← Clinical Trials
Hypertension Phase 3 Continuous Endpoint NCT00886600

A Study to Investigate the Magnitude and Duration of Response of MK0954 Compared to Placebo in Patients With Hypertension (0954-021)(COMPLETED): Complete Statistical Analysis

This analysis examines a randomized, double-blind, placebo-controlled study of losartan regimens and 24-hour diastolic ambulatory blood pressure change, alongside posted sitting blood pressure outcomes. It focuses on the size and precision of the posted comparisons and the limits of the registry record.

Trial start: 1991-05  ·  Enrollment: 122  ·  Sponsor: Merck Sharp & Dohme LLC
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 A Study to Investigate the Magnitude and Duration of Response of MK0954 Compared to Placebo in Patients With Hypertension (0954-021)(COMPLETED) (NCT00886600), a randomized phase 3 study. The primary outcome is Mean Change From Baseline in 24-hour Diastolic Ambulatory Blood Pressure Monitoring (ABPM) at Week 4.

122
Enrollment
Phase 3
4
Arms
In the primary outcome
-5.00
Mean difference
Losartan 50 mg q.d. / HCTZ 12.5 mg
-7.64–-2.36
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT00886600
PhasePhase 3
ConditionHypertension
AllocationRandomized
Design modelParallel
MaskingDouble
Enrollment122
Arms in the primary outcome4
Lead sponsorMerck Sharp & Dohme LLC
Results postedYes

2. Clinical Question

Population

Patients with hypertension were enrolled. The primary efficacy outcome used a per-protocol population: patients who completed the study according to the protocol. The registry record reports enrollment of 122, but the posted outcome counts differ by arm and outcome.

Intervention

The study evaluated losartan regimens of 50 mg once daily, 100 mg once daily, or 50 mg twice daily. Posted arm labels pair each regimen with HCTZ 12.5 mg. The registry title also describes MK0954 and lists losartan potassium among the interventions; the record's brief summary identifies the study drug as losartan.

Comparator

The posted comparison group is labelled Placebo / HCTZ 12.5 mg. The official title describes a placebo-controlled comparison and ambulatory blood pressure monitoring.

Primary question

At Week 4, how did mean change from baseline in 24-hour diastolic ambulatory blood pressure compare between each posted losartan regimen and the placebo-labelled group? The endpoint is expressed in mm Hg across a 24-hour period at baseline and Week 4.

The clinical question concerns the magnitude and duration of blood pressure response measured by ambulatory monitoring, as well as safety according to the study summary. The posted primary outcome concerns average change in diastolic pressure, not an individual patient's response or a clinical event. The available record supplies group means and standard deviations, plus simple unadjusted recalculations of differences between selected arms. Safety results are not included in the posted outcome data, so the quantitative interpretation is limited to blood pressure measures.

3. Trial Design

The registry describes a completed Phase 3 randomized, double-blind, parallel-group, placebo-controlled pilot study. Its official title identifies ambulatory blood pressure monitoring as the measurement approach and lists losartan regimens of 50 mg once or twice daily and 100 mg once daily. The registry record lists hypertension as the condition and reports enrollment of 122. The start and primary completion are recorded as 1991-05 and 1992-05.

The posted primary-outcome arms are labelled Placebo / HCTZ 12.5 mg, Losartan 50 mg once daily / HCTZ 12.5 mg, Losartan 100 mg once daily / HCTZ 12.5 mg, and Losartan 50 mg twice daily / HCTZ 12.5 mg. The record also lists hydrochlorothiazide (HCTZ) as an intervention. These labels are reported as recorded; the registry record does not provide enough detail to infer the timing or sequence of HCTZ use beyond the outcome and arm descriptions.

The primary efficacy population is explicitly described as per protocol: only patients who completed the study according to protocol were included. Posted primary outcome counts are 26.0 in the placebo-labelled group, 28.0 for each once-daily losartan group, and 30.0 for the twice-daily group. These are outcome-specific analysis counts, not a replacement for the registry's enrollment figure.

Three secondary outcomes are posted, covering sitting diastolic blood pressure at Week 4 and Week 6, including measures described in relation to adding HCTZ. Secondary outcome counts vary. The registry record does not report the original sample-size justification, allocation ratio, detailed visit schedule, or a full protocol description. The registry record also does not report the statistical plan or registered analysis details for the posted comparisons.

