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Major Depressive Disorder Phase 3 Continuous Endpoint NCT01185340

A Study in Participants With Major Depressive Disorder Who Are Partial Responders to Selective Serotonin Reuptake Inhibitor: Complete Statistical Analysis

This analysis examines a phase III randomized, double-blind comparison of adjunctive LY2216684 and placebo among participants with major depressive disorder who were partial responders to SSRI treatment. The primary result is the Week 8 change in MADRS total score, interpreted alongside the registry’s mixed-model analysis and secondary outcomes.

Trial start: 2011-03  ·  Enrollment: 1056  ·  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 in Participants With Major Depressive Disorder Who Are Partial Responders to Selective Serotonin Reuptake Inhibitor (NCT01185340), a randomized phase 3 study. The primary outcome is Change From Randomization to Week 8 in Montgomery-Asberg Depression Rating Scale (MADRS) Total Score.

1056
Enrollment
Phase 3
2
Arms
In the primary outcome
-0.24
Mean difference
LY2216684 + SSRI
-1.79–1.31
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT01185340
PhasePhase 3
ConditionMajor Depressive Disorder
AllocationRandomized
Design modelParallel
MaskingDouble
Enrollment1056
Arms in the primary outcome2
Lead sponsorEli Lilly and Company
Results postedYes

2. Clinical Question

Population

Participants with major depressive disorder who were partial responders to selective serotonin reuptake inhibitor (SSRI) treatment. The primary analysis population was randomized participants with non-missing values at randomization and at least one post-randomization value.

Intervention

LY2216684, given orally once daily at a flexible dose of 12 or 18 mg for 8 weeks, as an adjunct to an SSRI.

Comparator

Placebo, given once daily for 8 weeks as an adjunct to an SSRI.

Primary question

Did change from randomization to Week 8 in Montgomery-Asberg Depression Rating Scale (MADRS) total score differ between the LY2216684 + SSRI and placebo + SSRI groups?

The registry describes a placebo-controlled study of adjunctive treatment in people whose response to SSRI treatment was partial. The clinical question is therefore about the average change in depressive-symptom severity over the adjunctive-treatment period, not about LY2216684 used alone or as a replacement for an SSRI. The listed primary measure is a score change, rather than a count of participants reaching a threshold.

The posted arm estimates are least-squares means from a model that adjusts for treatment, investigator, visit, baseline score, treatment-by-visit, and baseline score-by-visit. A separate simple, unadjusted re-calculation compares the posted arm summaries. Those approaches answer related but not identical statistical questions: the registry’s mixed-model analysis is the sponsor’s reported analysis, while the re-calculation is a summary-statistic comparison and should not be treated as a substitute for the sponsor’s model.

3. Trial Design

This was a phase III, randomized, double-blind, parallel-group, placebo-controlled study sponsored by Eli Lilly and Company. The registry lists the condition as major depressive disorder and enrollment as 1056. The study start is recorded as 2011-03, primary completion as 2013-04, and status as completed.

The two randomized treatment groups were LY2216684 + SSRI and placebo + SSRI. The active-treatment description specifies a flexible oral dose of 12 or 18 mg once daily for 8 weeks; the comparator received oral placebo once daily for 8 weeks. Both are described as adjunctive to an SSRI. The arm descriptions state that, before entering the adjunctive-treatment phase, participants completed a 3-week confirmation phase involving placebo adjunctive to an SSRI. Further detail about that phase is not reported in the registry record.

Randomization and double masking are relevant to interpretation because they are design features intended to support a fair comparison and limit the influence of treatment knowledge. The registry does not report the randomization method, allocation-concealment procedures, or details of how masking was maintained. The parallel-group structure means the listed comparison is between participants assigned to the active adjunct and participants assigned to the placebo adjunct, rather than a crossover comparison within the same participant.

The registry’s enrollment figure describes the study record as a whole; it should not be read as the analysis count for the primary outcome. The primary endpoint entries list 225 participants for LY2216684 + SSRI and 217 for placebo + SSRI. The outcome population is defined as randomized participants with non-missing randomization values and at least one post-randomization value. Reasons that participants may not contribute to that analysis are not reported in the registry record.

The original protocol’s sample-size assumptions, including any design target or assumptions about the expected treatment difference, are not reported in the registry record. The sample-size illustrations based on the observed effect are separate planning calculations and do not describe the trial’s original design.

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: The first 3 weeks of the study was a double-blind Confirmation Phase during which participants continued to receive their SSRI with adjunctive placebo. If randomization criteria were met, participants were randomized to adjunctive LY2216684 or adjunctive placebo. If criteria were not met, participants continued on placebo to maintain the blind.

