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Diabetes Mellitus, Type 2 NA Continuous Endpoint NCT04286555

Dietary Approaches to Stop Hypertension for Diabetes: Complete Statistical Analysis

The randomized crossover feeding trial compared systolic blood pressure across four DASH4D and comparison diets at two sodium levels. The statistical reading distinguishes the registry’s mixed-model result from simple recalculations of the posted group summaries.

Trial start: 2021-06-02  ·  Enrollment: 105  ·  Sponsor: Johns Hopkins University
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 Dietary Approaches to Stop Hypertension for Diabetes (NCT04286555), a randomized na study. The primary outcome is Systolic Blood Pressure (SBP).

105
Enrollment
NA
4
Arms
In the primary outcome
4.80
Mean difference
DASH4D Diet With Higher Sodium
0.87–8.73
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT04286555
PhaseNA
ConditionDiabetes Mellitus, Type 2, Diabetes, Diabetes type2
AllocationRandomized
Design modelCrossover
MaskingDouble
Enrollment105
Arms in the primary outcome4
Lead sponsorJohns Hopkins University
Results postedYes

2. Clinical Question

Population

The trial concerns people with type 2 diabetes and hypertension, as indicated by its listed conditions and dietary objective. The primary outcome population includes participants who started a diet and completed at least one of the five blood pressure assessments during the last 2 weeks of that feeding period. A more detailed description of eligibility is not reported in the registry record.

Intervention

The intervention is the DASH4D dietary pattern, a DASH-style diet modified for people with diabetes. It was tested with lower sodium intake, specified as 1500 mg/day, and with higher sodium intake, specified as 3700 mg/day. The design also assessed each diet at the end of a 5-week feeding period.

Comparator

The comparison diet is described as a dietary pattern typical of what many Americans with diabetes eat. It was tested at the same lower and higher sodium levels: 1500 mg/day and 3700 mg/day. The primary contrast of interest was DASH4D with lower sodium versus the comparison diet with higher sodium.

Primary question

The primary outcome was mean systolic blood pressure, measured in mmHg at the end of a 5-week feeding period. The trial asks how this outcome differed across the dietary patterns and sodium levels, with particular interest in the DASH4D, lower-sodium diet compared with the higher-sodium comparison diet. The posted group summaries and the sponsor’s mixed-model analysis provide different forms of evidence about that contrast.

3. Trial Design

The Dietary Approaches to Stop Hypertension for Diabetes Trial was a randomized, double-masked, single-site, 4-period crossover feeding study. The registry reports an enrollment of 105 and a completed study. The recorded start date is 2021-06-02, and the primary completion date is 2024-06-13. The phase is listed as NA.

In a crossover design, participants receive more than one study condition in sequence, so each participant can contribute measurements under different conditions. Here, participants were fed each of four isocaloric diets in random order, with 5-week periods. The four conditions combined the DASH4D or comparison dietary pattern with lower or higher sodium. The lower sodium level was 1500 mg/day and the higher level was 3700 mg/day. Details about sequence allocation, any washout periods, or how period and sequence effects were handled are not reported in the registry record.

The primary contrast identified in the study description compares DASH4D with lower sodium against the comparison diet with higher sodium. The outcome was measured at the end of each feeding period. The registry describes a repeated blood pressure procedure: readings were taken after quiet seated rest, in triplicate, with readings separated by 30 seconds; blood pressure was assessed on five separate occasions during the last 2 weeks of a period. The mean systolic blood pressure from those five assessments, representing 15 readings, was the primary outcome.

Because this is a crossover feeding study, a participant could contribute observations to more than one diet condition. Therefore, the diet-specific outcome counts should not be read as independent groups of separate participants or added to estimate a unique participant total. The registry’s posted summaries include different numbers of observations across the four diet conditions. The analysis population is defined by starting the diet and completing at least one of the specified blood pressure assessments during the last 2 weeks of that period.

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: 105 participants were randomized to 1 of 24 possible sequences of the 4 study diets in random order (i.e., within-subjects crossover). However, 2 participants never started any study diets and 1 started the first diet but withdrew before any outcome assessments and were excluded from the analytic population (n=102). All participants were invited to the concurrent CGM Ancillary Study, but 3 did not consent, 8 changed their mind before outcome assessment, and 2 had contraindications (CGM n=89).

