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 Value of Liquid Potassium Magnesium Citrate in Controlling Hypertension (NCT01682837), a randomized phase 2 study. The primary outcome is 24-hour Average Systolic Blood Pressure.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT01682837 |
| Phase | Phase 2 |
| Condition | Hypertension |
| Allocation | Randomized |
| Design model | Crossover |
| Masking | Quadruple |
| Enrollment | 35 |
| Arms in the primary outcome | 4 |
| Lead sponsor | University of Texas Southwestern Medical Center |
| Results posted | Yes |
2. Clinical Question
Population
Participants with pre- or Stage I hypertension on their customary diet were the intended population. The registry lists an enrollment of 35; the primary outcome population is described as participants who completed all 4 phases.
Intervention
The intervention of interest was potassium magnesium citrate (KMgCit) powder, taken twice daily after dissolution in 250 ml water during its treatment phase.
Comparator
The study also included potassium citrate powder, potassium chloride powder and placebo. Each treatment phase was followed by at least 1 week of washout.
Primary question
Across a 4-week measurement timeframe, how did 24-hour average systolic blood pressure during the KMgCit phase compare with blood pressure during the placebo phase? The registry also reports a mixed-model analysis across all four phases.
This is a question about average blood pressure measurements under several assigned treatment conditions, not about a clinical event or a long-term outcome. The primary endpoint is continuous, so the posted arm summaries describe means and standard deviations. The direct KMgCit-versus-placebo recalculation estimates the difference between those phase means, while the registry’s reported mixed-model analysis covers all four treatment phases together.
The crossover arrangement means participants received more than one study condition in a sequence. That design can allow comparisons within participants, but interpretation depends on how the analysis handles repeated measurements and treatment sequence. The registry record describes the design and reports a mixed-model p-value; detailed model specifications and sequence-specific estimates are not reported in the registry record.
3. Trial Design
This completed Phase 2 study is registered as randomized, quadruple-masked and crossover, with an enrollment of 35. Its treatment conditions were potassium magnesium citrate powder, potassium citrate powder, potassium chloride powder and placebo. The arm descriptions list different orders in which these conditions could be received. Study medications were taken twice daily after dissolution in 250 ml water, and each phase was followed by at least 1 week of washout.
The primary outcome was 24-hour average systolic blood pressure at a 4-week timeframe. The outcome population is described as all participants who completed the study and all 4 phases. The posted summaries give 30 observations for each treatment phase. The record does not explain the relationship between the enrollment figure and the smaller number of observations in the outcome summaries, or how any missing measurements were handled.
Randomized crossover studies differ from parallel-group trials: participants experience multiple treatment conditions rather than remaining in one assigned condition throughout. Consequently, the order of conditions and possible effects carried from one phase to another can matter to the analysis. The registry describes sequence orders and washout, but does not report the randomization procedure, allocation concealment details, phase-specific adherence, or whether period and carryover effects were tested.
The registry reports a mixed-model analysis across the four groups, with p = 0.07 for the primary outcome. It does not report the model’s estimated treatment effects or confidence intervals. Detailed protocol dates, dose levels, and the original sample-size justification are not reported in the registry record. The trial’s own original design assumptions and any interim analysis plan are likewise not reported in the registry record.
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.
Baseline
| Stage | All Study Participants |
|---|---|
| STARTED | 35 |
| COMPLETED | 30 |
| NOT COMPLETED | 5 |
Reasons for not completing this period:
| Reason | All Study Participants |
|---|---|
| Withdrawal by Subject | 5 |
First Intervention (4 Weeks)
| Stage | All Study Participants |
|---|---|
| STARTED | 30 |
| Received KMgCit | 8 |
| Received KCit | 8 |
| Received KCl | 7 |
| Received Placebo | 7 |
| COMPLETED | 30 |
| NOT COMPLETED | 0 |
Second Intervention (4 Weeks)
| Stage | All Study Participants |
|---|---|
| STARTED | 30 |
| Received KMgCit | 7 |
| Received KCit | 6 |
| Received KCl | 8 |
| Received Placebo | 9 |
| COMPLETED | 30 |
| NOT COMPLETED | 0 |
Third Intervention (4 Weeks)
| Stage | All Study Participants |
|---|---|
| STARTED | 30 |
| Received KMgCit | 9 |
| Received KCit | 7 |
| Received KCl | 7 |
| Received Placebo | 7 |
| COMPLETED | 30 |
| NOT COMPLETED | 0 |
Analysis population for the primary outcome, as defined in the registry: All participants who completed the study completed all 4 phases.
