Cardiometabolic Effects of Pecans as a Snack: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Cardiometabolic Effects of Pecans as a Snack (NCT05071807), a randomized phase 2 study. The primary outcome is Flow Mediated Dilation.

2. Clinical Question

This question focuses on a measured vascular function outcome rather than on a diagnosis, clinical event, or long-term health outcome. Flow-mediated dilation is expressed as percentage points of change in arterial diameter and was measured by brachial ultrasound. The registry lists least-squares means for the two groups and a mean-difference comparison.

The primary outcome record reports results for 62 participants in the Pecan Group and 67 in the Usual Care Group. It does not report a separate population description for this outcome. The registry lists overall enrollment as 138, but the reason the primary outcome counts differ from the enrollment figure is not reported in the registry record.

3. Trial Design

This was a Phase 2, randomized, double-masked, parallel-group study sponsored by Penn State University. The registry lists enrollment of 138 and a completed status. The recorded start date is 2022-08-15, and the primary completion date is 2024-03-01. The study’s stated aim was to examine the effects of pecans on peripheral vascular health markers, lipids and lipoproteins, blood pressure, and glycemic control.

The two groups differed in their snack instructions. The Pecan Group was to replace one snack with unsalted raw pecans while continuing its usual diet. The Usual Care Group was to continue its usual diet without nuts. The allocation is recorded as randomized, the masking as double, and the model as parallel. Details about how randomization was generated, how allocation was concealed, and who was masked are not reported in the registry record.

The primary endpoint was assessed at 12 weeks. Secondary outcomes listed in the record include lipid and lipoprotein measures, brachial and central blood pressure, and carotid-femoral pulse wave velocity. The registry lists 18 outcome measures and 23 analyses. A complete account of all outcome measurements, visit schedules, and analysis populations is not reported in the registry record.

The primary outcome counts are 62 in the Pecan Group and 67 in the Usual Care Group. These are outcome-specific counts; they should not be taken as an explanation of participant flow or missingness. Reasons for differences between enrollment and outcome counts, withdrawals, and the number of participants included in each analysis are 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.

Overall Study

Reasons for not completing this period:

5. Baseline Characteristics

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

6. Primary Endpoint

The registry lists the primary outcome as Flow Mediated Dilation, measured over 12 weeks.

Flow-mediated dilation (FMD) measures a change in arterial diameter in response to a blood-flow stimulus. In this trial it was measured using brachial ultrasound and expressed as percentage points of change in arterial diameter. The recorded timeframe is 12 weeks. The registry reports least-squares means with standard errors for each group.

FMD is used in research as a measure of peripheral vascular function. It is a physiological measure, not a direct count of cardiovascular events or a measure of how participants feel or function in daily life. A between-group comparison addresses whether the recorded FMD values differed between the randomized groups at the stated assessment, subject to the trial’s measurement and analysis procedures.

The endpoint description does not state a clinically meaningful threshold for interpreting a difference in FMD. Such a threshold, the details of measurement standardization, and whether assessors were masked to group assignment are not reported in the registry record. Consequently, the numerical estimate can be interpreted as a difference on the stated measurement scale, but the registry record does not establish what size of difference would be important to participants or clinicians.

7. Results Posted in the Registry

• Pecan Group: mean 7.07 versus 7.25 on control; difference -0.18 (95% CI -1.12 to 0.76), standardized effect d = -0.07; z-test p = 0.708.

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.

LDL-cholesterol Concentration

• 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 errors.
• Result:
  • Pecan Group: mean 110.00 versus 117.00 on control; difference -7.00 (95% CI -10.62 to -3.38), standardized effect d = -0.67; z-test p = <0.001.
• Interpretation:
  • The 95% confidence interval excludes no difference, so the mean is statistically lower for Pecan Group than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

HDL-cholesterol Concentration

• 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 errors.
• Result:
  • Pecan Group: mean 54.00 versus 53.00 on control; difference 1.00 (95% CI -0.26 to 2.26), standardized effect d = 0.27; z-test p = 0.120.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Pecan Group and the control. The interval gives the range of effects that remain compatible with the data.

