Neurocognitive Benefits of a Weight Management Program: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Neurocognitive Benefits of a Weight Management Program (NCT04202133), a randomized phase 4 study. The primary outcome is Blood Oxygen Level-dependent (BOLD) Response to High-calorie Foods Cues Minus Neutral Objects in Left Anterior Cingulate Cortex.

2. Clinical Question

3. Trial Design

This completed Phase 4 study was a randomized, parallel-group trial of WW (formerly Weight Watchers) versus a waitlist control. The registry lists enrollment as 61 and describes the condition as overweight and obesity. The study began on 2019-11-20, with primary completion on 2021-04-02. Allocation was randomized, and masking was listed as none, so the study was open-label.

The WW group was assigned to the group-based program for 16 weeks. The waitlist group remained on the waitlist for 16 weeks and was then to receive the same group-based program for 16 weeks. The primary endpoint compared change from baseline to 16 weeks, the point at which the initial program period and waitlist period were specified. This is a waitlist comparison rather than a comparison with another weight-management intervention.

The primary outcome is reported for 29 participants in the WW group and 22 in the waitlist group. The registry does not explain why those outcome counts differ from the enrollment figure, nor does it describe the analysis population used for the primary endpoint. It also does not report the original sample-size justification or the statistical analysis plan. The posted outcome summaries therefore allow a descriptive comparison, but they do not establish how the original investigators planned to address all design and analysis issues.

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

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 Blood Oxygen Level-dependent (BOLD) Response to High-calorie Foods Cues Minus Neutral Objects in Left Anterior Cingulate Cortex, measured over Change from baseline to 16 weeks.

The primary endpoint was change from baseline to 16 weeks in the BOLD fMRI response to high-calorie food images minus the response to neutral objects in the left anterior cingulate cortex. The reported unit was percent BOLD signal change, and the summary statistic was a mean with standard error. The endpoint was intended to capture a difference in brain response to food-related cues, rather than a direct measure of weight change or task performance.

In general, BOLD fMRI measures changes in blood oxygenation associated with brain activity. It is an indirect functional signal: it does not directly record neuronal firing, and the contrast between high-calorie food cues and neutral objects represents a response difference between two kinds of image. This kind of endpoint can be used to study whether an intervention is associated with a change in neural response to a specified stimulus. Its meaning depends on the defined brain region, task or stimulus, and analysis method. The registry describes the region and stimulus contrast, but does not report additional technical details of image processing or the endpoint analysis.

The study summary also describes interest in working memory and neural responses to food images. Those aims provide context for the endpoint, but the primary result specifically concerns the left anterior cingulate cortex food-cue contrast.

7. Results Posted in the Registry

• WW (Formerly Weight Watchers): mean -0.05 versus -0.16 on control; difference 0.11 (95% CI -0.04 to 0.26), standardized effect d = 0.40; z-test p = 0.159.

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.

Percent Weight

• 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:
  • WW (Formerly Weight Watchers): mean -4.70 versus 0.20 on control; difference -4.90 (95% CI -16.70 to 6.90), standardized effect d = -0.21; z-test p = 0.416.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between WW (Formerly Weight Watchers) and the control. The interval gives the range of effects that remain compatible with the data.

Power of Food

• 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:
  • WW (Formerly Weight Watchers): mean -0.40 versus -0.10 on control; difference -0.30 (95% CI -2.11 to 1.51), standardized effect d = -0.09; z-test p = 0.745.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between WW (Formerly Weight Watchers) and the control. The interval gives the range of effects that remain compatible with the data.

The registry lists N-back Behavioral Performance, Percent Weight, Eating Behavior, and Power of Food among secondary outcomes. Numerical summaries are available for Percent Weight and Power of Food. Numerical results for N-back Behavioral Performance and Eating Behavior are not reported in the registry record. This means the listed outcome aims cannot all be evaluated from the posted numerical summaries.

Across the available continuous secondary results, the reported intervals include zero, and the unadjusted p-values do not provide strong evidence of between-group differences. The directions of the estimated differences are not uniform across outcomes. That overall pattern does not supply independent confirmation of the primary result: the secondary measures assess different constructs, and their estimates are also imprecise. Nor does a lack of clear differences on these outcomes establish that the groups were equivalent.

Secondary results generally carry less inferential weight when the registry does not document a prespecified testing hierarchy or multiplicity adjustment. Examining several outcomes creates multiple opportunities for apparently notable results by chance. The registry lists 12 outcome measures, while the detailed analysis plan and adjustment strategy are not reported. Interpretation should therefore focus on effect estimates and uncertainty, and should avoid treating any one unadjusted secondary finding as conclusive.