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: Patients could be randomized if sitting diastolic blood pressure (SiDBP) after 2 and 4 weeks of placebo washout was 95-115 mm Hg and the difference between measurements at the 2 visits was ≤7 mm Hg. At the end of placebo baseline the mean 24-hr DBP using ambulatory blood pressure monitoring (ABPM) had to be at least 85 mm Hg.

Double-blind Monotherapy

StagePlacebo / HCTZ 12.5 mgLosartan 50 mg q.d. / HCTZ 12.5 mgLosartan 100 mg q.d. / HCTZ 12.5 mgLosartan 50 mg b.i.d. / HCTZ 12.5 mg
STARTED32293031
COMPLETED30282929
NOT COMPLETED2112

Reasons for not completing this period:

ReasonPlacebo / HCTZ 12.5 mgLosartan 50 mg q.d. / HCTZ 12.5 mgLosartan 100 mg q.d. / HCTZ 12.5 mgLosartan 50 mg b.i.d. / HCTZ 12.5 mg
Adverse Event1111
Protocol Violation0001
Withdrawal by Subject1000

Combination Therapy Period

StagePlacebo / HCTZ 12.5 mgLosartan 50 mg q.d. / HCTZ 12.5 mgLosartan 100 mg q.d. / HCTZ 12.5 mgLosartan 50 mg b.i.d. / HCTZ 12.5 mg
STARTED28212123
COMPLETED28211923
NOT COMPLETED0020

Reasons for not completing this period:

ReasonPlacebo / HCTZ 12.5 mgLosartan 50 mg q.d. / HCTZ 12.5 mgLosartan 100 mg q.d. / HCTZ 12.5 mgLosartan 50 mg b.i.d. / HCTZ 12.5 mg
Adverse Event0010
Protocol Violation0010

Analysis population for the primary outcome, as defined in the registry: The efficacy analysis followed a "per protocol" approach in that only patients who completed the study according to the protocol were included in the analysis.

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.

CharacteristicUnitPlacebo / HCTZ 12.5 mgLosartan 50 mg q.d. / HCTZ 12.5 mgLosartan 100 mg q.d. / HCTZ 12.5 mgLosartan 50 mg b.i.d. / HCTZ 12.5 mgTotal
Participants analysed32293031122
Age, Continuousyears52.2 (SD 12.0)56.8 (SD 12.1)51.2 (SD 9.6)54.1 (SD 9.0)53.5 (SD 10.8)
Sex: Female, Male: FemaleParticipants71091339
Sex: Female, Male: MaleParticipants2519211883
Race/Ethnicity: Caucasianparticipants30293030119
Race/Ethnicity: Orientalparticipants00011
Race/Ethnicity: Filipinoparticipants10001
Race/Ethnicity: Indianparticipants10001
Diastolic 24-hr mean ambulatory blood pressure monitoring (ABPM)mm Hg94.8 (SD 5.9)94.0 (SD 6.9)93.8 (SD 6.0)94.4 (SD 6.9)94.2 (SD 6.4)
Sitting Diastolic Blood Pressure (SiDBP)mm Hg100.7 (SD 4.0)100.0 (SD 4.6)101.5 (SD 5.1)101.2 (SD 4.8)100.9 (SD 4.6)

6. Primary Endpoint

The registry lists the primary outcome as Mean Change From Baseline in 24-hour Diastolic Ambulatory Blood Pressure Monitoring (ABPM) at Week 4, measured over 24 hour period at Baseline and Week 4.

ElementRegistry entry
Result typeMean
Measure of spreadStandard Deviation
Unitmm Hg
Endpoint classificationContinuous Endpoint

The primary endpoint is mean change from baseline in 24-hour diastolic ambulatory blood pressure monitoring (ABPM) at Week 4, measured in mm Hg. It summarizes the average within-group change in diastolic pressure across a 24-hour period at baseline and Week 4. A negative mean change denotes a decrease from the baseline value. Comparing mean changes between groups describes how the average change differed between each losartan-labelled arm and the placebo-labelled arm.