Carotid-femoral Pulse Wave Velocity

• 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:
  • Pecan Group: mean 7.10 versus 7.30 on control; difference -0.20 (95% CI -0.65 to 0.25), standardized effect d = -0.15; z-test p = 0.381.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Pecan Group and the control. The interval gives the range of effects that remain compatible with the data.

The registry lists secondary measures spanning blood lipids and lipoprotein subclasses, blood pressure, and vascular stiffness. Sixteen secondary outcomes are posted, while detailed comparative values in the record include LDL-cholesterol, HDL-cholesterol, and carotid-femoral pulse wave velocity. Across those available comparisons, the pattern is not uniform: the LDL-cholesterol comparison is more clearly separated from zero than the HDL-cholesterol or pulse wave velocity comparisons. This differs from the primary FMD result, whose reported interval includes zero. The secondary outcomes therefore do not form a single consistent pattern that can be reduced to the primary endpoint alone.

Secondary endpoints can provide context about related biological measures, but they do not replace the primary outcome. They may also be exploratory or have different measurement properties and precision. The registry does not state whether these outcomes were designated as confirmatory or how their results were intended to contribute to a combined conclusion.

Unadjusted secondary results carry less weight when many outcomes or analyses are considered. Testing multiple measures creates more opportunities for a result to appear unusual by chance, even if there is no underlying effect. The registry lists 18 outcome measures and 23 analyses, but a correction for multiplicity or a hierarchy among outcomes is not reported in the registry record. As a result, the secondary pattern is best viewed as descriptive and hypothesis-generating rather than as independent confirmation of the primary result.

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

• LDL-cholesterol Concentration
• HDL-cholesterol Concentration
• Triglycerides
• LDL Lipoprotein Subclasses
• HDL Lipoprotein Subclasses
• Brachial Systolic and Diastolic Blood Pressure
• Central Systolic and Diastolic Blood Pressure
• Carotid-femoral Pulse Wave Velocity

9. Statistical Interpretation

10. Statistical Methods Explained

The posted primary outcome is continuous: it is measured on a numerical scale and reported as a group mean. The registry uses least-squares means, which are model-based group estimates, and gives a standard error for each. A mean difference expresses the contrast between the groups on the same outcome scale. In the unadjusted recalculation, the direction is defined as Pecan Group minus Usual Care Group, so a negative value corresponds to a lower estimate in the Pecan Group. The sponsor reports a regression-based net mean difference.

What does a least-squares mean represent?

In general, a least-squares mean is an estimate from a statistical model rather than necessarily the raw arithmetic average of every recorded measurement. Its value can depend on the model terms and any adjustment or standardization used. The registry identifies the reported analysis as linear regression, but the specific model terms, covariates, and handling of baseline values are not reported in the registry record. The term “net” appears in the reported analysis label, but the registry does not define it further.

What does the standard error describe?

In general, a standard error describes the uncertainty in an estimated mean, reflecting the variability of the estimate under repeated sampling assumptions. It is not the same quantity as the standard deviation, which describes variation among individual observations. The primary group summaries report standard errors of 0.35 and 0.33. For the unadjusted recalculation, variability estimates are approximated from the reported standard errors. That calculation is therefore a summary-statistic approximation, not a reconstruction of the trial’s regression model or participant-level analysis.

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

A confidence interval gives a range of values compatible with the observed data under the method used to construct it. A 95% interval is a measure of estimation uncertainty, not a guarantee that the true value lies in the interval. The sponsor reports a 95% confidence interval for the primary regression comparison. The unadjusted recalculation also reports a p-value, 0.708. A p-value measures how unusual data at least as incompatible with a specified null model would be if that model and its assumptions held. It is not the probability that the null hypothesis is true, and it does not measure clinical importance.

Why distinguish the sponsor analysis from a recalculation?