Confirmation (CF) Phase, 3 Weeks

StagePlacebo + SSRI (Pre-randomized Participants)LY2216684 + SSRI (Randomized Participants)Placebo + SSRI (Randomized Participants)Placebo + SSRI (Non-randomized Participants)
STARTED1056000
Entered Discontinuation (DC) Phase18000
COMPLETED968000
NOT COMPLETED88000

Reasons for not completing this period:

ReasonPlacebo + SSRI (Pre-randomized Participants)LY2216684 + SSRI (Randomized Participants)Placebo + SSRI (Randomized Participants)Placebo + SSRI (Non-randomized Participants)
Adverse Event24000
Lack of Efficacy6000
Lost to Follow-up5000
Physician Decision2000
Protocol Violation16000
Withdrawal by Subject32000
Sponsor Decision3000

Adjunctive Treatment (AT) Phase, 8 Weeks

StagePlacebo + SSRI (Pre-randomized Participants)LY2216684 + SSRI (Randomized Participants)Placebo + SSRI (Randomized Participants)Placebo + SSRI (Non-randomized Participants)
STARTED0230219519
Entered Discontinuation (DC) Phase0206204483
COMPLETED0195186458
NOT COMPLETED0353361

Reasons for not completing this period:

ReasonPlacebo + SSRI (Pre-randomized Participants)LY2216684 + SSRI (Randomized Participants)Placebo + SSRI (Randomized Participants)Placebo + SSRI (Non-randomized Participants)
Adverse Event013813
Lack of Efficacy0474
Lost to Follow-up0457
Physician Decision0101
Protocol Violation0525
Withdrawal by Subject08824
Sponsor Decision0037

Analysis population for the primary outcome, as defined in the registry: All randomized participants who have non-missing values at the time of randomization and at least one post-randomization value.

5. Baseline Characteristics

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

Population: Participants who completed the Confirmation (CF) Phase and were randomized to adjunctive LY2216684 or adjunctive placebo or who did not met randomization criteria and continued on placebo to maintain the blind.

CharacteristicUnitLY2216684 + SSRI (Randomized Participants)Placebo + SSRI (Randomized Participants)Placebo + SSRI (Non-randomized Participants)Total
Participants analysed230219519968
Age, Continuousyears48.29 (SD 11.90)48.44 (SD 11.39)47.39 (SD 12.68)47.84 (SD 12.21)
Sex: Female, Male: FemaleParticipants155145354654
Sex: Female, Male: MaleParticipants7574165314
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants19123162
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants164158370692
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants4749118214
Race (NIH/OMB): American Indian or Alaska NativeParticipants0033
Race (NIH/OMB): AsianParticipants2136
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants0000
Race (NIH/OMB): Black or African AmericanParticipants173153101
Race (NIH/OMB): WhiteParticipants207185457849
Race (NIH/OMB): More than one raceParticipants4228
Race (NIH/OMB): Unknown or Not ReportedParticipants0011
Region of Enrollment: United StatesParticipants9389195377
Region of Enrollment: BelgiumParticipants741324
Region of Enrollment: AustriaParticipants10102545
Region of Enrollment: AustraliaParticipants222084126
Region of Enrollment: GermanyParticipants586395216
Region of Enrollment: United KingdomParticipants19153064
Region of Enrollment: SwedenParticipants211877116

6. Primary Endpoint

The registry lists the primary outcome as Change From Randomization to Week 8 in Montgomery-Asberg Depression Rating Scale (MADRS) Total Score, measured over Randomization, 8 weeks.

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

The primary endpoint is change from randomization to Week 8 in MADRS total score. MADRS is a rating scale for severity of depressive mood symptoms. Its 10-item checklist rates each item on a scale from 0 to 6, producing a total score range from 0 to 60; lower scores indicate lower symptom severity. Change from randomization expresses how the score at follow-up differs from the randomization value.

A change score is useful for comparing average symptom trajectories over a defined follow-up period. The registry reports least-squares mean changes, rather than only raw averages. These model-adjusted estimates account for the listed treatment, investigator, visit, baseline, and interaction terms. The reported timeframe is randomization to 8 weeks.

The endpoint is a continuous measure, so the principal comparison concerns the difference in mean change between the randomized groups. It does not by itself describe how many participants improved, reached a particular score, or maintained a change over time. Those are distinct questions addressed by some of the listed secondary outcomes. The clinical importance of a particular score difference or threshold is not specified in the registry record.