ABPM measures pressure across a day rather than at a single clinic reading. As a general statistical point, repeated measurements over a 24-hour period can characterize average pressure across that monitoring period and can describe how a response varies over time. The registry's stated interest in magnitude and duration of response is consistent with measuring over 24 hours, although the posted primary summary is a single mean change and does not itself show a time-course profile.

The reported dispersion is the standard deviation, which describes variation among the individual observations around each group's mean. It is not the standard error of the mean and is not a confidence interval. The endpoint's per-protocol definition means that the posted primary summary applies to patients meeting the specified completion condition, rather than necessarily to every randomized participant. The record does not report how this outcome relates to a prespecified threshold for clinical importance.

7. Results Posted in the Registry

Mean difference: Losartan 50 mg q.d. / HCTZ 12.5 mg

-5.00

95% CI: -7.64 to -2.36

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals-12.2-9.1-6.1-3.1-0.12.9Placebo / HCTZ 12.5 mg (n=26)Losartan 50 mg q.d. / HCTZ 12… (n=28)Losartan 100 mg q.d. / HCTZ 1… (n=28)Losartan 50 mg b.i.d. / HCTZ … (n=30)mm Hg (95% CI)
Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Losartan 50 mg q.d. / HCTZ 12…Losartan 100 mg q.d. / HCTZ 1…Losartan 50 mg b.i.d. / HCTZ …-12-9.60-6.98-4.35-1.720.91mean 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
Mean Change From Baseline in Sitting Diastolic Blood Pressure (siDBP) 24 Hours After Morning Dose at Week 4Continuous EndpointMean difference-4.60 (-8.36 to -0.84)41 per arm
Mean Change From Baseline in Sitting Diastolic Blood Pressure (siDBP) After Adding HCTZ 24 Hours After Morning Dose at Week 6Continuous EndpointMean difference-5.30 (-8.87 to -1.73)22 per arm
Mean Change From Week 4 in Sitting Diastolic Blood Pressure (siDBP) Adding HCTZ 24 Hours After Morning Dose at Week 6Continuous EndpointMean difference-1.10 (-5.25 to 3.05)647 per arm

Mean Change From Baseline in Sitting Diastolic Blood Pressure (siDBP) 24 Hours After Morning Dose at Week 4

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Losartan 50 mg q.d. / HCTZ 12…Losartan 100 mg q.d. / HCTZ 1…-12-9.28-6.74-4.20-1.660.88mean difference vs control (95% CI)

Mean Change From Baseline in Sitting Diastolic Blood Pressure (siDBP) After Adding HCTZ 24 Hours After Morning Dose at Week 6

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Losartan 50 mg q.d. / HCTZ 12…Losartan 100 mg q.d. / HCTZ 1…-10-8.02-5.82-3.63-1.440.76mean difference vs control (95% CI)

Mean Change From Week 4 in Sitting Diastolic Blood Pressure (siDBP) Adding HCTZ 24 Hours After Morning Dose at Week 6

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Losartan 50 mg q.d. / HCTZ 12…Losartan 100 mg q.d. / HCTZ 1…-5.97-3.86-1.740.372.494.60mean difference vs control (95% CI)

The secondary outcomes broaden the measurement picture beyond the primary 24-hour ambulatory endpoint. They include sitting diastolic pressure at Week 4 and Week 6, with descriptions that distinguish changes from baseline and changes from Week 4 and refer to adding HCTZ. The posted summaries show that the direction and size of group differences are not identical across these settings and time points. This degree of variation is important: related outcomes can support a coherent account without producing the same contrast at every visit or under every outcome definition.

In broad terms, the Week 4 sitting-pressure comparisons often point toward more negative average changes in the losartan-labelled groups than in the placebo-labelled group. At Week 6, comparisons of change from baseline also show more negative changes for the posted losartan arms, whereas the Week 4-to-Week 6 change comparisons are much closer together. These observations provide context for the primary result, but sitting measurements are not the same endpoint as a 24-hour ambulatory average, and changes over different intervals answer different questions.

Some secondary comparisons are not available for every arm, and the registry record does not list reported analyses for these outcomes. The posted unadjusted comparisons therefore offer only a partial inferential picture. Their p-values are not adjusted for the collection of secondary outcomes, and the registry record does not describe a hierarchy of tests, a prespecified multiplicity strategy, or which secondary comparisons were intended as confirmatory.

