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Moderate or Severe Submental Fullness Phase 3 Binary Endpoint NCT01546142

Phase 3 Study of Deoxycholic Acid Injection (ATX-101) Versus Placebo for the Reduction of Localized Subcutaneous Fat in the Submental Area: Complete Statistical Analysis

A randomized, double-blind, placebo-controlled Phase 3 trial evaluated deoxycholic acid injection for submental fullness. The analysis focuses on the registry’s primary response outcome, its reported statistical comparison, secondary outcomes, missing-data information and serious adverse events.

Trial start: 2012-03  ·  Enrollment: 516  ·  Sponsor: Kythera Biopharmaceuticals
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 Phase 3 Study of Deoxycholic Acid Injection (ATX-101) Versus Placebo for the Reduction of Localized Subcutaneous Fat in the Submental Area (NCT01546142), a randomized phase 3 study. The primary outcome is Percentage of Participants Who Achieved a Composite 1-grade Response.

516
Enrollment
Phase 3
2
Arms
In the primary outcome
+44.6 pts
Risk difference
Deoxycholic Acid Injection
36.9 to 52.2 pts
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT01546142
PhasePhase 3
ConditionModerate or Severe Submental Fullness
AllocationRandomized
Design modelParallel
MaskingDouble
Enrollment516
Arms in the primary outcome2
Lead sponsorKythera Biopharmaceuticals
Results postedYes

2. Clinical Question

Population

The registry describes participants with moderate or severe submental fullness, meaning fullness from fat below the chin. The trial enrolled 516 participants. For the primary outcome, the intent-to-treat population included 258 participants in each arm, and missing values were imputed using a multiple imputation process. The registry does not provide further eligibility details in the record.

Intervention

Participants assigned to deoxycholic acid received 2 mg/cm² in 0.2 mL injections, up to 10 mL per treatment session. Sessions were scheduled at intervals of approximately 1 month, for a maximum of 6 treatments. The study evaluated the injection in the submental area.

Comparator

The comparison group received placebo in 0.2 mL injections, up to 10 mL per treatment session, at intervals of approximately 1 month, for a maximum of 6 treatments. The trial was randomized, double-blind and placebo-controlled, with a parallel-group model. The registry does not report additional details about how masking was maintained.

Primary question

The primary question was whether participants achieved at least a 1-grade improvement from baseline on both the clinician-reported and patient-reported Submental Fat Rating Scales, assessed 12 weeks after the last treatment. The timeframe was baseline and 12 weeks after last treatment, up to 32 weeks after first treatment. The endpoint therefore required improvement according to both the clinician and the participant, rather than either measure alone.

3. Trial Design

This was a randomized, double-blind, placebo-controlled, parallel-group Phase 3 study of deoxycholic acid injection, also identified in the title as ATX-101, versus placebo for localized subcutaneous fat in the submental area. Kythera Biopharmaceuticals was the sponsor. The registry lists the study as completed, with a start date of 2012-03 and primary completion in 2013-05. Enrollment was 516.

The two assigned regimens used the same injection volume and treatment-session schedule. The active arm received deoxycholic acid 2 mg/cm² in 0.2 mL injections, up to 10 mL per session. The placebo arm received placebo in 0.2 mL injections, also up to 10 mL per session. Sessions were approximately 1 month apart, for up to a maximum of 6 treatments. The registry does not report whether all participants received the maximum number of treatments.

The primary endpoint was a composite response based on two ordinal rating scales. A participant had to improve at least 1 grade from baseline on both the clinician-reported and patient-reported scales. The assessment was scheduled 12 weeks after the last treatment, with the stated overall timeframe extending up to 32 weeks after the first treatment. The primary population was intent-to-treat, and missing values were handled using multiple imputation.

The registry also lists an MRI response and change in the Patient-Reported Submental Fat Impact Scale as secondary outcomes. The posted record includes results for these outcomes, but it does not report the full protocol, the original sample-size justification, or detailed operational information such as the randomization procedure and any stratification factors. Those details should not be inferred from the trial title or from the statistical results.