The primary analysis population includes randomized participants with a non-missing value at randomization and at least one post-randomization value. This definition is narrower than simply referring to everyone enrolled, and the registry does not give further detail about how missing measurements were handled within the analysis.

7. Results Posted in the Registry

Mean difference: LY2216684 + SSRI

-0.24

95% CI: -1.79 to 1.31

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals-10.1-9.5-8.9-8.3-7.7-7.1LY2216684 + SSRI (n=225)Placebo + SSRI (n=217)units on a scale (95% CI)
Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)LY2216684 + SSRI-2.04-1.32-0.600.120.841.56mean 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 Randomization to Week 8 in Sheehan Disability Scale (SDS) Global Functional Impairment ScoreContinuous EndpointMean difference-0.12 (-1.44 to 1.20)52,373 per arm
Change From Randomization to Week 8 in Fatigue Associated With Depression (FAsD) Impact Subscale ScoreContinuous EndpointMean difference-0.10 (-0.28 to 0.08)1,416 per arm
Probability of Participants Achieving a Montgomery-Asberg Depression Rating Scale (MADRS) Total Score of Less Than or Equal to 10 at Week 8Continuous EndpointMean difference0.06 (-0.03 to 0.15)987 per arm

Change From Randomization to Week 8 in Sheehan Disability Scale (SDS) Global Functional Impairment Score

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)LY2216684 + SSRI-1.65-1.04-0.430.190.801.41mean difference vs control (95% CI)

Change From Randomization to Week 8 in Fatigue Associated With Depression (FAsD) Impact Subscale Score

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)LY2216684 + SSRI-0.31-0.23-0.14-0.060.030.11mean difference vs control (95% CI)

Probability of Participants Achieving a Montgomery-Asberg Depression Rating Scale (MADRS) Total Score of Less Than or Equal to 10 at Week 8

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)LY2216684 + SSRI-0.04-0.000.040.080.130.17mean difference vs control (95% CI)

The secondary outcomes cover several related but distinct domains: functional impairment, fatigue, symptom severity and thresholds, anxiety, depression, and MADRS items. The posted estimates do not present one uniform pattern of clear separation between the randomized groups. As with the primary result, the secondary comparisons should be read as estimates with uncertainty, rather than as a collection of definitive treatment conclusions.

These outcomes add context to the primary MADRS change endpoint, but they do not replace it. Some assess changes in continuous scores, while others describe probabilities or achievement of symptom thresholds. Their scales and interpretations differ, so apparent agreement or divergence across outcomes cannot be treated as a direct replication of the primary comparison. The registry lists 18 secondary outcomes, and only a subset have posted summary results in the record.

Unadjusted secondary results carry less weight when many outcomes are examined. General statistical context: testing many outcomes increases the chance that some comparisons appear notable by chance, even when there is no underlying difference. A multiplicity procedure can address this issue, but one is not reported in the registry record. The secondary outcomes are therefore most useful as supporting or exploratory information, interpreted with attention to their uncertainty and the primary result, rather than as independent proof of an effect.

The registry does not give a complete account of the prespecified hierarchy among secondary outcomes or identify a family-wise error-control strategy. Nor does it report enough detail to determine whether every listed secondary outcome was analyzed according to a prespecified plan. Those gaps make it difficult to distinguish confirmatory secondary findings from exploratory observations based on the registry record alone.

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

9. Statistical Interpretation

Clinical Biostats interpretation

The posted least-squares mean change in MADRS total score was -8.73 for LY2216684 + SSRI and -8.49 for placebo + SSRI. Because lower MADRS scores indicate lower symptom severity, negative changes indicate that the average score was lower at follow-up than at randomization in each group. The registry-reported mixed-model analysis gives p = 0.751 for the comparison.

A simple unadjusted re-calculation from the posted summaries estimates a mean difference of -0.24, with a 95% confidence interval from -1.792 to 1.312 and p = 0.762. The interval includes zero, so this re-calculation does not establish a clear difference between the group mean changes. It also spans values in either direction, meaning the summary estimate is not precise enough to rule out a range of possible differences. The sponsor’s reported result comes from its mixed-model analysis; the re-calculation uses posted group summaries and is not the same analysis.

The estimates are close in direction and size, but that observation is not proof that the treatments are equivalent. A failure to establish a difference is not the same as demonstrating that any difference is absent or clinically unimportant. The registry does not report an equivalence or non-inferiority objective, nor a margin defining an unimportant difference. No treatment-effect conclusion beyond the statistical comparison is warranted from these summaries alone.

