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Rheumatoid Arthritis Phase 2 Binary Endpoint NCT00966875

A Study in Patients With Rheumatoid Arthritis: Complete Statistical Analysis

This analysis examines the Week 12 ACR20 dose-response outcome in bDMARD-naive participants, alongside selected secondary results, safety counts, and statistical precision. The study was a randomized, quadruple-masked Phase 2 trial of LY2439821 in patients with active rheumatoid arthritis receiving concomitant DMARD therapy.

Trial start: 2009-08  ·  Enrollment: 448  ·  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 Patients With Rheumatoid Arthritis (NCT00966875), a randomized phase 2 study. The primary outcome is Dose-Response Relationship Measured by the Percentage of Participants With American College of Rheumatology (ACR) 20 Response in bDMARD-Naive Population.

448
Enrollment
Phase 2
6
Arms
In the primary outcome
+11.7 pts
Risk difference
3 mg LY2439821 (bDMARD-naive Population)
-8.2 to 31.6 pts
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT00966875
PhasePhase 2
ConditionRheumatoid Arthritis
AllocationRandomized
Design modelParallel
MaskingQuadruple
Enrollment448
Arms in the primary outcome6
Lead sponsorEli Lilly and Company
Results postedYes

2. Clinical Question

Population

The primary analysis population was the Part A full analysis set of participants who were bDMARD-naive, randomized, and received at least one dose of study drug. The trial enrolled patients with active rheumatoid arthritis on concomitant DMARD therapy. A separate TNFα-inadequate responder population was also studied.

Intervention

In the bDMARD-naive population, participants received subcutaneous LY2439821 at 3 mg, 10 mg, 30 mg, 80 mg, or 180 mg during Part A. Doses were given at Weeks 0, 1, 2, 4, 6, 8, and 10. Part B was optional and included a subsequent 160 mg regimen.

Comparator

The primary comparison was each LY2439821 dose group against placebo in the bDMARD-naive population. Placebo was given on the Part A schedule. Participants entering optional Part B received 160 mg LY2439821 according to the study arm descriptions.

Primary question

At Week 12, how did the percentage of bDMARD-naive participants meeting ACR20 response criteria vary across the LY2439821 dose groups and placebo? ACR20 required improvement in joint counts and in at least three additional core measures.

The study was registered as a Phase 2 dose-ranging trial. Its stated purposes included examining safety, whether LY2439821 could help participants with active rheumatoid arthritis, and how much LY2439821 should be given. The primary endpoint focused on the proportion meeting a defined response threshold rather than on an average change in a single measurement. The registry record also lists outcomes in the TNFα-inadequate responder population and continuous disease activity measures, so the study addressed more than one clinical subgroup and more than one way of characterizing response.

The primary result is a dose-group comparison at a specified time point, not an estimate of what would happen to every participant or over every duration of treatment. The study’s results describe the enrolled trial populations and the recorded endpoint definitions. They do not, by themselves, establish how the findings apply to people outside those populations or to treatment decisions.

3. Trial Design

This was a randomized, quadruple-masked, parallel-group Phase 2 study. The registry records enrollment of 448 participants and a completed status. The study began in 2009-08, with primary completion in 2011-03. Participants had active rheumatoid arthritis and were receiving concomitant DMARD therapy. The registry distinguishes a bDMARD-naive population from a TNFα-inadequate responder population.

In Part A, the bDMARD-naive population was assigned among placebo and five LY2439821 dose groups: 3 mg, 10 mg, 30 mg, 80 mg, and 180 mg. The TNFα-inadequate responder population had placebo, 80 mg, and 180 mg groups. The stated Part A schedule administered treatment at Weeks 0, 1, 2, 4, 6, 8, and 10. Part B was optional; the arm descriptions specify 160 mg LY2439821 beginning at Weeks 16, 18, and 20, followed by dosing every 4 weeks through Week 60. Participants assigned to placebo in Part A also had a Part B description involving 160 mg LY2439821.

The primary endpoint was evaluated at Week 12 in the bDMARD-naive population. The registry defines its analysis population as the Part A full analysis set: randomized participants who received at least one dose and were bDMARD-naive. The primary outcome is the percentage of participants with ACR20 response. Secondary outcomes include ACR20 response in the TNFα-inadequate responder population, response thresholds for ACR and DAS28 in the bDMARD-naive population, changes in DAS28, and ACR20, ACR50, and ACR70 response outcomes in Parts A and B.

The registry record does not report the randomization ratio, allocation concealment details, masking procedures, eligibility criteria beyond the population descriptions, or the rationale for the optional Part B structure. The original sample-size justification and the trial’s full statistical analysis plan are not reported in the registry record.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Before assignment: Participants were randomized to Part A and had the option of continuing in the open-label extension, Part B after completing Part A.

Only the first 6 of 9 groups are shown.