The sponsor’s analysis uses linear regression and is the analysis posted by the trial. The simple recalculation uses only the group-level means, standard errors, and sample sizes in the registry record. It does not account for unreported model adjustments, covariates, or participant-level features. The two estimates can therefore differ without either arithmetic result being a direct substitute for the other. For interpretation of the trial’s own result, the sponsor’s reported analysis takes precedence.

Why can over-dispersion matter?

In general, over-dispersion means that observed variation is greater than a model assumes. When a model understates variability, its standard errors may be too small and its intervals may be too narrow. When variability is appropriately represented, uncertainty estimates are more reliable. The registry record does not report an over-dispersion assessment for these outcomes, so no conclusion about it can be drawn for this trial.

What does an unadjusted secondary comparison mean?

An unadjusted comparison is interpreted without a correction for the number of outcomes or analyses being examined. In general, testing many outcomes increases the chance that at least one result will appear notable by chance alone. The registry lists 18 outcome measures and 23 analyses, but does not report a multiplicity adjustment. This is one reason secondary findings should be treated as less conclusive than a prespecified primary analysis, especially when the full analysis plan is unavailable.

11. Confidence Intervals and Precision

Precision concerns how narrowly the data locate a group difference. The sponsor’s primary regression estimate is 0.08, with a 95% confidence interval from -1.17 to 1.33. Because this interval includes zero and extends to values on both sides, the result does not pin down the direction of the primary group difference. It also allows for differences that may be more than negligible on the measured scale. The registry record does not state which differences in FMD would be clinically important.

The unadjusted recalculation gives an estimate of -0.18 and p = 0.708. The recalculated interval is not used as a substitute for the sponsor’s reported interval. The standard errors and group counts indicate that estimates are subject to sampling uncertainty, but the registry does not provide enough detail to assess every source of uncertainty in the regression analysis.

Confidence intervals are more informative than a single estimate alone because they show a range of values compatible with the analysis. In general, an interval that includes zero does not prove there is no difference; it indicates that the observed data do not distinguish zero from a range of possible positive and negative differences at the stated confidence level. Conversely, an interval excluding zero would not by itself establish clinical importance. Interpretation also depends on the outcome scale, study design, analysis, and an appropriate importance threshold, which is not reported for FMD.

Precision is specific to the endpoint, follow-up, and analysis. It should not be extended to long-term effects or to outcomes not represented by FMD.

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.

The sample-size values are planning illustrations based on the observed effect, not the trial’s own design calculation. For continuous outcomes, the figures are participants per arm; they are not total participants across both arms and are not event counts. The planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is the stated share of the observed effect. The trial’s original sample-size assumptions and justification are not reported in the registry record.

The 80% power column indicates the number of participants per arm in a hypothetical study that, under the planning assumptions, would have an 80% chance of detecting the stated effect if that effect were the true one. The 90% power column uses the same idea but aims for a higher chance of detection, so it generally calls for more participants. These are design targets, not guarantees about the results of a future study.

The rows use 100%, 75%, and 50% of the observed effect. For the primary outcome, planning for 100% of the observed effect gives 3,605 participants per arm for 80% power and 4,826 for 90% power; planning for 50% gives 14,419 and 19,302 per arm, respectively. This illustrates the general pattern: smaller effects need more participants to detect with the same power. The curve expresses that relationship across the planning choices. These figures are not observed power and do not describe the probability that this completed trial detected its true effect.

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 z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

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

Worked calculation for this trial

1. Observed difference Δ = -0.180; pooled standard deviation σ = 2.728.
2. n = 2 × (1.96 + 0.842)² × 2.728² / -0.180² = 3,604.6, rounded up to 3,605 participants per arm for 80% power.