For these reasons, secondary findings carry less weight than a fully specified primary analysis when judging the overall evidence. They can help identify patterns worth further study, but they should not be treated as independent replications or proof that an effect persists across settings. The registry record also does not report enough detail to determine how missing observations or repeated measurements were handled in the study's own analyses.

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

9. Statistical Interpretation

Clinical Biostats interpretation

For the primary endpoint, the posted mean changes were -0.2 mm Hg for the placebo-labelled group, -5.2 mm Hg for Losartan 50 mg once daily, -6.4 mm Hg for Losartan 100 mg once daily, and -8.5 mm Hg for Losartan 50 mg twice daily. Each arm label includes HCTZ 12.5 mg. The negative values indicate decreases from baseline on average; the group means alone do not describe the spread of individual responses.

Simple unadjusted recalculations from the posted summaries estimate the mean difference versus the placebo-labelled group as -5.0 mm Hg for Losartan 50 mg once daily, with a 95% confidence interval from -7.641 to -2.359 and p < 0.001. For Losartan 100 mg once daily, the recalculated difference is -6.2 mm Hg, with a 95% confidence interval from -8.949 to -3.451 and p < 0.001. For Losartan 50 mg twice daily, it is -8.3 mm Hg, with a 95% confidence interval from -11.33 to -5.275 and p < 0.001. Because the endpoint is change from baseline, a negative between-group difference indicates a more negative average change in the losartan-labelled group than in the placebo-labelled group.

These contrasts are unadjusted recalculations, not registry-reported model estimates. They use the posted group means, standard deviations, and counts. The registry record reports no outcome analyses, so no adjusted estimate, model specification, or multiplicity correction can be attributed to the trial's own analysis from this record. The recalculated intervals describe uncertainty around these simple group contrasts under their calculation assumptions; they do not account for unreported design or analysis features.

The secondary outcomes add information about sitting diastolic pressure at different recorded time points and after HCTZ is mentioned in the outcome descriptions. Their overall pattern is broadly consistent with lower average changes in the losartan-labelled groups in some comparisons, but it is not uniform across every endpoint or comparison. These outcomes are secondary, and the registry record does not provide a reported analysis plan or multiplicity adjustment. They should therefore be interpreted as supporting descriptive evidence rather than as independent confirmation of a definitive primary finding.

The summaries do not establish the clinical importance of the differences, the durability of effects beyond the reported observation periods, or comparative safety. The registry record gives no safety outcome results in the posted measures. It also does not provide an intention-to-treat analysis, participant flow details, or an explanation of missing outcome data. Thus the numerical patterns describe posted group summaries and limited unadjusted contrasts, not a complete assessment of all randomized participants or all study objectives.

10. Statistical Methods Explained

The primary outcome is continuous: it is a mean change in a blood pressure measurement. The registry reports a mean and standard deviation for each arm. The comparisons described in the statistical summary are simple unadjusted recalculations from those arm-level summaries, rather than analyses reported by the registry. The registry record does not report a statistical analysis plan or the model used by the study investigators.

What does a mean change represent?

A change score expresses the difference between a participant's measurement at follow-up and that participant's baseline measurement. The group mean is the average of those changes for the participants included in that outcome group. A negative group mean indicates an average decrease. A between-group mean difference compares the average change in one group with the average change in the reference group. For the primary outcome, negative recalculated differences mean a more negative average change in the losartan-labelled arm than in the placebo-labelled arm.

A mean does not show whether every participant changed in the same direction. The standard deviation gives a description of variation in individual observations around the group mean. A large spread relative to the mean difference can make the estimate less precise, while a smaller spread can make it more precise, all else being equal. This is a general statistical principle; it does not establish the shape of the data distribution in this trial.

What is the role of the unadjusted comparison?

The recalculated mean differences compare posted arm means directly. Their confidence intervals and p-values are based on the posted counts and standard deviations and do not represent an adjusted analysis. An adjusted model might account for baseline values, stratification, repeated measurements, or other factors, but the registry record does not report whether such methods were used by the investigators. It would therefore be inappropriate to describe the recalculations as the trial's prespecified analysis.

