Low Level Laser Treatment (LLLT) and Lorcaserin for Weight Management: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Low Level Laser Treatment (LLLT) and Lorcaserin for Weight Management (NCT02129608), a randomized phase 3 study. The primary outcome is Change in Waist Circumference.

2. Clinical Question

3. Trial Design

The registry identifies this as a randomized, parallel-group study with no masking. It is also labelled PHASE3, while the brief summary calls it a feasibility pilot. These are both descriptions in the record; the rationale for the phase designation and the pilot label is not reported in the registry record. The sponsor is Mayo Clinic, and the overall status is completed.

The listed enrollment is 44. The posted arm data report 15 participants for LLLT, 14 for lorcaserin, and 15 for the combination. These are arm-specific figures; the record does not explain how they relate to the enrollment figure or describe any exclusions from the outcome analysis. The study began in 2014-06, with primary completion in 2015-12.

LLLT was scheduled once a week for 12 weeks. Lorcaserin was scheduled at 10 mg twice daily for 12 weeks, and the combination arm used both schedules. The primary endpoint timeframe is 3 months. The registry does not report the method used to generate the random sequence, the allocation-concealment process, or whether treatment adherence was assessed. Masking is explicitly listed as none.

The primary measure is change in waist circumference from baseline to 3 months. The record lists two outcome measures, but no secondary outcomes are posted. It also lists four analyses, including sponsor-reported t-tests for the combination versus LLLT and the combination versus lorcaserin. Further details on the analysis population, handling of missing measurements, and prespecified statistical plan 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 Change in Waist Circumference, measured over 3 months.

Change in waist circumference measures the difference between a participant’s baseline waist measurement and the measurement at 3 months. The unit is cm, and the registry reports group means with standard deviations. A negative mean change indicates that the measured waist circumference was lower at follow-up than at baseline; it does not, on its own, describe the spread of individual changes or establish why the measurement changed.

Waist circumference is used as a measure of central adiposity, consistent with the study’s stated focus on reducing central adiposity in overweight individuals. The registry’s brief summary also identifies abdominal subcutaneous fat as an interest of the pilot, but the posted primary endpoint is waist circumference, not a direct measurement of abdominal fat. The measurement therefore answers a more specific question about change in waist size over the stated timeframe.

The record reports mean changes of -2.3 cm for LLLT, -6.0 cm for lorcaserin, and -4.0 cm for the combination. The corresponding standard deviations are 4.1, 7.3, and 5.5. Those standard deviations describe variation in participant-level changes around each arm’s mean. The record does not report the measurement protocol, the primary analysis population, or whether any adjustment was made for baseline waist circumference.

7. Results Posted in the Registry

• Lorcaserin: mean -6.00 versus -2.30 on control; difference -3.70 (95% CI -8.05 to 0.65), standardized effect d = -0.63; z-test p = 0.096.
• LLLT and Lorcaserin: mean -4.00 versus -2.30 on control; difference -1.70 (95% CI -5.17 to 1.77), standardized effect d = -0.35; z-test p = 0.337.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is a continuous measure, and the registry describes it as a mean. For each arm, the posted result is the average change in waist circumference from baseline to 3 months. A mean gives a central summary of the observed changes. The standard deviation describes how dispersed those changes are around the mean; it is not the standard error and does not directly express the uncertainty of the group mean.

What does a mean difference express?

A mean difference compares the average change in one arm with the average change in a reference arm. The recalculated lorcaserin comparison uses LLLT as the reference and reports -3.7 cm. The combination-versus-LLLT recalculation reports -1.7 cm. The negative signs indicate that the mean change in the named comparison arm was more negative than the mean change in the reference arm. These are unadjusted comparisons of the posted summaries, not adjusted estimates from a model using individual-level data.

A difference in means is expressed in the endpoint’s original unit, cm. It is therefore directly tied to the waist-circumference scale. The recalculations also list standardized effect-size estimates, but those values do not replace the original-unit differences and are not needed to understand the central interpretation. The record does not describe a covariate-adjusted analysis, a baseline-adjusted model, or any other modeling approach for the primary endpoint.

What does the t-test do?

