Treatment of Obesity and Binge Eating: Behavioral Weight Loss Versus Stepped Care: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Treatment of Obesity and Binge Eating: Behavioral Weight Loss Versus Stepped Care (NCT00829283), a randomized na study. The primary outcome is Number of Subjects Who Reached Binge Eating Remission.

2. Clinical Question

3. Trial Design

The registry identifies this as a randomized, quadruple-masked, factorial-model study. It records 191 participants enrolled and two named arms: Standard Care and Stepped-care. The primary outcome display includes 39 participants in Standard Care and 152 in Stepped-care. These figures describe the denominators shown for that outcome; the record does not explain the allocation ratio or why the arm sizes differ.

The trial is marked completed. Its recorded start is 2008-11 and its primary completion is 2013-11. The phase is listed as NA. The sponsor is Yale University. The conditions are obesity and binge eating.

The brief summary says the stepped-care approach begins with behavioral weight loss and uses early treatment response to guide additional interventions. The intervention list names behavioral weight loss, behavioral weight loss plus guided self-help cognitive-behavioral therapy, placebo, and sibutramine/orlistat. Although the study model is labeled factorial, the record does not describe the factorial factors, how the listed interventions map onto those factors, or how the treatment pathways were assigned. Those details are not reported in the registry record.

The primary outcome is a count of participants reaching binge-eating remission at 12 months follow-up. BMI is listed as a secondary outcome, measured at 12 months follow-up post-treatment. The record includes arm summaries and comparison estimates for these outcomes, but no reported analyses are listed. The original statistical analysis plan, sample-size justification, analysis populations, and reasons for any differences between outcome denominators 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 Number of Subjects Who Reached Binge Eating Remission, measured over 12 months follow-up.

The primary endpoint is the number of participants who reached binge-eating remission, with remission defined in the registry description as abstinence from binge eating. The recorded assessment timeframe is 12 months follow-up. This is a binary outcome at the participant level: each participant either meets the stated remission definition or does not. The posted arm summaries therefore present the number meeting the endpoint alongside the number of participants represented in each arm.

Remission is used to express whether participants reached the specified status by the follow-up assessment, rather than the amount or frequency of binge eating over time. That makes the endpoint directly interpretable as a count of participants reaching abstinence under the registry definition. However, the record does not provide the assessment instrument, the required duration of abstinence, the handling of intermittent symptoms, or the method used to collect and verify the outcome. These details are not reported in the registry record, and they limit how precisely the endpoint definition can be reconstructed.

The registry summary identifies remission as the major outcome relevant to the comparison of stepped care with standard behavioral treatment. The result should be read as a comparison of the recorded remission counts at the stated follow-up, not as a measure of every aspect of binge-eating severity or treatment experience.

7. Results Posted in the Registry

• Stepped-care: 42.8% (65/152) versus 41.0% (16/39) on control; risk difference 1.7 percentage points (95% CI -15.6 to 19.1), risk ratio 1.04 (0.69–1.58); unadjusted two-proportion z-test p = 0.845.

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.

BMI

• 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:
  • Stepped-care: mean 37.10 versus 35.90 on control; difference 1.20 (95% CI -1.37 to 3.77), standardized effect d = 0.18; z-test p = 0.359.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Stepped-care and the control. The interval gives the range of effects that remain compatible with the data.

BMI is the one secondary endpoint with posted results. It is a continuous measure, unlike the primary endpoint, which counts participants reaching remission. The BMI display summarizes group averages and their variability, while the primary result summarizes whether participants met the remission definition. These outcomes address related but distinct aspects of the study, so a secondary BMI comparison is not a substitute for the primary remission comparison.

The BMI comparison's interval includes values on either side of zero, and its unadjusted p value does not indicate a clear separation in the posted analysis. This broad pattern is consistent with the primary result in that neither displayed comparison tightly identifies a directional group difference. It does not establish that the outcomes are equivalent, and the two estimates should not be combined informally into a single overall treatment conclusion.