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

StageDeoxycholic Acid InjectionPlacebo
STARTED258258
Received Treatment257257
COMPLETED214224
NOT COMPLETED4434

Reasons for not completing this period:

ReasonDeoxycholic Acid InjectionPlacebo
Consent Withdrawn (Subject Convenience)1515
Subject Noncompliance11
Adverse Event63
Lost to Follow-up2015
Consent Withdrawn (Subject Discomfort)10
Subject Randomized but Not Treated10

Analysis population for the primary outcome, as defined in the registry: Intent-to-treat (ITT) population; missing values were imputed using a multiple imputation process.

5. Baseline Characteristics

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

Population: Intention-to-treat population

CharacteristicUnitDeoxycholic Acid InjectionPlaceboTotal
Participants analysed258258516
Age, Continuousyears48.2 (SD 9.30)47.6 (SD 8.99)47.9 (SD 9.14)
Age, Customized: 18-50 yearsparticipants149150299
Age, Customized: 51-65 yearsparticipants109108217
Sex: Female, Male: FemaleParticipants221224445
Sex: Female, Male: MaleParticipants373471
Race/Ethnicity, Customized: Whiteparticipants222222444
Race/Ethnicity, Customized: Black or African Americanparticipants242145
Race/Ethnicity, Customized: Asianparticipants459
Race/Ethnicity, Customized: American Indian or Alaskan Nativeparticipants123
Race/Ethnicity, Customized: Native Hawaiian or Pacific Islanderparticipants314
Race/Ethnicity, Customized: Multipleparticipants202
Race/Ethnicity, Customized: Otherparticipants279
Race/Ethnicity, Customized: Hispanic or Latinoparticipants403979
Race/Ethnicity, Customized: Non-Hispanic or Latinoparticipants218219437
Weightkg81.38 (SD 14.791)80.31 (SD 15.041)80.84 (SD 14.912)
Body Mass Index (BMI)kg/m²29.22 (SD 4.755)29.30 (SD 4.282)29.26 (SD 4.520)
Fitzpatrick Skin Type: I - IIIparticipants170176346
Fitzpatrick Skin Type: IV - VIparticipants8882170

6. Primary Endpoint

The registry lists the primary outcome as Percentage of Participants Who Achieved a Composite 1-grade Response, measured over Baseline and 12 weeks after last treatment (up to 32 weeks after first treatment).

ElementRegistry entry
Result typeNumber
Measure of spreadnot applicable
Unitpercentage of participants
Endpoint classificationBinary Endpoint

The primary endpoint was the percentage of participants who achieved a composite 1-grade response. To qualify, a participant needed at least a 1-grade improvement from baseline on both the Clinician-Reported Submental Fat Rating Scale and the Patient-Reported Submental Fat Rating Scale. The response was assessed 12 weeks after the last treatment, within a timeframe of baseline and 12 weeks after the last treatment, up to 32 weeks after the first treatment.

The clinician-reported scale was based on the investigator’s clinical evaluation. It used a 5-point ordinal scale from 0, absent, to 4, extreme. The patient-reported scale asked how much fat the participant had under the chin, with response options ranging from 0, no chin fat at all, to 4, a very large amount of chin fat. Each scale captures a different perspective: one is the investigator’s assessment, and the other is the participant’s own report.

Requiring improvement on both scales makes the outcome a joint threshold rather than a change on either scale alone. It was used to express the proportion meeting a defined response criterion, rather than to describe the average change in a score. The registry identifies the intent-to-treat population and says missing values were imputed using a multiple imputation process. The endpoint does not, by itself, describe the size of each participant’s change or how long a response continued after the assessment.