Part A

StagePlacebo [bDMARD-naive Population]3 mg LY2439821 [bDMARD-naive Population]10 mg LY2439821 [bDMARD-naive Population]30 mg LY2439821 [bDMARD-naive Population]80 mg LY2439821 [bDMARD-naive Population]180 mg LY2439821[bDMARD-naive Population]
STARTED544035375737
Received ≥1 Doses of Study Drug544035375737
COMPLETED483633345233
NOT COMPLETED642354

Reasons for not completing this period:

ReasonPlacebo [bDMARD-naive Population]3 mg LY2439821 [bDMARD-naive Population]10 mg LY2439821 [bDMARD-naive Population]30 mg LY2439821 [bDMARD-naive Population]80 mg LY2439821 [bDMARD-naive Population]180 mg LY2439821[bDMARD-naive Population]
Adverse Event210101
Entry Criteria000002
Lack of Efficacy010000
Lost to Follow-up200001
Parent/Caregiver Decision000100
Physician Decision000010
Sponsor Decision001010
Withdrawal by Subject221130
Protocol Violation000000

Part B

StagePlacebo [bDMARD-naive Population]3 mg LY2439821 [bDMARD-naive Population]10 mg LY2439821 [bDMARD-naive Population]30 mg LY2439821 [bDMARD-naive Population]80 mg LY2439821 [bDMARD-naive Population]180 mg LY2439821[bDMARD-naive Population]
STARTED463633345132
COMPLETED413327314426
NOT COMPLETED536376

Reasons for not completing this period:

ReasonPlacebo [bDMARD-naive Population]3 mg LY2439821 [bDMARD-naive Population]10 mg LY2439821 [bDMARD-naive Population]30 mg LY2439821 [bDMARD-naive Population]80 mg LY2439821 [bDMARD-naive Population]180 mg LY2439821[bDMARD-naive Population]
Adverse Event011010
Death001000
Lack of Efficacy211123
Lost to Follow-up000100
Physician Decision001021
Sponsor Decision100001
Withdrawal by Subject212121
Entry Criteria000000

Analysis population for the primary outcome, as defined in the registry: Part A FAS: All randomized participants who received at least 1 dose of study drug and were bDMARD-naive.

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: Full Analysis Set (FAS): All randomized participants who received at least 1 dose of study drug.

Only the first 6 of 10 groups are shown.

CharacteristicUnitPlacebo [bDMARD-naive Population]3 mg LY2439821 [bDMARD-naive Population]10 mg LY2439821 [bDMARD-naive Population]30 mg LY2439821 [bDMARD-naive Population80 mg LY2439821 [bDMARD-naive Population]180 mg LY2439821[bDMARD-naive Population]
Participants analysed544035375737
Age, Categorical: <=18 yearsParticipants000000
Age, Categorical: Between 18 and 65 yearsParticipants453730294832
Age, Categorical: >=65 yearsParticipants935895
Age, Continuousyears52.99 (SD 10.18)52.19 (SD 9.67)53.86 (SD 10.62)53.03 (SD 12.16)52.60 (SD 10.91)52.21 (SD 11.33)
Sex: Female, Male: FemaleParticipants473327315230
Sex: Female, Male: MaleParticipants778657
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants9787106
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants453224294630
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants013111
Race (NIH/OMB): American Indian or Alaska NativeParticipants232124
Race (NIH/OMB): AsianParticipants161310121710
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants000000
Race (NIH/OMB): Black or African AmericanParticipants420131
Race (NIH/OMB): WhiteParticipants292021203122
Race (NIH/OMB): More than one raceParticipants322340
Race (NIH/OMB): Unknown or Not ReportedParticipants000000
Region of Enrollment: United Statesparticipants12988129
Region of Enrollment: Taiwanparticipants543443
Region of Enrollment: Argentinaparticipants100110
Region of Enrollment: Polandparticipants1188797
Region of Enrollment: Romaniaparticipants543463
Region of Enrollment: Peruparticipants644464
Region of Enrollment: Chileparticipants012022
Region of Enrollment: Russian Federationparticipants310132
Region of Enrollment: Germanyparticipants000010
Region of Enrollment: Korea, Republic ofparticipants221121

6. Primary Endpoint

The registry lists the primary outcome as Dose-Response Relationship Measured by the Percentage of Participants With American College of Rheumatology (ACR) 20 Response in bDMARD-Naive Population, measured over Week 12.

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

The primary endpoint was the percentage of participants in the bDMARD-naive population who achieved an ACR20 response at Week 12. ACR20 is a composite response definition. It required at least 20% improvement from baseline in both tender joint count and swollen joint count, together with improvement in at least three of five other core measures: HAQ-DI, C-reactive protein, patient assessment of arthritis pain, patient global assessment of disease activity, and physician global assessment of disease activity.

This type of endpoint combines several aspects of a participant’s status rather than relying on a single symptom or laboratory measure. The threshold gives a clear responder classification for comparing the proportions in randomized groups. It is different from an average change score: it records whether each participant met the criteria, then summarizes the share meeting them in each group. Consequently, the percentage depends on the particular response definition and the treatment of missing observations.