A t-test evaluates whether a difference in group means is large relative to the variability and uncertainty in the observations, under the assumptions of the test. The registry reports two-sided t-tests for the combination compared with LLLT and for the combination compared with lorcaserin. A two-sided test considers departures in either direction rather than only a difference in a specified direction. The sponsor-reported p-values are 0.398 and 0.436. The exact implementation and any assumptions checks are not reported in the registry record.

The recalculated comparisons use the posted means, standard deviations, and arm-specific sample sizes. They are described as unadjusted because they do not incorporate adjustment for other variables. Their p-values are 0.096 for lorcaserin versus LLLT and 0.337 for the combination versus LLLT. The registry does not report whether the sponsor’s analyses used the same variance assumptions, the same analysis population, or the same endpoint data as the recalculations.

Why do confidence intervals matter?

A confidence interval describes a range of estimates compatible with the data under the method used to construct it. It helps show the uncertainty around a point estimate rather than presenting the estimate as exact. The recalculated interval for lorcaserin versus LLLT runs from -8.051 to 0.650. The interval for the combination versus LLLT runs from -5.172 to 1.772. Both include zero, which represents no average difference. Their width indicates that the recalculated summaries do not pin down a narrow range of plausible differences.

The confidence level for these recalculated intervals is not reported in the registry record. The sponsor-reported tests do not include confidence intervals or comparison estimates. A p-value and an interval are related summaries of uncertainty, but they do not answer identical questions: the p-value assesses compatibility with a specified null under a test, while an interval presents a range of estimates under an interval procedure. Neither alone gives the probability that a treatment effect is true.

Why can variability affect the result?

The standard deviations are 4.1 cm for LLLT, 7.3 cm for lorcaserin, and 5.5 cm for the combination. They indicate variation in observed changes within each arm. Greater variability makes it harder to estimate an arm mean or a difference between means precisely, all else being equal. The group summaries do not reveal the shape of each arm’s distribution, whether there were unusual observations, or whether the t-test assumptions were checked.

Over-dispersion is a general concern when observed variability exceeds what a chosen statistical model assumes. In a continuous-outcome comparison, a variance assumption that understates the actual spread can make uncertainty appear too small. The posted standard deviations provide some information about spread, but the registry does not report a diagnostic assessment or a method for dealing with unusual variance patterns. The recalculations use pooled standard deviations as part of their comparison calculations; they should be read as simple summary-based estimates rather than a full reanalysis.

What do the results not establish?

The presence of randomized allocation does not, by itself, supply all details needed to assess risk of bias. The method of sequence generation and allocation concealment are not reported in the registry record, and masking is listed as none. The analysis population, missing-data strategy, and protocol for handling deviations from the treatment schedule are also not reported. These omissions limit assessment of how the outcome data were assembled and analyzed.

The registry identifies the study as PHASE3 and describes it as a feasibility pilot. It does not report the original sample-size justification or the original design assumptions. The separate planning illustrations use the observed effects and specified assumptions; they are not descriptions of the trial’s actual design. In general, a pilot’s observed effect estimate can be unstable, particularly when group sizes are small. A later study would need its own design assumptions and a prespecified analysis plan rather than treating these recalculations as definitive evidence.

10. Confidence Intervals and Precision

The recalculated mean difference for lorcaserin versus LLLT is -3.7 cm. The interval is reported from -8.051 to 0.650. Its span across zero means that the posted summaries do not rule out no average difference, and the interval also permits estimates in either direction. The upper endpoint is retained in the reported interval rather than rounded.

For the combination versus LLLT, the recalculated mean difference is -1.7 cm, with an interval from -5.172 to 1.772. This interval also includes zero and extends to values on both sides of the point estimate. The width is a practical indication that the estimate is not precise enough to isolate a narrow range of differences from the posted data.

The registry does not report the confidence level for these recalculated intervals. The sponsor’s own comparison results are given as two-sided t-test p-values, 0.398 for combination versus LLLT and 0.436 for combination versus lorcaserin, without corresponding estimates or intervals. Therefore, the precision of those sponsor-reported contrasts cannot be assessed from the reported p-values alone.

