Safety Study of Deoxycholic Acid for the Reduction of Localized Subcutaneous Fat in the Submental Area in Subjects 65 to 75 Years of Age: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Safety Study of Deoxycholic Acid for the Reduction of Localized Subcutaneous Fat in the Submental Area in Subjects 65 to 75 Years of Age (NCT02123134), a randomized phase 3 study. The primary outcome is Percentage of Participants With at Least a 1-Grade Reduction (Improvement) at 12 Weeks From Last Treatment Based on Both the Clinician-Reported Submental Fat Rating Scale (CR-SMFRS) and Patient-Reported Submental Fat Rating Scale (PR-SMFRS) Assessments.

2. Clinical Question

3. Trial Design

This was a randomized, double-blind, parallel-group phase 3 study comparing ATX-101 with placebo. The registry record lists the study as completed, with 55 participants enrolled. The study began in 2014-04, and primary completion was recorded in 2015-08. The sponsor was Kythera Biopharmaceuticals. The registry record describes the objective as exploring the safety and efficacy of subcutaneous deoxycholic acid injections relative to placebo in participants aged 65 to 75 years.

In the ATX-101 group, participants received deoxycholic acid 2 mg/cm^2 in 0.2 mL subcutaneous injections. The protocol description allowed up to 10 mL in a treatment session, with sessions at intervals of approximately 1 month and no more than 6 treatments. The placebo group had the same stated injection volume, session limit, interval, and maximum number of treatments. Other details about treatment delivery or adherence are not reported in the registry record.

The primary outcome was assessed at 12 weeks after the last treatment. The registry timeframe also describes assessment from baseline and up to Week 32. The investigator rated the chin and neck area using the clinician-reported scale, while participants rated their own chin and neck area using the patient-reported scale. The registry record states that the primary result was based on both assessments. The record does not report the allocation procedure, details of how blinding was maintained, or the original sample-size justification.

Although 55 participants were enrolled, the primary outcome lists 25 participants in the ATX-101 group and 24 in the placebo group. The registry record does not explain the difference between the enrollment total and these outcome denominators, or report participant flow and reasons for any missing outcome data.

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:

Analysis population for the primary outcome, as defined in the registry: Intent-to treat (ITT) population included all randomized participants, whether or not they received the assigned study drug.

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 Percentage of Participants With at Least a 1-Grade Reduction (Improvement) at 12 Weeks From Last Treatment Based on Both the Clinician-Reported Submental Fat Rating Scale (CR-SMFRS) and Patient-Reported Submental Fat Rating Scale (PR-SMFRS) Assessments, measured over Baseline and up to Week 32 (12 weeks after last treatment).

The primary endpoint is the percentage of participants with at least a 1-grade improvement at 12 weeks after the last treatment, based on both clinician and participant assessments. The clinician-rated Submental Fat Rating Scale and the patient-reported Submental Fat Rating Scale each use a 5-point scale. On the clinician scale, 0 means absent submental convexity and 4 means extreme submental convexity. On the patient scale, 0 means no chin fat at all and 4 means a very large amount of chin fat. Lower scores therefore represent less submental fat on each scale.

Using both ratings makes the endpoint a joint measure: the result is intended to reflect improvement identified by the investigator as well as improvement reported by the participant. It is a binary outcome for each participant—meeting the specified improvement criterion or not—and the group result is expressed as a percentage. This format is readily interpretable as the share of participants who met the endpoint, but it does not show the size of improvement beyond the 1-grade threshold. Nor does it convey the full distribution of scale scores or changes over time.

The record specifies the assessment time as 12 weeks after the last treatment and gives a broader timeframe of baseline and up to Week 32. Other details about endpoint handling, including how missing scale ratings were treated, are not reported in the registry record.

7. Results Posted in the Registry

• ATX-101 (Deoxycholic Acid) Injection: 68.0% (17/25) versus 25.0% (6/24) on control; risk difference 43.0 percentage points (95% CI 17.8 to 68.2), risk ratio 2.72 (1.29–5.72); unadjusted two-proportion z-test p = 0.003.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary result is a binary outcome summarized as a percentage: each participant either met the endpoint or did not. The endpoint required at least a 1-grade reduction on both the clinician-reported and patient-reported scales. The group percentages are therefore the number meeting that criterion divided by the group outcome denominator. This type of result is useful when the clinical question is about the proportion crossing a defined improvement threshold, although it discards information about the amount of change beyond that threshold.

What does the risk difference express?

The risk difference compares the endpoint probabilities in the two groups by subtracting one group probability from the other. It is expressed on the same probability scale as the percentages. Here, the listed risk difference is 0.43, using the ATX-101 group as the treatment group and placebo as the control. A value of zero would correspond to equal endpoint probabilities. The risk difference is an absolute comparison, unlike a ratio measure, and directly describes the separation between the group rates.