First Feeding Period (5 Weeks)

StageDASH4D Trial Analytic Population
STARTED102
DASH4D Diet With Lower Sodium (DL)23
DASH4D Diet With Higher Sodium (DH)27
Comparison Diet With Lower Sodium (CL)25
Comparison Diet With Higher Sodium (CH)27
Participated in CGM Assessment During First Feeding Period86
COMPLETED101
NOT COMPLETED1

Reasons for not completing this period:

ReasonDASH4D Trial Analytic Population
1 participant on the CL diet did not complete the first feeding period.1

Break 1 (at Least 1 Week)

StageDASH4D Trial Analytic Population
STARTED101
COMPLETED98
NOT COMPLETED3

Second Feeding Period (5 Weeks)

StageDASH4D Trial Analytic Population
STARTED98
DASH4D Diet With Lower Sodium26
DASH4D Diet With Higher Sodium23
Comparison Diet With Lower Sodium24
Comparison Diet With Higher Sodium25
Participated in CGM Assessment During Second Feeding Period80
COMPLETED97
NOT COMPLETED1

Break 2 (at Least 1 Week)

StageDASH4D Trial Analytic Population
STARTED97
COMPLETED90
NOT COMPLETED7

Analysis population for the primary outcome, as defined in the registry: The analysis population reflects the number of participants who started the diet and completed at least one of the five blood pressure assessments during the last 2 weeks of the feeding period.

5. Baseline Characteristics

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

CharacteristicUnitDASH4D All Participants
Participants analysed102
Age, Continuousyears66.0 (SD 8.8)
Sex: Female, Male: FemaleParticipants67
Sex: Female, Male: MaleParticipants35
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants2
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants100
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants0
Race (NIH/OMB): American Indian or Alaska NativeParticipants0
Race (NIH/OMB): AsianParticipants6
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants0
Race (NIH/OMB): Black or African AmericanParticipants89
Race (NIH/OMB): WhiteParticipants6
Race (NIH/OMB): More than one raceParticipants1
Race (NIH/OMB): Unknown or Not ReportedParticipants0

6. Primary Endpoint

The registry lists the primary outcome as Systolic Blood Pressure (SBP), measured over At the end of 5-week feeding period.

ElementRegistry entry
Result typeMean
Measure of spreadStandard Deviation
UnitmmHg
Endpoint classificationContinuous Endpoint

The primary endpoint is mean systolic blood pressure (SBP), recorded in mmHg at the end of a 5-week feeding period. SBP is the pressure measured when the heart contracts. The endpoint is a continuous measure: each participant’s repeated blood pressure readings are reduced to a mean for the feeding period, and the posted arm summaries report means and standard deviations.

The registry describes careful repeated measurement rather than relying on a single reading. After at least 5 minutes of quiet seated rest, an Omron device was used to take three readings, each separated by 30 seconds, and their average was recorded. Blood pressure was assessed on five separate occasions during the last 2 weeks of the period. The mean systolic blood pressure across those five occasions, corresponding to 15 total readings, was designated as the primary outcome.

General statistical context: repeated measurements can make an endpoint less dependent on any single reading and can represent blood pressure during the end of a feeding period. A mean is useful for comparing average levels across diet conditions, while a standard deviation describes the spread of individual measurements around that average. Neither summary alone describes the full distribution or the pattern of within-person change.

The endpoint is a measure of blood pressure during the feeding period, not a measure of later cardiovascular events or long-term health. The registry record does not report a clinically important difference threshold for SBP, so statistical evidence about mean differences should not be treated as proof that a difference is clinically important.