For this primary outcome, missing values were imputed using non-responder imputation. Under that approach, participants with missing response information are counted as not having achieved the response. The registry states that the percentage was calculated as the number of ACR20 responders divided by the number of participants treated, multiplied by 100. The analysis population was the Part A full analysis set of randomized participants who received at least one dose and were bDMARD-naive. These definitions determine what the reported percentages mean; they should not be interpreted as a continuous measure of the amount of improvement or as an outcome at other time points.

7. Results Posted in the Registry

Risk difference: 3 mg LY2439821 (bDMARD-naive Population)

+11.7

95% CI: -8.2 to 31.6 percentage points

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals17.628.840.051.262.473.6Placebo (bDMARD-naive Populat… (n=54)3 mg LY2439821 (bDMARD-naive … (n=40)10 mg LY2439821 (bDMARD-naive… (n=35)30 mg LY2439821 (bDMARD-naive… (n=37)80 mg LY2439821 (bDMARD-naive… (n=57)180 mg LY2439821 (bDMARD-naiv… (n=37)% of participants (95% CI)
Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)3 mg LY2439821 (bDMARD-naive …10 mg LY2439821 (bDMARD-naive…30 mg LY2439821 (bDMARD-naive…80 mg LY2439821 (bDMARD-naive…180 mg LY2439821 (bDMARD-naiv…-12-0.7311223445risk difference (percentage points) vs control (95% CI)

8. Secondary Efficacy Endpoints

The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.

Secondary outcomeTypeEffect measureEstimate (95% CI)Planning size, 80% power
Percentage of Participants With ACR20 Response in Tumor Necrosis Factor Alpha-Inadequate Responder (TNFα-IR) PopulationBinary EndpointRisk difference+16.6 pts (0.8 to 32.4)123 per arm
Change From Baseline in Disease Activity Score (DAS28)-Part AContinuous EndpointMean difference-0.49 (-0.92 to -0.06)70 per arm
Change From Baseline in DAS28 - Part BContinuous EndpointMean difference0.31 (-0.19 to 0.81)202 per arm

Percentage of Participants With ACR20 Response in Tumor Necrosis Factor Alpha-Inadequate Responder (TNFα-IR) Population

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)80 mg LY2439821 (TNFα-IR Popu…180 mg LY2439821 (TNFα-IR Pop…-3.304.3612202735risk difference (percentage points) vs control (95% CI)

Change From Baseline in Disease Activity Score (DAS28)-Part A

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)3 mg LY2439821 (bDMARD-naive …10 mg LY2439821 (bDMARD-naive…-1.39-1.09-0.80-0.50-0.200.10mean difference vs control (95% CI)

Change From Baseline in DAS28 - Part B

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)3 mg/160 mg LY2439821(bDMARD-…10 mg/160 mg LY2439821(bDMARD…-0.90-0.53-0.170.200.570.94mean difference vs control (95% CI)

The secondary outcomes extend the primary ACR20 question in two directions: they examine a separate TNFα-inadequate responder population and use additional response thresholds or disease activity measures. The outcome list includes ACR20, ACR50, and ACR70 responses, dose levels associated with specified fractions of maximum response, and changes in DAS28. This range gives a broader descriptive view of the trial’s endpoints, but it also means that the results address multiple questions rather than one single confirmatory contrast.

The posted results include ACR20 percentages for the TNFα-inadequate responder groups and mean DAS28 changes in Part A and Part B. The numerical results for the remaining listed secondary outcomes are not reported in the registry record. The secondary findings that are available are relevant as additional descriptions, but they do not replace the primary Week 12 ACR20 result in the bDMARD-naive population. Differences in population, endpoint definition, time point, and analysis method mean that results should be interpreted within their own context rather than combined as though they were the same measure.

Unadjusted secondary comparisons carry less weight because the record includes many outcomes, dose groups, time points, and analyses. When many tests are conducted, some results may appear notable by chance even if there is no underlying difference. The registry record does not report a multiplicity adjustment or a hierarchy that would distinguish confirmatory from exploratory secondary analyses. The sponsor reports Fisher exact tests for the TNFα-inadequate responder ACR20 comparisons and ANCOVA for selected Part A DAS28 comparisons, but the record does not provide a complete statistical analysis plan for all secondary outcomes.

Accordingly, secondary results are best treated as supporting or exploratory evidence about patterns across endpoints and populations. They can add context to the primary result, but they should not be used to claim a consistent treatment effect across outcomes without the complete prespecified analysis plan and multiplicity strategy.

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

9. Statistical Interpretation

Clinical Biostats interpretation

At Week 12, the registry-reported ACR20 percentages in the bDMARD-naive population were 34.1 for placebo, 46.2 for 3 mg, 52.2 for 10 mg, 55.0 for 30 mg, 55.3 for 80 mg, and 54.0 for 180 mg LY2439821. The pattern across the active-dose groups rises from the lower doses and is similar across the higher doses, with the largest posted percentage in the 80 mg group. The percentages describe the observed trial groups; they do not alone establish the size or certainty of a treatment effect.

