)100.8 (SD 3.79)101.3 (SD 4.14)101.2 (SD 4.09)
Pulse Ratebeats per minute78.8 (SD 11.41)81.9 (SD 9.88)78.5 (SD 10.59)78.9 (SD 10.94)

6. Primary Endpoint

The registry lists the primary outcome as Change From Baseline to Week 8 in Trough, Cuff, Seated Diastolic Blood Pressure (SDBP), measured over Day 0, Week 8.

ElementRegistry entry
Result typeLeast Squares Mean
Measure of spreadStandard Error
UnitmmHg
Endpoint classificationContinuous Endpoint

The primary endpoint was change from baseline to Week 8 in trough, cuff, seated systolic blood pressure? No: the primary endpoint is specifically seated diastolic blood pressure (SDBP), measured in mmHg. The outcome title identifies the change from baseline to Week 8; its timeframe is Day 0 to Week 8. The posted group values are least-squares means, with standard errors as the accompanying measure of dispersion.

Blood pressure was measured using an Omron monitor. On study visit days, participants took their morning study medication after the examination, so the examination measurement was taken at the medication trough, when medication levels were at their lowest. After a 5-minute rest, three seated blood pressure measurements were taken, with a full 2-minute interval between readings that did not exceed 5 minutes. The cuff was fully deflated between readings, and the mean of the three readings constituted the visit blood pressure value.

Change from baseline expresses how the measured outcome at follow-up differs from the participant's baseline value; it is a continuous outcome, so group means describe average changes rather than counts of events. A trough measurement is intended to characterize blood pressure at the point in the dosing interval when medication levels are lowest, as described in the registry. A seated, repeated-measure protocol gives a defined way to obtain the visit value, while averaging the three readings reduces reliance on any one measurement.

These features explain what the endpoint measures, not whether a particular change is clinically important. The registry does not report a threshold for clinical importance or additional validation details for the endpoint. The standard error describes precision of an estimated group mean, not the spread of individual participants' blood pressure values.

7. Results Posted in the Registry

Mean difference: Combined Olmesartan

0.10

95% CI: -1.22 to 1.42

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals-11.2-10.1-9.0-8.0-6.9-5.8Olmesartan (n=384)Combined Olmesartan (n=424)Losartan (n=426)mmHg (95% CI)
Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Combined OlmesartanLosartan-1.64-0.420.792.013.224.44mean difference vs control (95% CI)

8. Secondary Efficacy Endpoints

The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.

Secondary outcomeTypeEffect measureEstimate (95% CI)Planning size, 80% power
Change From Baseline to Week 4 in Trough, Cuff, Seated Systolic Blood Pressure (SSBP)Continuous EndpointMean difference0.30 (-1.52 to 2.12)32,800 per arm
Change From Baseline to Week 8 in Trough, Cuff, Seated Systolic Blood Pressure (SSBP)Continuous EndpointMean difference0.00 (-2.02 to 2.02)n/a
Change From Baseline to Week 4 in Trough, Cuff, Seated Diastolic Blood Pressure (SDBP)Continuous EndpointMean difference0.20 (-0.99 to 1.39)31,804 per arm

Change From Baseline to Week 4 in Trough, Cuff, Seated Systolic Blood Pressure (SSBP)

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Combined OlmesartanLosartan-2.09-0.431.222.884.536.19mean difference vs control (95% CI)

Change From Baseline to Week 8 in Trough, Cuff, Seated Systolic Blood Pressure (SSBP)

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Combined OlmesartanLosartan-2.66-0.821.032.874.726.56mean difference vs control (95% CI)

Change From Baseline to Week 4 in Trough, Cuff, Seated Diastolic Blood Pressure (SDBP)

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Combined OlmesartanLosartan-1.39-0.230.922.083.234.39mean difference vs control (95% CI)

The secondary outcomes cover systolic blood pressure at Week 4 and Week 8, and diastolic blood pressure at Week 4. Across the posted group summaries, the mean changes are negative for the blood-pressure outcomes, and the losartan group has less negative changes than the olmesartan-based groups. The sponsor's ANCOVA comparisons of combined olmesartan with losartan report estimates with confidence intervals that do not include zero for each of these listed secondary outcomes. Taken together, the outcomes describe a consistent pattern across measurement type and follow-up visit, rather than an isolated finding on the primary endpoint alone.

