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Fibromyalgia Phase 4 Continuous Endpoint NCT00673452

A Study Comparing Duloxetine and Placebo in the Treatment of Fibromyalgia: Complete Statistical Analysis

This analysis examines a randomized, quadruple-masked comparison of duloxetine and placebo for fibromyalgia, focusing on patients’ perceived improvement at week 12. It also explains the registry’s reported analysis, secondary outcomes, safety counts, and planning illustrations.

Trial start: 2008-06  ·  Enrollment: 530  ·  Sponsor: Eli Lilly and Company
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 A Study Comparing Duloxetine and Placebo in the Treatment of Fibromyalgia (NCT00673452), a randomized phase 4 study. The primary outcome is Patient's Global Impressions of Improvement (PGI-I) at Week 12.

530
Enrollment
Phase 4
2
Arms
In the primary outcome
-0.57
Mean difference
Duloxetine
-0.83–-0.31
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT00673452
PhasePhase 4
ConditionFibromyalgia
AllocationRandomized
Design modelParallel
MaskingQuadruple
Enrollment530
Arms in the primary outcome2
Lead sponsorEli Lilly and Company
Results postedYes

2. Clinical Question

Population

Adults aged 18 and older who met the study’s criteria for fibromyalgia were the intended population. The primary endpoint analysis population was defined as randomized patients with baseline PGI-S data and at least one post-baseline PGI-I assessment. The registry record does not report further eligibility details in the information available for this analysis.

Intervention

The intervention was flexible-dosed oral duloxetine, described as 60-120 mg daily for 12 weeks. The study summary says that all patients would receive duloxetine at some point, but the timing and details of that exposure are not reported in the registry record.

Comparator

The comparator was oral placebo, taken daily for 12 weeks. Participants were randomized to duloxetine or placebo. The registry identifies the study as parallel-group, but it does not provide further detail about the period during which each group received its assigned treatment.

Primary question

At week 12, did the average patient-rated impression of improvement differ between the duloxetine and placebo groups? The PGI-I scale ranges from 1, very much improved, to 7, very much worse; 4 means no change. Consequently, a lower group mean represents a more favorable reported impression on this scale. The statistical comparison describes the observed group contrast, not a guarantee of an individual patient’s experience.

3. Trial Design

The registry describes a Phase 4, randomized, quadruple-masked, parallel-group study comparing flexible-dosed duloxetine with placebo in people with fibromyalgia. Enrollment is listed as 530. The study status is completed, with a start date of 2008-06 and primary completion in 2009-04. Eli Lilly and Company is listed as sponsor.

The registered treatment descriptions specify oral duloxetine at 60-120 mg daily and oral placebo daily, each for 12 weeks. The study summary also says that all patients would receive duloxetine at some point. How that exposure was arranged, including its timing relative to the randomized comparison, is not reported in the registry record. The meaning of quadruple masking for specific roles is likewise not reported in the registry record.

The primary outcome was the Patient’s Global Impressions of Improvement score at week 12. The reported primary analysis population required baseline PGI-S and at least one post-baseline PGI-I measurement. The arm counts associated with the primary endpoint are 245 for duloxetine and 255 for placebo; these endpoint counts are not the same thing as the enrollment figure, and the registry record does not explain the difference.

The registry lists 15 outcome measures and 14 secondary outcomes. These include measures of pain, fatigue, depression, anxiety, global severity, health status, functioning, and mood, among others. Results for several secondary measures are included in the posted information, but the analysis plan, the hierarchy among outcomes, and the intended multiplicity strategy 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.

Before assignment: All patients were on duloxetine in the continuation phase. The continuation phase was for exploratory purpose only, and the results will not be presented further.