The secondary outcomes provide context for the trial’s broader aims concerning weight, eating-related measures, and working memory, but they do not replace the defined primary endpoint. The available secondary evidence is best considered exploratory unless the analysis plan establishes otherwise; no such plan is reported in the registry record.

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

• N-back Behavioral Performance
• Percent Weight
• Eating Behavior
• Power of Food

9. Statistical Interpretation

10. Statistical Methods Explained

The registry identifies the study as randomized and parallel-group, with no masking. Randomization is intended to balance measured and unmeasured characteristics between groups on average, although it does not guarantee balance in a study of this size. A parallel design compares groups assigned to different conditions over the same initial period. Because masking was listed as none, participants and study personnel were not described as blinded to assignment. The registry does not report whether those assessing or processing the imaging outcome were masked.

What does a mean difference represent?

For a continuous endpoint, a mean summarizes the average observed value or change in a group. The primary results are means of change from baseline to 16 weeks. The reported mean difference compares the WW group’s mean change with the waitlist group’s mean change. A positive difference means the WW group’s reported change was numerically higher under the stated comparison direction; it does not determine whether that direction represents clinical or neurological benefit. Interpretation depends on the endpoint’s scale and the scientific meaning of an increase or decrease.

The registry reports standard errors beside the group means. In general, a standard error describes the sampling uncertainty around an estimated mean, rather than the spread of individual participant values. A standard error is affected by both the variability in observations and the amount of information available. It should not be interpreted as showing the full range of individual responses. The registry does not provide standard deviations for the primary endpoint as reported by the study; the posted dispersion is standard error.

How should the p-value be read?

The unadjusted p-value of 0.159 is a measure of how compatible the observed comparison is with a null model of no difference, conditional on the statistical assumptions used. In general, a p-value is not a measure of effect size, clinical importance, or the probability that a hypothesis is correct. It also does not indicate the chance that the findings will replicate. The registry does not report the test used to produce this p-value or a full analysis specification, so further assumptions about the calculation should not be made.

Unadjusted means the p-value is reported without a stated adjustment for multiple comparisons. When several outcomes, contrasts, or analyses are considered, the chance of at least one apparently notable result can increase. Adjustment procedures or a prespecified hierarchy can address that concern, but a multiplicity plan is not reported in the registry record. The posted p-value should consequently be interpreted as an unadjusted result, not as evidence that the full set of analyses was protected against multiplicity.

Why do confidence intervals matter?

A confidence interval presents a range of effect estimates compatible with the observed data under the method’s assumptions. In general, a narrower interval indicates greater precision, while a wider interval indicates more uncertainty. A confidence interval crossing zero for a difference means the data do not clearly distinguish a positive difference from no difference and a negative difference. This does not prove that the true difference is zero. The primary interval crosses zero, so the point estimate should not be read in isolation.

The registry gives the primary interval limits to four decimal places, but reporting is limited to three decimal places; the interpretation is therefore stated without reproducing those limits. No confidence level is specified in the registry record, so a confidence level should not be assumed from the posted limits alone.

What assumptions are not documented?

The registry record does not report the primary analysis model, assumptions about the distribution of the imaging measure, handling of baseline values, covariate adjustment, missing-data procedures, or the population included in the analysis. Those details can affect estimates and uncertainty. For example, a model that adjusts for baseline values may differ from an unadjusted comparison of change scores. Without a reported method, the posted summary statistics should be treated as the available results rather than as a complete account of the analysis.

More generally, over-dispersion occurs when variability is greater than a model expects. If it is not addressed, standard errors can be too small and intervals too narrow. That concept is relevant to statistical modeling in general, but the registry does not report a model for this endpoint that would establish whether over-dispersion was assessed or relevant. The available endpoint is continuous and summarized as a mean with standard error; no additional distributional diagnostic is reported.

11. Confidence Intervals and Precision

The primary mean difference was 0.11, with a confidence interval that extends from a negative value to a positive value and therefore includes zero. This interval indicates uncertainty about both the direction and magnitude of the between-group difference. The estimate is not precise enough to distinguish clearly between no difference and differences in either direction that remain compatible with the data.

The primary group means were reported with standard errors of 0.05 for WW and 0.06 for waitlist. These standard errors describe uncertainty around the means, not the variability among individual participants. The confidence interval for the difference is the more direct summary for judging uncertainty about the comparison itself. Its width, together with the modest outcome group counts, cautions against treating the point estimate as a stable or definitive quantity.

In general, confidence intervals convey a range of values that remain plausible under the analysis assumptions, rather than a list of equally likely possibilities or a guarantee that the true effect lies within the interval. A wide interval can leave substantial uncertainty even when the point estimate is near zero. Conversely, an interval including zero does not establish that the effect is absent. The registry does not state the confidence level or document all assumptions behind the interval, limiting how fully its calibration can be assessed.