These secondary results complement the primary Week 8 diastolic outcome because they consider another blood-pressure measure, an earlier visit, and the systolic measure at both follow-up visits. They do not replace the prespecified primary endpoint, and they do not establish that all endpoints were independently planned or analyzed under a single multiplicity-controlled procedure. The registry does not report a multiplicity adjustment or a hierarchy for these secondary tests.

In general, when multiple outcomes and comparisons are tested, the chance of obtaining at least one apparently notable result by chance can increase unless the analysis plan controls for multiplicity. Without a reported adjustment, secondary p-values and intervals are best read as supporting descriptive evidence, not as a separate set of confirmatory claims. The posted outcome summaries can show whether directions are broadly coherent, but concordance among outcomes does not eliminate shared sources of bias, dependence among blood-pressure measures, or uncertainty related to missing data and model specification.

The registry identifies 16 outcome measures and 100 analyses overall, while three secondary outcomes are detailed in the posted information described for this trial. The remaining outcome definitions and their analysis details are not reported in the registry record in this information. That limits the ability to evaluate the full testing burden or know whether the reported secondary outcomes were selected from a larger set. Interpretation should therefore give the primary endpoint and the sponsor's reported analysis greater weight than unadjusted secondary calculations.

Secondary outcomes registered for this trial, for reference (only those above were recalculated):

9. Statistical Interpretation

Clinical Biostats interpretation

For the primary Week 8 SDBP outcome, the posted least-squares mean change was -9.8 mmHg for Olmesartan, -9.7 mmHg for Combined Olmesartan, and -7.1 mmHg for Losartan. These are group-level changes from baseline. Negative values indicate that the follow-up mean was lower than baseline under the registry's change-from-baseline definition; they do not describe the response of every participant.

The unadjusted recalculation comparing Combined Olmesartan with Olmesartan estimated a mean difference of 0.1 mmHg, with a confidence interval from -1.218 to 1.418 and p = 0.882. The interval includes zero, and the posted unadjusted p-value does not indicate a clear difference in this recalculated comparison. This comparison is not the sponsor's primary reported comparison of combined olmesartan with losartan.

For Losartan compared with Olmesartan, the unadjusted recalculation estimated a mean difference of 2.7 mmHg, with a confidence interval from 1.382 to 4.018 and p < 0.001. This estimate is calculated from the posted group change means, with the contrast expressed as Losartan minus Olmesartan. The positive estimate therefore reflects the less negative mean change in the Losartan group. Because the registry flags a discrepancy between its posted summary statistics and the sponsor analysis, the sponsor's own analysis takes precedence for the sponsor-reported comparison.

The sponsor's ANCOVA analysis comparing Combined Olmesartan with Losartan reports a mean difference in final values of -2.5, a 95% confidence interval from -3.8 to -1.3, and p < 0.001. The posted parameter is a difference in final values, while the recalculation above is an unadjusted difference in change-from-baseline means. These are not identical analysis quantities, and their contrast signs need to be read according to each analysis's group order and parameter definition. They should not be treated as interchangeable estimates.

The broad pattern in the blood-pressure outcomes is that the reported group mean changes are negative, and the sponsor's posted ANCOVA comparisons of combined olmesartan with losartan have confidence intervals that do not include zero. Such statistical evidence describes the analyses and their uncertainty; it does not establish the importance of a difference for an individual, nor does it by itself establish a treatment effect free of bias. The registry provides no clinical-importance threshold. Interpretation also depends on the study population, endpoint measurement, missing-data handling, multiplicity, and the difference between adjusted sponsor analyses and unadjusted recalculations.

10. Statistical Methods Explained

The registry presents continuous blood-pressure outcomes as least-squares means with standard errors. A least-squares mean is a model-based estimate of a group mean; unlike a simple raw average, it can reflect adjustments specified by the model. The primary endpoint description identifies this parameter, but the exact model used to calculate the posted least-squares group means is not reported in the registry record. The standard error describes uncertainty in an estimated mean. It is not the standard deviation of individual participant measurements.

What does the sponsor's ANCOVA comparison represent?