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.
Population: Thirty (30) subjects participated in the trial. Each subject completed all four phases of the trial.
| Characteristic | Unit | All Study Participants |
|---|---|---|
| Participants analysed | 30 | |
| Age, Continuous | years | 54 (SD 12) |
| Sex: Female, Male: Female | Participants | 16 |
| Sex: Female, Male: Male | Participants | 14 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 4 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 26 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 0 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 0 |
| Race (NIH/OMB): Asian | Participants | 0 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 0 |
| Race (NIH/OMB): Black or African American | Participants | 12 |
| Race (NIH/OMB): White | Participants | 18 |
| Race (NIH/OMB): More than one race | Participants | 0 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 0 |
| Region of Enrollment: United States | participants | 30 |
| BMI | kg/m^2 | 31 (SD 5) |
| Office Systolic Blood Pressure | mmHg | 125 (SD 11) |
| Office Diastolic Blood Pressure | mmHg | 81 (SD 8) |
| Office Heart Rate | beats per minute | 72 (SD 11) |
| 24-hr Systolic Blood Pressure Average | mmHg | 126 (SD 10) |
| 24-hr Diastolic Blood Pressure Average | mmHg | 79 (SD 10) |
| 24-hr Heart Rate Average | beats per minute | 76 (SD 11) |
| 24-hr Daytime Systolic Blood Pressure | mmHg | 129 (SD 10) |
| 24-hr Daytime Diastolic Blood Pressure | mmHg | 81 (SD 11) |
6. Primary Endpoint
The registry lists the primary outcome as 24-hour Average Systolic Blood Pressure, measured over 4 weeks.
| Element | Registry entry |
|---|---|
| Result type | Mean |
| Measure of spread | Standard Deviation |
| Unit | mmHg |
| Endpoint classification | Continuous Endpoint |
The primary endpoint is 24-hour average systolic blood pressure, measured in mmHg, with a 4-week timeframe. Systolic pressure is the pressure recorded during the heart’s contraction; averaging measurements over a 24-hour period represents blood pressure across a full day rather than relying only on a single office reading. The registry describes the endpoint as the average systolic blood pressure over a 24-hour period.
A continuous endpoint preserves information about the magnitude of measurements. Reporting a mean and standard deviation describes the central value in each treatment phase and the spread of participant measurements around that mean. The comparison of interest for the recalculation is the difference between the KMgCit phase mean and the placebo phase mean. This difference is expressed in mmHg, with negative values indicating a lower observed mean during the KMgCit phase relative to placebo under the stated subtraction direction.
That descriptive comparison is not the same as the registry’s mixed-model analysis. A mixed model can account for the repeated observations arising when participants take multiple treatments, depending on its specification. The registry reports the method and an overall p-value, but not model-based effect estimates or confidence intervals. The endpoint can therefore be described from posted phase summaries and an unadjusted pairwise recalculation, while the sponsor’s reported analysis remains the registry’s own inferential result.
7. Results Posted in the Registry
- Potassium Magnesium Citrate Powder Phase: mean 127.00 versus 129.00 on control; difference -2.00 (95% CI -8.09 to 4.09), standardized effect d = -0.17; z-test p = 0.520.
- Potassium Citrate Powder Phase: mean 127.00 versus 129.00 on control; difference -2.00 (95% CI -7.87 to 3.87), standardized effect d = -0.17; z-test p = 0.504.