Acute Double-Blind Phase

StageDuloxetinePlacebo
STARTED263267
COMPLETED176187
NOT COMPLETED8780

Reasons for not completing this period:

ReasonDuloxetinePlacebo
Adverse Event4124
Lack of Efficacy914
Lost to Follow-up1619
Physician Decision06
Protocol Violation53
Sponsor Decision01
Withdrawal by Subject1613

Continuation Double-Blind Phase

StageDuloxetinePlacebo
STARTED176187
COMPLETED151153
NOT COMPLETED2534

Reasons for not completing this period:

ReasonDuloxetinePlacebo
Adverse Event513
Withdrawal by Subject95
Lost to Follow-up45
Lack of Efficacy25
Protocol Violation23
Sponsor Decision03
Physician Decision20
Death - Cervical vertebral fracture10

Analysis population for the primary outcome, as defined in the registry: Number of randomized patients with baseline PGI-S and at least one post-baseline PGI-I data.

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.

CharacteristicUnitDuloxetinePlaceboTotal
Participants analysed263267530
Age Continuousyears50.74 (SD 11.26)49.62 (SD 10.84)50.18 (SD 11.05)
Sex: Female, Male: FemaleParticipants244250494
Sex: Female, Male: MaleParticipants191736
Race/Ethnicity, Customized: Caucasianparticipants204206410
Race/Ethnicity, Customized: Hispanicparticipants374683
Race/Ethnicity, Customized: Other - Not Specifiedparticipants221537
Region of Enrollment: United Statesparticipants263267530
Alcohol Consumption: Yesparticipants8990179
Alcohol Consumption: Noparticipants174177351
Generalized Anxiety Disorder (GAD) Status: Yesparticipants192443
Generalized Anxiety Disorder (GAD) Status: Noparticipants244243487
Major Depressive Disorder (MDD) Status: Yesparticipants445397
Major Depressive Disorder (MDD) Status: Noparticipants219214433
Tobacco Use: Yesparticipants574299
Tobacco Use: Noparticipants206225431
Beck Anxiety Inventory (BAI) Total Scoreunits on a scale12.83 (SD 9.28)13.18 (SD 9.77)13.00 (SD 9.52)
Beck Depression Inventory II (BDI-II) Total Scoreunits on a scale16.16 (SD 10.43)16.20 (SD 10.35)16.18 (SD 10.38)
Brief Pain Inventory (BPI) Average Pain Scoreunits on a scale6.45 (SD 1.54)6.46 (SD 1.62)6.45 (SD 1.58)
Heightcentimeters (cm)163.00 (SD 8.38)163.75 (SD 8.48)163.38 (SD 8.43)
Likert Scale Rating of Mood, Anxiety, Sleep, Pain, and Stiffness: Anxietyunits on a scale3.68 (SD 2.81)4.08 (SD 2.90)3.88 (SD 2.86)
Likert Scale Rating of Mood, Anxiety, Sleep, Pain, and Stiffness: Moodunits on a scale3.78 (SD 2.76)4.04 (SD 2.77)3.91 (SD 2.77)
Likert Scale Rating of Mood, Anxiety, Sleep, Pain, and Stiffness: Painunits on a scale7.25 (SD 1.87)7.45 (SD 1.83)7.35 (SD 1.85)
Likert Scale Rating of Mood, Anxiety, Sleep, Pain, and Stiffness: Sleepunits on a scale6.74 (SD 2.56)6.81 (SD 2.67)6.78 (SD 2.62)
Likert Scale Rating of Mood, Anxiety, Sleep, Pain, and Stiffness: Stiffnessunits on a scale7.02 (SD 2.00)7.12 (SD 1.84)7.07 (SD 1.92)
Massachusetts General Hospital Cognitive and Physical Functioning Questionnaire (MGH-CPFQ) Totalunits on a scale26.71 (SD 6.33)26.63 (SD 6.29)26.67 (SD 6.30)

6. Primary Endpoint

The registry lists the primary outcome as Patient's Global Impressions of Improvement (PGI-I) at Week 12, measured over 12 weeks.

ElementRegistry entry
Result typeLeast Squares Mean
Measure of spreadStandard Error
Unitunits on a scale
Endpoint classificationContinuous Endpoint

The primary endpoint is the Patient’s Global Impressions of Improvement (PGI-I) at week 12. It is a patient-rated measure of perceived symptom change. The scale runs from 1, very much improved, through 4, no change, to 7, very much worse. It therefore asks patients for an overall judgment of how their condition has changed, rather than measuring a single symptom or a laboratory quantity.