7. Results Posted in the Registry

Risk difference: Deoxycholic Acid Injection

+44.6

95% CI: 36.9 to 52.2 percentage points

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals12.025.138.251.464.577.6Deoxycholic Acid Injection (n=258)Placebo (n=258)% of participants (95% CI)
Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Deoxycholic Acid Injection-4.187.9420324456risk difference (percentage points) 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
Percentage of Participants With a Magnetic Resonance Imaging (MRI) ResponseBinary EndpointRisk difference+34.5 pts (24.5 to 44.4)22 per arm
Change From Baseline in Patient-Reported Submental Fat Impact Scale (PR-SMFIS)Continuous EndpointMean difference-2.06 (-2.50 to -1.62)25 per arm

Percentage of Participants With a Magnetic Resonance Imaging (MRI) Response

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Deoxycholic Acid Injection-3.556.7517273848risk difference (percentage points) vs control (95% CI)

Change From Baseline in Patient-Reported Submental Fat Impact Scale (PR-SMFIS)

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Deoxycholic Acid Injection-2.70-2.12-1.54-0.96-0.380.20mean difference vs control (95% CI)

The registry posts two secondary outcomes: MRI response and change from baseline in the Patient-Reported Submental Fat Impact Scale. The posted comparisons favor the deoxycholic acid injection arm on both measures, but these endpoints assess different aspects of the outcome and use different statistical methods. Their overall direction is consistent with the primary response comparison, while their meaning remains specific to each measure.

The MRI outcome is a binary response measure, whereas the impact scale is a continuous change score. They are not alternate versions of the primary composite. The primary endpoint required a threshold improvement on both clinician- and patient-rated fullness scales; the MRI and impact-scale outcomes do not share that same response definition. Agreement in direction can provide context, but it does not make the endpoints interchangeable or demonstrate that they measure an identical effect.

Secondary outcomes generally carry less inferential weight than a designated primary outcome when the registry does not report a plan controlling the chance of false-positive findings across multiple tests. The record does not report a multiplicity adjustment or testing hierarchy for these secondary comparisons. Their p-values should therefore be read as outcome-specific, unadjusted evidence rather than as definitive family-wide tests.

The MRI outcome has fewer participants in its posted summaries than the primary outcome. The registry record does not explain the reason for that difference, so it should not be attributed to a particular missingness or assessment process. For the impact scale, the sponsor reports an ANCOVA p-value but does not report its adjusted estimate or confidence interval. These reporting limits constrain comparisons of precision across the secondary findings.

Taken together, the secondary results provide additional outcome-specific context that is directionally consistent with the primary result. They do not resolve unreported questions about multiplicity, missingness, model details, durability, or generalizability. Their role is supportive and descriptive in the registry record, rather than a replacement for the primary endpoint.

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

9. Statistical Interpretation

Clinical Biostats interpretation

For the primary composite response, 66.5% of participants in the deoxycholic acid injection arm and 22.2% in the placebo arm met the endpoint. The posted sponsor analysis reports a risk ratio of 2.983, with a 95% confidence interval from 2.311 to 3.849 and p < 0.001. In statistical terms, the reported response proportion was higher in the active arm than in the placebo arm under this analysis. This is a comparison of the registry-defined response at the stated assessment, not a description of every outcome or every participant’s experience.

The reported endpoint is deliberately specific: improvement had to occur on both the clinician-rated and patient-rated scales. A participant who improved on only one scale would not meet the composite response definition. The percentage therefore answers a threshold-based question. It does not show the average grade change, the distribution of changes, or whether responses persisted beyond the scheduled assessment.

The recalculated comparison is an unadjusted analysis of the posted summary statistics. It estimates the difference between the two response proportions, while the sponsor’s reported analysis uses a Cochran-Mantel-Haenszel risk ratio. These are different summaries of a binary outcome and can have different numerical values without being contradictory. The reported analysis is the sponsor’s own analysis; the registry record does not give enough detail to reconstruct all features of that analysis.

The p-value indicates that the observed data are inconsistent with a null comparison under the model used for the reported analysis, assuming the model’s conditions. It is not a measure of the probability that the null hypothesis is true, nor does it quantify the size or importance of the result. The confidence interval conveys uncertainty around the risk ratio estimate, conditional on the analysis method. It excludes the no-difference value for a risk ratio, but the interval does not address possible limitations in endpoint measurement, missing-data assumptions, or the conduct of the trial.