A p-value is a measure of how compatible the observed data are with a specified null hypothesis under the calculation's assumptions. It is not the probability that the null hypothesis is true, nor does it measure clinical importance. The posted primary comparisons have unadjusted p-values of <0.001. Since the record does not state how many comparisons were prespecified or whether adjustments were used, these p-values should be read as unadjusted summaries and not as a family-wise error controlled set of tests.

Why does the per-protocol population matter?

The primary efficacy population is described as patients who completed the study according to protocol. Per-protocol analyses can answer a question about outcomes among participants who met the specified completion conditions, but the resulting groups may not represent all randomized participants. If exclusions or discontinuations are related to treatment or outcome, estimates among completers can differ from estimates based on all randomized participants. This is a general concern, not a claim that such bias occurred. Reasons for exclusion, adherence information, and an intention-to-treat analysis are not reported in the registry record.

Outcome counts also vary by outcome. This can happen when measurement availability differs across time points, but the reason for the differences is not reported in the registry record. Without a missing-data description, the group summaries cannot establish whether missing measurements affected the comparisons.

How should secondary tests be understood?

The secondary endpoints examine sitting diastolic pressure at Week 4 and Week 6, with outcome descriptions referring to adding HCTZ. They provide related but not identical measurements to the 24-hour ambulatory primary endpoint. Clinic-style sitting measurements and ambulatory averages capture different measurement settings. As a general point, outcomes that differ in setting, time, or definition may complement one another but should not be treated as interchangeable.

Multiple comparisons create more opportunities for a nominally unusual result to occur by chance across a collection of tests. A multiplicity adjustment can address this issue, but the registry record does not report one. The unadjusted secondary p-values are consequently exploratory in interpretation. The registry record also does not report whether the secondary outcomes or their analysis methods were prespecified in a statistical plan.

Finally, the reported planning illustrations are calculations based on observed effects, not evidence about the original design or the probability that the completed study detected an effect. Their assumptions are described with the planning figures. They serve as hypothetical planning aids and depend on the assumed effect and variability being relevant to a future study.

11. Confidence Intervals and Precision

The recalculated primary confidence intervals quantify uncertainty around simple unadjusted mean differences. For Losartan 50 mg once daily, the interval is -7.641 to -2.359 mm Hg; for Losartan 100 mg once daily, it is -8.949 to -3.451 mm Hg; and for Losartan 50 mg twice daily, it is -11.33 to -5.275 mm Hg. All three intervals are entirely below zero. Under the assumptions used for these recalculations, the intervals are compatible with a more negative average change in each losartan-labelled arm than in the placebo-labelled arm.

A confidence interval is a range generated by a method that, under its assumptions, would contain the underlying parameter at the stated confidence level over repeated applications. It is not a range containing a specified proportion of individual participant responses, and it is not a guarantee that the true effect lies within the particular interval. The intervals are recalculations rather than registry-reported estimates, and the registry record does not report an adjusted analysis.

The widths of intervals depend on the estimated contrast, the variability in the groups, and the number of observations contributing to each estimate. In general, more variable measurements or fewer observations tend to produce less precise estimates. The posted primary analysis counts are 26.0, 28.0, 28.0, and 30.0 across the four arm labels, and the standard deviations range from 4.8 to 6.7 mm Hg. Those features provide context for precision, but they do not remedy the absence of information about missing data, the analysis plan, or the original model.

Statistical precision is not the same as clinical importance. The registry record does not report a threshold for a meaningful difference, so the confidence intervals cannot be classified against such a threshold. Nor do the intervals establish how well the results generalize beyond the analyzed per-protocol population.

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 effect1621
75% of the observed effect2837
50% of the observed effect6283
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect10205010020040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, two-sample comparison of means with the pooled standard deviation. Calculated for the comparison: Losartan 50 mg q.d. / HCTZ 12.5 mg.

The planning figures are participants per arm for 80% power and participants per arm for 90% power. They are not total events: the sample-size assumptions specify that non-time-to-event outcomes are expressed as participants per arm. The calculations use 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 80% power column gives the illustrative number of participants per arm for a design with an 80% chance of detecting the assumed effect under the stated calculation assumptions, if that effect and the other assumptions apply. The 90% power column expresses the corresponding planning target for 90% power. These are design-planning concepts, not probabilities that the observed trial result is correct or that a treatment has an effect.