- Potassium Chloride Powder Phase: mean 126.00 versus 129.00 on control; difference -3.00 (95% CI -8.66 to 2.66), standardized effect d = -0.27; z-test p = 0.299.
Mean difference: Potassium Magnesium Citrate Powder Phase
95% CI: -8.09 to 4.09
Recalculated from the posted summary statistics
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 outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Office Systolic Blood Pressure | Continuous Endpoint | Mean difference | -5.00 (-10.83 to 0.83) | 84 per arm |
| Office Diastolic Blood Pressure | Continuous Endpoint | Mean difference | 0.00 (-4.55 to 4.55) | n/a |
| Serum C-terminal Telopeptide (CTX) | Continuous Endpoint | Mean difference | -0.03 (-0.18 to 0.12) | 1,634 per arm |
Office Systolic Blood Pressure
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
- Result:
- Potassium Magnesium Citrate Powder Phase: mean 124.00 versus 129.00 on control; difference -5.00 (95% CI -10.83 to 0.83), standardized effect d = -0.43; z-test p = 0.093.
- Potassium Citrate Powder Phase: mean 125.00 versus 129.00 on control; difference -4.00 (95% CI -10.33 to 2.33), standardized effect d = -0.32; z-test p = 0.216.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Potassium Magnesium Citrate Powder Phase and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Potassium Citrate Powder Phase and the control. The interval gives the range of effects that remain compatible with the data.
Office Diastolic Blood Pressure
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
- Result:
- Potassium Magnesium Citrate Powder Phase: mean 81.00 versus 81.00 on control; difference 0.00 (95% CI -4.55 to 4.55), standardized effect d = 0.00; z-test p = 1.000.
- Potassium Citrate Powder Phase: mean 81.00 versus 81.00 on control; difference 0.00 (95% CI -4.31 to 4.31), standardized effect d = 0.00; z-test p = 1.000.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Potassium Magnesium Citrate Powder Phase and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Potassium Citrate Powder Phase and the control. The interval gives the range of effects that remain compatible with the data.
Serum C-terminal Telopeptide (CTX)
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
- Result:
- Potassium Magnesium Citrate Powder Phase: mean 0.46 versus 0.49 on control; difference -0.03 (95% CI -0.18 to 0.12), standardized effect d = -0.10; z-test p = 0.704.
- Potassium Citrate Powder Phase: mean 0.46 versus 0.49 on control; difference -0.03 (95% CI -0.18 to 0.12), standardized effect d = -0.10; z-test p = 0.704.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Potassium Magnesium Citrate Powder Phase and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Potassium Citrate Powder Phase and the control. The interval gives the range of effects that remain compatible with the data.
The registry lists seven secondary outcomes, including office systolic and diastolic blood pressure, serum C-terminal Telopeptide (CTX), urinary calcium, pulse wave velocity and central aortic blood pressure measures. Numerical summaries are available in the posted results for office systolic blood pressure, office diastolic blood pressure and CTX. Numerical results for the other listed secondary outcomes are not reported in the registry record.
Across the posted secondary measures, the broad pattern is that the phase summaries do not establish a clear, precise separation from placebo. The secondary outcomes therefore do not substantially alter the interpretation of the primary endpoint: the posted evidence remains uncertain rather than providing a precise estimate of a treatment difference. The registry’s mixed-model p-values for the posted secondary analyses do not include model-based estimates or confidence intervals, limiting assessment of effect magnitude and precision.
Secondary analyses are generally less conclusive when many outcomes or comparisons are examined. Testing multiple outcomes increases the chance that some results appear noteworthy by chance, unless a prespecified multiplicity strategy is used. Whether the study specified or applied such a strategy is not reported in the registry record. The recalculated pairwise p-values are unadjusted, so they should not be treated as confirmatory evidence across a collection of outcomes.