The sponsor reports an analysis of covariance (ANCOVA) for the comparison of Combined Olmesartan with Losartan. In general, ANCOVA compares outcome values between groups while accounting for one or more covariates included in the model. The registry labels the reported parameter as Mean Difference (Final Values). It reports a point estimate, a 95% confidence interval, and a p-value. The specific covariates and full model specification are not reported in the registry record, so those details cannot be assessed from the posted analysis alone.

For the primary outcome, the sponsor's ANCOVA estimate is -2.5, its 95% confidence interval is -3.8 to -1.3, and its p-value is < 0.001. The sponsor's analysis is the registered reported analysis and takes precedence over a simple recalculation when the record flags a discrepancy. The separate recalculation uses posted group summary statistics and is not a replacement for the sponsor's adjusted model.

What is recalculated from the group summaries?

The recalculated comparisons are simple, unadjusted comparisons of the posted change-from-baseline means. They use the group means, sample sizes, and standard errors in the registry summary. The summary does not provide standard deviations directly for these outcomes; the recalculation therefore uses an approximate pooled standard deviation derived from the reported standard errors and group sizes. Because that standard deviation is approximate, the recalculated intervals and p-values are also approximate.

An unadjusted comparison does not account for baseline covariates or any other model adjustment. It provides a transparent comparison from the posted group summaries, but it may differ from an ANCOVA analysis of final values. The primary sponsor estimate and the recalculated estimate also use different analysis quantities: final values in the ANCOVA report versus changes from baseline in the recalculation. This distinction, along with the discrepancy flag, is why they should not be combined or presented as if they were the same calculation.

How should a confidence interval and p-value be read?

In general, a confidence interval gives a range of estimates compatible with the data and the statistical procedure, under its assumptions. It indicates uncertainty around the point estimate: a narrower interval is more precise than a wider interval. An interval crossing zero for a difference is compatible with no difference as well as with differences in either direction at the confidence level used. An interval wholly on one side of zero indicates that the values in that interval share a direction, but it does not establish clinical importance or resolve possible bias.

In general, a p-value measures how unusual data at least as incompatible with a specified null hypothesis would be if that null hypothesis and the test assumptions held. It is not the probability that the null hypothesis is true, nor a measure of the size or importance of an effect. The sponsor's reported p-values and the unadjusted recalculated p-values arise from different analysis approaches. The registry reports no multiplicity adjustment for the displayed analyses, so p-values for multiple outcomes or comparisons should not be interpreted as though they automatically account for all testing.

Why does over-dispersion matter?

In general, over-dispersion means that observed variability is greater than a model's assumed variability. It matters because an analysis that understates variability can produce standard errors that are too small and confidence intervals that are too narrow. The posted endpoint is continuous, and the recalculations use approximate pooled standard deviations; the registry does not report an over-dispersion model or a specific assessment of this issue. It is therefore a general statistical consideration rather than a claim that over-dispersion occurred in this trial.

What does last observation carried forward do?

The efficacy population definition includes participants with baseline and at least 1 post-baseline blood pressure measurement, and the registry specifies last observation carried forward. In general, this method substitutes a participant's last observed value for a later missing value. It can retain participants with incomplete follow-up, but it makes an assumption about how the unobserved later value relates to the last measurement. If outcomes would have changed after that measurement, the carried-forward value may not represent the missing value. The registry does not report the extent or reasons for missing primary endpoint data, sensitivity analyses, or the assumptions used to assess missing-data bias.

11. Confidence Intervals and Precision

The sponsor's primary ANCOVA estimate for combined olmesartan versus losartan is -2.5, with a 95% confidence interval from -3.8 to -1.3 and p < 0.001. The interval communicates uncertainty around the adjusted estimate under the sponsor's model. Its endpoints are both below zero, so the reported interval does not include zero. The direction of the estimate must be interpreted using the sponsor's parameter and group coding: the registry labels the parameter Mean Difference (Final Values), but does not give additional detail on the sign convention.

The recalculated unadjusted estimate is a different quantity. For Losartan compared with Olmesartan, the estimated difference in change from baseline is 2.7 mmHg, with a confidence interval from 1.382 to 4.018 and p < 0.001. The contrast is expressed as Losartan minus Olmesartan; the interval lies above zero. This interval is derived from posted summary statistics using an approximate pooled standard deviation, rather than from the sponsor's ANCOVA model. It should therefore be read as a summary-based, unadjusted estimate, not as the sponsor's primary inferential result.