The displayed scenarios use 100%, 75%, and 50% of the observed effect. A smaller assumed effect requires more participants to detect under otherwise unchanged assumptions. This is why planning for 75% or 50% of the observed effect generally produces larger per-arm figures than planning for the full observed effect. The calculations are specific to the posted comparisons and should not be treated as universal sample-size requirements.

These illustrations are based on observed effects and are not observed power. The original trial's sample-size justification and design assumptions are not reported in the registry record. The planning figures do not establish what assumptions investigators used when they designed the study, and they do not correct for uncertainty in using an observed effect as a planning input.

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 = -5.000; pooled standard deviation σ = 4.958.
  2. n = 2 × (1.96 + 0.842)2 × 4.9582 / -5.0002 = 15.4, rounded up to 16 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 <- -5                      # observed difference in means
sigma <- 4.95803543599835                     # 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(886600)
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 = 16 (80% power), 21 (90% power)
 75% of observed effect: n per arm = 28 (80% power), 37 (90% power)
 50% of observed effect: n per arm = 62 (80% power), 83 (90% power)
power.t.test: 16.5 
Simulated power at n = 16 per arm: 0.789 (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.

Very small required sample. The formula gives a very small requirement because the observed effect is very large relative to the variability. Normal-approximation formulas are unreliable at such sizes, and the simulation above shows the power actually achieved. An exact or simulation-based design would be needed in practice.

14. Multiplicity, Missing Data and Analysis Populations

The registry record does not report a statistical analysis plan, investigator-reported outcome analyses, or a multiplicity adjustment. The recalculated primary p-values are unadjusted, and the secondary p-values are also unadjusted. When several outcomes, time points, or treatment comparisons are examined, the chance of at least one small p-value can increase. This general issue makes a prespecified testing hierarchy or adjustment useful for confirmatory interpretation, but no such procedure can be attributed to this registry record.

The primary efficacy analysis is described as per protocol, restricted to patients who completed the study according to protocol. This differs conceptually from an intention-to-treat analysis that retains participants according to randomized assignment regardless of completion or adherence. The registry record does not report an intention-to-treat result, how protocol completion was defined in practice, or how many participants were excluded from the primary analysis and for what reasons.

The posted counts vary across outcome measures, including the primary and secondary summaries. The record does not explain why counts vary, how missing values were handled, whether observations were imputed, or whether missingness was assessed by treatment arm. Without that information, it is not possible to judge whether missing outcome data could have altered the reported group means or comparisons.

Nor does the record report a model for repeated observations or adjustment for baseline measurements. The simple recalculations compare arm-level changes and should not be confused with an analysis using individual participant data. Information about allocation concealment, protocol deviations, and a prespecified approach to multiple comparisons is also not reported in the registry record. These gaps limit assessment of analysis robustness, even though randomization and double masking are recorded design features.

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

The posted primary summaries show decreases in mean 24-hour diastolic ambulatory blood pressure from baseline in all four outcome groups, with more negative group means in the losartan-labelled groups than in the placebo-labelled group. The simple recalculated contrasts are negative, and their confidence intervals lie below zero. This describes the posted per-protocol summaries and their unadjusted comparisons; it does not by itself establish a causal effect or a clinically important difference.

Randomization and double masking are recorded in the registry, but interpreting results still depends on how participants were analyzed, how missing data were handled, and whether the published comparisons match the intended analysis. The primary population is per protocol, and those details are not fully documented in the registry record. The numerical estimates should therefore be read as evidence about the recorded outcome groups, not as a complete analysis of all randomized participants.

The posted results do not establish the effect in populations or settings beyond those represented in the study. The registry record does not report a threshold for clinical importance, longer-term outcome results, or safety findings among the posted measures. It therefore cannot support a conclusion about overall benefit and risk, nor about durability beyond the specified measurement periods.