The registry reports a logistic regression analysis across the six primary endpoint groups with p = 0.031. This is the sponsor’s reported analysis for the multi-group dose-response outcome. A separate set of simple, unadjusted recalculations compares each active-dose group with placebo using the posted summary statistics. Those calculations yield risk-difference estimates ranging from 0.117 to 0.228 across the five doses. Their intervals vary in width, and some include zero while others do not. These pairwise recalculations are not the same analysis as the sponsor’s logistic regression across all six groups.

The registry percentages and the recalculated summary proportions are not identical in every case. Because a discrepancy is flagged, the sponsor’s own analysis takes precedence when interpreting the primary result. The recalculations are useful as descriptive contrasts from the posted group summaries, but they should not replace the registered analysis or be treated as adjusted estimates.

Selected secondary results also describe differences between groups. In the TNFα-inadequate responder population, the posted ACR20 percentages were 23.4 for placebo, 40.0 for 80 mg, and 39.0 for 180 mg. The posted Part A DAS28 mean changes in the bDMARD-naive population ranged from -0.818 for placebo to -1.94 for 180 mg. Such outcomes provide additional perspectives, but they do not redefine the primary endpoint and involve separate populations or measurement scales.

The registry’s outcome set is broad, with 37 outcome measures and 108 analyses recorded. Multiple doses, populations, endpoints, and time periods create many opportunities for results to differ by chance. The record does not report a multiplicity adjustment for the results, so isolated unadjusted comparisons warrant more caution than the prespecified primary analysis. The reported numbers characterize this trial and its analysis methods; they are not sufficient to make a general claim about treatment effectiveness or safety.

10. Statistical Methods Explained

The primary outcome is binary at the participant level: each participant either meets the ACR20 definition or does not. The group result is expressed as a percentage. A risk difference compares the response proportions between two groups by subtracting one group’s proportion from the other. In the recalculated comparisons, a positive estimate means the observed responder proportion was higher in the active-dose group than in placebo. The risk-difference interval describes uncertainty around that unadjusted contrast. If an interval includes zero, values compatible with no difference are among the values covered by that interval; this does not prove that the groups are identical.

The posted primary percentages and the recalculated risk differences are related descriptions, but they are not interchangeable analyses. The recalculations use the posted summary statistics and are simple pairwise comparisons. They do not account for the trial’s full design or necessarily reproduce the sponsor’s model. The registry reports a logistic regression analysis across placebo and all five active-dose groups, with p = 0.031. Logistic regression is a method for modeling a binary outcome; in a multi-group setting it can evaluate an overall group or dose-response pattern. The record does not provide enough detail to identify every model term or assumption used in that analysis.

Other reported analyses use different methods because their endpoints or comparisons differ. Fisher exact tests are listed for the TNFα-inadequate responder ACR20 comparisons. This test evaluates association in a two-group table of binary outcomes and can be used when the observed counts are limited. For the Part A DAS28 change outcome, the registry lists ANCOVA comparisons. ANCOVA models a continuous outcome while adjusting for one or more covariates; the covariates used in the sponsor’s analysis are not reported in the registry record. The posted DAS28 results are group means and standard deviations, whereas the ACR20 results are percentages of responders.

For ACR20, missing response values were handled by non-responder imputation. This assigns missing observations to the non-responder category for the endpoint calculation. It is a conservative convention in the sense that missing participants do not contribute as responders, but it does not eliminate the possibility that missingness affects interpretation. The amount and pattern of missing data, reasons for missingness, and sensitivity analyses using alternative assumptions are not reported in the registry record. The specific missing-data handling for every secondary outcome is also not reported.

The primary analysis population is described as the Part A full analysis set: all randomized participants who received at least one dose and were bDMARD-naive. This definition is more specific than simply stating the number enrolled. The arm-specific denominators for the primary outcome range from 35 to 57 participants. Differences between enrolled participants and participants included in a particular analysis can arise from population definitions and available observations, but the registry record does not give a complete accounting of those differences.

Several statistical concepts help distinguish the results. The percentage in an arm is a descriptive estimate of the response frequency in that group. A risk difference expresses the contrast on an absolute scale, while a risk ratio compares the frequencies proportionally and an odds ratio compares the odds. These scales answer related but not identical questions. The recalculated intervals and p-values are unadjusted; they do not incorporate a correction for the many doses, secondary endpoints, and analyses in the record.

General statistical explanation: a p-value describes how incompatible the observed data are with a specified null model, under the assumptions of the analysis. It is not the probability that the null hypothesis is true, and it does not measure the magnitude or clinical importance of an effect. A confidence interval gives a range of estimates compatible with the data and the interval procedure. Wider intervals indicate less precision than narrower intervals, all else being equal. Neither a p-value nor an interval resolves questions about bias, missing data, or whether the endpoint is important to patients.

The trial’s original sample-size assumptions, planned target effect, and statistical analysis plan are not reported in the registry record. Planning illustrations based on observed effects are separate from the study’s original design. They can show how sample requirements change under stated assumptions, but they cannot establish that the original trial was adequately powered or recover its design rationale.