For the recalculated Combined Olmesartan versus Olmesartan contrast, the estimate is 0.1 mmHg, with a confidence interval from -1.218 to 1.418 and p = 0.882. This interval includes zero and spans values in either direction. It expresses greater uncertainty about the direction of this particular unadjusted contrast than an interval lying entirely to one side of zero would. It is not the comparison that the sponsor reports as the primary ANCOVA contrast.

In general, confidence intervals convey both direction and precision, while p-values alone do not show the range of estimates compatible with the data. Precision of a group mean is not the same as the distribution of individual responses. The registry reports standard errors for the group least-squares means, not standard deviations of individual outcomes. As a result, those standard errors should not be read as describing how much participants' measurements varied. The discrepancy flag, different analysis parameters, and approximate inputs to recalculation are important qualifications when comparing intervals.

12. 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.

Effect to detectParticipants per arm, 80% powerParticipants per arm, 90% power
100% of the observed effect142,345190,560
75% of the observed effect253,058338,772
50% of the observed effect569,380762,237
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect100,000200,000500,0001,000,0002,000,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Treat these figures cautiously. The observed difference is imprecise: its confidence interval includes no difference at all. A sample size built on a noisy estimate can be far too small or too large, so the smaller-effect rows are the more cautious guide.
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, two-sample comparison of means with the pooled standard deviation. Standard deviation was approximated from model-based standard errors, so treat it as rough. Calculated for the comparison: Combined Olmesartan.

The planning illustrations express required sample size as participants per arm, not as a total across arms and not as total events. The assumptions listed for these illustrations are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each illustration uses the stated fraction of the observed effect as the effect to detect. The original trial's sample-size assumptions and justification are not reported in the registry record.

The 80% power column gives the planning number of participants per arm for an analysis with an 80% chance of detecting the stated effect under the illustration's assumptions, if the effect and model assumptions are correct. The 90% power column uses a higher target chance of detection, so its required participant count is larger for the same stated effect. These are prospective planning calculations based on observed summary effects, not observed power.

Rows planning for 100% of the observed effect use the full observed effect as the target. Rows planning for 75% or 50% of the observed effect use smaller target effects. Smaller effects need more participants to distinguish them from random variation under the same assumptions. This is particularly consequential when the observed difference is small: the corresponding planning counts can become very large. Such illustrations do not establish that the original trial was designed for those effects, or that a future study should use those assumptions.

The counts are conditional on the stated calculation assumptions and on the estimated effect and variability used for each contrast. They do not include any additional adjustment for missing outcomes or multiple comparisons unless that is part of the stated calculation; the planning assumptions do not list such adjustments. The registry does not report the trial's original target effect, target power, planned sample size calculation, or whether the original design incorporated other considerations. Treat the planning figures as illustrations of how sample size changes with the target effect and desired power, not as a reconstruction of the trial protocol.

13. 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 z1−α/2 = 1.960) and the desired power (z1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n = 2 (z1−α/2 + z1−β)2 σ2 / Δ2

n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

  1. Observed difference Δ = 0.100; pooled standard deviation σ = 9.523.
  2. n = 2 × (1.96 + 0.842)2 × 9.5232 / 0.1002 = 142,344.8, rounded up to 142,345 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
delta <- 0.100000000000001                      # observed difference in means
sigma <- 9.52251999718426                     # pooled standard deviation
n_per_arm <- function(power, frac = 1) {
  ceiling(round(2 * (z_a + qnorm(power))^2 * sigma^2 / (delta * frac)^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 (t-based, so very slightly larger)
cat("power.t.test:", round(power.t.test(delta = delta, sd = sigma, power = 0.80)$n, 1), "\n")

# Simulation: exact two-sample t-test using simulated means and variances
set.seed(949884)
n    <- n_per_arm(0.80)
reps <- 20000
m_diff <- rnorm(reps, delta, sigma * sqrt(2 / n))             # difference in sample means
s2     <- sigma^2 * rchisq(reps, 2 * (n - 1)) / (2 * (n - 1))   # pooled sample variance
tstat  <- m_diff / sqrt(s2 * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(tstat) > qt(0.975, 2 * (n - 1))), reps))

Output from running the code

100% of observed effect: n per arm = 142,345 (80% power), 190,560 (90% power)
 75% of observed effect: n per arm = 253,058 (80% power), 338,772 (90% power)
 50% of observed effect: n per arm = 569,380 (80% power), 762,237 (90% power)
power.t.test: 142345.7 
Simulated power at n = 142,345 per arm: 0.797 (20000 replicates)

The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-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.

14. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
ANCOVAMean Difference (Final Values) -2.5-3.8 to -1.3< 0.001
Where the two analyses differ, rely on the sponsor's. The simple re-calculation above reaches a different conclusion from the sponsor's analysis, usually because the sponsor adjusts for covariates, stratification or repeated measures, or (for event rates) uses a negative binomial model that allows for over-dispersion and so gives wider intervals.

The sponsor's reported primary comparison is an ANCOVA analysis of final values for Combined Olmesartan versus Losartan. It gives a mean difference of -2.5, a 95% confidence interval from -3.8 to -1.3, and p < 0.001. This is the sponsor's own analysis and takes precedence because the registry flags a discrepancy between the posted summary statistics and the recalculation.

The recalculation is not a reproduction of that ANCOVA. It compares posted change-from-baseline means without adjustment, and its uncertainty calculation uses approximate pooled standard deviations derived from group standard errors and sample sizes. For the Losartan versus Olmesartan comparison, it estimates a mean difference of 2.7 mmHg, with a confidence interval from 1.382 to 4.018 and p < 0.001. This estimate uses the reverse group order from the sponsor's combined-olmesartan-versus-losartan contrast, as well as a different endpoint summary quantity. The numeric estimates and signs therefore should not be compared without accounting for their definitions.

The sponsor analyses for the secondary outcomes are also ANCOVA comparisons of final values. The recalculations are based on the posted group changes. No full model specification, covariates, or explanation of the discrepancy is reported in the registry record. The recalculations can serve as a check on the direction and approximate scale of contrasts constructed from the summary statistics, but they do not supersede the sponsor analyses or provide a basis for resolving why the estimates differ.

15. Multiplicity, Missing Data and Analysis Populations

The registry lists 16 outcome measures and 100 analyses overall, and identifies three secondary blood-pressure endpoints in the posted outcome information. It does not report a multiplicity adjustment, a formal testing hierarchy, or which outcomes were designated as confirmatory beyond identifying the primary endpoint. When several outcomes or contrasts are tested, unadjusted p-values do not account for the full set of tests. In general, this can make nominal evidence from secondary analyses less persuasive than evidence from a prespecified primary analysis with an appropriate testing plan. The actual impact cannot be quantified from the registry information.

The registry states that the efficacy population comprised participants who received at least 1 dose of double-blind randomized study medication and had a baseline and at least 1 post-baseline blood pressure measurement. It also specifies last observation carried forward. That is an analysis-population definition and missing-data rule, but the number of participants with missing primary endpoint observations, reasons for missingness, and follow-up completeness are not reported in the registry record. The registry also does not report sensitivity analyses using alternative missing-data assumptions or a comparison of the efficacy population with all randomized participants.

In general, last observation carried forward assumes that the last observed value is an adequate substitute for an unobserved later value. This assumption may not hold if the outcome changes over time after the last measurement. The method can also affect group comparisons if missingness or the timing of last observations differs between groups. Without information about missingness patterns and sensitivity analyses, it is not possible to judge how robust the posted estimates are to alternative assumptions.

The sponsor's reported ANCOVA model details, including covariates and handling of incomplete observations beyond the listed population rule, are not reported in the registry record. The original statistical analysis plan, details of any interim analyses, and the original sample-size justification are also not reported in the registry record. These omissions constrain assessment of prespecification, model choice, multiplicity control, and the potential influence of missing data. They do not invalidate the reported results, but they limit the scope of what can be concluded about their robustness.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Olmesartan04200.0%
Placebo Followed by Olmesartan0520.0%
Losartan44690.9%
Participants with at least one serious adverse event
Serious adverse events by armOlmesartan0.0%Placebo Followed by Olmesartan0.0%Losartan0.9%% of participants with at least one serious adverse event

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 0% reporting threshold.