Secondary outcomes generally carry less confirmatory weight than a prespecified primary outcome, especially when the analysis plan and any multiplicity procedure are not available. Each additional outcome creates another opportunity for an apparently notable result to arise by chance. A multiplicity adjustment can help control this issue, but whether one was planned or used is not reported in the registry record. The BMI p value is unadjusted, and the record lists no reported analyses.

The BMI denominators differ from those shown for the primary outcome. The reasons are not reported, so it is not possible to determine whether the secondary comparison reflects the same participant set, a particular follow-up subset, or another analysis population. The record also does not report an analysis of how BMI changes relate to remission within individuals. Accordingly, the secondary endpoint adds descriptive context but cannot explain the primary comparison or establish a mechanism for it.

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

• BMI

9. Statistical Interpretation

10. Statistical Methods Explained

What does a risk difference describe?

A risk difference compares the proportions of participants reaching a binary outcome in two groups. Here, the outcome is reaching binge-eating remission. The posted estimate, 0.017, is the difference on the risk scale for Stepped-care relative to Standard Care. A positive estimate points toward a higher observed remission proportion in Stepped-care; a negative estimate points toward a higher proportion in Standard Care. The estimated difference is small in the posted summary, but its interval is broad enough to include values in both directions.

The counts and denominators give the context for this comparison: 16 of 39 participants in Standard Care and 65 of 152 in Stepped-care reached remission. A risk difference is an absolute contrast between group proportions. It is distinct from a risk ratio or odds ratio, which describe relative contrasts on different scales. The registry display includes relative measures as well, but this explanation focuses on the risk-difference estimate, which is the stated primary comparison metric in the posted results.

How should the interval be read?

A confidence interval expresses uncertainty around an estimate under the method used to construct it. It is not a range of individual participant outcomes, nor does it identify the exact value of the underlying effect. For the primary comparison, the estimate is 0.017 and the interval extends from -0.156 to 0.191. Because the interval includes values below and above zero, the posted data do not tightly locate the direction or magnitude of the group difference. The confidence level and the exact interval-construction procedure are not reported in the registry record, so they should not be inferred.

The unadjusted p value of 0.845 is another summary of the comparison under a statistical model. It does not state the probability that the groups are equivalent, and it does not tell us the probability that a treatment has a particular effect. Estimates and intervals are useful alongside a p value because they show the direction and range of effects compatible with the calculation, rather than reducing interpretation to a threshold decision.

What is being compared for BMI?

BMI is a continuous secondary outcome, summarized by a mean and standard deviation in each arm. The displayed means are 35.9 for Standard Care and 37.1 for Stepped-care. The posted mean difference is 1.2, with an interval from -1.367 to 3.767 and an unadjusted p value of 0.359. A mean difference describes a contrast in group averages, not a difference experienced by every participant. The displayed standard deviations describe variation among participants within each group; they are not uncertainty intervals around the group means.

The BMI comparison is based on 32 participants in Standard Care and 127 in Stepped-care, whereas the primary remission summary uses 39 and 152. The record does not explain why these denominators differ. The calculation shown for BMI is based on the posted summary statistics, not on an individual-participant model reported in the registry. No adjusted analysis is listed.

What can be concluded from unadjusted calculations?

The comparison estimates and p values should be understood as unadjusted calculations from the posted group summaries. They do not account for covariates, stratification, repeated observations, or other design features unless those are reflected in the summary statistics; the record does not report such an adjustment. The registry labels the design factorial, but it does not report a factorial analysis, interaction estimates, or how the listed intervention components enter an analysis. The record also lists no reported analyses. Thus, these calculations summarize the available group-level display and should not be mistaken for a complete reconstruction of the trial's planned or sponsor-conducted analysis.

In general, adjustment can affect both an estimate and its uncertainty, particularly when the planned analysis accounts for design features or prognostic variables. In general, an unadjusted comparison is not necessarily biased, but it may not match a prespecified analysis. Since the analysis plan and analysis population are not reported in the registry record, readers cannot establish whether these calculations reproduce the intended primary analysis.

Why can over-dispersion matter?