11. Confidence Intervals and Precision

The recalculated risk differences are estimates from the observed group summaries, and their intervals express uncertainty in those estimates. For the primary bDMARD-naive comparisons, the posted intervals are narrower for some contrasts and broader for others. The 3 mg and 10 mg intervals include zero; the 30 mg, 80 mg, and 180 mg intervals do not. These interval boundaries should be read as measures of precision for the unadjusted pairwise estimates, not as proof that any particular dose has a definite effect. The registry’s separate logistic regression result addresses the overall six-group analysis and should not be conflated with these pairwise intervals.

Arm sizes were modest, ranging from 35 to 57 participants in the primary outcome groups. In general, estimates from smaller groups tend to be less precise, although the observed event proportions and analysis method also affect interval width. The observed percentages themselves are point estimates; an interval conveys that the underlying response frequency or group contrast is not known exactly from the sample.

The registry record does not state the confidence level for the recalculated intervals, so no confidence percentage is assigned to them in this interpretation. The sponsor’s reported primary analysis gives a p-value but does not include an effect estimate or interval in the posted analysis details. As a result, the sponsor-reported overall test and the recalculated pairwise contrasts contribute different information: one is a model-based multi-group test, while the other set supplies unadjusted estimates and intervals for individual dose-versus-placebo contrasts.

Precision is also limited by the scope of the analysis population and outcome. The primary result concerns ACR20 at Week 12 among the defined bDMARD-naive participants. It does not directly quantify uncertainty for other endpoints, other populations, or later time points. Interpreting numerical precision alongside the endpoint definition, analysis population, missing-data rule, and multiplicity context gives a more complete view than relying on a single interval or p-value.

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 effect274366
75% of the observed effect481643
50% of the observed effect1,0651,426
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect2005001,0002,00040%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, pooled-variance normal approximation for two proportions. Counts were reconstructed from the posted percentages and arm sizes, so small rounding differences are possible. Calculated for the comparison: 3 mg LY2439821 (bDMARD-naive Population).

The planning figures are stated as participants per arm for the binary outcomes in this trial. They are not total event counts. The illustrations assume a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. Each planning row uses the stated fraction of the observed effect as the effect to detect. The original trial’s own design assumptions and sample-size justification are not reported in the registry record.

The 80% power column gives the estimated participants needed in each arm under those planning assumptions to have an 80% chance of detecting the specified effect if that effect is present. The 90% power column uses a higher chance of detection and therefore generally calls for more participants per arm. These are planning calculations, not observed power. They are conditional on the assumed effect, allocation, significance level, and approximation; they do not describe the probability that the trial’s result is true.

Rows for 100% of the observed effect use the full recalculated contrast as the planning target. Rows for 75% or 50% of the observed effect represent smaller targets. Smaller effects are harder to distinguish from random variation, so they require more participants per arm under the same assumptions. For example, for the primary 80 mg comparison, the illustration gives 74 participants per arm for 80% power at 100% of the observed effect, 130 at 75%, and 287 at 50%. The figures are not recommendations for a future study; they show how the assumed effect size changes the planning requirement.

The illustrations are generated from observed trial effects and should not be mistaken for the actual enrollment target or a retrospective judgment of adequacy. The registry reports total enrollment of 448, but the primary bDMARD-naive arm sizes differ from one another. A planning calculation using equal allocation between two arms therefore does not reproduce the full multi-dose trial design.

13. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z1−α/2 = 1.960) and the desired power (z1−β = 0.842 for 80% and 1.282 for 90%).

Formula

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

n is the number of participants in each arm, p0 and p1 are the control and treatment proportions, and p̄ is their average.

Worked calculation for this trial

  1. Control proportion p0 = 0.333; treatment proportion p1 = 0.450; average p̄ = 0.392.
  2. First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6903 = 1.3530.
  3. Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.6854 = 0.5768.
  4. n = (1.3530 + 0.5768)2 / (0.1167)2 = 273.6, rounded up to 274 participants per arm for 80% power.

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

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
p0 <- 0.333333333333333                          # control proportion
p1 <- 0.45                          # treatment proportion
n_per_arm <- function(power, frac = 1) {
  q1 <- p0 + (p1 - p0) * frac               # smaller effect = fraction of the observed difference
  pbar <- (p0 + q1) / 2
  z_b <- qnorm(power)
  ceiling(round((z_a * sqrt(2 * pbar * (1 - pbar)) + z_b * sqrt(p0 * (1 - p0) + q1 * (1 - q1)))^2 / (q1 - p0)^2, 6))
}
for (f in c(1, 0.75, 0.5))
  cat(sprintf("%3.0f%% of observed effect: n per arm = %s (80%% power), %s (90%% power)\n", 100 * f,
              format(n_per_arm(0.80, f), big.mark = ","), format(n_per_arm(0.90, f), big.mark = ",")))

# Check against R's built-in function (unrounded n per arm)
cat("power.prop.test:", round(power.prop.test(p1 = p0, p2 = p1, power = 0.80)$n, 1), "\n")

# Simulation: how often does the z-test reject at the 80%-power sample size?
set.seed(966875)
n    <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z  <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))

Output from running the code

100% of observed effect: n per arm = 274 (80% power), 366 (90% power)
 75% of observed effect: n per arm = 481 (80% power), 643 (90% power)
 50% of observed effect: n per arm = 1,065 (80% power), 1,426 (90% power)
power.prop.test: 273.6 
Simulated power at n = 274 per arm: 0.799 (20000 replicates)

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

14. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
Regression, Logisticnot reported0.031
Where the two analyses differ, rely on the sponsor's. The simple re-calculation above reaches a different conclusion from the sponsor's analysis, usually because the sponsor adjusts for covariates, stratification or repeated measures, or (for event rates) uses a negative binomial model that allows for over-dispersion and so gives wider intervals.