ArmParticipants affected of at risk
Olmesartan133 of 420
Placebo Followed by Olmesartan21 of 52
Losartan148 of 469

Most frequent serious adverse event terms

Event termOrgan systemOlmesartanPlacebo Followed by OlmesartanLosartan
Non-cardiac chest painGeneral disorders0 of 4200 of 521 of 469
AsthmaRespiratory, thoracic and mediastinal disorders0 of 4200 of 521 of 469
Cerebrovasular accidentNervous system disorders0 of 4200 of 521 of 469
Urinary tract infectionInfections and infestations0 of 4200 of 521 of 469

Most frequent non-serious adverse event terms

Event termOrgan systemOlmesartanPlacebo Followed by OlmesartanLosartan
HeadacheNervous system disorders18 of 4205 of 5224 of 469
NasopharyngitisInfections and infestations8 of 4200 of 5213 of 469
NauseaGastrointestinal disorders7 of 4202 of 529 of 469
Upper respiratory tract infectionInfections and infestations4 of 4202 of 5210 of 469
DizzinessNervous system disorders8 of 4201 of 526 of 469
ConstipationGastrointestinal disorders5 of 4201 of 524 of 469
DiarrhoeaGastrointestinal disorders5 of 4201 of 523 of 469
Back painMusculoskeletal and connective tissue disorders4 of 4202 of 523 of 469
BronchitisInfections and infestations6 of 4200 of 522 of 469
HypertensionVascular disorders3 of 4201 of 524 of 469

Serious events with the highest arm-level rate: non-cardiac chest pain (0.2%), asthma (0.2%), cerebrovasular accident (0.2%), urinary tract infection (0.2%).

Do not overextend the safety comparison. Serious-adverse-event counts are safety observations, not efficacy outcomes, and should not be combined with the primary result into a single benefit-risk number.

The registry reports serious adverse event counts for Olmesartan, Placebo Followed by Olmesartan, and Losartan. The serious adverse event counts are 0 among 420 at risk for Olmesartan, 0 among 52 at risk for Placebo Followed by Olmesartan, and 4 among 469 at risk for Losartan. These are counts within the listed groups and risk denominators; they are not estimates of comparative risk adjusted for differences between groups.

For other, non-serious adverse events, the posted counts are 133 among 420 at risk for Olmesartan, 21 among 52 at risk for Placebo Followed by Olmesartan, and 148 among 469 at risk for Losartan. These counts summarize reported events in the registry and do not establish that a treatment caused an event. The serious-event terms listed include Non-cardiac chest pain, Asthma, Cerebrovasular accident, and Urinary tract infection, each reported as 0.2%.

Deaths are not reported in the registry record. The safety figures should be interpreted as descriptive counts, not as proof that no unlisted events occurred or as a complete safety comparison. The registry does not provide further detail in the reported information about event severity beyond the serious classification, event timing, attribution, or exposure-adjusted rates.

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

The posted results describe average blood-pressure changes among the analyzed participants and the statistical comparisons recorded for the trial. For the primary Week 8 SDBP endpoint, the sponsor reports an ANCOVA comparison of Combined Olmesartan with Losartan with a mean difference of -2.5 and a 95% confidence interval from -3.8 to -1.3. The registry also provides group mean changes and recalculated, unadjusted comparisons. Because the sponsor analysis and recalculation use different quantities and methods, the sponsor's analysis takes precedence for the reported comparison.

These results do not establish how much an individual participant's blood pressure would change. Group averages can conceal variation among participants, and the reported standard errors describe precision of group means rather than individual variability. The registry does not report a threshold for clinical importance, so the numerical differences cannot by themselves determine whether the observed change is important in a clinical sense.

The results also do not show that any effect is free from bias. Interpretation depends on randomization and blinding as implemented, the analysis population, the endpoint measurement protocol, missing-data handling, model assumptions, and the complete set of analyses. Some of these details are not reported in the registry record. Last observation carried forward can affect estimates when follow-up data are missing, and the registry does not report the amount or pattern of missingness or sensitivity analyses.

The trial's status is completed and its listed enrollment is 941, but enrollment alone does not describe the number contributing to each endpoint analysis. The group counts differ across posted outcomes, reflecting the reported analysis samples; the registry does not provide a complete explanation of those differences. Nor do these findings answer questions about outcomes not reported in the posted results or about longer-term follow-up beyond the listed study period.