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

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
delta <- -0.18                      # observed difference in means
sigma <- 2.72759419245975                     # 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(5071807)
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 = 3,605 (80% power), 4,826 (90% power)
 75% of observed effect: n per arm = 6,409 (80% power), 8,579 (90% power)
 50% of observed effect: n per arm = 14,419 (80% power), 19,302 (90% power)
power.t.test: 3605.5 
Simulated power at n = 3,605 per arm: 0.799 (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

The sponsor’s own primary analysis is a linear regression comparison reported as a net mean difference of 0.08, with a 95% confidence interval from -1.17 to 1.33. The registry does not report a p-value for that analysis. The unadjusted recalculation from the posted group summaries estimates -0.18 and reports p = 0.708. These are distinct analyses, and the recalculation does not reproduce the regression model.

The recalculation uses the group means, standard errors, and sample sizes posted for the endpoint. It does not have participant-level data or the model specification. The sponsor’s result can therefore reflect regression details that are not available in the registry record. The reported summaries do not give enough information to explain the difference between the two estimates.

The registry record does not flag a discrepancy between the sponsor analysis and recalculation. Nevertheless, interpretation of the trial’s reported result should prioritize the sponsor’s regression analysis, while treating the recalculation as a simple unadjusted check. Neither estimate should be described as a proven effect, and neither resolves the uncertainty indicated by the confidence interval.

15. Multiplicity, Missing Data and Analysis Populations

The registry lists 18 outcome measures and 23 analyses, including a primary endpoint and a broad set of secondary measures. When many outcomes are examined, the chance of at least one apparently notable result can increase. Statistical approaches to address this include adjusting the threshold for interpretation, controlling an error rate across a family of tests, or specifying an ordered testing strategy. These are general options; which, if any, was used in this trial is not reported in the registry record.

The posted secondary comparisons include unadjusted p-values in the recalculations, and the sponsor analyses report estimates and confidence intervals. The registry does not describe whether the trial used multiplicity adjustment, which outcome family any adjustment would cover, or whether secondary analyses were confirmatory. This missing information limits how strongly individual secondary findings can be interpreted alongside the primary endpoint.

Missing-data methods and analysis populations are also not fully described. The registry gives enrollment as 138 and primary endpoint counts of 62 in the Pecan Group and 67 in the Usual Care Group. Outcome-specific counts differ among some secondary entries. Reasons for these counts, missing-measurement patterns, exclusions, and the methods used to handle missing observations are not reported in the registry record. The record also does not state whether the primary analysis followed an intention-to-treat principle, a per-protocol definition, or another population rule.

These omissions do not establish that the analysis was inappropriate; they mean the registry record does not allow readers to evaluate those aspects of the analysis in detail. A fuller statistical plan and participant-flow account would help clarify how multiplicity, missing data, and analysis populations were handled.

16. Safety Results

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

Deaths

Other (non-serious) adverse events

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

Most frequent non-serious adverse event terms

The adverse-event record lists 69 participants at risk for serious adverse events in each group. It reports zero serious adverse events in the Pecan Group and zero in the Usual Care Group. It reports zero deaths in both groups. For other adverse events, the record lists 2 affected participants in the Pecan Group and 0 in the Usual Care Group, with 69 at risk in each group.

These figures describe the events recorded in the registry; they do not establish that no events occurred outside the reporting period or that uncommon events can be ruled out. The registry does not provide event descriptions for the two other adverse events in the Pecan Group, and no serious adverse-event terms are listed. The period covered by adverse-event collection and the criteria used to classify events are not reported in the registry record.

Counts alone do not show whether an event was related to an intervention. The record does not report such an attribution for these other adverse events. Safety figures should therefore be read as a limited account of recorded events in this study, not as a complete assessment of risk.

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

The primary endpoint result is an estimate of the difference in FMD between the two randomized groups at 12 weeks. The sponsor’s regression estimate is 0.08, and its 95% confidence interval ranges from -1.17 to 1.33. The interval includes zero, so the posted analysis does not establish a clear direction of difference. The unadjusted recalculation is also close to zero, but it is a separate summary-statistic analysis and does not replace the sponsor’s result.

This finding does not demonstrate that the groups are equivalent. Equivalence requires a prespecified range of differences considered sufficiently small, and such a margin is not reported in the registry record. A non-significant result also does not prove the absence of an effect. The confidence interval reflects uncertainty; it includes a range of possible differences, and the registry does not define which values would matter clinically.