Secondary endpoints can help describe whether patterns are consistent across different measurements, but they do not replace the primary analysis. Their interpretation also depends on how they were selected, whether they were prespecified, and how missing data were handled; those details are not reported in the registry record. The limited posted secondary results should therefore be read as exploratory context rather than as independent proof of a treatment effect.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Office Systolic Blood Pressure
- Office Diastolic Blood Pressure
- Serum C-terminal Telopeptide (CTX)
- 24-hour Urinary Calcium
- Carotid to Femoral Pulse Wave Velocity
- Central Aortic Systolic Blood Pressure
- Central Aortic Diastolic Blood Pressure
9. Statistical Interpretation
For 24-hour average systolic blood pressure, the posted means were 127.0 mmHg during the potassium magnesium citrate phase and 129.0 mmHg during the placebo phase. The unadjusted recalculation gives a mean difference of -2.0 mmHg, with a 95% confidence interval from -8.094 to 4.094 and p = 0.52. The interval includes no difference and also spans effects in either direction. Thus, the pairwise estimate is not precise enough to establish the direction or size of a difference from these summary data alone.
The registry’s own mixed-model analysis across the four treatment phases reports p = 0.07. It does not report a model-based estimate or confidence interval. This is an overall analysis across the treatment groups, not the same calculation as the unadjusted KMgCit-versus-placebo contrast. The two results answer related but not identical statistical questions, and their p-values should not be treated as interchangeable. The registry model result takes precedence as the sponsor’s reported analysis; the recalculation is a supplementary, unadjusted comparison of posted summary statistics.
The other pairwise recalculations for the primary endpoint are also uncertain: the potassium citrate phase mean was 127.0 mmHg and its difference from placebo was -2.0 mmHg, with a confidence interval from -7.869 to 3.869 and p = 0.504. The potassium chloride phase mean was 126.0 mmHg, with a difference from placebo of -3.0 mmHg, a confidence interval from -8.658 to 2.658 and p = 0.299. These unadjusted comparisons do not replace the trial’s mixed-model analysis and do not account for the crossover structure.
Standard deviations in the phase summaries range from 9.0 to 13.0 mmHg. Variation among measurements is substantial relative to the observed differences between phase means, which helps explain why the confidence intervals remain broad. The number of observations listed for each phase is 30, while the registered enrollment is 35. The primary outcome population is restricted to participants who completed all phases, so conclusions relate to that analyzed population rather than necessarily to every enrolled participant.
Overall, the registry offers an across-treatment model p-value and descriptive summaries, but it does not provide the model’s estimated contrasts or their precision. The unadjusted comparisons are useful for understanding the scale of the observed phase differences, but they are not a substitute for a crossover-aware estimate. The record does not establish that any observed difference is clinically important; a threshold for clinical importance is not reported in the registry record.
10. Statistical Methods Explained
Several statistical ideas help distinguish the posted summaries from the trial’s own analysis. The primary endpoint is continuous, and the registry reports a mean and standard deviation for each treatment phase. A mean gives the arithmetic average of measurements; a standard deviation describes how dispersed the measurements are around that average. Neither quantity alone describes the uncertainty in a treatment comparison. For that, an estimated difference and its confidence interval are more informative.
A mean difference expresses the distance between two group means in the endpoint’s original units. For the primary pairwise recalculation, the KMgCit phase is compared with the placebo phase. A negative estimate means the observed average was lower in the KMgCit phase under the stated comparison direction. This recalculation uses posted summary statistics and treats the comparison as unadjusted. It does not reproduce the trial’s mixed model or account for within-participant correlation from the crossover design.
The registry’s reported method is Mixed Models Analysis across the four treatment conditions. In general, mixed models can represent repeated measurements from the same participant and account for correlation among those measurements. They can also include fixed effects for treatment or other design features, depending on the model specification. The registry record does not report the model formula, covariance structure, covariates, degrees-of-freedom method, or treatment-specific estimates. It is therefore not possible to determine from the registry record exactly how these features were handled.