In short, the record supports a statistical description of the posted endpoint analyses, with the sponsor's ANCOVA result as the primary reported comparison and the summary-based recalculations as approximate, unadjusted checks. It does not, on its own, establish clinical importance, individual response, long-term effects, or a complete characterization of benefits and harms.

18. Why This Trial Matters Statistically

This trial is statistically instructive because its registry contains both model-based sponsor analyses and summary-based recalculations. The sponsor reports ANCOVA contrasts of final values, while the recalculations compare posted change-from-baseline means. The approaches can produce different estimates because they use different outcome summaries, adjustments, and possibly contrast coding. Recognizing that distinction prevents a recalculated result from being mistaken for a replication of the sponsor's analysis.

The record also illustrates why uncertainty must be described alongside an estimate. The sponsor's primary comparison includes a confidence interval and p-value, and the recalculations provide their own intervals based on approximate inputs. Those intervals indicate statistical precision under their respective methods; they do not establish clinical importance or eliminate uncertainty about model assumptions and missing data.

Multiple outcomes and analyses make the question of multiplicity important. The registry lists 16 outcome measures and 100 analyses, but does not report a multiplicity adjustment or testing hierarchy in the posted information. Secondary findings can help assess whether the broad pattern is coherent across measurement types and visits, but they should not automatically be treated as independent confirmation.

Finally, the efficacy population and last-observation-carried-forward rule show how an analysis can depend on decisions about which participants contribute and how missing outcomes are handled. The original sample-size justification and fuller statistical plan are not reported in the registry record. These features make the distinction between a reported result, a recalculation, and a planning illustration essential to sound statistical reading.

19. Limitations

Several limitations specific to this record restrict interpretation. The registry reports a discrepancy between its posted summary statistics and the sponsor analysis. The primary sponsor comparison uses ANCOVA on final values, whereas the recalculation uses unadjusted changes from baseline and approximate pooled variability. The two estimates are not interchangeable, and the record does not explain the source of the discrepancy or provide the full model specification needed to reproduce the sponsor analysis.

The posted primary group means are least-squares means with standard errors, but individual-level data and standard deviations are not reported. The recalculated intervals therefore depend on an approximate standard deviation derived from the reported summaries. Their precision should not be treated as equivalent to that of the sponsor's model-based results.

The registry specifies an efficacy population and last observation carried forward, but does not report the amount, timing, or reasons for missing endpoint data. It also does not report sensitivity analyses that could show whether conclusions change under different missing-data assumptions. The counts contributing to posted outcomes differ, and a full accounting of those differences is not reported in the registry record.

The exact ANCOVA covariates, the original sample-size justification, any interim analyses, and a multiplicity plan are not reported in the registry record. Although the record lists many outcome measures and analyses, only three secondary blood-pressure endpoints are detailed in the posted information. The full set of outcomes and the rationale for their selection cannot be assessed from these data.

Finally, safety results are presented as counts, with deaths not reported in the registry record. Further details on event timing, attribution, or exposure-adjusted comparisons are not reported. These limitations do not negate the posted estimates, but they narrow the conclusions that can be drawn from them.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

Continue through the Clinical Biostats statistical pathway

Use this trial's endpoint as a starting point for deeper study of effect measures, confidence intervals, and sample-size planning.

23. Record Summary

The registry describes a completed, randomized, double-blind, parallel-group, Phase 4 active-comparator trial of olmesartan medoxomil and losartan potassium in participants with hypertension. Total enrollment was 941. The primary endpoint was change from baseline to Week 8 in trough, cuff, seated diastolic blood pressure, measured in mmHg.

The sponsor's ANCOVA comparison of Combined Olmesartan with Losartan reports a mean difference of -2.5, a 95% confidence interval from -3.8 to -1.3, and p < 0.001. The registry flags a discrepancy with summary-based recalculations, so the sponsor's own analysis takes precedence. Recalculated contrasts are unadjusted and use approximate variability derived from posted summaries.

The record specifies an efficacy population and last observation carried forward, but does not report the original sample-size justification, multiplicity plan, full ANCOVA model, or extent of missing endpoint data. Safety findings are reported as event counts, and deaths are not reported in the registry record.

Clinical Biostats