The posted secondary results also point in the same broad direction: both the MRI response outcome and the patient-reported impact-scale outcome favored the injection arm in their respective statistical comparisons. These measures differ from the primary composite and should not be treated as interchangeable confirmations. Their interpretation depends on their own measurement properties and analyses, and the registry record does not report a multiplicity adjustment across the secondary outcomes.

Overall, the registry results describe between-arm differences on the stated outcomes at the stated assessment. They do not establish how results generalize beyond the enrolled study population, identify which participants are most likely to meet the endpoint, or establish long-term outcomes. The trial record is a report of statistical comparisons, not a basis for individual medical advice.

10. Statistical Methods Explained

Several statistical ideas help interpret the registry results. The primary outcome is binary at the participant level: each participant either met the composite response definition or did not. A percentage summarizes the proportion meeting that definition in each arm. It is straightforward to read, but it depends on the exact threshold used. Here, the threshold required improvement on both rating scales, so the percentage is not the proportion improving on either scale alone.

What does a risk ratio describe?

A risk ratio compares the response proportion in one group with the response proportion in another. A value of 1 represents equal proportions under this measure. Values greater than 1 indicate a higher proportion in the group in the numerator; values less than 1 indicate a lower proportion. The registry’s sponsor-reported primary analysis gives a risk ratio of 2.983. This is a relative comparison, not an absolute difference in percentage points, and it does not mean that every participant had the same response.

A risk difference answers a different question: it subtracts one group’s response proportion from the other group’s proportion. It expresses the comparison on an absolute scale. The recalculated estimates in the statistical material use unadjusted calculations from posted summaries. They can provide a useful independent description, but they are not a replacement for the sponsor’s own analysis. Relative and absolute measures can both be informative, and their numerical scales should not be compared as though they were the same quantity.

Why can the reported and recalculated estimates differ?

The registry reports a Cochran-Mantel-Haenszel analysis for the primary risk ratio. The recalculation is an unadjusted comparison based on the posted summary statistics. An adjusted or stratified method and an unadjusted method need not produce identical estimates or confidence intervals. The registry record does not report the strata or other details needed to reproduce the reported method fully. There is no flagged discrepancy between the posted sponsor analysis and the recalculated result, but the sponsor’s reported method remains the primary record of its analysis.

A confidence interval describes a range of estimates compatible with the observed data under the statistical method and its assumptions. Its width reflects statistical precision: a narrower interval indicates less sampling uncertainty than a wider interval on the same scale. A confidence interval is not a guarantee that the true value lies within the specific interval, and it does not incorporate every possible source of uncertainty, such as measurement limitations or unreported design details.

What does the p-value contribute?

The reported p-value is p < 0.001. Under the null comparison and the assumptions of the analysis, a p-value this small indicates that data at least as incompatible with the null would be uncommon. It does not measure effect size, practical importance, or the probability that a result is due to chance. Nor does it account for the number of outcomes examined unless the analysis explicitly addresses multiplicity. The registry record does not report an adjustment for the secondary outcome comparisons.

For the change in the Patient-Reported Submental Fat Impact Scale, the outcome is continuous rather than binary. The posted group summaries are means with standard deviations. A mean describes the average score change, while a standard deviation describes the spread of participant-level changes around the mean. The sponsor reports an ANCOVA analysis with p < 0.001, but the registry does not post an adjusted estimate or confidence interval for that analysis. The unadjusted recalculation based on the group summaries is not the same as an ANCOVA result, which can account for baseline values and other model terms; those details are not reported in the registry record.

Why can over-dispersion matter?

For count outcomes, over-dispersion occurs when variability is greater than a model assumes. A model that understates variability can produce intervals that are too narrow and tests that are too optimistic. That general concern is not directly the central issue for this primary binary response, which is analyzed as a proportion, but it illustrates why the chosen statistical model should match the outcome and its variability. The registry’s posted primary analysis is a risk-ratio analysis, not a count-rate model.

For binary outcomes, precision depends in part on the number of observed responses and nonresponses in each group. For continuous outcomes, precision depends on the group sizes and variability. These are general statistical principles; they do not reveal the study’s original design assumptions, which are not reported in the registry record. The sample-size illustrations use the observed effects and stated planning assumptions, rather than documenting the original design calculation.