The reported p-value is a measure of how compatible the data are with a specified null hypothesis under the analysis model. It is not the probability that the null hypothesis is true, and it does not measure the size or importance of an effect. The registry reports p = 0.07 for its primary mixed-model analysis. The recalculated pairwise p-values are separate, unadjusted tests based on summary statistics. They should be read as supplementary rather than as a replacement for the sponsor’s model-based analysis.
Confidence intervals describe a range of effect estimates compatible with the observed data and the calculation’s assumptions. A wide interval signals substantial uncertainty about the effect’s magnitude or direction. A confidence interval that includes zero is consistent with no difference, while also allowing the other values in its range. This does not prove that there is no effect. The confidence intervals for the recalculated primary comparisons all include zero, and their breadth leaves considerable uncertainty about the true difference.
Because the study is a crossover, each participant may contribute observations under multiple conditions. In general, within-participant comparisons can be more informative than comparisons between unrelated groups, but that benefit relies on appropriate handling of repeated observations and the order of treatment. Carryover is a concern when effects from one phase persist into another; washout periods are intended to reduce that possibility. The record says each phase was followed by at least 1 week of washout, but whether carryover was assessed is not reported in the registry record. The protocol’s treatment doses and details about measurement procedures are also not reported in the registry record.
The pairwise calculations use the arm-level means, standard deviations and sample sizes as posted. They are unadjusted recalculations. In general, an unadjusted calculation does not incorporate the design-specific features that may be included in a trial’s prespecified model. It also does not address multiplicity across several comparisons. The trial’s own mixed-model analysis takes precedence as the sponsor-reported result, and the registry does not report enough model detail to independently reproduce that analysis.
Over-dispersion is a general concern when observed variability is greater than a statistical model expects. If the model understates variability, standard errors may be too small and confidence intervals too narrow; if it accounts for variability appropriately, uncertainty is better represented. There is no over-dispersion assessment reported in the registry record, so this issue cannot be evaluated for the sponsor’s model from the posted information.
Planning calculations based on observed effects are a different use of statistics from analysis of the completed trial. They illustrate how the number of participants per arm would vary under stated assumptions and hypothetical target effects. They do not establish what sample size the investigators selected or why. The original sample-size justification is not reported in the registry record.
11. Confidence Intervals and Precision
The recalculated primary comparison estimates a mean difference of -2.0 mmHg between the potassium magnesium citrate phase and placebo. Its 95% confidence interval is -8.094 to 4.094 mmHg. This interval includes zero, so the posted summary statistics are compatible with no difference as well as with a lower or higher mean during the KMgCit phase. Its width indicates that the estimate is imprecise: the data do not pin down a narrow range of plausible effects.
A confidence interval is not a guarantee that the true effect lies within the particular interval, nor does it assign a probability to each value inside it. In general, it reflects the variability in the data and the assumptions used to construct it. Here, the recalculated interval is unadjusted and based on summary statistics; it does not incorporate the crossover structure in the way a correctly specified repeated-measures model might.
The posted standard deviations are 11.0 mmHg for the KMgCit phase and 13.0 mmHg for placebo, with 30 observations in each phase. These summaries show considerable spread around the means compared with the estimated difference. The confidence interval therefore leaves room for effects meaningfully different in magnitude from the point estimate, in either direction. The clinical importance of any particular value is not reported in the registry record.
The sponsor’s mixed-model result has p = 0.07, but its treatment effect estimate and confidence interval are not reported in the registry record. That means precision for the sponsor’s own model-based contrast cannot be described from the posted results. The unadjusted confidence interval is informative about the simple summary-data comparison, but it should not be mistaken for a model-based interval from the crossover analysis.
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 detect | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 570 | 762 |
| 75% of the observed effect | 1,012 | 1,355 |
| 50% of the observed effect | 2,277 | 3,048 |
The planning figures are participants per arm, not total event counts. They are illustrations for comparisons of continuous outcomes under a two-sided significance level of 0.05, equal allocation between the two arms and a normal approximation. Each planning row uses the stated fraction of the observed effect as the effect to detect. The trial’s own original sample-size assumptions are not reported in the registry record.