7. Results Posted in the Registry

Mean difference: DASH4D Diet With Higher Sodium

4.80

95% CI: 0.87 to 8.73

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals119121124126129131DASH4D Diet With Lower Sodium (n=89)DASH4D Diet With Higher Sodium (n=92)Comparison Diet With Lower So… (n=95)Comparison Diet With Higher S… (n=97)mmHg (95% CI)
Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)DASH4D Diet With Higher SodiumComparison Diet With Lower So…Comparison Diet With Higher S…-2.56-0.132.294.727.149.57mean 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
Diastolic Blood Pressure (DBP)Continuous EndpointMean difference2.50 (-0.41 to 5.41)252 per arm

Diastolic Blood Pressure (DBP)

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)DASH4D Diet With Higher SodiumComparison Diet With Lower So…-2.23-0.591.052.704.345.98mean difference vs control (95% CI)

The registry posts diastolic blood pressure as a secondary endpoint. Its condition means are 67.4 mmHg for DASH4D with lower sodium, 69.9 mmHg for DASH4D with higher sodium, 68.8 mmHg for the comparison diet with lower sodium, and 69.4 mmHg for the comparison diet with higher sodium. The standard deviations are 10.0, 10.0, 11.2, and 9.5 mmHg, respectively. The registry also reports a mixed-model result for comparison diet with higher sodium versus DASH4D with lower sodium: a mean difference of -2.3 mmHg with a 95% confidence interval from -3.7 to -0.9. No p-value is reported for that analysis.

At a broad level, the posted secondary SBP and DBP summaries have a similar ordering: the DASH4D, lower-sodium condition has the lowest mean among the listed conditions, and the higher-sodium comparison condition has a higher mean. This is a descriptive pattern across the posted endpoints, not independent confirmation of the primary result. The secondary mixed-model result is also a separate outcome and should be interpreted in the context of its own analysis and uncertainty.

The registry lists 31 outcome measures and 10 analyses, while one secondary endpoint is posted in the available record. It does not report a multiplicity-adjustment procedure for the secondary analyses. General statistical context: when multiple outcomes or contrasts are examined, the chance of obtaining at least one apparently notable result by chance can increase if each is assessed without adjustment. Therefore, unadjusted secondary results generally carry less confirmatory weight than the primary analysis specified for the trial.

The secondary result does not establish that the same effect applies to every outcome, nor does it replace the primary SBP contrast. The registry record does not report a complete secondary analysis plan or explain how all outcomes and comparisons were selected or interpreted. That missing context limits conclusions about how much evidential weight to assign to the secondary pattern.

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

9. Statistical Interpretation

Clinical Biostats interpretation

For the primary outcome, the posted means were 122.4 mmHg for DASH4D with lower sodium, 127.2 mmHg for DASH4D with higher sodium, 124.8 mmHg for the comparison diet with lower sodium, and 127.0 mmHg for the comparison diet with higher sodium. The standard deviations were 13.3, 13.7, 15.2, and 13.5 mmHg, respectively. These are descriptive summaries for the diet conditions, not the sponsor’s adjusted crossover-model estimates.

The registry reports a mixed-model analysis for the primary contrast between DASH4D with lower sodium and the comparison diet with higher sodium. Its mean difference in final values is -4.6 mmHg, with a 95% confidence interval from -7.2 to -2.0 and p < 0.001. Given the order of the groups in that reported analysis, the negative sign corresponds to a lower final SBP in the DASH4D, lower-sodium condition. This is the sponsor’s own analysis and takes precedence over a simple recalculation from the posted summaries.

Simple unadjusted recalculations comparing the posted means give a different presentation of the contrasts. For DASH4D with higher sodium versus DASH4D with lower sodium, the recalculated mean difference is 4.8 mmHg, with a 95% confidence interval from 0.867 to 8.733 and p = 0.017. For the comparison diet with lower sodium versus DASH4D with lower sodium, the recalculated difference is 2.4 mmHg, with a 95% confidence interval from -1.72 to 6.52 and p = 0.254. For the comparison diet with higher sodium versus DASH4D with lower sodium, the recalculated difference is 4.6 mmHg, with a 95% confidence interval from 0.746 to 8.454 and p = 0.019. These calculations use the first named condition as the reference and compare arm means without the sponsor’s mixed-model analysis. The registry marks a discrepancy, so these recalculations should not replace the reported sponsor result.

The posted descriptive means are also lower for DASH4D with lower sodium than for each of the other listed diet conditions. That pattern is consistent with the direction of the sponsor’s primary contrast, but the descriptive comparisons do not account for the crossover structure in the same way as the mixed model. The confidence intervals for recalculated comparisons are unadjusted and should not be interpreted as the sponsor’s inferential analysis.