The primary analysis population is intent-to-treat, meaning the registry identifies participants according to the assigned study groups for that analysis. The record states that missing primary outcome values were imputed using multiple imputation. In general, multiple imputation uses a statistical model to create plausible values for missing observations, analyzes the resulting completed datasets, and combines their results to reflect imputation uncertainty. The registry does not report the imputation model, variables included, number of imputations, or sensitivity analyses. Thus, the label alone cannot establish whether missingness assumptions were reasonable.

Finally, multiple outcomes create a multiplicity question. If several endpoints are tested, the chance of at least one apparently notable result can increase when each is assessed independently. An adjustment or a prespecified hierarchy can address that issue, but such details are not reported in the registry record. The primary result and secondary results should therefore be distinguished rather than treated as a single collection of equivalent tests.

11. Confidence Intervals and Precision

The sponsor-reported primary risk ratio is 2.983, with a 95% confidence interval from 2.311 to 3.849. The interval is entirely above the value representing equal response proportions under a risk ratio. This indicates that the reported analysis is compatible with a range of relative response contrasts, not a single exact value. The interval does not show the absolute difference in response proportions; that is a separate statistical measure.

The primary arm percentages, 66.5% and 22.2%, give the observed response proportions in the registry’s posted primary population. Those percentages are point estimates: they describe the analyzed data but are subject to sampling variability. The sponsor’s interval applies to the reported risk ratio, not directly to each displayed percentage. The registry does not provide confidence intervals for the arm percentages in the primary outcome record.

A confidence interval’s width is one way to assess precision on its own scale. It should be interpreted together with the estimate and the outcome definition. A relatively precise estimate can still be affected by limitations that a confidence interval does not include, such as errors in measurement, missing-data assumptions, or the applicability of the enrolled population to other settings. Statistical precision is not the same as certainty about every aspect of the result.

The secondary MRI response comparison has a sponsor-reported risk ratio of 7.838, with a 95% confidence interval from 3.299 to 18.622. The interval is wider on the relative scale than the primary risk-ratio interval, indicating greater uncertainty around that secondary estimate. The MRI outcome has fewer participants in its posted arm summaries than the primary outcome. This comparison should be interpreted as a secondary finding, with the additional caution that the registry does not report a multiplicity adjustment.

The sponsor’s posted ANCOVA result for the patient-reported impact scale gives p < 0.001, but no adjusted estimate or confidence interval is reported. The unadjusted recalculation has an interval for the mean difference, but it is not the sponsor’s ANCOVA interval. Precision for the sponsor’s adjusted comparison cannot be fully assessed from the reported p-value alone.

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 effect1924
75% of the observed effect3343
50% of the observed effect6992
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect205010020040%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, pooled-variance normal approximation for two proportions. Counts were reconstructed from the posted percentages and arm sizes, so small rounding differences are possible. Calculated for the comparison: Deoxycholic Acid Injection.

The sample-size illustrations describe hypothetical future planning based on fractions of the observed effect. For these outcomes, the figures are participants per arm, not total events. The planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each planning row uses the stated fraction of the observed effect as the effect to detect. These calculations are illustrations based on the observed result, not the trial’s original design calculation; the original sample-size assumptions are not reported in the registry record.

The 80% power column gives the illustrative number of participants per arm for a design with an 80% chance of detecting the specified effect under the planning assumptions, if that effect and the assumptions were correct. The 90% power column gives the corresponding per-arm number for a design with a 90% chance. Power is a design property calculated before results are observed; it is not a measure of how likely the observed result is to be true.

Rows planning for 100% of the observed effect use the full observed effect as the target. Rows planning for 75% or 50% use smaller target effects. Smaller effects are harder to distinguish from random variation and therefore require more participants per arm to achieve the same planned power, all else equal. This relationship is a general planning principle and is reflected in the increasing illustrative sample sizes as the target effect becomes smaller.