In general, an interval is more informative than a point estimate by itself because it communicates sampling uncertainty. It does not account for every possible source of uncertainty, such as missing outcome data, measurement error, or bias arising from study conduct. Those features are not fully described in the registry record. The intervals should consequently be read as uncertainty summaries for the recalculated comparisons, not as a complete measure of uncertainty about the study or its broader implications.

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 sample-size planning figures are participants per arm, not total events. They are planning illustrations based on the observed effect, not the original design calculations; the trial’s own sample-size justification and original design assumptions are not reported in the registry record. The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect targeted in each planning scenario is the stated fraction of the observed effect.

For lorcaserin compared with LLLT, planning for 100% of the observed effect gives 40 participants per arm for 80% power and 53 participants per arm for 90% power. Planning for 75% of the observed effect gives 71 participants per arm for 80% power and 94 participants per arm for 90% power. Planning for 50% of the observed effect gives 158 participants per arm for 80% power and 212 participants per arm for 90% power.

For the combination compared with LLLT, planning for 100% of the observed effect gives 128 participants per arm for 80% power and 172 participants per arm for 90% power. Planning for 75% of the observed effect gives 228 participants per arm for 80% power and 305 participants per arm for 90% power. Planning for 50% of the observed effect gives 512 participants per arm for 80% power and 685 participants per arm for 90% power.

The 80% power column describes the planned number per arm under which the assumed test would have an 80% chance of detecting the stated effect if that effect and the planning assumptions held. The 90% column describes the corresponding target at 90% power. Planning for a smaller fraction of the observed effect requires more participants, because a smaller difference is harder to distinguish from variability. These figures are not observed power.

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, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = -3.700; pooled standard deviation σ = 5.863.
2. n = 2 × (1.96 + 0.842)² × 5.863² / -3.700² = 39.4, rounded up to 40 participants per arm for 80% power.

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

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
delta <- -3.7                      # observed difference in means
sigma <- 5.86297232165089                     # pooled standard deviation
n_per_arm <- function(power, frac = 1) {
  ceiling(round(2 * (z_a + qnorm(power))^2 * sigma^2 / (delta * frac)^2, 6))
}
for (f in c(1, 0.75, 0.5))
  cat(sprintf("%3.0f%% of observed effect: n per arm = %s (80%% power), %s (90%% power)\n", 100 * f,
              format(n_per_arm(0.80, f), big.mark = ","), format(n_per_arm(0.90, f), big.mark = ",")))

# Check against R's built-in function (t-based, so very slightly larger)
cat("power.t.test:", round(power.t.test(delta = delta, sd = sigma, power = 0.80)$n, 1), "\n")

# Simulation: exact two-sample t-test using simulated means and variances
set.seed(2129608)
n    <- n_per_arm(0.80)
reps <- 20000
m_diff <- rnorm(reps, delta, sigma * sqrt(2 / n))             # difference in sample means
s2     <- sigma^2 * rchisq(reps, 2 * (n - 1)) / (2 * (n - 1))   # pooled sample variance
tstat  <- m_diff / sqrt(s2 * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(tstat) > qt(0.975, 2 * (n - 1))), reps))

Output from running the code

100% of observed effect: n per arm = 40 (80% power), 53 (90% power)
 75% of observed effect: n per arm = 71 (80% power), 94 (90% power)
 50% of observed effect: n per arm = 158 (80% power), 212 (90% power)
power.t.test: 40.4 
Simulated power at n = 40 per arm: 0.798 (20000 replicates)

The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

13. Analyses Reported by the Sponsor

The registry reports two sponsor analyses, each using a two-sided t-test. One compares the combination with LLLT and has a reported p-value of 0.398. The other compares the combination with lorcaserin and has a reported p-value of 0.436. No sponsor-reported mean differences or confidence intervals are included for these comparisons.

The unadjusted recalculations address a different set of contrasts: lorcaserin versus LLLT and the combination versus LLLT. They use the posted arm means, standard deviations, and sample sizes. Their mean differences are -3.7 cm and -1.7 cm, with p-values of 0.096 and 0.337, respectively. Because the contrasts differ, the sponsor’s p-values should not be read as direct checks of both recalculated comparisons.