In general, over-dispersion occurs when variability in the data is greater than a statistical model assumes. For count or binary outcomes, a model that understates variability can produce uncertainty estimates that are too narrow. Methods that allow extra variability may widen intervals or change test results. The registry does not report an over-dispersion assessment or a model for the primary endpoint, so there is no basis to say whether over-dispersion was assessed or affected the trial's analysis. This is a general statistical consideration, not a claim about this study.

11. Confidence Intervals and Precision

The primary estimate is 0.017, and its interval runs from -0.156 to 0.191. The interval includes zero and extends in both directions. This means that the posted summary does not pin down whether the underlying risk difference favors Stepped-care, favors Standard Care, or is close to zero. The data are therefore imprecise with respect to the direction and size of the difference. The unadjusted p value of 0.845 is consistent with the absence of a clear separation in this comparison, but it does not establish equivalence.

Precision is about how narrowly an estimate is located, not simply whether the estimate is positive or negative. The primary interval is wide relative to its point estimate. That breadth matters: a near-zero point estimate alone could give an overly reassuring impression of similarity, while the interval shows that a range of potentially meaningful differences remains compatible with the posted calculation. The record does not state the confidence level or interval method, so this page does not assign one.

The BMI mean-difference interval also spans zero, running from -1.367 to 3.767 around an estimate of 1.2. It likewise leaves uncertainty about the direction and size of the group contrast. The BMI result is secondary and has different arm denominators from the primary endpoint, so its precision should not be treated as direct confirmation or refutation of the remission comparison.

Intervals from group-level recalculations reflect sampling uncertainty under their calculation assumptions. They do not address every possible source of uncertainty, such as missing outcomes, outcome measurement, departures from the registered treatment pathways, or analysis choices not described in the record. Those features are not reported in the registry record. The intervals are useful summaries of the posted comparisons, but they cannot substitute for a full statistical analysis plan and participant-level analysis.

12. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

The sample-size table and curve are planning illustrations based on the observed effects, not a reconstruction of the trial's original design. For these outcomes, the table gives participants per arm. It assumes a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The planning effect is set to the stated fraction of the observed effect: the full observed effect, 75% of that effect, or 50% of that effect. The trial's own sample-size justification and original design assumptions are not reported in the registry record.

The 80% power column represents the number of participants per arm that the planning calculation indicates would be needed for an 80% chance of detecting the specified effect under those assumptions. The 90% power column gives the corresponding planning requirement for a 90% chance. These are conditional design calculations: they depend on the effect size and assumptions used, and they are not statements about what happened in the completed trial.

The table and curve illustrate that smaller effects require more participants to detect under the same assumptions. For the primary binary endpoint, the displayed requirements rise as the assumed effect is reduced from the observed effect to smaller fractions. The same pattern applies to the BMI illustration. These figures should be read as hypothetical planning guidance rather than as evidence that the trial had a particular probability of success. This is not observed power.

Because the calculations assume equal allocation, they do not reproduce the arm sizes shown in the registry results. The planning figures also do not incorporate any unreported features of the trial design or analysis. The curve is a visual representation of the planning relationship; it does not add information about the trial's original target or actual operating characteristics.

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, p₀ and p₁ are the control and treatment proportions, and p̄ is their average.

Worked calculation for this trial

1. Control proportion p₀ = 0.410; treatment proportion p₁ = 0.428; average p̄ = 0.419.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6978 = 1.3676.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.6976 = 0.5872.
4. n = (1.3676 + 0.5872)² / (0.0174)² = 12,656.5, rounded up to 12,657 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
p0 <- 0.41025641025641                          # control proportion
p1 <- 0.427631578947368                          # treatment proportion
n_per_arm <- function(power, frac = 1) {
  q1 <- p0 + (p1 - p0) * frac               # smaller effect = fraction of the observed difference
  pbar <- (p0 + q1) / 2
  z_b <- qnorm(power)
  ceiling(round((z_a * sqrt(2 * pbar * (1 - pbar)) + z_b * sqrt(p0 * (1 - p0) + q1 * (1 - q1)))^2 / (q1 - p0)^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 (unrounded n per arm)
cat("power.prop.test:", round(power.prop.test(p1 = p0, p2 = p1, power = 0.80)$n, 1), "\n")