The registry also posts diastolic blood pressure (DBP) summaries and a mixed-model comparison for the comparison diet with higher sodium against DASH4D with lower sodium. That secondary analysis reports a mean difference of -2.3 mmHg, with a 95% confidence interval from -3.7 to -0.9. The posted DBP summaries show the same broad ordering as the SBP summaries, but the secondary endpoint does not replace the prespecified primary outcome. The registry does not report a p-value for that secondary mixed-model result.

Overall, the primary sponsor analysis supports a difference in final SBP for the specified diet contrast in this feeding study, with the estimate and interval indicating its direction and precision. It does not establish the effect of the diets outside the study conditions, the persistence of any difference after feeding ends, or an effect on clinical events. The registry record does not report a clinically important difference threshold, so the magnitude should be interpreted as a blood pressure difference rather than as a judgment about clinical importance.

10. Statistical Methods Explained

The registry’s primary inferential result comes from a mixed models analysis of final values. A mixed model is a statistical approach that can represent both measured outcomes and aspects of the study structure. General statistical context: in a crossover design, measurements from the same participant can be related because they come from the same person. A model that accounts for this dependence can give a more appropriate estimate and uncertainty than treating all condition summaries as if they came from unrelated participants. The registry names a mixed-model method, but further details of its specification, such as the exact terms included, are not reported in the registry record.

What does a mean difference describe?

A mean difference expresses the separation between the average outcome in one condition and the average in another, using the measurement unit of the outcome. Here the unit is mmHg. Its sign depends on which group is subtracted from which. For the sponsor’s primary analysis, the reported group order is DASH4D with lower sodium and then the comparison diet with higher sodium; the mean difference is -4.6 mmHg. The negative value therefore indicates a lower final SBP for the first condition under that ordering. In the simple recalculations, the comparison means are presented relative to DASH4D with lower sodium, so positive values indicate higher means in the named comparison condition.

A difference in means is an estimate, not a guarantee that every participant experienced that amount of change. The diet-condition means describe averages, while the standard deviations describe variation among the observed values. General statistical context: an average can conceal substantial variation between individuals, and an estimate of an average contrast does not by itself describe how many individuals had a change in either direction.

What does the confidence interval add?

A confidence interval gives a range of values compatible with the data and the statistical model at the stated confidence level. The sponsor’s primary 95% confidence interval extends from -7.2 to -2.0 mmHg. The interval is entirely below zero, which is consistent with a lower mean SBP in the DASH4D, lower-sodium condition under the sponsor’s group ordering. General statistical context: a confidence interval reflects sampling uncertainty under the method used; it is not a range containing every participant’s response, and it does not include every possible source of bias or uncertainty.

For the recalculated comparisons, the confidence intervals come from simple unadjusted calculations using posted summary statistics. They are not the same as the sponsor’s crossover mixed-model intervals. For instance, the recalculated comparison of the lower-sodium comparison diet with DASH4D lower sodium has an interval that includes zero, while the recalculated higher-sodium comparisons have intervals that do not include zero. These results are descriptive inferential checks, not a substitute for the reported primary analysis. The discrepancy flag in the registry record means the sponsor’s analysis takes precedence.

Why distinguish the reported analysis from recalculation?

The recalculations use the posted condition means, standard deviations, and sample counts to form simple between-condition contrasts. Such calculations are useful for checking how the displayed averages relate to one another. They do not reproduce the study’s complete mixed-model analysis. In particular, the summarized arm-level information does not retain the participant-level pattern of observations across the crossover periods. The registry does not report enough model details to reconstruct the sponsor’s analysis independently.

The reported primary mean difference is -4.6 mmHg, whereas the unadjusted recalculated comparison of the same named conditions is expressed as 4.6 mmHg because its subtraction order is reversed. The numerical magnitudes correspond, but the two estimates are not interchangeable: the sponsor’s result is from the mixed model, and the recalculated result is based on unadjusted posted summary statistics. The sponsor’s model is the relevant registry-reported inferential analysis for the primary contrast.

What does a p-value indicate?