The 80% power column gives the illustrative number of participants per arm needed for an analysis to have an 80% chance of detecting the specified effect, if that effect and the planning assumptions were correct. The 90% power column uses a higher target chance of detecting that same specified effect, and therefore generally calls for more participants per arm. These are planning targets, not guarantees about what a future study would find.
Rows describing planning for 75% or 50% of the observed effect ask what the sample size might be if the true effect were smaller than the observed estimate. Smaller effects are harder to distinguish from random variation, so they require more participants for the same power target. This relationship is reflected in the increasing participant counts across those planning scenarios. The posted figures use the observed effect as a starting point; an observed effect from a small study can itself be uncertain.
These calculations are not observed power. They are hypothetical planning illustrations based on the stated assumptions, not a retrospective measure of whether the completed trial was adequately powered. The crossover design and the sponsor’s mixed-model approach may have different information characteristics from the equal-allocation, two-arm normal approximation used for these illustrations. The planning numbers should therefore be read as rough comparisons of hypothetical sample-size needs, not as a reconstruction of the trial’s design rationale.
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 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
- Observed difference Δ = -2.000; pooled standard deviation σ = 12.042.
- n = 2 × (1.96 + 0.842)2 × 12.0422 / -2.0002 = 569.0, rounded up to 570 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 <- -2 # observed difference in means
sigma <- 12.0415945787923 # 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(1682837)
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 = 570 (80% power), 762 (90% power)
75% of observed effect: n per arm = 1,012 (80% power), 1,355 (90% power)
50% of observed effect: n per arm = 2,277 (80% power), 3,048 (90% power)
power.t.test: 570
Simulated power at n = 570 per arm: 0.800 (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
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| Mixed Models Analysis | not reported | 0.070 |
The sponsor’s reported primary analysis is a Mixed Models Analysis across the four treatment phases, with p = 0.07. The registry does not report a model-based treatment estimate, confidence interval, or further model details. The sponsor’s p-value is therefore the registry’s own inferential result, but its magnitude and precision cannot be fully interpreted without those additional outputs.
The recalculated pairwise comparison between potassium magnesium citrate and placebo uses the posted phase means, standard deviations and sample sizes. It gives a mean difference of -2.0 mmHg, a 95% confidence interval from -8.094 to 4.094, and p = 0.52. This is an unadjusted recalculation, not a reproduction of the mixed model. It does not account for repeated measurements or the crossover sequence in a model-based way.
The p-values need not match because the analyses are not identical: one is reported as a mixed-model analysis across all four phases, and the other is a simple pairwise recalculation from summary statistics. The record identifies no discrepancy between the sponsor’s reported analysis and the posted results. Accordingly, the sponsor’s own analysis takes precedence, while the recalculation serves as a transparent, limited description of the two phase means and their unadjusted uncertainty.
15. Multiplicity, Missing Data and Analysis Populations
The registry reports one primary outcome and lists seven secondary outcomes. It also reports an overall mixed-model analysis across the four treatment phases for the primary endpoint and the posted secondary outcomes. Multiple outcomes and treatment comparisons create a multiplicity issue: when many hypotheses are tested, the chance of at least one apparently unusual result can increase even if there is no real effect. A prespecified strategy can address this, for example by defining which comparisons are primary or adjusting inference for multiple testing.
Multiplicity handling is not reported in the registry record. The recalculated pairwise p-values are unadjusted and should not be interpreted as if they account for all comparisons across treatment phases and outcomes. The record also does not report whether the mixed-model p-values were adjusted, how the testing hierarchy was defined, or whether the primary contrast was prespecified separately from an overall treatment test.