# Simulation: how often does the z-test reject at the 80%-power sample size?
set.seed(829283)
n    <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z  <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))

Output from running the code

100% of observed effect: n per arm = 12,657 (80% power), 16,943 (90% power)
 75% of observed effect: n per arm = 22,469 (80% power), 30,079 (90% power)
 50% of observed effect: n per arm = 50,480 (80% power), 67,577 (90% power)
power.prop.test: 12656.5 
Simulated power at n = 12,657 per arm: 0.803 (20000 replicates)

The simulation draws many pairs of event counts at the planned sample size and counts how often the two-proportion z-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 labels the study model factorial and lists multiple intervention entries, a primary outcome, and BMI as a secondary outcome. Yet the record does not describe the factorial factors, specify which comparisons were prespecified, or report whether the analysis controlled for multiple comparisons. It also lists no reported analyses. As a result, readers cannot determine whether the displayed comparisons reflect a single planned hypothesis, a subset of a broader analysis plan, or a particular multiplicity strategy.

Multiplicity matters when several outcomes, treatment contrasts, time points, or subgroup analyses are examined. In general, the more comparisons considered, the greater the chance that at least one result will appear notable by chance. Adjustments or a prespecified testing hierarchy can address some of this concern. Neither the analysis plan nor any adjustment for multiplicity is reported in the registry record. The posted p values are unadjusted, so they should not be read as if they account for a family of tests.

The registry provides different denominators for the primary remission endpoint and BMI. It does not report the amount, reasons, or pattern of missing outcome data, or how missing observations were handled. It also does not identify an intention-to-treat population, a per-protocol population, or another analysis population. Without these details, it is not possible to establish which enrolled participants contributed to each comparison or how exclusions and incomplete follow-up may have affected the summaries.

Interim analyses, stopping rules, and a detailed statistical analysis plan are also not reported in the registry record. This does not show that such procedures were or were not used; it means their use cannot be assessed from the posted information. The factorial label alone does not establish the actual analysis model, and the registry does not report interaction tests or estimates. These gaps limit interpretation of the reported comparisons and make it important to distinguish the posted summary-based calculations from a documented sponsor analysis.

15. Safety Results

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

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 5% reporting threshold.

The adverse-event display lists 39 participants at risk in Standard Care and 152 in Stepped-care. It records 0 participants affected by serious adverse events in each group and 0 affected by other adverse events in each group. No serious adverse-event terms are listed. These are the figures shown in the registry record; they describe what is posted, not necessarily every event that may have occurred or been collected.

The death fields are blank in the record, so death information is not reported in the registry record. A zero count in the event fields should not be interpreted as proof that no events occurred outside the recorded categories or reporting process. The record does not provide definitions, ascertainment methods, follow-up duration for safety, or details about event severity beyond the serious/other categories. It also does not give a comparison estimate or uncertainty interval for safety outcomes.

These sparse registry figures permit only a limited description of reported events. They do not support a broad safety conclusion or a comparison of the treatments' overall safety profiles.

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

The posted primary results describe similar observed remission proportions in the two named arms, with a risk-difference estimate close to zero. The interval around that estimate is broad and crosses zero, and the unadjusted p value is 0.845. Together, these figures show that the posted group-level comparison does not clearly distinguish the arms, while leaving substantial uncertainty about the size and direction of a possible difference.

This does not demonstrate that the approaches are equivalent. Equivalence requires a defined margin and an analysis designed to assess whether the difference falls within that margin; neither is reported in the registry record. Nor does the result establish that both approaches have the same effect, or that one approach has no effect. It is a comparison between the named groups in this trial, using the available posted endpoint summaries.

The record's summary frames stepped care as an approach that begins with behavioral weight loss and uses early response to guide additional intervention. The result should not be attributed to any one component in the intervention list. The registry does not provide component-specific estimates, pathway adherence, or the detailed mapping from interventions to the arms. The factorial label is not enough to infer those details.