The record also lists ratio measures, including a risk ratio of 2.72 with a 95% confidence interval from 1.293 to 5.72, and an odds ratio of 6.375 with a 95% confidence interval from 1.828 to 22.23. These measures compare groups on relative scales, but their interpretation differs: the risk ratio compares probabilities, whereas the odds ratio compares odds. When an outcome is not rare, an odds ratio can appear farther from the null value than a risk ratio. The risk difference, risk ratio, and odds ratio answer related but distinct questions; they should not be treated as interchangeable.

How should the p-value be read?

The unadjusted p-value of 0.003 is associated with the comparison of the two group results. In general, a p-value assesses how compatible the observed data are with a specified null model, assuming the model and analysis conditions are appropriate. A small p-value is not the probability that the null hypothesis is true, and it does not quantify the magnitude or importance of an effect. It also does not account for multiple testing unless a suitable adjustment is made. Whether any adjustment was planned or used is not reported in the registry record.

Why do confidence intervals matter?

A confidence interval communicates uncertainty around an estimate. In repeated use of a valid interval procedure, the stated confidence level describes the long-run coverage of the intervals produced by that procedure. For an individual study, the interval indicates a range of effect estimates that are reasonably compatible with the data under the method's assumptions. It is not a guarantee about the true value. A narrow interval generally indicates greater precision than a wide interval, while both the point estimate and the interval are needed to understand the result.

The registry lists 95% confidence intervals for the group percentages and for the risk difference. The intervals for each group percentage describe uncertainty in each group's event rate; the risk-difference interval describes uncertainty in the between-group contrast. The two group intervals should not be used as a substitute for the interval on the risk difference, since the latter directly addresses the comparison.

What assumptions affect count-based comparisons?

For a binary outcome, the analysis treats participants' endpoint status as a count of events and non-events. In a simple comparison, each participant contributes an outcome, and the calculation relies on assumptions about how outcomes are sampled and how observations relate to one another. If outcomes vary more than a model assumes, that is over-dispersion: standard errors may be too small and intervals too narrow if the extra variability is ignored. This is a general statistical issue; the registry record does not report whether an over-dispersion assessment was relevant or performed for this trial.

The posted outcome is based on both clinician and patient ratings, but the record does not provide a detailed analysis specification, explain the handling of missing ratings, or describe adjustments for any baseline variables. Those choices can affect estimates and uncertainty. Details of the trial's statistical plan, including any interim analyses, are not reported in the registry record. Consequently, the reported comparison should be interpreted with the methods information that is actually recorded, rather than assuming unlisted modeling or adjustment decisions.

What can recalculation add?

A simple unadjusted recalculation from posted summary statistics can help readers understand a comparison, but it is not a replacement for a sponsor's full analysis when results differ. The posted results list the group counts, denominators, percentages, risk difference, and an unadjusted p-value; the discrepancy flag is false. No discrepancy between the posted comparison and a separate sponsor analysis is identified in the record. Details such as covariate adjustment or other analysis choices cannot be inferred from the summary figures alone.

10. Confidence Intervals and Precision

The ATX-101 group percentage is 68%, with a 95% confidence interval from 49.7% to 86.3%. The placebo group percentage is 25%, with a 95% confidence interval from 7.7% to 42.3%. These intervals show substantial uncertainty around each group's rate, which is expected when the outcome denominators are limited. The point estimates are useful summaries, but they should not be read as exact values for the broader population.

The comparison is more directly captured by the risk difference of 0.43, with a 95% confidence interval from 0.178 to 0.682. The range includes values reflecting a smaller or larger group separation than the point estimate, and its lower bound remains above zero. The interval communicates uncertainty in the contrast itself; comparing whether the separate group intervals overlap is not a substitute for assessing this contrast interval.

Precision depends on the amount of information in the data and on the variation in outcomes. Here, the primary outcome denominators are 25 and 24. The record lists 55 participants enrolled but does not explain the difference between enrollment and the denominators used for the primary result. The reason for any unavailable outcomes, and their treatment in the analysis, are not reported in the registry record. This limits the ability to assess how missing information may affect the precision or representativeness of the estimates.

A confidence interval does not capture every source of uncertainty. It reflects the statistical method used and its assumptions, not uncertainty arising from unreported design details, endpoint handling, or possible analysis choices. The registry record does not report a detailed statistical analysis plan. The intervals should therefore be read as precision measures for the posted estimates, not as a complete accounting of uncertainty about the study's design and conduct.