A patient-rated global measure can capture an overall impression that may incorporate several aspects of the experience of illness. It is useful for asking whether participants perceive improvement, while remaining distinct from measures focused on pain, fatigue, mood, or function. As a continuous endpoint in this registry analysis, the reported group values are least-squares means, with standard errors. A group average summarizes responses but does not show how responses were distributed among individual participants.

The registry defines the primary analysis population as randomized patients with baseline PGI-S and at least one post-baseline PGI-I assessment. This definition makes clear that the endpoint result is based on participants with the specified measurements, rather than necessarily every randomized participant. Details of how missing assessments were handled beyond this population definition are not reported in the registry record.

Because lower PGI-I scores indicate a more favorable perceived change, the direction of the mean contrast can be interpreted using the scale anchors. The score remains a patient-reported measure; the group contrast alone does not establish why participants reported their impressions or whether the same pattern applies to every participant.

7. Results Posted in the Registry

Mean difference: Duloxetine

-0.57

95% CI: -0.83 to -0.31

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals2.52.73.03.23.43.6Duloxetine (n=245)Placebo (n=255)units on a scale (95% CI)
Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Duloxetine-0.90-0.71-0.51-0.32-0.130.07mean difference 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
Change From Baseline in Beck Depression Inventory-II (BDI-II) at 12 Week EndpointContinuous EndpointMean difference-1.90 (-3.36 to -0.44)282 per arm
Change From Baseline in Clinical Global Impressions of Severity (CGI-S) at 12 Week EndpointContinuous EndpointMean difference-0.34 (-0.53 to -0.15)156 per arm
Change From Baseline in Beck Anxiety Inventory (BAI) at 12 Week EndpointContinuous EndpointMean difference0.08 (-1.20 to 1.36)119,893 per arm

Change From Baseline in Beck Depression Inventory-II (BDI-II) at 12 Week Endpoint

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Duloxetine-3.62-2.85-2.07-1.29-0.510.27mean difference vs control (95% CI)

Change From Baseline in Clinical Global Impressions of Severity (CGI-S) at 12 Week Endpoint

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Duloxetine-0.58-0.45-0.33-0.21-0.080.04mean difference vs control (95% CI)

Change From Baseline in Beck Anxiety Inventory (BAI) at 12 Week Endpoint

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Duloxetine-1.40-0.81-0.220.380.971.56mean difference vs control (95% CI)

The registry lists 14 secondary outcomes, spanning measures of depression, global severity, anxiety, pain, fatigue, health status, functioning, and other symptom domains. Among the secondary outcomes with numerical results described in this analysis, the pattern is not uniform: some contrasts are in the direction of lower scores for duloxetine, while another is close to no mean difference. This variation is a reminder that a primary endpoint result does not imply the same pattern across every measured domain.

These outcomes can add context by showing whether the primary patient-rated impression is accompanied by changes in related measures. They are not substitutes for the primary endpoint, and they address different constructs. The specific secondary comparisons and their sponsor-reported analyses are reported with their respective results; interpreting them together requires attention to their scales, analysis populations, and methods rather than treating all outcomes as interchangeable evidence.

Unadjusted secondary results carry less weight when many outcomes are examined. In general, testing multiple outcomes creates more opportunities for apparently notable results even when no corresponding effects exist. Adjustments or a prespecified hierarchy can address this concern, but the multiplicity strategy and analysis hierarchy are not reported in the registry record. Consequently, isolated secondary p-values should be treated as exploratory context unless the trial’s planned approach to multiple testing is known.

The registry record does not report a complete interpretive framework for the secondary outcomes, such as which were confirmatory or how missing observations were handled for each measure. The secondary pattern can therefore inform a cautious reading of breadth and consistency, but it does not by itself establish a comprehensive effect across symptoms or functioning.