Both groups’ estimates describe change during a study in which the comparator also received an SSRI. The comparison therefore concerns adding LY2216684 rather than placebo to SSRI treatment in the studied population. It cannot isolate an effect of SSRI treatment itself, and it does not directly address people who are not partial responders to SSRI treatment.

Statistical significance is not the only consideration in reading this result. The effect estimate describes the observed contrast, and its interval describes uncertainty around that estimate under the re-calculation. The registry’s p-value is from the sponsor’s adjusted model, while the recalculated p-value is unadjusted. Neither p-value conveys clinical importance on its own. A threshold for a clinically meaningful MADRS difference is not reported in the registry record.

The registry lists 18 secondary outcomes, including functional impairment, fatigue, symptom thresholds, anxiety, depression, and individual MADRS items. These provide additional outcome perspectives, but they do not change the definition of the primary endpoint. Secondary analyses should be interpreted in the context of their number, their analysis methods, and the uncertainty around each estimate. A multiplicity adjustment for those outcomes is not reported in the registry record.

10. Statistical Methods Explained

The trial used randomized allocation, double masking, and a parallel-group comparison. In general, randomization aims to make treatment groups comparable at the start, while masking can reduce the influence of knowledge of assignment on care, reporting, or assessment. These are general purposes of the design features; the registry does not provide operational detail about sequence generation, concealment, or masking procedures.

What does the primary model estimate?

The registry reports least-squares mean changes from a mixed-model repeated-measures analysis. A least-squares mean is a model-based estimate, adjusted for the factors included in the model, rather than an unadjusted arithmetic mean. The stated model adjusts for treatment, investigator, visit, baseline score, treatment-by-visit, and baseline score-by-visit. This allows the estimated treatment comparison to account for those modeled features of the data. The registry does not report additional model details, such as the covariance structure or degrees-of-freedom method.

Repeated-measures models are generally used when an outcome is measured at multiple visits. General statistical context: such models can use measurements across visits and account for their within-participant relationship. The registry names mixed model repeated measures, but its detailed assumptions and implementation are not reported in the registry record. In particular, the record does not state the missing-data assumptions used for the primary model or describe sensitivity analyses for departures from those assumptions.

How does the re-calculation differ?

The recalculated comparison uses the posted arm-level least-squares means and standard errors to form a simple unadjusted mean difference, confidence interval, and p-value. It is a summary-statistic re-calculation, not a reproduction of the sponsor’s mixed model. The pooled standard deviation used for the standardized effect is marked as approximate because it is inferred from the posted standard errors. That approximation and the absence of participant-level data limit what can be reconstructed independently.

The recalculated mean difference is -0.24, with a confidence interval from -1.792 to 1.312 and an unadjusted p-value of 0.762. The registry-reported mixed-model p-value is 0.751. These values arise from different calculations. The sponsor’s model result is the result reported by the registry; the unadjusted calculation is useful as a transparent check of the posted summaries, not as a replacement for the prespecified analysis. Whether the original protocol specified this exact model or additional analyses is not reported in the registry record.

What do standard errors and confidence intervals convey?

A standard error describes the estimated sampling uncertainty of a model-based mean. It is not the same as the spread of individual participant outcomes. A confidence interval expresses a range of estimates compatible with the data and the calculation’s assumptions; wider intervals indicate less precision. General statistical explanation: a confidence interval is not a guarantee that the true value lies within the interval, and it does not by itself identify clinical importance.

The posted primary estimates have standard errors of 0.55 for LY2216684 + SSRI and 0.57 for placebo + SSRI. The re-calculated interval concerns the difference between the group means, not the range of individual participant scores. The registry’s primary outcome entries do not include arm-specific confidence limits, and the comparison interval is a recalculated, unadjusted interval.

Why can over-dispersion matter?

General statistical context: over-dispersion occurs when observed variability is greater than a model assumes. It can make standard errors too small if the model does not account for the extra variability, which can make confidence intervals too narrow and tests too optimistic. The primary endpoint is continuous, and the registry does not report a specific over-dispersion assessment. This concept is relevant when interpreting statistical models generally, not evidence that over-dispersion occurred in this study.

What does the sample-size illustration assume?

The planning illustrations use a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. They consider effects set at the stated fractions of the observed effect. General statistical explanation: smaller effects are harder to distinguish from random variation and therefore require more participants for a given target power. The illustrations are planning calculations based on the observed effect, not observed power. The trial’s original sample-size justification and design assumptions are not reported in the registry record.

What is not specified?