Missing-data handling is also not reported in the registry record. The primary outcome population is described as all participants who completed all 4 phases, and the posted summaries list 30 observations per phase, while enrollment is 35. The record does not explain why fewer observations appear in the outcome summaries, whether participants withdrew or lacked particular measurements, or whether any imputation or sensitivity analysis was used. The population wording suggests a completer analysis, but the handling of participants who did not complete all phases is not described in enough detail to assess potential selection effects.
The registry does not report whether the analysis was based on intention-to-treat, per-protocol, or another population definition beyond the completer description for the primary outcome. The exact mixed-model specification and assumptions about missing observations are not reported either. These omissions limit assessment of robustness and reproducibility. They do not show that the analysis was inappropriate; they mean the relevant methods cannot be evaluated from the registry record.
16. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Potassium Magnesium Citrate Powder Phase | 0 | 30 | 0.0% |
| Potassium Citrate Powder Phase | 0 | 30 | 0.0% |
| Potassium Chloride Powder Phase | 0 | 30 | 0.0% |
| Placebo Phase | 0 | 30 | 0.0% |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 0% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Potassium Magnesium Citrate Powder Phase | 5 of 30 |
| Potassium Citrate Powder Phase | 5 of 30 |
| Potassium Chloride Powder Phase | 16 of 30 |
| Placebo Phase | 4 of 30 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Potassium Magnesium Citrate Powder Phase | Potassium Citrate Powder Phase | Potassium Chloride Powder Phase | Placebo Phase |
|---|---|---|---|---|---|
| Dysgeusia | Gastrointestinal disorders | 2 of 30 | 2 of 30 | 12 of 30 | 2 of 30 |
| Nausea | Gastrointestinal disorders | 2 of 30 | 1 of 30 | 1 of 30 | 1 of 30 |
| Loose Bowel Movement | Gastrointestinal disorders | 0 of 30 | 0 of 30 | 4 of 30 | 0 of 30 |
| Belching | Gastrointestinal disorders | 0 of 30 | 1 of 30 | 2 of 30 | 0 of 30 |
| Diarrhea | Gastrointestinal disorders | 1 of 30 | 0 of 30 | 1 of 30 | 1 of 30 |
| Pain and/or Cramps | Gastrointestinal disorders | 0 of 30 | 1 of 30 | 1 of 30 | 1 of 30 |
| Dyspepsia | Gastrointestinal disorders | 0 of 30 | 0 of 30 | 0 of 30 | 1 of 30 |
The adverse-event record lists 30 participants at risk for serious adverse events in each phase: potassium magnesium citrate, potassium citrate, potassium chloride and placebo. The number affected by serious adverse events is recorded as 0 for each phase. The record therefore reports no serious adverse events in the listed phase groups.
This is a count from the registry’s adverse-event reporting, not proof that serious harms are impossible or that the treatment conditions have equivalent safety. The sample is limited, and the record does not provide a detailed description of surveillance, event adjudication or the duration of safety follow-up beyond the treatment-phase information. Death counts are not reported in the registry record.
The registry also lists other, non-serious adverse events, but those counts are distinct from the serious-event figures. Safety interpretation should keep these categories separate. The serious-event counts alone do not provide a complete account of tolerability or establish comparative safety across the phases.
17. What the Result Does, and Does Not, Mean
The registry record presents a randomized crossover comparison of four treatment conditions, with 24-hour average systolic blood pressure as the primary endpoint. The sponsor’s mixed-model analysis across the phases reports p = 0.07, while the unadjusted recalculation comparing the potassium magnesium citrate phase with placebo estimates a difference of -2.0 mmHg and a confidence interval from -8.094 to 4.094. The confidence interval includes zero and spans values in both directions, so the pairwise estimate is uncertain.
These results do not establish that potassium magnesium citrate lowers blood pressure, nor do they establish that it has no effect. The registry’s model-based result lacks a reported effect estimate and confidence interval, while the recalculation does not account for the crossover design in the way the trial’s mixed model may. The registry’s own analysis remains the principal reported inferential result, but its precision and estimated magnitude cannot be assessed from the posted information.