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

9. Statistical Interpretation

Clinical Biostats interpretation

At week 12, the posted least-squares mean PGI-I was 2.79 for duloxetine and 3.36 for placebo. Since 1 means very much improved and 7 means very much worse, these group averages lie on the favorable side of the scale’s no-change anchor of 4. The mean difference, expressed as duloxetine minus placebo, is -0.57. Its negative direction indicates a lower average score in the duloxetine group, consistent with a more favorable average patient impression on this measure.

The simple unadjusted re-calculation from the posted summary statistics gives a 95% confidence interval from -0.834 to -0.306 and p < 0.001. The interval is entirely below zero, so the re-calculated contrast is inconsistent with no mean difference under the assumptions of that calculation. The interval also conveys uncertainty about the size of the contrast; it does not say that every participant experienced improvement, nor does it describe the full distribution of scores.

The registry’s own primary analysis is identified as a Mixed Models Analysis, with p < 0.001. The registry does not report an estimate or confidence interval for that analysis in the information. The re-calculated estimate and interval are therefore a separate, unadjusted summary-based analysis, not a replacement for the sponsor’s model. The registry-reported test and the re-calculated contrast point in the same general direction, but their methods and reported quantities differ.

The endpoint analysis includes 245 duloxetine participants and 255 placebo participants. The primary population definition required baseline PGI-S and at least one post-baseline PGI-I measurement. The registry record does not report why these counts differ from enrollment, the amount or pattern of missing data, or the details of the mixed-model specification. Such details matter when interpreting how a model uses repeated observations and how results may depend on incomplete follow-up.

The result is specific to a patient-rated global improvement score at week 12 in this trial. It should not be read as a direct estimate of change in every symptom assessed, as a measure of long-term outcomes, or as an individual prediction. Nor does a small p-value quantify the importance of the observed difference. Interpretation requires considering the scale, the uncertainty interval, the analysis population, and the registry’s limited reporting of model and missing-data details.

10. Statistical Methods Explained

The primary endpoint is continuous: each participant’s PGI-I is a score on a 7-point scale, and the registry reports a group least-squares mean for each arm. The primary comparison is between duloxetine and placebo at week 12. Several statistical quantities help distinguish the estimated group contrast, its uncertainty, and the evidence against a zero contrast.

What does the mean difference describe?

The arm means are 2.79 for duloxetine and 3.36 for placebo. The mean difference is -0.57, defined in the re-calculation as the duloxetine mean minus the placebo mean. A negative value means the duloxetine group’s average score is lower. Because lower PGI-I scores correspond to more favorable perceived improvement, the direction is favorable on this scale. A difference in group means does not imply that every person in one arm had a lower score than every person in the other arm.

The reported arm summaries are least-squares means rather than simple raw averages. Least-squares means generally represent model-based averages, but the registry record does not give the full model specification for this primary result. The sample counts associated with the arm summaries are 245 and 255. The posted standard errors are 0.1 and 0.09, respectively. A standard error describes the statistical uncertainty of an estimated mean, not the spread of individual participant scores.

How should the confidence interval be read?

The re-calculated 95% confidence interval for the mean difference runs from -0.834 to -0.306. In general, a confidence interval is a range of values compatible with the data and the method used, under that method’s assumptions. Here, both endpoints are below zero. This indicates that the simple summary-based interval does not include a zero mean difference. It also shows that the re-calculated estimate is not exact: a range of negative contrasts remains compatible with the calculation.

The interval is derived from posted summary statistics, not from the registry’s mixed-model output. Its construction uses an approximate pooled standard deviation reconstructed from the arm standard errors; the underlying standard deviation is therefore marked as approximate. This makes the interval useful as a transparent, unadjusted re-calculation, but it should not be mistaken for the sponsor’s model-based interval, which is not reported in the registry record.

What does the p-value add?

The re-calculated p-value is p < 0.001. In general, a p-value describes how incompatible the observed data, or more extreme data, would be with a specified null model in which the mean contrast is zero. It is not the probability that the null hypothesis is true, and it does not measure the probability that the result happened by chance in an everyday sense. It also does not quantify the size or practical importance of the difference.