The sponsor-reported primary analysis is a logistic regression across the placebo group and five LY2439821 dose groups in the bDMARD-naive population. The registry reports p = 0.031 for that analysis. This is the sponsor’s analysis of the multi-group primary dose-response outcome, rather than a collection of separate placebo-versus-dose tests.

The recalculated results are simple, unadjusted pairwise risk differences based on posted summary statistics. They provide an absolute-scale contrast and an interval for each dose versus placebo, but they do not reproduce the sponsor’s logistic regression. The posted arm percentages and recalculated proportions also show a discrepancy. Because that discrepancy is flagged, the sponsor’s own analysis takes precedence over the recalculations for interpreting the primary result.

The recalculations can still help describe the size and precision of individual contrasts, provided they are identified as unadjusted. Their p-values should not be substituted for the sponsor’s overall test, and they do not account for multiplicity across the dose groups or other outcomes. The registry record does not report enough model detail to independently reconstruct the sponsor’s analysis or determine whether the posted overall test was adjusted for any other comparisons.

15. Multiplicity, Missing Data and Analysis Populations

Multiplicity is a central interpretive issue because the registry records 37 outcome measures and 108 analyses. The primary endpoint compares five active doses with placebo, while secondary outcomes cover another population, multiple response thresholds, dose-response summaries, change scores, and Part B results. Testing many hypotheses increases the chance of observing apparently unusual results by chance. An adjustment or a prespecified testing hierarchy can address that issue, but a multiplicity plan is not reported in the registry record.

The sponsor-reported primary logistic regression has p = 0.031 for the six-group analysis. The recalculated dose-versus-placebo p-values are unadjusted, as are the simple recalculated intervals. They should not be read as though they had automatically controlled the error rate across all comparisons. The registry also reports Fisher exact tests for the TNFα-inadequate responder ACR20 comparisons and ANCOVA for selected DAS28 comparisons; a comprehensive account of the sponsor’s testing strategy is not reported.

Missing data are handled explicitly for the primary ACR20 endpoint through non-responder imputation. Participants with missing response values are counted as non-responders in the primary calculation. The registry record does not report the amount or reasons for missing data, the assumptions underlying that rule, or sensitivity analyses using alternative missing-data approaches. Missing-data methods for all secondary outcomes are not reported in the registry record.

The primary population is the Part A full analysis set, defined as randomized participants who received at least one dose and were bDMARD-naive. The registry does not provide a detailed participant flow for every analysis or a complete accounting of exclusions and missing observations. The original sample-size justification and full statistical analysis plan are also not reported. These gaps limit assessment of whether the reported analyses followed a prespecified strategy and how robust the results are to alternative analysis choices.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
3 mg LY2439821 (bDMARD-naive Population) Part A0400.0%
10 mg LY2439821 (bDMARD-naive Population) Part A1352.9%
30 mg LY2439821 (bDMARD-naive Population) Part A1372.7%
80 mg LY2439821 (bDMARD-naive Population) Part A4577.0%
180 mg LY2439821(bDMARD-naive Population) Part A1372.7%
Placebo (bDMARD-naive Population) Part A1541.9%
80 mg LY2439821 (TNFa-IR Population) Part A5657.7%
180 mg LY2439821 (TNFa-IR Population) Part A65910.2%
Placebo (TNFa-IR Population) Part A1641.6%
3 mg/160 mg LY2439821 (bDMARD-naive Population) Part B3368.3%
10 mg/160 mg LY2439821 (bDMARD-naive Population) Part B3339.1%
30 mg/160 mg LY2439821 (bDMARD-naive Population) Part B2345.9%
80 mg/160 mg LY2439821 (bDMARD-naive Population) Part B4517.8%
180 mg/160 mg LY2439821 (bDMARD-naive Population) Part B1323.1%
Placebo/160 mg LY2439821 (bDMARD-naive Population) Part B4468.7%
80 mg/160 mg LY2439821 (TNFa-IR Population) Part B75712.3%
180 mg/160 mg LY2439821 (TNFa-IR Population) Part B4508.0%
Placebo/160 mg LY2439821 (TNFa-IR Population) Part B75113.7%
Participants with at least one serious adverse event
Serious adverse events by arm3 mg LY2439821 (bDMARD-naive …0.0%10 mg LY2439821 (bDMARD-naive…2.9%30 mg LY2439821 (bDMARD-naive…2.7%80 mg LY2439821 (bDMARD-naive…7.0%180 mg LY2439821(bDMARD-naive…2.7%Placebo (bDMARD-naive Populat…1.9%80 mg LY2439821 (TNFa-IR Popu…7.7%180 mg LY2439821 (TNFa-IR Pop…10.2%% 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 5% reporting threshold.