These values are not observed power. They do not establish that the completed trial was adequately or inadequately designed, because the registry does not report the original design assumptions. They are conditional planning calculations, and changing assumptions about the effect, allocation, significance level, analysis, or outcome could change the resulting sample-size needs.

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 = [ z1−α/2 √(2p̄(1−p̄)) + z1−β √(p0(1−p0) + p1(1−p1)) ]2 / (p1 − p0)2

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 = 0.221; treatment proportion p1 = 0.667; average p̄ = 0.444.
  2. First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.7026 = 1.3771.
  3. Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.6280 = 0.5285.
  4. n = (1.3771 + 0.5285)2 / (0.4457)2 = 18.3, rounded up to 19 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 <- 0.22093023255814                          # control proportion
p1 <- 0.666666666666667                          # 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(1546142)
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 = 19 (80% power), 24 (90% power)
 75% of observed effect: n per arm = 33 (80% power), 43 (90% power)
 50% of observed effect: n per arm = 69 (80% power), 92 (90% power)
power.prop.test: 18.3 
Simulated power at n = 19 per arm: 0.823 (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.

Very small required sample. The formula gives a very small requirement because the observed effect is very large relative to the variability. Normal-approximation formulas are unreliable at such sizes, and the simulation above shows the power actually achieved. An exact or simulation-based design would be needed in practice.

14. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
Cochran-Mantel-HaenszelRisk Ratio (RR) 2.9832.311 to 3.849< 0.001

The registry reports the sponsor’s primary comparison as a Cochran-Mantel-Haenszel risk ratio of 2.983, with a 95% confidence interval from 2.311 to 3.849 and p < 0.001. The recalculated comparison uses the posted group summaries and is unadjusted. It is a separate descriptive calculation, not a reconstruction of every feature of the sponsor’s analysis.

The reported result and recalculation address the same broad contrast in primary response, but they use different summary measures and methods. The sponsor reports a relative measure, the risk ratio; the recalculation also includes an absolute risk-difference measure. Differences in scale and adjustment mean these estimates should not be expected to match numerically. The registry record does not provide the strata or other analysis details needed to independently reproduce the Cochran-Mantel-Haenszel result.

No discrepancy is flagged between the posted sponsor analysis and the recalculated comparison. The sponsor’s own analysis is therefore the main reported inferential result. The recalculation is useful as a transparent, unadjusted check based on the available summaries, but it should not be treated as more authoritative than the sponsor’s stated analysis or as evidence that the sponsor used an unadjusted method.

For the continuous secondary outcome, the sponsor reports ANCOVA and p < 0.001, without an adjusted effect estimate or interval. Its recalculated mean difference is based on posted group summaries and is likewise not a substitute for the adjusted analysis.

15. Multiplicity, Missing Data and Analysis Populations

The registry identifies one primary outcome and posts two secondary outcomes. It does not report whether the secondary tests were adjusted for multiplicity, arranged in a formal testing hierarchy, or treated as exploratory. When multiple outcomes are tested, independent unadjusted tests can increase the chance of at least one apparently notable result even when no underlying difference exists across the family of outcomes. This general issue is why the secondary p-values should not automatically be interpreted as though each were the sole prespecified test.

The primary outcome uses an intent-to-treat population, and the registry states that missing values were imputed using a multiple imputation process. This is important information because an analysis of a binary response requires an outcome classification for participants included in the analysis. Multiple imputation is a method for handling missing data by estimating plausible values under a model and incorporating uncertainty from that process. It does not eliminate the need for assumptions about why data are missing and how missingness relates to observed information.

The registry record does not report the imputation model, variables used, number of imputed datasets, assumptions about the missingness process, or sensitivity analyses comparing alternative assumptions. It is therefore not possible to assess from the record alone how robust the primary result is to different missing-data scenarios. The registry also does not specify the missing-data handling for each secondary outcome.