The secondary BMI comparison does not resolve the primary uncertainty. It is a different outcome, has different displayed denominators, and is also presented as an unadjusted summary. The registry record does not report how missing measurements were handled or whether the secondary analysis was prespecified as confirmatory.

In practical terms, the available record supports a careful description of the posted counts and comparisons, not a definitive conclusion about superiority, equivalence, or the contribution of individual treatment elements. The trial question is clinically focused, but the interpretation is constrained by the breadth of the intervals and by missing details about analysis, outcome assessment, and follow-up. These findings should not be converted into treatment advice.

17. Why This Trial Matters Statistically

This trial raises a statistical question that is common in evaluating stepped care: whether adapting treatment according to early response leads to a different outcome from a standard approach. That question concerns not only whether an average result differs, but also how the adaptive pathway is defined, how participants move through it, and what contrast the analysis estimates. The registry describes the broad idea of response-guided additional interventions, but does not report enough detail to reconstruct those pathways or their analysis.

The results also illustrate why an estimate should be read together with its interval. A point estimate near zero can appear to suggest little difference, but the primary interval covers effects in both directions. The uncertainty is central to interpretation. The unadjusted p value alone would not convey the range of contrasts compatible with the posted calculation, nor would it establish equivalence.

The factorial-model label and multiple listed intervention components make reporting of the design and analysis especially important. Without the factors, planned contrasts, or any interaction results, readers cannot identify which treatment dimensions were tested independently or jointly. The posted comparison remains interpretable at the level of the two named arms, but not as a component-level evaluation.

Finally, the trial highlights the distinction between a completed study and a fully reported statistical record. The record includes outcome summaries and adverse-event counts, but does not report the analysis plan, missing-data handling, analysis populations, or original sample-size rationale. Transparent reporting of these elements is essential for readers to judge precision, bias, and how closely published calculations match the intended design.

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.

Several limitations specific to this record affect interpretation. First, the primary comparison shows markedly different arm denominators: 39 for Standard Care and 152 for Stepped-care. The registry labels the study randomized but does not explain the allocation ratio or the reason for this imbalance. The posted effect estimate and interval should therefore be interpreted as summaries of the displayed groups, without assuming an unreported allocation or analysis strategy.

Second, the BMI summaries use 32 participants in Standard Care and 127 in Stepped-care, rather than the primary outcome denominators. The reasons for the differing outcome counts, the extent of missing data, and the handling of incomplete measurements are not reported in the registry record. This makes it difficult to assess whether missingness could affect the comparisons.

Third, the trial is labeled factorial and includes several intervention entries, but only two arm descriptions are presented in the outcome display. The record does not explain the factorial structure, the treatment sequence, or the mapping of listed interventions to the named arms. Consequently, the results cannot be separated into effects of individual intervention components from the information.

Fourth, the record does not report the remission assessment method, a full analysis plan, multiplicity handling, interim analyses, or the original sample-size justification. It also lists no reported analyses. These omissions limit assessment of outcome validity, analysis choices, and the relationship between the posted recalculations and any intended primary analysis. The adverse-event section is similarly limited: death information is not reported, and event definitions and ascertainment details are absent.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Treatment of Obesity and Binge Eating: Behavioral Weight Loss Versus Stepped Care — NCT00829283.
• Registry record last updated 2020-04-03; status last verified 2020-04.
• Results first posted 2016-02-01.
• 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

The registry record describes a completed randomized, quadruple-masked, factorial-model study of standard care versus stepped care for obesity and binge eating, sponsored by Yale University. It records 191 participants enrolled. The primary endpoint is the number reaching binge-eating remission at 12 months follow-up; BMI is the posted secondary endpoint.

The primary comparison is a summary-based, unadjusted risk-difference calculation with an interval that spans zero. The BMI comparison is also unadjusted, and its interval spans zero. The record lists no reported analyses. The original analysis plan, sample-size justification, missing-data handling, analysis populations, and details of the factorial structure are not reported in the registry record.