ArmParticipants affected of at risk
3 mg LY2439821 (bDMARD-naive Population) Part A16 of 40
10 mg LY2439821 (bDMARD-naive Population) Part A16 of 35
30 mg LY2439821 (bDMARD-naive Population) Part A16 of 37
80 mg LY2439821 (bDMARD-naive Population) Part A23 of 57
180 mg LY2439821(bDMARD-naive Population) Part A16 of 37
Placebo (bDMARD-naive Population) Part A22 of 54

Most frequent serious adverse event terms

Event termOrgan system3 mg LY2439821 (bDMARD-naive Population) Part A10 mg LY2439821 (bDMARD-naive Population) Part A30 mg LY2439821 (bDMARD-naive Population) Part A80 mg LY2439821 (bDMARD-naive Population) Part A180 mg LY2439821(bDMARD-naive Population) Part APlacebo (bDMARD-naive Population) Part A
Ischaemic strokeNervous system disorders0 of 400 of 350 of 371 of 570 of 371 of 54
Acute vestibular syndromeEar and labyrinth disorders0 of 400 of 350 of 371 of 570 of 370 of 54
Non-cardiac chest painGeneral disorders0 of 400 of 350 of 371 of 570 of 370 of 54
Systemic inflammatory response syndromeGeneral disorders0 of 400 of 350 of 371 of 570 of 370 of 54
Serum sickness-like reactionImmune system disorders0 of 400 of 350 of 370 of 571 of 370 of 54
CellulitisInfections and infestations0 of 400 of 350 of 371 of 570 of 370 of 54
SepsisInfections and infestations0 of 400 of 350 of 371 of 570 of 370 of 54
HypoaesthesiaNervous system disorders0 of 400 of 350 of 371 of 570 of 370 of 54
AnxietyPsychiatric disorders0 of 400 of 351 of 370 of 570 of 370 of 54
Renal failure acuteRenal and urinary disorders0 of 400 of 350 of 371 of 570 of 370 of 54

Most frequent non-serious adverse event terms

Event termOrgan system3 mg LY2439821 (bDMARD-naive Population) Part A10 mg LY2439821 (bDMARD-naive Population) Part A30 mg LY2439821 (bDMARD-naive Population) Part A80 mg LY2439821 (bDMARD-naive Population) Part A180 mg LY2439821(bDMARD-naive Population) Part APlacebo (bDMARD-naive Population) Part A
HeadacheNervous system disorders0 of 404 of 352 of 372 of 571 of 376 of 54
Urinary tract infectionInfections and infestations1 of 402 of 353 of 372 of 572 of 374 of 54
NasopharyngitisInfections and infestations2 of 402 of 350 of 373 of 573 of 373 of 54
Upper respiratory tract infectionInfections and infestations1 of 400 of 353 of 373 of 572 of 370 of 54
HypertensionVascular disorders0 of 402 of 352 of 374 of 571 of 370 of 54
Injection site painGeneral disorders1 of 401 of 351 of 372 of 572 of 371 of 54
ArthralgiaMusculoskeletal and connective tissue disorders3 of 400 of 351 of 370 of 573 of 371 of 54
Rheumatoid arthritisMusculoskeletal and connective tissue disorders1 of 402 of 352 of 372 of 570 of 371 of 54
PyrexiaGeneral disorders0 of 401 of 352 of 372 of 570 of 372 of 54
DizzinessNervous system disorders1 of 401 of 350 of 371 of 571 of 372 of 54

Serious events with the highest arm-level rate: meningitis (3.1%), pancreatitis acute (3.0%), death (3.0%), urinary tract infection (3.0%), aortic aneurysm (3.0%).

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 event counts by arm and study part, with the number at risk and number affected. In Part A among bDMARD-naive participants, serious adverse events were reported in 0 of 40 participants in the 3 mg group, 1 of 35 in the 10 mg group, 1 of 37 in the 30 mg group, 4 of 57 in the 80 mg group, 1 of 37 in the 180 mg group, and 1 of 54 in the placebo group. The TNFα-inadequate responder Part A groups had 5 of 65 affected in the 80 mg group, 6 of 59 in the 180 mg group, and 1 of 64 in the placebo group.

Part B counts are reported separately for participants continuing or switching to 160 mg LY2439821. They should not be pooled with Part A counts without accounting for the different study periods and group definitions. The registry also lists serious-event terms and percentages, including meningitis at 3.1%, pancreatitis acute at 3.0%, death at 3.0%, urinary tract infection at 3.0%, aortic aneurysm at 3.0%, and pneumonia at 2.9%. The group-level death counts are not reported in the registry record.