The findings also do not establish whether any observed difference is clinically important. A clinically meaningful threshold is not reported in the registry record. The study’s sample and completer-defined outcome population constrain how broadly its estimates can be generalized, and the record does not provide enough information to assess missing-data handling or the impact of treatment sequence.
More broadly, a p-value is not a measure of treatment benefit, and a confidence interval containing zero is not proof of no effect. The posted findings describe uncertainty in the available comparisons. They do not justify medical advice or conclusions about an individual’s care.
18. Why This Trial Matters Statistically
This trial illustrates why a reported p-value should not be read in isolation. The sponsor reports a mixed-model p-value for an analysis across four treatment conditions, while the recalculated pairwise comparison gives a different p-value because it addresses a narrower contrast using arm-level summary statistics. The methods answer related but distinct questions, and the registry’s own analysis takes precedence over a simple recalculation.
It also demonstrates the importance of confidence intervals. The pairwise estimate is accompanied by an interval broad enough to include zero and effects in either direction. That range communicates uncertainty more directly than the point estimate alone. A numerical difference between phase means is not, by itself, evidence that the difference is reliable or clinically important.
The crossover design makes analysis choices particularly consequential. Repeated measurements from the same participants can be correlated, and phase order may matter. A mixed model can address repeated observations, but the registry does not provide enough specifications to evaluate how the model represented treatment, period, sequence or carryover. The treatment schedules and washouts are described, but the analysis details are not.
Finally, the registry separates an observed trial analysis from sample-size planning illustrations. The planning figures show how hypothetical sample sizes change with effect assumptions; they do not explain the original design or quantify the completed trial’s power. Keeping those uses distinct is important when judging what a small completed study can and cannot tell us.
19. 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.
The outcome population is described as participants who completed the study and all 4 phases. The registry lists enrollment of 35 but gives 30 observations per phase for the posted outcomes. The reason for this difference and the treatment of participants without complete measurements are not reported in the registry record. A completer-focused result may not represent all enrolled participants if completion is related to outcomes or tolerability, but the record does not allow that possibility to be assessed.
Although the study is identified as a randomized crossover trial and treatment orders are listed, the randomization procedure and the allocation of participants to specific sequences are not reported in the registry record. The washout period is described as at least 1 week, but whether carryover or period effects were assessed is not reported. These design features matter when interpreting phase comparisons.
The sponsor’s mixed-model estimate, confidence interval and detailed model specification are absent. The unadjusted recalculations cannot fill that gap because they use summary statistics and do not reproduce a repeated-measures analysis. The original sample-size justification, prespecified multiplicity approach and missing-data methods are also not reported in the registry record.
Several listed secondary outcomes lack numerical results in the posted information. The registry provides limited detail about measurement procedures and does not report the clinical importance threshold for the primary endpoint. These limitations restrict independent assessment of reproducibility, precision, generalizability and the practical meaning of observed differences.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Value of Liquid Potassium Magnesium Citrate in Controlling Hypertension — NCT01682837.
- Registry record last updated 2017-04-28; status last verified 2017-03.
- Results first posted 2017-04-28.
- 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.
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
This completed Phase 2 randomized, quadruple-masked crossover trial enrolled 35 participants with pre- or Stage I hypertension. Participants received potassium magnesium citrate, potassium citrate, potassium chloride and placebo in different sequences, with each treatment phase followed by at least 1 week of washout.
The primary endpoint was 24-hour average systolic blood pressure at 4 weeks. The registry reports a mixed-model analysis across the four conditions with p = 0.07, but does not report its estimated effects or confidence intervals. An unadjusted recalculation for potassium magnesium citrate versus placebo gives a mean difference of -2.0 mmHg, with a 95% confidence interval from -8.094 to 4.094.
The posted primary comparison is imprecise, and the registry does not report enough model detail to independently reproduce the sponsor’s analysis. The primary outcome population is described as participants completing all phases; missing-data and multiplicity methods are not reported in the registry record.