General statistical context: a p-value measures how incompatible the observed data, or data more extreme, would be with a specified null model, assuming that model and the analysis assumptions are correct. It is not the probability that the null hypothesis is true, nor does it measure the size or clinical importance of an effect. The sponsor reports p < 0.001 for the primary mixed-model result. The recalculated comparisons also have unadjusted p-values. These should be read as results of separate simple comparisons, with no multiplicity adjustment reported for them.

The model’s validity depends on its assumptions and implementation. The registry record does not report model diagnostics, the exact covariance structure, or details about adjustment for period or sequence. It is therefore not possible to assess those features from the registry summary alone. This limitation does not alter the fact that the registry reports the mixed-model result; it limits independent evaluation of how the analysis was constructed.

How does the crossover structure affect interpretation?

General statistical context: crossover studies can make efficient use of within-participant comparisons because each person can receive multiple conditions. This structure also means that observations across conditions are not generally independent. The order and timing of conditions may matter if an earlier condition has effects that carry into a later period, or if measurements change over time for reasons unrelated to the assigned diet. The study description says the four diets were given in random order, but washout procedures and the model’s handling of period, sequence, and carryover are not reported in the registry record.

The observed diet-condition counts are not counts of separate, non-overlapping groups. The primary outcome population is defined by starting a diet and completing at least one of the five blood pressure assessments in the last 2 weeks of that period. Since the same person could contribute data under different conditions, the condition summaries should not be added to derive a total number of participants. A participant-level analysis is needed to account for the repeated condition measurements; the sponsor’s mixed-model analysis is the reported approach.

Finally, the results concern average blood pressure at the end of the feeding periods. General statistical context: statistical evidence for a mean difference is distinct from evidence about durability, clinical events, individual responses, or the practical importance of an effect. Those questions require outcomes and follow-up that are not reported in this registry record.

11. Confidence Intervals and Precision

The sponsor’s primary estimate is a mean difference of -4.6 mmHg, with a 95% confidence interval from -7.2 to -2.0. The interval gives a range of effect values compatible with the reported model and data at the stated confidence level. Because the full interval is on the negative side of zero under the sponsor’s group ordering, the reported analysis is consistent with lower final SBP for DASH4D with lower sodium compared with the higher-sodium comparison diet.

The interval also communicates uncertainty about the magnitude. It does not identify a single exact effect, and the difference between its endpoints should not be mistaken for an individual response range. General statistical context: a confidence interval is influenced by both variability in the data and the amount of information available, as well as by the model used. Its interpretation depends on the analysis being appropriate for the study design.

The unadjusted recalculated interval for the same contrast is 0.746 to 8.454 mmHg when expressed as comparison-diet higher sodium minus DASH4D lower sodium. The reversed direction explains why its sign differs from the sponsor’s reported estimate. The recalculated interval is not the sponsor’s interval and does not account for the crossover model in the same way. Since the registry identifies a discrepancy, the sponsor’s mixed-model estimate and confidence interval should be treated as the primary inferential result.

The registry does not report a clinically important difference threshold for SBP. Consequently, interval precision can be discussed statistically, but the interval alone cannot determine whether all values within it would represent an important difference in practice. Nor does this interval capture uncertainty about design features or model choices that are not described in the registry record.

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 effect125167
75% of the observed effect221296
50% of the observed effect498666
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect1002005001,0002,00040%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: DASH4D Diet With Higher Sodium.

The sample-size figures are planning illustrations based on the observed effect, not the trial’s original design calculation. For continuous outcomes such as SBP and DBP, the displayed figures refer to participants per arm, not total events. The assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each planning scenario uses the stated fraction of the observed effect as the effect to detect. The registry record does not report the original trial’s sample-size assumptions or justification.

The 80% power column gives the number of participants per arm that the planning calculation estimates would be needed for an 80% chance of detecting the specified effect under those assumptions, if that effect were present and the analysis assumptions held. The 90% power column gives the corresponding number per arm for a 90% chance. These are design targets, not statements about what the completed trial achieved.

Planning for the full observed effect uses the observed contrast as the target. The smaller-effect scenarios plan for 75% and 50% of that observed effect. Smaller effects require more participants because they are harder to distinguish from random variation, all else held constant. The figures increase accordingly across the smaller-effect scenarios for each listed comparison.