The registry does not report the primary model’s detailed covariance specification, the handling of missing data, a multiplicity procedure, or the full prespecified statistical analysis plan. It also does not report whether interim analyses were planned or conducted. These omissions limit assessment of how the posted analysis relates to every planned analysis and how robust the findings are to alternative assumptions. They do not negate the reported estimates, but they constrain how completely the statistical analysis can be audited from the registry record.

11. Confidence Intervals and Precision

The recalculated primary mean difference is -0.24, and its 95% confidence interval extends from -1.792 to 1.312. The interval includes zero. Thus, the posted summary data are compatible with no difference in mean change as well as with differences in either direction under this unadjusted calculation. The point estimate alone should not be read as a precise estimate of the treatment contrast.

Confidence intervals express uncertainty in an estimate, conditional on the statistical method and its assumptions. They are not ranges containing most individual participant outcomes. Here, the interval is for the difference between group mean changes, not for the distribution of MADRS scores among participants. A confidence interval also does not say whether an estimate is clinically important; the registry does not state a threshold for clinical importance.

The recalculated interval is based on posted summary statistics and is not the interval from the sponsor’s mixed-model analysis. The registry reports the sponsor’s mixed-model p-value as 0.751 but does not provide a confidence interval for that comparison. The re-calculated p-value is 0.762. Differences between these values reflect the use of different analytical approaches and should not be interpreted as contradictory estimates of a single identical calculation.

Precision also depends on which participants contributed data and how missing values were handled. The registry defines the primary analysis population as randomized participants with non-missing randomization values and at least one post-randomization value, but detailed missing-data methods are not reported in the registry record. The posted interval should therefore be understood in the context of the stated re-calculation and its available summary information, not as a complete account of uncertainty under every possible analysis.

12. Planning a Similar Trial: Sample Size

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

Effect to detectParticipants per arm, 80% powerParticipants per arm, 90% power
100% of the observed effect18,87625,270
75% of the observed effect33,55744,923
50% of the observed effect75,503101,077
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect20,00050,000100,000200,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Treat these figures cautiously. The observed difference is imprecise: its confidence interval includes no difference at all. A sample size built on a noisy estimate can be far too small or too large, so the smaller-effect rows are the more cautious guide.
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: LY2216684 + SSRI.

The planning figures are participants per arm for the continuous and other non-time-to-event outcomes in this study; they are not total events. The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The calculations use the observed effect or a stated fraction of it as the effect to detect. They are planning illustrations, not observed power. The trial’s original sample-size assumptions are not reported in the registry record.

The 80% power column describes the number of participants per arm a hypothetical study would require, under those assumptions, to have an 80% chance of detecting the specified effect if that effect were real. The 90% power column gives the corresponding planning target for a 90% chance. These are prospective design concepts, not measures of how likely the observed result is to be true and not a retrospective assessment of the completed study.

Rows that plan for 100% of the observed effect use the full observed effect as the target; rows for 75% or 50% of the observed effect use smaller targets. Smaller effects need more participants to detect at the same power and significance level. The calculations are sensitive to the observed effect, so they should not be treated as a definitive sample-size recommendation or as evidence that the original trial was designed around these assumptions. For time-to-event outcomes, the stated convention is total events using the Schoenfeld method; the primary outcome is continuous.

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 = -0.240; pooled standard deviation σ = 8.322.
  2. n = 2 × (1.96 + 0.842)2 × 8.3222 / -0.2402 = 18,875.7, rounded up to 18,876 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 <- -0.24                      # observed difference in means
sigma <- 8.32230201981945                     # 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(1185340)
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 = 18,876 (80% power), 25,270 (90% power)
 75% of observed effect: n per arm = 33,557 (80% power), 44,923 (90% power)
 50% of observed effect: n per arm = 75,503 (80% power), 101,077 (90% power)
power.t.test: 18876.6 
Simulated power at n = 18,876 per arm: 0.799 (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 reported0.751

The registry reports the sponsor’s primary comparison as a mixed-model analysis with p = 0.751. The model-based least-squares means are -8.73 for LY2216684 + SSRI and -8.49 for placebo + SSRI. The model adjusts for treatment, investigator, visit, baseline score, treatment-by-visit, and baseline score-by-visit.

The separate re-calculation from the posted summaries estimates a mean difference of -0.24, with a 95% confidence interval from -1.792 to 1.312 and p = 0.762. This is an unadjusted calculation based on group summaries, whereas the sponsor’s result comes from the reported repeated-measures model. The values are therefore not identical tests. The recalculation is best read as a check of the posted summaries, not a replacement for the sponsor’s model-based analysis.