11. 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 illustrations based on the observed risk difference, not the trial's original sample-size calculation. They assume a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each planning scenario uses a stated fraction of the observed effect as the effect to detect. These are participants per arm, not total events. The entries are not observed power.

For planning around 100% of the observed effect, the illustration gives 20 participants per arm for 80% power and 27 participants per arm for 90% power. For planning around 75% of the observed effect, it gives 36 participants per arm for 80% power and 47 participants per arm for 90% power. For planning around 50% of the observed effect, it gives 77 participants per arm for 80% power and 103 participants per arm for 90% power.

In plain language, the 80% power column gives the estimated number per arm under the stated assumptions for a design with an 80% chance of detecting the specified effect if that effect is the true one and the model assumptions hold. The 90% power column uses the corresponding higher target probability. These are prospective planning concepts, not statements about the chance that this completed study found a real effect.

The pattern across scenarios reflects a general principle: smaller effects are harder to distinguish from random variation and therefore require more participants for the same target power. The registry record does not report the trial's original sample-size justification or design assumptions, so these planning illustrations should not be mistaken for the basis on which the study was designed.

12. 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 = 0.250; treatment proportion p₁ = 0.680; average p̄ = 0.465.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.7054 = 1.3825.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.6365 = 0.5357.
4. n = (1.3825 + 0.5357)² / (0.4300)² = 19.9, rounded up to 20 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 <- 0.25                          # control proportion
p1 <- 0.68                          # 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(2123134)
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 = 20 (80% power), 27 (90% power)
 75% of observed effect: n per arm = 36 (80% power), 47 (90% power)
 50% of observed effect: n per arm = 77 (80% power), 103 (90% power)
power.prop.test: 19.9 
Simulated power at n = 20 per arm: 0.786 (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.

13. Multiplicity, Missing Data and Analysis Populations

The registry record lists 7 outcome measures and no posted secondary outcome results. The listed primary endpoint combines clinician and patient assessments and is evaluated at the specified follow-up. However, a detailed hierarchy of outcomes, time points, or planned comparisons is not reported in the registry record. The record also does not report whether there were interim analyses or whether any multiplicity procedure was prespecified.

Multiplicity arises when several outcomes, time points, subgroups, or comparisons are tested. Conducting multiple tests can increase the chance of at least one apparently noteworthy result under a setting where none of the tested effects is present. Adjustments or a prespecified testing hierarchy can address this concern, but whether such approaches were planned or used in this study is not reported in the registry record. The p-value listed for the primary comparison is unadjusted, so it should not be described as adjusted for other testing.

The primary outcome population is identified as intent-to-treat and defined as all randomized participants, whether or not they received the assigned study drug. Yet the primary outcome denominators are 25 and 24, while total enrollment is 55. The record does not explain the difference, give participant flow by group, or state how missing outcome data were handled. It is therefore not possible to determine from the registry record whether all randomized participants contributed to the primary outcome analysis or what assumptions were used for unavailable ratings.

Missing outcome data can affect both the estimated percentages and their uncertainty, especially if participants without recorded assessments differ from those with observed assessments. This is a general concern, not a claim about what happened in this study. Without reasons for missingness and the analysis approach, the direction or size of any effect on the result cannot be established. Baseline-adjustment methods and other analysis details are also not reported in the registry record.

14. 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.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: urosepsis (3.8%).

The serious adverse event counts list 0 of 28 participants in the ATX-101 group and 1 of 26 in the placebo group. The registry record lists Urosepsis as a serious-event term at 3.8%. These counts describe the recorded serious adverse events in the groups; they do not by themselves establish whether an event was caused by study treatment. The listed number of deaths is 0 in each group.

The record also lists other adverse events for 28 of 28 participants in the ATX-101 group and 23 of 26 in the placebo group. Serious and other adverse event categories are distinct entries in the record, and the counts should not be combined. The registry record does not provide additional detail in these summary figures about event timing, severity beyond the serious classification, duration, or individual-level overlap among events. These summary counts are descriptive and do not constitute a full comparative safety analysis.

Because the groups and outcome denominators are limited, the absence or presence of a small number of recorded events should be interpreted cautiously. The registry record does not report a detailed safety analysis plan or additional safety results beyond those listed.

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

The posted primary result describes a higher percentage meeting the combined improvement criterion in the ATX-101 group than in the placebo group: 68% versus 25%. The risk difference is 0.43, with a 95% confidence interval from 0.178 to 0.682, and the unadjusted p-value is 0.003. These statistics describe the observed comparison and its uncertainty for the recorded endpoint, at 12 weeks after the last treatment.