These calculations are illustrations based on simple assumptions, including equal allocation, rather than a reconstruction of the crossover study’s full design or model. They should not be used to infer that the completed study had a particular probability of success. This is not observed power. The registry does not report the original design assumptions, and these planning values should not be interpreted as evidence about whether the trial was adequately designed.

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 = 4.800; pooled standard deviation σ = 13.505.
  2. n = 2 × (1.96 + 0.842)2 × 13.5052 / 4.8002 = 124.3, rounded up to 125 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 <- 4.8                      # observed difference in means
sigma <- 13.504832571835                     # 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(4286555)
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 = 125 (80% power), 167 (90% power)
 75% of observed effect: n per arm = 221 (80% power), 296 (90% power)
 50% of observed effect: n per arm = 498 (80% power), 666 (90% power)
power.t.test: 125.2 
Simulated power at n = 125 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
Mixed Models AnalysisMean Difference (Final Values) -4.6-7.2 to -2.0< 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 registry’s own primary analysis is a mixed-model comparison of final values for DASH4D with lower sodium versus the comparison diet with higher sodium. It reports a mean difference of -4.6 mmHg, a 95% confidence interval from -7.2 to -2.0, and p < 0.001. This is the sponsor’s inferential analysis for the primary contrast.

The simple recalculation from the posted means expresses the same named contrast in the reverse direction: comparison diet with higher sodium minus DASH4D with lower sodium. It gives 4.6 mmHg, with a 95% confidence interval from 0.746 to 8.454 and an unadjusted p-value of 0.019. The opposing signs reflect the reversed subtraction order. The simple recalculation uses posted summary statistics and does not reproduce the sponsor’s mixed model or retain the participant-level crossover pattern.

The registry marks a discrepancy between the sponsor analysis and the recalculation. Accordingly, the sponsor’s own analysis takes precedence. The recalculation can help readers understand how the displayed means are ordered, but it should not be presented as an alternative adjusted result or used to replace the reported mixed-model estimate. The registry does not report enough detail about the model specification to reconstruct the sponsor’s analysis independently.

15. Multiplicity, Missing Data and Analysis Populations

The registry identifies systolic blood pressure as the primary outcome and posts diastolic blood pressure as a secondary endpoint. It also reports 31 outcome measures and 10 analyses. The record does not report a multiplicity strategy describing whether, or how, statistical testing across outcomes and contrasts was adjusted. The unadjusted recalculated p-values should therefore be understood as separate comparisons rather than as results corrected for a broader family of tests. The registry also does not report whether the secondary analysis was intended to be confirmatory or exploratory.

Multiplicity matters because repeated testing can make some results appear statistically notable by chance, even when no corresponding underlying effect exists. General statistical context: adjustment methods can control error across a defined family of tests, but they require a clear description of which tests belong to that family. Without a reported plan, it is not possible to determine whether the posted secondary analyses meet a particular family-wise or false-discovery criterion. The sponsor’s primary analysis remains the most direct registry-reported result for the primary question.

The analysis population for the primary endpoint includes participants who started the diet and completed at least one of the five blood pressure assessments during the last 2 weeks of that feeding period. The condition-specific outcome counts differ, but the registry record does not explain why observations are missing for some participants or conditions. It does not report the amount or pattern of missing outcome data, any imputation method, or sensitivity analyses addressing missingness.

The study is a crossover trial in which participants can contribute measurements under multiple diets. In that setting, incomplete outcomes could leave some participants with data for some conditions but not others. General statistical context: the implications of incomplete repeated measurements depend on why data are missing and how the analysis handles the observed pattern. The registry summary does not provide enough information to evaluate those assumptions or determine how missing observations affected the model estimate.

The registry record also does not report interim analyses, stopping rules, or a detailed statistical analysis plan. Their absence from the record should not be interpreted as evidence that a particular procedure was or was not used. They are simply not reported in the registry record.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
DASH4D Diet With Lower Sodium1921.1%
DASH4D Diet With Higher Sodium0930.0%
Comparison Diet With Lower Sodium1951.1%
Comparison Diet With Higher Sodium0970.0%
CGM Ancillary Study0890.0%
Participants with at least one serious adverse event
Serious adverse events by armDASH4D Diet With Lower Sodium1.1%DASH4D Diet With Higher Sodium0.0%Comparison Diet With Lower So…1.1%Comparison Diet With Higher S…0.0%CGM Ancillary Study0.0%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
DASH4D Diet With Lower Sodium0 of 92
DASH4D Diet With Higher Sodium0 of 93
Comparison Diet With Lower Sodium0 of 95
Comparison Diet With Higher Sodium0 of 97
CGM Ancillary Study0 of 89

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 2% reporting threshold.