The sponsor’s reported primary method is Mixed Models Analysis, with p < 0.001. The record does not report the model’s estimate, confidence interval, covariates, covariance structure, or missing-data assumptions. The re-calculated p-value and interval are therefore not equivalent to the reported model test. They are calculated from posted group summaries using a simpler, unadjusted approach. General statistical practice distinguishes these analyses because a model can account for features of the data that a summary-based comparison does not, but the exact role of such features in this trial is not reported.

Why can over-dispersion matter?

General explanation: over-dispersion means that observed variation is greater than a chosen statistical model expects. If a model assumes less variation than is present, its standard errors can be too small and its confidence intervals too narrow. That concern is especially relevant for outcomes whose variability is not well described by the assumed distribution. The primary measure is a bounded rating scale, and the registry reports a continuous-measure analysis. Whether the sponsor assessed distributional assumptions or used any adjustment for them is not reported in the registry record. The re-calculation uses an approximate pooled standard deviation and does not establish that all model assumptions hold.

How do secondary analyses fit?

The secondary outcomes include continuous changes from baseline, including depression, global severity, and anxiety measures. For the reported comparisons, the registry gives ANCOVA results and the re-calculation gives unadjusted mean contrasts. In general, ANCOVA compares outcomes while accounting for specified covariates, often including baseline values; the covariates used in these analyses are not reported in the registry record. The sponsor’s reported ANCOVA estimates and p-values are distinct from the simple summary-based calculations. Secondary tests also raise the issue of multiplicity: when many outcomes are tested, the chance of at least one apparently notable result can increase. Whether and how the trial addressed that issue is not reported in the registry record.

The listed primary analysis population requires baseline PGI-S and at least one post-baseline PGI-I observation. This is an eligibility definition for the analysis, not a complete account of missing-data handling. The registry record does not report whether missing values were imputed, how repeated measurements were incorporated, or whether sensitivity analyses were conducted. Those omissions limit independent assessment of robustness, while leaving the reported primary test and the separate re-calculation as distinct pieces of statistical evidence.

11. Confidence Intervals and Precision

The re-calculated primary mean difference is -0.57, with a 95% confidence interval from -0.834 to -0.306. The whole interval is below zero, so the summary-based calculation supports a negative contrast. On the PGI-I scale, that direction corresponds to a lower, more favorable average impression in the duloxetine group. The interval’s width also matters: it indicates that the data do not identify one exact value for the difference, even though the possible values in this calculation share the same direction.

A confidence interval is not a range containing a fixed proportion of individual participant scores. It describes uncertainty about an estimated quantity under a statistical method and its assumptions. It does not show the spread of responses, the proportion of participants who improved, or the probability that the true difference lies within the particular interval. Those questions require other summaries or analyses, which are not reported for the primary endpoint in the registry record.

The interval is a simple unadjusted re-calculation from the posted arm summaries, using an approximate pooled standard deviation. The registry’s mixed-model primary analysis reports p < 0.001 but does not report its estimate or confidence interval in the information. The confidence interval from the re-calculation should therefore not be attributed to the sponsor’s model. The registry record also does not provide enough detail about the mixed model or missing-data handling to assess how those choices affect precision.

Precision and statistical evidence are related but not identical to practical importance. The interval addresses uncertainty in the average contrast; the scale anchors provide context for its direction. The registry record does not give a threshold for a clinically important difference, so the interval alone cannot establish whether the contrast is important to patients. It also cannot describe variation in individual responses or the result at time points beyond week 12.

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 effect109146
75% of the observed effect194260
50% of the observed effect436584
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect1002005001,00040%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, two-sample comparison of means with the pooled standard deviation. Standard deviation was approximated from model-based standard errors, so treat it as rough. Calculated for the comparison: Duloxetine.

The sample-size figures are planning illustrations based on the observed effect, not the trial’s original design calculations. For this continuous outcome, figures are participants per arm, not total events. The planning assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. The assumed effect is the stated fraction of the observed effect. The original design assumptions, including any original target power or effect size, are not reported in the registry record.