The registry record does not state whether the sponsor used the same analysis population, variance assumptions, or handling of missing observations as the recalculation. For those reasons, the recalculations are best treated as simple unadjusted analyses of posted summaries. The sponsor’s own analyses take precedence when describing the analyses reported by the study; the recalculations offer a separate, limited way to inspect other contrasts from the posted summary data. The available record does not provide enough detail to reconcile any differences in methods or to reproduce the sponsor analyses fully.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists four analyses and two outcome measures, but only the primary waist-circumference outcome has posted numerical results in the record. No secondary outcome results are posted. The brief summary mentions preliminary interest in abdominal subcutaneous fat, inflammatory biomarkers, blood sugar, and cholesterol; numerical findings for those measures are not reported in the registry record.

Multiple comparisons can raise the chance of observing at least one apparently notable result by chance when several hypotheses are tested. Statistical approaches can address this issue by controlling an error rate, prioritizing outcomes, or defining a testing sequence in advance. The record does not report a multiplicity adjustment, a hierarchy of hypotheses, or a prespecified strategy for interpreting multiple analyses. The sponsor-reported comparisons and recalculated comparisons should therefore be read as the results of the particular contrasts described, without assuming a family-wise adjustment or another correction.

The record identifies randomization and no masking, but it does not report the random-sequence method or allocation concealment. It also does not specify the primary analysis population, whether analyses followed an intention-to-treat principle, or how participants with missing endpoint data were handled. The amount and pattern of missing outcome data are not reported in the registry record. These details matter because exclusions and missingness can affect which participants contribute to the estimated means and how representative those estimates are.

There is no reported description of protocol deviations, adherence analyses, imputation, or sensitivity analyses. The registry also does not report a prespecified statistical analysis plan or interim analyses. These absences do not show that such procedures were or were not used; they mean the relevant details are not available in the registry record. Consequently, the posted means and tests can be described, but the full analysis pathway and robustness to missing data cannot be assessed from the record.

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 0% reporting threshold.

Most frequent non-serious adverse event terms

The serious adverse event figures report zero affected participants in the LLLT group, zero in the lorcaserin group, and zero in the LLLT and lorcaserin group. The corresponding numbers at risk are 15, 14, and 15. These are the serious-event figures in the registry record; they do not establish that no other health events occurred or that the interventions are free of risk.

The record separately lists other adverse events affecting zero participants in LLLT, 2 in lorcaserin, and 4 in the combination. Those are not the serious adverse event counts and should not be conflated with them. The record does not give serious-event terms because no serious terms are listed. Death counts are not reported in the registry record.

Adverse-event summaries are limited by the observation period, how events were sought and classified, and the completeness of reporting. The registry gives the treatment schedules as 12 weeks, but the safety-data collection details are not reported. The figures should be read as counts recorded for the listed groups, not as comparative proof of safety or as a basis for treatment decisions.

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

The posted primary outcome describes average waist-circumference change from baseline to 3 months. The group means are negative in all arms: -2.3 cm with LLLT, -6.0 cm with lorcaserin, and -4.0 cm with the combination. The recalculated comparison of lorcaserin with LLLT estimates a difference of -3.7 cm, while the combination-versus-LLLT estimate is -1.7 cm. These are descriptive estimates from the posted summaries, with uncertainty that includes zero for both comparisons.

The data do not establish that the observed arm differences are precise. The recalculated intervals extend across zero, and the sponsor-reported comparisons provide p-values without estimated differences or intervals. Nor do these results establish that two arms are equivalent. Failure to identify a clear difference is not the same as evidence that the treatments have the same effect; an equivalence assessment would require a specified margin and appropriate design details, which are not reported in the registry record.

The study is described as a feasibility pilot, and the record does not report a sample-size justification. Its planning illustrations are based on the observed effects and should not be mistaken for the original design. The arm-specific sample sizes and the variability in the outcome are relevant to how precisely the means and differences can be estimated. The results can therefore be read as preliminary estimates, rather than as a definitive resolution of comparative effects.