Precision is also distinct from statistical significance. The unadjusted p-value was 0.159, and the interval crosses zero. Together, these results indicate that the trial did not estimate the primary comparison with enough precision to rule out no difference or effects in either direction represented by the interval. They do not establish equivalence or exclude every meaningful effect.

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 planning figures are participants per arm, not total events. They are illustrations based on the observed effect and are not the sample-size assumptions used to design the original trial; those original design assumptions are not reported in the registry record. The illustrations use a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. Each row considers detecting the stated fraction of the observed effect.

The 80% power column gives the estimated participants per arm for a future study to have an 80% chance of detecting the specified effect under those assumptions, if that effect is the true one. The 90% column gives the corresponding planning count for a 90% chance. For the primary endpoint, planning for 100% of the observed effect gives 98 participants per arm for 80% power and 131 participants per arm for 90% power. Planning for 75% of the observed effect gives 174 participants per arm for 80% power and 233 participants per arm for 90% power. Planning for 50% of the observed effect gives 392 participants per arm for 80% power and 524 participants per arm for 90% power.

Smaller target effects require more participants because they are harder to distinguish from random variation. These figures should be read as planning illustrations, not as a claim that the trial had a particular probability of detecting its result. This is not observed power. The displayed curve applies the same planning logic across the effect sizes represented in the analysis; it does not replace a design calculation based on prespecified assumptions about a future study.

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 = 0.110; pooled standard deviation σ = 0.275.
2. n = 2 × (1.96 + 0.842)² × 0.275² / 0.110² = 97.8, rounded up to 98 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 <- 0.11                      # observed difference in means
sigma <- 0.274538573922552                     # 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(4202133)
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 = 98 (80% power), 131 (90% power)
 75% of observed effect: n per arm = 174 (80% power), 233 (90% power)
 50% of observed effect: n per arm = 392 (80% power), 524 (90% power)
power.t.test: 98.8 
Simulated power at n = 98 per arm: 0.794 (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. Multiplicity, Missing Data and Analysis Populations

The registry identifies a primary endpoint and lists secondary outcomes, but the statistical plan for managing multiple comparisons is not reported in the registry record. In particular, it does not state whether outcomes were tested in a prespecified order, whether a family of hypotheses was defined, or whether any adjustment was planned. The primary p-value is explicitly unadjusted, and the secondary analyses do not have reported analyses in the registry record. Without these details, it is not possible to determine how the reported results relate to a broader multiplicity strategy.

Multiplicity matters because repeated testing can increase the chance of finding at least one result that appears unusual under a no-effect model. This general issue does not mean that any particular result is false; it means that unadjusted p-values should be interpreted in the context of how many outcomes and comparisons were considered. A prespecified hierarchy or adjustment procedure can clarify which results are confirmatory and how error rates are controlled. Such information is not reported in the registry record.

Missing-data methods are also not reported. The primary endpoint summaries include 29 participants in the WW group and 22 in the waitlist control group, while the registry lists enrollment as 61. The record does not explain the relationship between enrollment and the outcome counts, whether missing measurements occurred, why any measurements might be absent, or whether imputation or another method was used. It would be inappropriate to assume that the posted analysis included all randomized participants or that missingness had no effect.

The analysis population is not described in the primary outcome entry. The registry does not specify whether the analysis followed assigned treatment, included participants who completed the intervention, or used another population definition. Nor does it report whether the imaging analysis adjusted for baseline response, or how deviations from assignment were handled. These omissions limit assessment of possible bias and the applicability of the estimate to all randomized participants.

These reporting gaps do not invalidate the posted summaries, but they constrain their interpretation. A fuller account of multiplicity, missing data, and analysis populations would help readers assess how robust the inferences are and how the primary and secondary findings were selected and tested.

15. 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 5% reporting threshold.

The registry reports zero serious adverse events and zero deaths in the WW group, among 31 participants at risk, and zero serious adverse events and zero deaths in the waitlist control group, among 30 participants at risk. It also reports zero other adverse events in each group, using the same respective at-risk counts. No serious adverse-event terms are listed.

These figures describe the events recorded in the registry for the stated groups and at-risk counts. A zero count means no events of that category were reported in those groups; it does not establish that the intervention has no risks or that no unrecorded events occurred. The registry record does not provide further detail about event collection, severity definitions beyond the serious category, follow-up completeness, or the safety analysis population. The outcome counts for the primary imaging endpoint differ from the at-risk counts used in the adverse-event entry, and the record does not explain that difference. Safety interpretation should remain limited to the reported event counts and their stated denominators.