The endpoint is specific: it requires at least a 1-grade improvement on both the clinician-reported and patient-reported scales. It does not report the degree of improvement beyond that threshold, the complete distribution of scale changes, or other measures of participant experience. The registry record also does not provide posted secondary outcome results, so this primary result should not be taken to represent every outcome the study may have considered.

The results do not establish how the comparison would apply to other age groups, populations, schedules, or settings. The study focused on participants aged 65 to 75 years, and the registry record does not report detailed characteristics of those enrolled. Differences between the total enrollment of 55 and the primary outcome denominators are not explained, and missing-data handling is not reported. These gaps limit assessment of how representative the outcome estimates are of all randomized participants.

The serious adverse event summaries are descriptive counts. They do not establish a causal relationship between an event and treatment, and they are not a complete account of all possible safety outcomes. Likewise, a p-value is not a measure of clinical importance, and statistical significance does not remove uncertainty or replace consideration of study design and data limitations. The registry record does not report the original sample-size justification, a detailed statistical analysis plan, or interim-analysis details.

16. Why This Trial Matters Statistically

This study illustrates how a clinical question can be translated into a defined binary endpoint: the percentage meeting a specified improvement threshold on both clinician- and participant-rated scales. The joint endpoint is statistically meaningful only in relation to that definition. A reader should distinguish it from improvement on one scale alone, from average score change, and from broader notions of benefit or experience.

The comparison also shows why an effect estimate and its uncertainty should be read together. The risk difference of 0.43 is a direct measure of the observed separation in group percentages, while its 95% confidence interval from 0.178 to 0.682 conveys the range of estimates compatible with the data under the calculation. The unadjusted p-value addresses a different question about compatibility with a no-difference model. None of these summaries alone describes every source of uncertainty or determines the importance of the result.

Outcome denominators and analysis populations are central to interpretation. The record names an intent-to-treat population but lists primary outcome denominators smaller than the enrollment total. Because participant flow and missing-data methods are not reported, readers cannot fully assess how the analyzed data relate to all randomized participants. This is a practical reminder that a stated analysis population and the denominators underlying results need to be considered together.

Finally, a completed study can have posted outcome results while still leaving important methods details unreported. The registry record does not give the original sample-size justification, multiplicity approach, or interim-analysis details. Planning illustrations based on an observed effect can aid understanding of future designs, but they do not reveal the study's original design rationale or its observed power.

17. 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.
• Participant counts were reconstructed from posted percentages and arm sizes, so small rounding differences are possible.

The trial enrolled 55 participants, but the primary outcome results list 25 in the ATX-101 group and 24 in the placebo group. The registry record does not explain the difference, provide participant flow, or describe why some enrolled participants are not represented in those denominators. Missing-data handling is not reported, so the effect of unavailable assessments cannot be evaluated from the record.

The registry record describes an intent-to-treat population, but it does not provide enough detail to confirm how that population was implemented in the reported endpoint analysis. It also does not report the original sample-size justification, the statistical analysis plan, any interim analyses, or whether multiplicity was addressed. These omissions constrain assessment of prespecification and the relationship between the listed unadjusted comparison and the full planned analysis.

The primary endpoint is a threshold-based combination of two rating scales. The posted percentage does not show the amount of improvement beyond the threshold, the distribution of ratings, or the individual contribution of each scale. The record lists 7 outcome measures but no posted secondary results, limiting the ability to assess outcomes beyond the primary measure.

The safety data are summary counts and do not report event timing, detailed severity, or additional context needed for a comprehensive safety assessment. The study's age range is 65 to 75 years, and the registry record does not provide detailed enrolled-participant characteristics. Generalizability beyond the population and treatment conditions described cannot be established from these summary results alone.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Safety Study of Deoxycholic Acid for the Reduction of Localized Subcutaneous Fat in the Submental Area in Subjects 65 to 75 Years of Age — NCT02123134.
• Registry record last updated 2020-02-17; status last verified 2020-01.
• Results first posted 2020-02-17.
• 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.

21. Record Summary

NCT02123134 is a completed randomized, double-blind, parallel-group phase 3 study sponsored by Kythera Biopharmaceuticals. It enrolled 55 participants and compared ATX-101 deoxycholic acid injections with placebo in participants aged 65 to 75 years. The study began in 2014-04, and primary completion was recorded in 2015-08.

The primary endpoint was the percentage with at least a 1-grade improvement on both clinician- and patient-reported submental fat scales at 12 weeks after the last treatment. The posted percentages were 68% for ATX-101 and 25% for placebo, with a risk difference of 0.43 and an unadjusted p-value of 0.003. The listed outcome denominators were 25 and 24. The registry record does not explain the difference between these denominators and total enrollment, or report detailed missing-data and analysis-plan information.