The 80% power column gives the estimated participants per arm for a future study to have an 80% chance of detecting the assumed effect at the stated significance level, if the planning assumptions hold. The 90% column gives the corresponding planning figure for a 90% chance. These are design calculations for hypothetical future comparisons, not evidence about the probability that the completed trial’s result is correct.

The rows consider planning for 100%, 75%, and 50% of the observed effect. A smaller assumed effect is harder to distinguish from random variation, so the required number of participants per arm increases. The displayed figures should be read as conditional illustrations: changing the expected effect, analysis method, allocation, or other assumptions can change the planning requirements.

This is not observed power. It does not retrospectively measure the trial’s success or explain its p-value. The calculations use the observed contrast as their starting point, so they are particularly sensitive to how well that observed effect represents the effect a future study should expect. The registry record does not report the trial’s own sample-size justification or planned assumptions.

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 = 2 (z1−α/2 + z1−β)2 σ2 / Δ2

n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

  1. Observed difference Δ = -0.570; pooled standard deviation σ = 1.501.
  2. n = 2 × (1.96 + 0.842)2 × 1.5012 / -0.5702 = 108.9, rounded up to 109 participants per arm for 80% power.

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

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
delta <- -0.57                      # observed difference in means
sigma <- 1.50129595957391                     # 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(673452)
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 = 109 (80% power), 146 (90% power)
 75% of observed effect: n per arm = 194 (80% power), 260 (90% power)
 50% of observed effect: n per arm = 436 (80% power), 584 (90% power)
power.t.test: 109.9 
Simulated power at n = 109 per arm: 0.794 (20000 replicates)

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

14. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
Mixed Models Analysisnot reported< 0.001

The registry’s own primary result is a Mixed Models Analysis comparing the duloxetine and placebo groups, with p < 0.001. It does not report the model-based estimate or confidence interval for the primary outcome in the information available for this analysis. That reported test is the sponsor’s analysis and should be distinguished from the simple unadjusted re-calculation made from the posted arm summaries.

The re-calculation estimates a mean difference of -0.57, with a 95% confidence interval from -0.834 to -0.306 and p < 0.001. It uses the posted least-squares means and standard errors, with an approximate pooled standard deviation. It is not a reconstruction of the mixed model: the model details, including its covariates and handling of repeated or missing observations, are not reported in the registry record.

Both the registry-reported test and the re-calculation indicate evidence of a group difference, and the re-calculated direction is a lower PGI-I mean for duloxetine. Their agreement in direction does not make their estimates interchangeable. The sponsor’s result remains the trial’s reported analysis; the additional calculation is best understood as a transparent check based on available summary statistics, with its own assumptions and limitations.

15. Multiplicity, Missing Data and Analysis Populations

Multiplicity concerns arise because the registry lists 15 outcome measures, including 14 secondary outcomes, and reports multiple analyses. When many statistical tests are performed, the chance of at least one result appearing notable can rise even if all corresponding null hypotheses are true. A prespecified hierarchy, adjustment procedure, or distinction between confirmatory and exploratory outcomes can help readers interpret that family of tests. The multiplicity strategy is not reported in the registry record.

The primary outcome is identified separately as PGI-I at week 12, and the registry reports a Mixed Models Analysis with p < 0.001. The record does not say whether the primary endpoint was formally protected from other testing, whether secondary outcomes were adjusted, or whether the reported secondary analyses were prespecified. Without that information, the primary result and secondary findings should not be treated as having identical confirmatory status.

The primary analysis population includes randomized patients with baseline PGI-S and at least one post-baseline PGI-I observation. This definition identifies which participants qualified for that analysis, but it does not explain why some randomized participants may lack required data or how missing measurements were addressed. The registry record does not report imputation methods, assumptions about missingness, sensitivity analyses, or the extent and reasons for missing data.