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

The posted primary result estimates the difference in mean change in a specified fMRI response between a group assigned to WW and a waitlist group over 16 weeks. The WW mean change was -0.05 percent BOLD signal change, the waitlist mean change was -0.16, and the mean difference was 0.11. The interval crosses zero, so the estimate remains uncertain about the direction and magnitude of the difference.

This result does not show that the program changed brain health, protected neurocognitive function, or improved memory. The primary endpoint is a BOLD response contrast to images in a specified brain region; it is not itself a direct measure of cognitive ability, everyday functioning, or long-term brain health. The study summary describes working memory as an area of interest, but the primary result is about the imaging contrast.

The result also does not establish that the intervention is ineffective. An interval that includes zero indicates uncertainty rather than proof of no effect. The study’s open-label design and the absence of reported details about the analysis model, missing-data handling, and analysis population further limit what can be concluded from the summary statistics.

More generally, statistical results should be separated from clinical importance. A small p-value would not by itself establish that an effect matters in practice, and a non-small p-value does not establish that an effect is absent. The registry does not provide a threshold for a meaningful change in the primary imaging endpoint. The available evidence therefore supports a careful description of the observed group averages and their uncertainty, not a clinical recommendation or a claim of benefit or lack of benefit.

17. Why This Trial Matters Statistically

This trial is statistically informative because it tests an intervention with a neuroimaging endpoint rather than relying only on body weight or self-reported behavior. The primary endpoint defines a specific contrast between high-calorie food images and neutral objects in the left anterior cingulate cortex. That specificity makes the question measurable, while also making interpretation dependent on the imaging task, brain region, and analysis method.

The registry result illustrates why an estimate should be considered alongside its uncertainty. The mean difference is positive, but its confidence interval crosses zero and the unadjusted p-value is 0.159. Neither the point estimate nor the p-value alone supports a definitive conclusion. This is particularly important in a study with modest outcome group counts and a continuous imaging outcome.

The design also highlights the value of complete statistical reporting. Randomization and a parallel comparison are useful design features, but interpretation would be strengthened by a reported analysis plan, a clear account of the analysis population, and details of missing-data and multiplicity handling. Those elements are not reported in the registry record. Their absence makes it harder to evaluate how the posted estimates were generated and how they should be weighed against the broader set of outcomes.

Finally, the posted secondary outcomes demonstrate that a broad research question can involve several distinct measures. The imaging endpoint, weight change, food-related measures, and working-memory performance address related but non-identical questions. Keeping those outcomes distinct, and interpreting unadjusted results cautiously, is central to a sound statistical reading.

18. 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 primary endpoint is a specialized fMRI contrast in a single named brain region. The registry describes the stimulus comparison and unit, but does not report image-processing details, quality-control procedures, or the full statistical model. Those omissions make it difficult to assess the sensitivity of the result to analytic choices or to compare it with other measures of brain function.

The trial was open-label and compared WW with a waitlist rather than an active program. Differences between groups could therefore reflect aspects of participation beyond the specific program content, and the registry does not describe procedures to separate those influences. The waitlist group was to receive WW after 16 weeks, so the posted primary comparison addresses the initial period, not a long-term comparison between ongoing treatment strategies.

Outcome counts were 29 in the WW group and 22 in the waitlist group for the primary endpoint, while enrollment was 61. The record does not explain the difference, describe missing observations, or specify the analysis population. It also does not report the original sample-size justification or the statistical analysis plan. These limitations restrict evaluation of precision, potential attrition bias, and the role of planned analyses.

The registry lists additional secondary outcomes, but numerical results are not reported for all listed measures. It also does not report a multiplicity strategy, so the relationship between the primary finding and the wider set of outcomes is unclear. These reporting limitations are specific to the available registry record and should not be mistaken for evidence that no further methods or analyses existed outside it.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Neurocognitive Benefits of a Weight Management Program — NCT04202133.
• Registry record last updated 2025-02-10; status last verified 2025-01.
• Results first posted 2025-02-10.
• 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.

22. Record Summary

NCT04202133 is a completed, randomized, open-label, parallel-group Phase 4 study sponsored by the University of Pennsylvania. It compared a 16-week group-based WW program with a 16-week waitlist period in people with overweight and obesity. The primary outcome was change from baseline to 16 weeks in the BOLD response to high-calorie food cues minus neutral objects in the left anterior cingulate cortex.

The reported primary mean difference was 0.11 percent BOLD signal change, with an unadjusted p-value of 0.159 and a confidence interval that crosses zero. Secondary summaries are available for Percent Weight and Power of Food; additional listed outcomes do not have numerical results reported in the registry record. The record reports zero serious adverse events, other adverse events, and deaths in the stated groups. Important details about analysis methods, missing data, multiplicity, and the original design assumptions are not reported in the registry record.