ArmParticipants affected of at risk
DASH4D Diet With Lower Sodium9 of 92
DASH4D Diet With Higher Sodium6 of 93
Comparison Diet With Lower Sodium13 of 95
Comparison Diet With Higher Sodium8 of 97
CGM Ancillary Study0 of 89

Most frequent serious adverse event terms

Event termOrgan systemDASH4D Diet With Lower SodiumDASH4D Diet With Higher SodiumComparison Diet With Lower SodiumComparison Diet With Higher SodiumCGM Ancillary Study
myocardial infarctionCardiac disorders1 of 920 of 930 of 950 of 970 of 89
decompensated heart failureCardiac disorders0 of 920 of 931 of 950 of 970 of 89

Most frequent non-serious adverse event terms

Event termOrgan systemDASH4D Diet With Lower SodiumDASH4D Diet With Higher SodiumComparison Diet With Lower SodiumComparison Diet With Higher SodiumCGM Ancillary Study
hypotensionCardiac disorders5 of 921 of 936 of 952 of 970 of 89
hypoglycemiaEndocrine disorders2 of 925 of 934 of 953 of 970 of 89
hypertension escape level 2Cardiac disorders0 of 920 of 933 of 953 of 970 of 89
hyperkalemiaMetabolism and nutrition disorders2 of 920 of 931 of 950 of 970 of 89

Serious events with the highest arm-level rate: myocardial infarction (1.1%), decompensated heart failure (1.1%).

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 events by diet condition and lists the number at risk and the number affected. For DASH4D with lower sodium, 92 were at risk and 1 was affected; for DASH4D with higher sodium, 93 were at risk and 0 were affected. For the comparison diet with lower sodium, 95 were at risk and 1 was affected; for the comparison diet with higher sodium, 97 were at risk and 0 were affected. The ancillary CGM study lists 89 at risk and 0 affected. Deaths are recorded as 0 in each listed group.

The registry lists myocardial infarction and decompensated heart failure among the serious adverse event terms, each at 1.1%. It does not make clear in this summary how those terms map to the diet-condition groups. The group figures and event terms should therefore be read as registry safety reporting, not as a basis for attributing a particular event to a specific diet.

These figures describe the events recorded during the study; they do not establish whether a diet caused an event or whether risks differ between conditions. The crossover design and group-specific at-risk counts also mean that condition counts should not be added as if they represented separate, non-overlapping groups of participants. Details of event adjudication, timing, and causal assessment are not reported in the registry record.

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

The primary result describes a difference in average systolic blood pressure at the end of feeding periods in this randomized crossover study. The sponsor’s mixed-model estimate for DASH4D with lower sodium compared with the higher-sodium comparison diet is -4.6 mmHg, with a 95% confidence interval from -7.2 to -2.0. This supports a lower mean final SBP in the first condition under the reported group ordering. The posted condition means have a corresponding descriptive pattern.

This result does not mean that every participant had a lower reading on the DASH4D diet, or that each participant’s blood pressure changed by the amount of the mean difference. The registry reports group means and standard deviations, not individual response distributions. General statistical context: an average treatment contrast describes a group-level estimate and may not represent the experience of each person.

The result also does not show that a difference persists after the feeding periods end. The outcome was measured at the end of a 5-week feeding period, and later blood pressure follow-up is not reported in the registry record. The primary endpoint is a blood pressure measure, not a cardiovascular event outcome. No conclusion about events, long-term outcomes, or effects in populations beyond the trial conditions follows from this endpoint alone.

The comparison involved specified diets and sodium levels, including 1500 mg/day and 3700 mg/day. The study description says the diets were isocaloric and delivered in random order. The record does not establish how results would generalize to other dietary patterns, other sodium exposures, or settings outside the single-site feeding study. Nor does it report a threshold for a clinically important SBP difference.