These counts describe reported events within the recorded risk groups. They do not by themselves establish whether an event was caused by study treatment, and comparisons are limited by group size and the study structure. They should be read as safety reporting, not as individualized risk estimates.

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

The primary result describes the percentage of participants meeting the study’s ACR20 definition at Week 12 in the bDMARD-naive population. The posted percentages were higher in each active-dose group than in placebo, and the sponsor reported an overall logistic regression p-value of 0.031 across the six groups. The pattern across doses rises at lower doses and is broadly similar among the higher-dose groups. These are observations from this trial, not a guarantee of an outcome for any individual participant.

The endpoint is a threshold-based composite. Meeting ACR20 means meeting the specified improvement criteria across joint counts and other core measures; it does not mean every measure improved by the same amount, nor does it describe the magnitude of change beyond the response threshold. The DAS28 change outcomes are separate measures and should not be treated as interchangeable with ACR20 response.

The primary analysis concerns a particular population, treatment schedule, and time point. The trial also included a TNFα-inadequate responder population and an optional Part B, but those results answer different questions. The findings do not establish effects at all doses, for all participants with rheumatoid arthritis, or beyond the time points reported. The registry record does not report all details needed to assess generalizability or reconstruct the sponsor’s full statistical model.

Statistical evidence and clinical importance are also distinct. A p-value does not measure the size or value of an outcome, and an observed difference does not alone show that the difference is meaningful to participants. Interpretation depends on the endpoint, precision, missing-data handling, multiplicity, safety reporting, and applicability of the trial population. The record supports a description of the posted trial results; it does not by itself support medical advice or a broad conclusion about treatment.

18. Why This Trial Matters Statistically

This trial offers a useful statistical example of dose-ranging analysis: several active dose groups are compared with placebo, while the primary question concerns an overall response pattern across doses. The sponsor’s logistic regression result and the recalculated pairwise risk differences illustrate how different analyses can address related but distinct questions. An overall multi-group test is not the same as five separate estimates of the absolute difference from placebo.

It also shows why effect estimates and precision matter alongside p-values. The recalculated risk differences are accompanied by intervals that vary in width, while the sponsor’s reported primary analysis supplies a p-value without an effect estimate or interval in the posted analysis details. Reading those pieces together prevents a single test result from being mistaken for a complete account of the evidence.

The endpoint and population definitions are equally important. ACR20 is a composite responder outcome, the primary population excludes participants outside the specified bDMARD-naive full analysis set, and missing primary responses were handled as non-responders. Secondary outcomes include different populations and measurement scales. Those distinctions affect what can be concluded from each result.

Finally, the record’s many outcome measures and analyses make multiplicity, transparent analysis planning, and careful labeling of unadjusted calculations especially relevant. The registry illustrates both the value and limits of posted results: they permit readers to examine observed group patterns, but missing details about the original design assumptions and full analysis plan restrict independent evaluation of every statistical choice.

19. Limitations

The primary outcome group sizes range from 35 to 57 participants, so precision for individual dose comparisons is limited. The study distributes the bDMARD-naive population across placebo and five active doses, rather than concentrating all participants in a single active-versus-control comparison. The simple planning illustrations use equal allocation between two arms, which does not reproduce that multi-arm structure.

The primary endpoint is a composite threshold, and its calculation uses non-responder imputation for missing values. The registry record does not report the amount or pattern of missingness, reasons for missing observations, or sensitivity analyses. The record also does not report the original sample-size justification, the full statistical analysis plan, the randomization ratio, or a multiplicity strategy. These omissions limit assessment of prespecification and robustness.

The registry identifies a discrepancy between posted primary summary results and recalculated summaries. The sponsor’s reported logistic regression therefore takes precedence; the recalculated pairwise estimates are descriptive, unadjusted analyses and should not be treated as substitutes. In addition, only selected secondary outcome statistics are available in the record described, and the remaining listed secondary outcome values are not reported in the registry record.

Safety counts are given by arm and study part, but they do not establish causality, and group-level death counts are not reported. Part B was optional and involved a subsequent 160 mg regimen, so Part B group summaries reflect a different stage and group definition from the primary Part A comparison. These features constrain direct comparisons across periods and populations.

20. Related Tutorials

21. Related Statistical Calculators

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23. Record Summary

NCT00966875 is a completed randomized, quadruple-masked, parallel-group Phase 2 study of LY2439821 in patients with active rheumatoid arthritis on concomitant DMARD therapy. The registry records enrollment of 448, a start of 2009-08, and primary completion in 2011-03. The primary endpoint was Week 12 ACR20 response in the bDMARD-naive Part A full analysis set.

Across placebo and five LY2439821 dose groups, the registry reports an overall logistic regression p-value of 0.031. The posted ACR20 percentages were 34.1 for placebo and 46.2 to 55.3 across the active-dose groups. Selected secondary results cover the TNFα-inadequate responder population and DAS28 change. Interpretation is constrained by the discrepancy between posted summaries and recalculations, unadjusted secondary analyses, and statistical-plan details not reported in the registry record.

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