These details matter because incomplete follow-up can affect both the population represented by an analysis and the uncertainty around its estimate. General statistical practice distinguishes analyses based on observed measurements from methods that model repeated data or impute missing values; their interpretation depends on assumptions. The sponsor’s primary method is described as mixed models, but its specification and missing-data assumptions are not reported. Thus, the available record supports description of the reported test and the stated analysis population, but not a full independent audit of multiplicity or missing-data handling.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Duloxetine12630.4%
Placebo62672.2%
Participants with at least one serious adverse event
Serious adverse events by armDuloxetine0.4%Placebo2.2%% 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 4% reporting threshold.

ArmParticipants affected of at risk
Duloxetine217 of 263
Placebo189 of 267

Most frequent serious adverse event terms

Event termOrgan systemDuloxetinePlacebo
Myocardial infarctionCardiac disorders0 of 2631 of 267
PancreatitisGastrointestinal disorders0 of 2631 of 267
Chest painGeneral disorders0 of 2631 of 267
Non-cardiac chest painGeneral disorders0 of 2631 of 267
Intervertebral disc protrusionMusculoskeletal and connective tissue disorders1 of 2630 of 267
Muscle spasmsMusculoskeletal and connective tissue disorders0 of 2631 of 267
Suicidal ideationPsychiatric disorders0 of 2631 of 267

Most frequent non-serious adverse event terms

Event termOrgan systemDuloxetinePlacebo
NauseaGastrointestinal disorders83 of 26326 of 267
HeadacheNervous system disorders45 of 26324 of 267
ConstipationGastrointestinal disorders35 of 26311 of 267
FatigueGeneral disorders25 of 26319 of 267
Dry mouthGastrointestinal disorders31 of 26312 of 267
InsomniaPsychiatric disorders24 of 26319 of 267
DizzinessNervous system disorders26 of 26314 of 267
DiarrhoeaGastrointestinal disorders27 of 26312 of 267
HyperhidrosisSkin and subcutaneous tissue disorders23 of 2634 of 267
Upper respiratory tract infectionInfections and infestations13 of 26313 of 267

Serious events with the highest arm-level rate: intervertebral disc protrusion (0.4%), myocardial infarction (0.4%), pancreatitis (0.4%), chest pain (0.4%), non-cardiac chest pain (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 reports serious adverse events among 263 participants at risk in the duloxetine group and 267 at risk in the placebo group. The serious adverse event counts are 1 and 6, respectively. These are counts within the registry’s stated at-risk groups; they should not be confused with the primary endpoint analysis counts or interpreted as a complete measure of safety.

For other adverse events, the registry reports 217 among 263 at risk in the duloxetine group and 189 among 267 at risk in the placebo group. The record lists intervertebral disc protrusion, myocardial infarction, pancreatitis, chest pain, non-cardiac chest pain, and muscle spasms among the top serious-event terms, each shown as 0.4%. The registry record does not report deaths in the adverse-event information.

These counts are descriptive. They do not establish that a treatment caused or prevented an event, and the event counts alone do not account for event timing, duration, severity beyond the serious classification, or differences in exposure. The registry record does not provide further details needed to assess those issues. Safety interpretation should therefore remain limited to the recorded counts and terms, rather than treating them as comparative causal estimates.

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

The posted primary outcome shows a lower average PGI-I score in the duloxetine group than in the placebo group at week 12. Since a score of 1 means very much improved, 4 means no change, and 7 means very much worse, the mean difference of -0.57 is in the direction of a more favorable average patient-rated impression for duloxetine. The re-calculated 95% confidence interval is entirely below zero, and the registry’s mixed-model analysis reports p < 0.001.

This is a group-level result on one patient-reported scale. It does not mean that every participant improved, that participants experienced the same degree of change, or that an individual can expect a particular outcome. Group averages can conceal substantial variation in responses. The registry record does not report the distribution of individual PGI-I scores or the proportion of participants in each response category.

The result is limited to the endpoint and time point assessed: PGI-I at week 12. It does not establish a longer-term pattern, address every symptom or functional outcome, or determine whether the difference meets a threshold for clinical importance. No clinically important difference threshold is reported in the registry record. A statistically clear contrast and a clinically important contrast are related questions, but they are not the same.