The registry does not report a numerical test statistic, confidence interval, or additional model details for the sponsor’s comparison. The sponsor’s full analysis plan and any sensitivity analyses are not reported in the registry record. The posted p-value alone should not be used to infer those missing details or to establish clinical importance.

15. Multiplicity, Missing Data and Analysis Populations

The registry identifies one primary outcome and lists 18 secondary outcomes. It reports a mixed-model analysis for the primary comparison, but a multiplicity adjustment for the secondary outcomes is not reported in the registry record. The record also does not specify whether the primary and secondary outcomes were organized into a testing hierarchy or whether any family of tests was controlled at a stated error rate.

General statistical context: when many outcomes are tested, the chance of at least one apparently unusual result can increase. Adjustment procedures or a prespecified testing sequence can help control that risk. Without a reported approach, unadjusted secondary p-values, if available, should be treated cautiously and should not be interpreted as though each arose from an isolated confirmatory test. The registry does not report a full statistical analysis plan, so it is not possible to determine from the record whether multiplicity was addressed elsewhere.

The primary analysis population is described as all randomized participants with non-missing values at randomization and at least one post-randomization value. This is the registry’s stated population definition; it does not establish that every randomized participant contributed to the primary analysis. The record does not report the number or reasons for missing outcome measurements, the detailed handling of those measurements, or sensitivity analyses for missing data.

General statistical context: missing-data methods rely on assumptions about why values are absent, and those assumptions can affect estimates. Mixed-model repeated-measures methods can incorporate observed repeated measurements, but their interpretation depends on model specification and missingness assumptions. The registry does not state those assumptions or describe checks of their robustness, so they cannot be evaluated from the record.

The registry also does not report whether interim analyses were planned or conducted, or whether any stopping rules were used. Those details, along with the original protocol’s statistical plan and sample-size justification, are not reported in the registry record. Their absence limits assessment of the full analysis process; it does not justify inferring that any particular procedure was or was not used.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Placebo + SSRI (Pre-randomized) - CF Phase910520.9%
LY2216684 + SSRI (Randomized) - AT Phase72283.1%
Placebo + SSRI (Randomized) - AT Phase72183.2%
Placebo + SSRI (Non-randomized) - AT Phase125192.3%
Placebo + SSRI (Pre-randomized) - DC Phase1185.6%
LY2216684 + SSRI (Randomized) - DC Phase22061.0%
Placebo + SSRI (Randomized) - DC Phase42022.0%
Placebo + SSRI (Non-randomized) - DC Phase44820.8%
Participants with at least one serious adverse event
Serious adverse events by armPlacebo + SSRI (Pre-randomize…0.9%LY2216684 + SSRI (Randomized)…3.1%Placebo + SSRI (Randomized) -…3.2%Placebo + SSRI (Non-randomize…2.3%Placebo + SSRI (Pre-randomize…5.6%LY2216684 + SSRI (Randomized)…1.0%Placebo + SSRI (Randomized) -…2.0%Placebo + SSRI (Non-randomize…0.8%% of participants with at least one serious adverse event

Other (non-serious) adverse events

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

ArmParticipants affected of at risk
Placebo + SSRI (Pre-randomized) - CF Phase270 of 1052
LY2216684 + SSRI (Randomized) - AT Phase87 of 228
Placebo + SSRI (Randomized) - AT Phase44 of 218
Placebo + SSRI (Non-randomized) - AT Phase128 of 519
Placebo + SSRI (Pre-randomized) - DC Phase5 of 18
LY2216684 + SSRI (Randomized) - DC Phase39 of 206

Most frequent serious adverse event terms

Event termOrgan systemPlacebo + SSRI (Pre-randomized) - CF PhaseLY2216684 + SSRI (Randomized) - AT PhasePlacebo + SSRI (Randomized) - AT PhasePlacebo + SSRI (Non-randomized) - AT PhasePlacebo + SSRI (Pre-randomized) - DC PhaseLY2216684 + SSRI (Randomized) - DC Phase
DepressionPsychiatric disorders1 of 10522 of 2280 of 2180 of 5190 of 181 of 206
Suicidal ideationPsychiatric disorders0 of 10520 of 2282 of 2181 of 5190 of 180 of 206
Suicide attemptPsychiatric disorders1 of 10520 of 2282 of 2180 of 5190 of 180 of 206
Atrial fibrillationCardiac disorders0 of 10520 of 2282 of 2180 of 5190 of 180 of 206
Myocardial infarctionCardiac disorders0 of 10521 of 2280 of 2180 of 5190 of 181 of 206
Postoperative wound infectionInfections and infestations1 of 10520 of 2280 of 2181 of 5190 of 180 of 206
Tibia fractureInjury, poisoning and procedural complications1 of 10520 of 2280 of 2181 of 5190 of 180 of 206
Blood creatinine increasedInvestigations0 of 10521 of 2281 of 2180 of 5190 of 180 of 206
Diabetes mellitusMetabolism and nutrition disorders1 of 10520 of 2280 of 2181 of 5190 of 180 of 206
Rotator cuff syndromeMusculoskeletal and connective tissue disorders1 of 10520 of 2281 of 2180 of 5190 of 180 of 206