The scope is also limited to the posted primary endpoint and its 3-month timeframe. The brief summary identifies other scientific interests, but no secondary outcome results are posted. The waist-circumference findings do not answer questions about abdominal subcutaneous fat, inflammatory biomarkers, blood sugar, cholesterol, durability beyond the stated timeframe, or outcomes not recorded in the registry. No medical conclusion or treatment recommendation follows from these registry results alone.

17. Why This Trial Matters Statistically

This record illustrates how a continuous clinical endpoint can be described at several levels: the arm means, the variability within arms, the difference between means, and the uncertainty around that difference. Reporting only the arm means would make the changes easy to compare visually but would not show how much participant-level variation accompanied them. Reporting the recalculated intervals makes clear that the estimated differences are imprecise.

It also illustrates why the sponsor’s reported analysis and an unadjusted recalculation should be kept distinct. The sponsor reports combination-versus-monotherapy tests, while the recalculations compare each of lorcaserin and the combination with LLLT. Those contrasts answer different questions. A p-value alone does not give the magnitude or precision of a difference, and analyses of different contrasts should not be treated as interchangeable.

The sample-size illustrations show the dependency between the effect chosen for planning and the number of participants needed under stated assumptions. Smaller target effects require larger planned numbers per arm. Because the calculations use observed effects from a feasibility pilot, they are planning illustrations rather than evidence about the trial’s achieved power or a substitute for a prespecified future design.

Finally, the record makes visible several reporting features that shape statistical interpretation: randomization is listed, masking is absent, and key information about missing data, analysis populations, multiplicity, and the original design assumptions is not reported. A result’s meaning depends not only on its point estimate and p-value, but also on the design and analysis details that determine what was measured and how the estimate should be understood.

18. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.

The registry record does not report the primary analysis population or explain how participants with missing waist measurements were handled. It gives arm-specific counts but does not describe exclusions, withdrawals, protocol deviations, or the completeness of outcome measurement. Without those details, it is difficult to assess whether the posted means represent all randomized participants or a subset with available data.

Masking is listed as none. The record does not describe safeguards against measurement or assessment bias, nor does it give the waist-measurement protocol. Randomization is listed, but the sequence-generation and allocation-concealment methods are not reported. These gaps limit assessment of possible bias in treatment assignment and outcome measurement.

The study is labelled PHASE3 while also being described in the summary as a feasibility pilot. The registry does not explain the relationship between those descriptions or report the original sample-size justification. The trial’s original design assumptions, including any intended effect size or power target, are not reported in the registry record. The posted planning calculations based on observed effects cannot fill that gap.

Only the primary waist-circumference results are posted, despite the stated interest in abdominal subcutaneous fat and in inflammatory biomarkers, blood sugar, and cholesterol. The record does not provide longer-term results beyond the 3-month endpoint timeframe. It also does not report a multiplicity plan, a detailed statistical analysis plan, or whether interim analyses occurred.

For the sponsor’s comparisons, the record supplies p-values but not estimates or confidence intervals. For the recalculated contrasts, the intervals are broad and their confidence level is not reported. Taken together, these reporting limitations mean that the results support a description of the posted summaries, but not a complete assessment of bias, robustness, or the full analysis plan.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Low Level Laser Treatment (LLLT) and Lorcaserin for Weight Management — NCT02129608.
• Registry record last updated 2016-11-22; status last verified 2016-09.
• Results first posted 2016-11-22.
• 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, unmasked, parallel study sponsored by Mayo Clinic and labelled PHASE3. It is also characterized as a feasibility pilot. The listed enrollment is 44, and the treatment schedules lasted 12 weeks. The primary endpoint is change in waist circumference from baseline to 3 months.

Posted mean changes are -2.3 cm for LLLT, -6.0 cm for lorcaserin, and -4.0 cm for the combination. Recalculated unadjusted comparisons with LLLT have mean differences of -3.7 cm for lorcaserin and -1.7 cm for the combination; both reported intervals include zero. Sponsor-reported two-sided t-test p-values are 0.398 for combination versus LLLT and 0.436 for combination versus lorcaserin.

The registry reports zero serious adverse events in each arm and separately lists other adverse events. Secondary results, the analysis population, missing-data procedures, and the original sample-size justification are not reported in the registry record.