The record does not report a full statistical analysis plan, the original sample-size justification, interim analyses, or whether any outcome definitions or analyses changed during the study. Those details should not be inferred from the completed status or from the statistical significance of the posted results. Their absence limits independent evaluation of prespecification and the consequences of missingness or multiple testing.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Deoxycholic Acid Injection72582.7%
Placebo102563.9%
Participants with at least one serious adverse event
Serious adverse events by armDeoxycholic Acid Injection2.7%Placebo3.9%% of participants with at least one serious adverse event

Other (non-serious) adverse events

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

ArmParticipants affected of at risk
Deoxycholic Acid Injection251 of 258
Placebo216 of 256

Most frequent serious adverse event terms

Event termOrgan systemDeoxycholic Acid InjectionPlacebo
DiverticulitisInfections and infestations0 of 2581 of 256
InfluenzaInfections and infestations0 of 2581 of 256
Spinal cord infectionInfections and infestations0 of 2581 of 256
Urinary tract infectionInfections and infestations1 of 2580 of 256
Breast cancerNeoplasms benign, malignant and unspecified (incl cysts and polyps)0 of 2581 of 256
Breast cancer recurrentNeoplasms benign, malignant and unspecified (incl cysts and polyps)1 of 2580 of 256
Ovarian cancerNeoplasms benign, malignant and unspecified (incl cysts and polyps)1 of 2580 of 256
Uterine cancerNeoplasms benign, malignant and unspecified (incl cysts and polyps)1 of 2580 of 256
Uterine leiomyomaNeoplasms benign, malignant and unspecified (incl cysts and polyps)1 of 2580 of 256
Hip surgerySurgical and medical procedures0 of 2581 of 256

Most frequent non-serious adverse event terms

Event termOrgan systemDeoxycholic Acid InjectionPlacebo
Injection site haematomaGeneral disorders188 of 258186 of 256
Injection site painGeneral disorders190 of 258100 of 256
Injection site oedemaGeneral disorders175 of 25893 of 256
Injection site anaesthesiaGeneral disorders169 of 25818 of 256
Injection site erythemaGeneral disorders91 of 25865 of 256
Injection site swellingGeneral disorders75 of 25840 of 256
Injection site indurationGeneral disorders73 of 2589 of 256
Injection site pruritusGeneral disorders42 of 25821 of 256
Injection site paraesthesiaGeneral disorders38 of 25811 of 256
Injection site noduleGeneral disorders37 of 25811 of 256

Serious events with the highest arm-level rate: diverticulitis (0.4%), influenza (0.4%), spinal cord infection (0.4%), breast cancer (0.4%), hip surgery (0.4%).

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 lists serious adverse events affecting 7 participants in the deoxycholic acid injection group and 10 in the placebo group. The serious-event risk sets are 258 and 256, respectively. These counts describe the registry’s reported serious adverse event summary; they do not identify whether events were considered related to treatment. The registry lists deaths as not reported in the record.

For other adverse events, the registry lists 251 participants affected in the injection group and 216 in the placebo group, with risk sets of 258 and 256. These are aggregate figures, and the record does not provide a complete event-by-event account in the information summarized. The labels and counts should not be interpreted as a comparison of severity or causation without further detail.

The registry lists six serious-event terms, each reported as 0.4%: Diverticulitis, Influenza, Spinal cord infection, Breast cancer, Hip surgery and Vaginal operation. These terms describe reported events; the record does not establish that the study intervention caused them. The serious adverse event figures are descriptive and do not, by themselves, establish comparative safety.

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

The results describe how the randomized groups compared on registry-defined outcomes at the specified follow-up. For the primary endpoint, the reported response proportion was higher in the deoxycholic acid injection group than in the placebo group, and the sponsor’s risk-ratio interval was above the value representing equal response proportions. The posted secondary comparisons were also directionally consistent, though they have their own definitions and limitations.

The primary endpoint is a threshold measure requiring improvement on both clinician- and patient-reported rating scales. It does not express the average amount of change, the full range of responses, or how an individual participant’s outcome might differ from the group result. The assessment timing also bounds the interpretation: the endpoint concerns the stated follow-up after the last treatment, not an unreported longer-term period.

These statistics do not establish that every participant benefited, that the result applies to people outside the enrolled population, or that the same results would occur under different treatment schedules or settings. They also do not answer all questions about safety, durability, or how participants valued the changes. The registry does not report enough detail to evaluate all design and analysis assumptions independently.