Most frequent non-serious adverse event terms

Event termOrgan systemPlacebo + SSRI (Pre-randomized) - CF PhaseLY2216684 + SSRI (Randomized) - AT PhasePlacebo + SSRI (Randomized) - AT PhasePlacebo + SSRI (Non-randomized) - AT PhasePlacebo + SSRI (Pre-randomized) - DC PhaseLY2216684 + SSRI (Randomized) - DC Phase
HeadacheNervous system disorders117 of 105226 of 22814 of 21853 of 5193 of 1827 of 206
NauseaGastrointestinal disorders54 of 105219 of 2287 of 21816 of 5192 of 184 of 206
NasopharyngitisInfections and infestations36 of 105212 of 22811 of 21831 of 5191 of 182 of 206
HyperhidrosisSkin and subcutaneous tissue disorders29 of 105227 of 2282 of 21814 of 5190 of 184 of 206
DizzinessNervous system disorders28 of 105214 of 2286 of 2187 of 5191 of 183 of 206
Dry mouthGastrointestinal disorders33 of 10529 of 2284 of 2187 of 5191 of 182 of 206
VomitingGastrointestinal disorders7 of 105214 of 2284 of 2187 of 5191 of 182 of 206
SomnolenceNervous system disorders11 of 10520 of 2281 of 2183 of 5191 of 180 of 206
TremorNervous system disorders4 of 10524 of 2280 of 2184 of 5191 of 182 of 206
Abdominal discomfortGastrointestinal disorders6 of 10522 of 2280 of 2182 of 5191 of 181 of 206

Serious events with the highest arm-level rate: anxiety (5.6%), suicidal ideation (1.0%), atrial fibrillation (0.9%), suicide attempt (0.9%), depression (0.9%).

Do not overextend the safety comparison. Serious-adverse-event counts are safety observations, not efficacy outcomes, and should not be combined with the primary result into a single benefit-risk number.

The registry lists serious adverse events by phase and treatment-group label, with the number at risk and the number affected. During the randomized adjunctive-treatment phase, the LY2216684 + SSRI group lists 7 serious adverse events among 228 at risk, and the placebo + SSRI group lists 7 among 218 at risk. These are reported counts, not a recalculated comparison of risk.

The record also includes pre-randomized confirmation and discontinuation-phase entries, as well as non-randomized placebo + SSRI groups. Those entries describe different phases or populations and should not be combined with the randomized adjunctive-treatment groups to infer a randomized treatment contrast. Serious adverse event terms listed include Anxiety at 5.6%, Suicidal ideation at 1.0%, Atrial fibrillation at 0.9%, Suicide attempt at 0.9%, Depression at 0.9%, and Rotator cuff syndrome at 0.5%. The registry does not provide details in this summary to establish the denominators or attribution for each listed term.

Deaths are not reported in the registry record. These adverse-event listings do not by themselves establish causation or a comparative safety conclusion; they are descriptive counts reported across phase-specific groups.

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

The primary result describes the average change in MADRS total score from randomization to Week 8 for the two randomized adjunctive-treatment groups. The posted least-squares means are -8.73 for LY2216684 + SSRI and -8.49 for placebo + SSRI. The sponsor-reported mixed-model comparison has p = 0.751. A separate unadjusted re-calculation estimates a difference of -0.24, with a 95% confidence interval from -1.792 to 1.312 and p = 0.762.

These results do not establish a clear difference in average change between the groups, but they also do not establish that the groups are equivalent. The confidence interval includes zero and permits a range of possible contrasts. The registry does not report an equivalence or non-inferiority framework or a margin defining an acceptably small difference. Statistical non-significance should not be translated into proof that no difference exists.

The result concerns an adjunctive-treatment comparison in participants with major depressive disorder who were partial responders to SSRI treatment. It does not answer whether LY2216684 alone has an effect, whether SSRI treatment itself has an effect, or whether the result applies to people with a different treatment history. The primary outcome is a scale-based mean change, not a direct measure of every aspect of symptoms or functioning.