The arm descriptions include HCTZ 12.5 mg alongside the losartan regimens and placebo. The registry record's brief summary describes evaluation of losartan against placebo, while the posted arm labels include HCTZ. Interpretation should retain those exact labels rather than infer a more detailed treatment sequence or attribute the outcomes to a component separately. The record also does not provide enough detail to resolve all differences in naming between the study title, official title, brief summary, and intervention listings.

These statistical results describe averages and uncertainty; they do not predict an individual response. They also do not constitute medical advice or a recommendation about treatment. Their meaning is bounded by the specific endpoint, follow-up descriptions, analysis population, and incomplete analysis details recorded for this study.

16. Why This Trial Matters Statistically

This study illustrates why the measurement and analysis population are central to interpreting a clinical trial result. The primary endpoint is an average change in 24-hour ambulatory diastolic pressure, while the secondary outcomes include sitting measurements at specified follow-up times. These are related measures, but they represent different observation settings and intervals. Keeping those distinctions visible avoids treating all blood pressure summaries as interchangeable.

The study also makes clear that group averages and uncertainty need to be read together. A mean difference describes the estimated contrast, while its confidence interval conveys precision under the calculation assumptions. Standard deviations describe variability within each group, not uncertainty in the group mean. This distinction is foundational in biostatistics and helps prevent overreading a point estimate alone.

Another statistical lesson is that registry-posted summaries may not provide the full analysis needed for confirmatory conclusions. Here, the outcome record describes a per-protocol efficacy population, but does not report an analysis plan, adjusted investigator results, missing-data methods, or multiplicity handling. Simple recalculations can make the posted summaries easier to compare, but they do not substitute for a prespecified analysis based on participant-level data.

Finally, planning illustrations derived from observed effects are useful for exploring how assumed effect size relates to future sample size, but they do not reveal the original design rationale. Separating planning assumptions from the completed trial's observed results is important for sound interpretation. The registry record offers a useful case for learning how design labels, outcome definitions, population restrictions, uncertainty, and incomplete reporting jointly shape statistical conclusions.

17. Limitations

Several limitations are specific to interpreting this registry record. The primary efficacy analysis is per protocol, and the record does not report the corresponding intention-to-treat analysis or detail how protocol completion was determined. The outcome counts vary across the posted measures, but reasons for this variation and methods for handling missing observations are not reported.

The registry record does not include investigator-reported analyses for the outcomes. The displayed contrasts are simple unadjusted recalculations from posted arm means, standard deviations, and counts. The record does not report whether the investigators used a baseline-adjusted model, how repeated measurements were handled, or whether there were prespecified covariates. The recalculations therefore cannot reproduce or verify an unreported trial analysis.

The primary endpoint focuses on a 24-hour ambulatory measure at Week 4, while secondary outcomes use sitting measurements and Week 6 descriptions. The outcome definitions are not identical, and the registry record provides no posted results for every possible arm-by-outcome comparison. Safety outcomes are not among the posted results, despite the study's stated safety objective.

The treatment naming is also not fully resolved by the record: the title refers to MK0954, the brief summary identifies losartan, and the posted arms pair losartan regimens with HCTZ 12.5 mg. The record does not report enough detail to infer treatment sequencing beyond the labels. Finally, the original sample-size justification and statistical plan are not reported in the registry record, limiting evaluation of how the study was designed to address its objectives.

18. Related Tutorials

19. Related Statistical Calculators

20. 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.

21. Record Summary

The registry describes a completed, randomized, double-blind, parallel-group, placebo-controlled Phase 3 pilot study in patients with hypertension. It reports enrollment of 122 and evaluates losartan-labelled regimens against a placebo-labelled group, with HCTZ 12.5 mg included in the posted arm labels.

The primary endpoint is mean change from baseline in 24-hour diastolic ABPM at Week 4. The primary outcome summaries use a per-protocol efficacy population. Posted secondary outcomes concern sitting diastolic pressure at Week 4 and Week 6. Simple unadjusted recalculations show negative primary mean differences versus the placebo-labelled group, with confidence intervals below zero.

The registry record does not report the investigator analysis plan, adjusted analyses, multiplicity handling, missing-data methods, or the original sample-size justification. The results should therefore be interpreted as posted group summaries and unadjusted recalculations, with those reporting limitations in view.

Clinical Biostats