Accordingly, the result is best understood as statistical evidence about the average final SBP contrast under the study conditions, not as a universal claim about diets or a prediction for an individual. The registry does not report details sufficient to assess all model assumptions, missing-data mechanisms, or multiplicity procedures. Those limitations qualify interpretation without changing the reported estimate itself.

18. Why This Trial Matters Statistically

This trial raises a statistical question that is especially relevant to crossover feeding studies: how to compare conditions when the same participant can contribute measurements under multiple diets. The design offers within-participant information, while also requiring analysis that respects dependence among repeated observations. The registry’s reported mixed-model result is therefore important to distinguish from simple comparisons of the posted means.

The primary contrast also combines two dietary features: the DASH4D pattern with lower sodium is compared with a typical comparison diet with higher sodium. The four diet conditions additionally include DASH4D with higher sodium and the comparison diet with lower sodium. The descriptive summaries allow readers to see the outcomes across those conditions, but the primary sponsor analysis directly addresses the stated contrast. Separating the pattern from the sodium level is a matter of the study’s planned contrasts and model, not something that can be inferred by casually comparing means alone.

The record illustrates why an effect estimate, confidence interval, and analysis method need to be read together. The sponsor reports an interval from -7.2 to -2.0 mmHg for the primary mean difference. A simple recalculation from summaries produces a contrast in the reverse direction and an interval based on a different method. Because the registry marks a discrepancy, the reported sponsor analysis takes precedence rather than allowing the recalculation to stand in for a crossover analysis.

Finally, the registry provides planning illustrations based on observed effects, alongside posted outcome summaries. Such illustrations are useful for understanding how the required sample size changes when the target effect is smaller, but they are not the original design justification and are not observed power. Keeping planning calculations, observed outcomes, and the trial’s own inferential model separate is essential to a sound statistical reading.

19. Limitations

The registry record provides a concise description of the crossover feeding design but does not report several details needed to assess it fully. Washout procedures, the exact timing between periods, and methods for assessing or accounting for carryover are not reported. The random order of the four diets is described, but the sequence-generation and allocation details are not reported in the registry record.

The record names a mixed models analysis but does not provide its full specification. It does not report the model terms, covariance structure, diagnostics, or details on how period and sequence were handled. Those omissions limit independent reproduction and assessment of the sponsor’s primary estimate. The discrepancy flagged between the sponsor analysis and simple recalculations reinforces the importance of giving precedence to the sponsor’s model rather than treating arm-level summaries as a complete substitute.

The outcome population is defined by starting a diet and completing at least one of the blood pressure assessments during the last 2 weeks of a period. However, the registry does not describe the reasons for missing assessments, the pattern of missing data, or any imputation or sensitivity analysis. Because the crossover design allows a participant to contribute in multiple conditions, the condition-level counts cannot be treated as separate independent groups or summed to infer a unique participant count.

The registry does not report a clinically important SBP threshold, a complete multiplicity plan, or the original sample-size justification. The posted planning illustrations use the observed effect and stated planning assumptions; they are not evidence of the original trial’s design rationale. Although a single site and feeding protocol are reported, broader generalizability beyond these study conditions is not established by the registry record. Finally, the primary measurements concern the end of 5-week feeding periods; longer-term outcomes are not reported.

20. Related Tutorials

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22. Sources

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23. Record Summary

The completed Dietary Approaches to Stop Hypertension for Diabetes Trial was a randomized, double-masked, single-site, 4-period crossover feeding study with 5-week periods. Its stated primary contrast was DASH4D with lower sodium versus a comparison diet with higher sodium. The primary endpoint was mean systolic blood pressure at the end of a feeding period.

The sponsor’s mixed-model analysis reports a mean difference of -4.6 mmHg, with a 95% confidence interval from -7.2 to -2.0 and p < 0.001, for DASH4D with lower sodium compared with the higher-sodium comparison diet. Simple unadjusted recalculations from the posted summaries are not equivalent to that crossover analysis; because the registry flags a discrepancy, the sponsor’s result takes precedence.

The registry also posts diastolic blood pressure as a secondary endpoint and reports serious adverse event counts by condition. Details of multiplicity handling, missing-data methods, the full model specification, and the original design assumptions are not reported in the registry record.

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