The study summary states that participants would receive duloxetine at some point, while the registry also describes randomized duloxetine and placebo arms and a parallel model. The timing and details of that exposure are not reported in the registry record, which limits interpretation of the comparator period. The available result should be read as a comparison between the registered randomized groups at the stated endpoint, not as a complete account of every phase of exposure.

Finally, the reported model details, multiplicity plan, and missing-data methods are limited. Those gaps do not erase the posted result, but they constrain how fully its robustness can be assessed from the registry record alone.

18. Why This Trial Matters Statistically

This trial illustrates why the statistical interpretation of a clinical result needs more than a p-value. The primary registry analysis reports p < 0.001, while the posted arm means and standard errors permit a separate, unadjusted estimate and confidence interval. Keeping those analyses distinct helps readers understand what the registry reported and what can be reconstructed from summary statistics without implying that the reconstruction reproduces the sponsor’s model.

The scale’s direction is also important. A negative mean difference might be confusing without knowing that lower PGI-I scores represent more favorable perceived improvement. Interpreting a contrast requires linking the sign of the estimate to the actual measurement scale and its anchors, rather than relying on statistical direction alone.

The record also demonstrates the difference between precision and importance. The confidence interval quantifies uncertainty in the estimated mean contrast under the re-calculation’s assumptions; it does not establish a threshold for meaningful change, describe individual responses, or determine long-term outcomes. Similarly, the planning illustrations are not retrospective evidence about the trial’s power. They show how assumed effects and design choices influence future sample-size requirements.

Finally, a primary result sits within a wider record of secondary measures, safety counts, analysis-population definitions, and reporting gaps. Multiplicity and missing-data methods affect how confidently findings across outcomes can be interpreted. Distinguishing what is reported from what is not reported supports a measured reading of the evidence without overstating the scope of any one analysis.

19. Limitations

The registry record gives limited detail about the primary mixed-model analysis. It reports the method and p-value, but not the model-based estimate, confidence interval, covariates, or covariance structure. The re-calculated estimate is based on posted summaries and an approximate pooled standard deviation; it is not a substitute for the missing model output.

The primary endpoint population is defined as randomized participants with baseline PGI-S and at least one post-baseline PGI-I observation. The record does not explain why endpoint counts differ from enrollment, report the extent or reasons for missing measurements, or describe sensitivity analyses. The stated mixed-model method does not by itself reveal the assumptions used to handle incomplete data.

The registry lists multiple secondary outcomes, but does not report the multiplicity strategy or the hierarchy of confirmatory and exploratory tests. This limits the weight that can be placed on individual secondary findings as evidence beyond the primary analysis. The record also does not identify a clinically important difference threshold for PGI-I, so the clinical importance of the mean contrast cannot be determined from the reported statistics alone.

The study summary says that all patients would receive duloxetine at some point, but the timing and details are not reported in the registry record. That limits understanding of the randomized placebo comparison over the full study course. The study’s reported treatment period is 12 weeks, so the posted endpoint does not establish longer-term outcomes.

Safety information is summarized as event counts and selected serious-event terms. Details about event timing, exposure, and further clinical context are not reported in the registry record. These limitations call for a focused interpretation of the posted group comparison rather than broad conclusions across outcomes, follow-up, or individual experience.

20. Related Tutorials

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23. Record Summary

The registry describes a completed Phase 4 randomized, quadruple-masked, parallel-group study of flexible-dosed oral duloxetine versus oral placebo in fibromyalgia. Enrollment is listed as 530. The primary endpoint was patient-rated PGI-I at week 12, with lower scores indicating more favorable perceived improvement.

The duloxetine and placebo least-squares means were 2.79 and 3.36. The summary-based mean difference was -0.57, with a 95% confidence interval from -0.834 to -0.306 and p < 0.001. The registry’s Mixed Models Analysis also reports p < 0.001, but its estimate and confidence interval are not reported in the registry record.

The record lists multiple secondary outcomes and adverse-event counts. Details of multiplicity, missing-data handling, and several analysis methods are not reported in the registry record, limiting independent assessment beyond the posted results.

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