FMD is a physiological measure of peripheral vascular function. The result does not directly answer whether the groups differed in cardiovascular events, symptoms, daily function, or long-term health. The registry record does not report such outcomes as the primary endpoint. Nor does a 12-week result determine what might happen over a longer period or in populations with different characteristics.

The secondary findings offer additional measurements but require caution. There are multiple posted outcomes and analyses, and multiplicity handling is not reported. Those findings should not be treated as a definitive confirmation of a broad effect across cardiometabolic measures. The study’s completed status records that the trial is complete; it does not, on its own, settle the interpretation of the estimates or their importance.

18. Why This Trial Matters Statistically

This trial is statistically useful because it illustrates the difference between an estimated effect and the certainty around that estimate. The primary outcome supplies a group contrast and a confidence interval, rather than only a claim of whether a statistical threshold was crossed. The interval’s inclusion of zero makes clear that the data do not tightly determine the direction of the primary difference.

It also highlights the distinction between a sponsor-reported model-based analysis and an unadjusted recalculation using group summaries. Such a recalculation can serve as a check, but it cannot reconstruct an analysis that depends on regression details or participant-level information not reported in the registry. The sponsor’s regression analysis remains the trial’s own reported analysis.

The range of secondary cardiometabolic measures raises a further statistical issue: evidence across many outcomes is harder to interpret if the analysis plan and multiplicity approach are unavailable. A result on one measure does not automatically establish a consistent pattern across related outcomes, and multiple unadjusted comparisons deserve restrained interpretation.

Finally, planning illustrations based on observed effects show how strongly sample-size requirements depend on the effect a future study aims to detect. They are not a substitute for the trial’s original design assumptions, which are not reported in the registry record. Together, these features make the record a useful example of why effect estimates, uncertainty, analysis choices, and planning assumptions should be read separately.

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 registry record leaves several trial-specific questions unresolved. It does not provide detailed eligibility criteria or a fuller description of the participants, limiting assessment of how broadly the findings might apply. It also does not describe the randomization sequence, allocation concealment, or which participants and study personnel were masked.

The primary outcome entry reports least-squares means and standard errors, but the regression specification and covariates are not reported. The sponsor’s result is therefore not fully reproducible from the registry record. The unadjusted recalculation is based on group summaries, and some variability estimates are approximated from standard errors; it should not be mistaken for a participant-level reanalysis.

Outcome counts vary across entries. The record lists enrollment of 138, while the primary analysis counts are 62 and 67, and some secondary counts differ. Participant flow, reasons for missing observations, exclusions, and missing-data methods are not reported in the registry record. The analysis population is also not defined.

The registry lists many outcomes and analyses but does not report whether multiplicity was handled or which secondary outcomes were considered confirmatory. It does not state a clinically meaningful threshold for FMD or provide a sample-size justification for the original trial. Adverse-event descriptions, event-collection details, and attribution are limited. These reporting gaps restrict assessment of reproducibility, precision, clinical importance, and the full context of the results.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

• ClinicalTrials.gov: Cardiometabolic Effects of Pecans as a Snack — NCT05071807.
• Registry record last updated 2025-02-25; status last verified 2025-02.
• Results first posted 2025-02-25.
• 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.

23. Record Summary

NCT05071807 is a completed Phase 2 randomized, double-masked, parallel-group study sponsored by Penn State University. It compared replacing one usual-diet snack with unsalted raw pecans against a usual diet without nuts. Registry enrollment is 138.

The primary endpoint was flow-mediated dilation measured by brachial ultrasound at 12 weeks. The sponsor’s linear regression analysis reports a net mean difference of 0.08, with a 95% confidence interval from -1.17 to 1.33. An unadjusted recalculation from posted group summaries estimates -0.18 and reports p = 0.708.

The registry also lists secondary lipid, blood pressure, and vascular measures. It does not report the original sample-size justification, detailed regression specification, multiplicity approach, missing-data handling, or analysis population.