The registry lists secondary outcomes in several domains, but their multiplicity handling is not reported. The adverse-event counts are presented across multiple phases and population labels, so they are not a single randomized comparative safety estimate. The record’s limitations in analysis detail, missing-data reporting, and safety attribution should be kept in view when drawing broader conclusions.

No medical decision follows from these statistics alone. The result is a description of the posted estimates and their uncertainty, within the population, interventions, outcome definition, and analysis information recorded for this trial. The clinical importance of the observed score changes is not defined in the registry record.

18. Why This Trial Matters Statistically

This trial illustrates why a clinical comparison should be read through its estimand and analysis population, not just its treatment labels. The primary question concerns adding LY2216684 or placebo to ongoing SSRI treatment for partial responders. The primary outcome is change in a symptom-rating scale over a stated follow-up period, and the analysis population has a specific requirement for observed post-randomization data.

It also demonstrates the distinction between an adjusted sponsor analysis and a simple recalculation from posted summaries. The sponsor reports a mixed-model analysis that accounts for listed baseline, visit, investigator, treatment, and interaction terms. The recalculation provides a transparent unadjusted contrast and interval, but it does not reproduce the model. Statistical interpretation depends on keeping those analyses distinct.

The interval is especially informative: it shows that the re-calculated group contrast is uncertain and includes zero. Reporting only a point estimate or p-value would conceal that range of compatible values. Conversely, an interval including zero is not evidence of equivalence; that requires a different question and a prespecified margin, neither of which is reported in the registry record.

The record also highlights the importance of outcome multiplicity and analysis transparency. A broad set of secondary endpoints can illuminate different domains, but unreported multiplicity procedures and missing-data assumptions limit their confirmatory weight. Likewise, adverse-event counts across randomized, non-randomized, and phase-specific groups should not be collapsed into a single treatment comparison.

These features make the trial useful for teaching careful interpretation: distinguish the target population, endpoint, analysis method, estimate, uncertainty, and scope of the record before drawing conclusions. The posted findings are informative about the registered comparison, while unreported design and analysis details place limits on how far they can be generalized.

19. Limitations

The registry’s primary endpoint summaries provide arm-level least-squares means and standard errors, but not sponsor-reported confidence limits for the treatment contrast. The interval and p-value from the separate re-calculation are based on summary statistics and do not reproduce the reported mixed model. The pooled standard deviation used in the standardized-effect calculation is approximate, inferred from standard errors rather than calculated from participant-level observations.

The primary analysis population requires non-missing randomization values and at least one post-randomization value. The registry does not report the full missing-data strategy, the number and reasons for missing measurements, or sensitivity analyses. The repeated-measures model is named and its adjustment factors are listed, but further implementation details are not reported in the registry record.

The record lists many secondary outcomes but does not state a multiplicity procedure or a complete testing hierarchy. Consequently, secondary findings cannot be assigned confirmatory status from the record alone. The original sample-size justification, any interim analyses, and the full prespecified statistical analysis plan are also not reported.

Safety entries are divided by phase and group, including non-randomized and pre-randomized categories. The summary does not provide a single harmonized comparative safety analysis, and deaths are not reported in the registry record. Serious-event terms are listed with percentages, but the record summary does not give enough detail to interpret those terms as an adjusted randomized comparison.

The registry describes the intervention as flexible-dose LY2216684 at 12 or 18 mg alongside SSRI treatment. It does not provide enough information to assess how dose selection related to outcomes. The record also does not report a clinical-importance threshold for MADRS change. These limitations constrain independent appraisal and generalization, without changing the numerical results that are posted.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

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23. Record Summary

NCT01185340 is a completed phase III randomized, double-blind, parallel-group, placebo-controlled study sponsored by Eli Lilly and Company. It enrolled participants with major depressive disorder who were partial responders to SSRI treatment and compared adjunctive LY2216684 with adjunctive placebo over 8 weeks.

The primary endpoint was change from randomization to Week 8 in MADRS total score. The registry reports least-squares mean changes of -8.73 for LY2216684 + SSRI and -8.49 for placebo + SSRI, with a sponsor-reported mixed-model p-value of 0.751. The unadjusted re-calculation estimates a mean difference of -0.24, with a 95% confidence interval from -1.792 to 1.312 and p = 0.762.

The recalculated interval includes zero and does not establish a clear group difference; it does not establish equivalence. Multiplicity procedures, detailed missing-data methods, and the trial’s original sample-size assumptions are not reported in the registry record.

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