A statistically small p-value does not mean that the result is free from bias or that its practical significance is settled. The confidence interval captures sampling uncertainty under the reported analysis, not every form of uncertainty. Missing-data assumptions, multiplicity, outcome measurement and unreported analysis details remain relevant to interpretation.

The findings should be understood as statistical evidence from a particular randomized, double-blind, placebo-controlled study, not as individualized medical advice. The registry record gives a bounded account of outcomes and comparisons; it does not resolve decisions for a particular person or establish conclusions beyond the measures and timeframe it reports.

18. Why This Trial Matters Statistically

This trial is statistically informative because its primary outcome combines two perspectives on submental fullness: an investigator rating and a participant rating. Requiring improvement on both makes the endpoint more specific than a response on either scale alone. It also means that the reported percentage answers a precise threshold question, which should be kept in view when interpreting the result.

The randomized, double-blind, placebo-controlled, parallel-group design provides a structured comparison between the intervention and a placebo regimen. The posted primary result includes both arm response proportions and a sponsor-reported risk ratio with a confidence interval and p-value. Considering the absolute group proportions alongside the relative comparison helps readers distinguish how common the response was in each arm from how the proportions relate to one another.

The record also illustrates why analysis method matters. The sponsor’s reported Cochran-Mantel-Haenszel analysis and an unadjusted recalculation are not identical procedures or measures. Clear separation of the sponsor analysis from recalculated summary-statistic comparisons helps avoid treating a convenient calculation as though it were the original trial analysis.

Finally, the registry contains secondary outcomes, a stated multiple-imputation approach for missing primary values, and adverse-event summaries, but leaves important methodological details unreported. That combination shows why statistical interpretation requires attention not just to p-values, but also to outcome definitions, precision, missing data, multiplicity and the limits of registry reporting. The result is most useful when read as a defined comparison with a defined follow-up, rather than as a universal or complete account of every possible outcome.

19. Limitations

The registry record does not report the original sample-size justification or the assumptions used to design the trial. The planning illustrations based on observed effects cannot fill that gap. Nor does the record provide the full protocol or statistical analysis plan, so prespecification of all outcomes and methods cannot be independently assessed from the registry information.

For the primary outcome, missing values were imputed using multiple imputation, but the imputation model and assumptions are not reported. No sensitivity analyses for missing data are described in the record. The degree to which the result might change under other missing-data assumptions is therefore not established by the posted information.

The record does not report whether or how multiplicity was controlled for secondary outcomes. It also omits details needed to reproduce the reported Cochran-Mantel-Haenszel and ANCOVA analyses fully. In particular, the adjusted estimate and confidence interval for the ANCOVA result are not posted. The recalculated summaries do not substitute for those missing sponsor-analysis details.

The MRI response summaries include fewer participants than the primary summaries, but the registry does not state why. The primary outcome’s threshold definition also compresses potentially different degrees of improvement into a response category, and the posted result does not describe the distribution of individual changes. Finally, the follow-up assessment is at the specified time after treatment; longer-term outcomes are not reported in the record. These limitations constrain claims about durability, broader applicability and the full clinical meaning of the measured differences.

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23. Record Summary

The registry record describes a completed randomized, double-blind, placebo-controlled, parallel-group Phase 3 trial sponsored by Kythera Biopharmaceuticals. It enrolled 516 participants with moderate or severe submental fullness and compared deoxycholic acid injection with placebo. The listed study dates are 2012-03 for start and 2013-05 for primary completion.

The primary outcome was a composite 1-grade response on both clinician- and patient-reported submental fat rating scales. The sponsor reported a risk ratio of 2.983, with a 95% confidence interval from 2.311 to 3.849 and p < 0.001. Missing primary outcome values were handled using multiple imputation in the intent-to-treat population.

The registry also reports MRI response and patient-reported impact-scale outcomes, as well as serious adverse event summaries. It does not report several details needed for a full independent assessment, including the original sample-size justification, complete missing-data assumptions and multiplicity procedures.

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