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Asthma Phase 3 Event-Rate Endpoint NCT01875003

A Study of Lebrikizumab in Adolescent Participants With Uncontrolled Asthma Who Are on Inhaled Corticosteroids and a Second Controller Medication: Complete Statistical Analysis

The registry record reports a terminated, randomized, double-blind trial of lebrikizumab versus placebo in adolescents with uncontrolled asthma on background controller treatment. The primary result is the adjusted rate of asthma exacerbations during the 52-week placebo-controlled period.

Trial start: 2013-08-13  ·  Enrollment: 346  ·  Sponsor: Hoffmann-La Roche
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 of Lebrikizumab in Adolescent Participants With Uncontrolled Asthma Who Are on Inhaled Corticosteroids and a Second Controller Medication (NCT01875003), a randomized phase 3 study. The primary outcome is Rate of Asthma Exacerbations During 52-Week Placebo Controlled Period.

346
Enrollment
Phase 3
3
Arms
In the primary outcome
0.60
Rate ratio
Lebrikizumab 37.5 mg
0.38–0.95
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT01875003
PhasePhase 3
ConditionAsthma
AllocationRandomized
Design modelParallel
MaskingDouble
Enrollment346
Arms in the primary outcome3
Lead sponsorHoffmann-La Roche
Results postedYes

2. Clinical Question

Population

Adolescent participants with asthma that remained uncontrolled while they were receiving inhaled corticosteroids and a second controller medication. The registry describes inhaled corticosteroid doses of 500-2000 micrograms of fluticasone propionate dry powder inhaler or equivalent in the arm descriptions.

Intervention

Subcutaneous lebrikizumab, at the 37.5 mg or 125 mg dose, administered every 4 weeks during the 52-week placebo-controlled period alongside standard-of-care therapy. The study description also includes an optional active-treatment extension.

Comparator

Matching placebo administered every 4 weeks during the 52-week placebo-controlled period, alongside standard-of-care therapy. The registry describes a randomized, double-blind, placebo-controlled comparison.

Primary question

How did the adjusted rate of asthma exacerbations during the 52-week placebo-controlled period compare between each lebrikizumab dose group and placebo? An exacerbation was defined by new or increased asthma symptoms leading to systemic corticosteroid treatment or hospitalization.

The primary endpoint expresses exacerbations as events per patient year, so it relates the number of events to the follow-up time contributed by participants. The registry reports adjusted rate ratios for each dose versus placebo, estimated using a Poisson regression model in the ITT population. This is a rate comparison, not a comparison of the proportion of participants who experienced an exacerbation.

The registry record lists an enrollment of 346 and a terminated study status. It does not report why the trial was terminated or whether termination affected the analysis. The results therefore describe the posted endpoint and analyses, rather than establishing why the study ended or what its planned completion would have been.

3. Trial Design

This was a Phase III, randomized, double-blind, parallel-group, placebo-controlled study sponsored by Hoffmann-La Roche. It enrolled adolescents with uncontrolled asthma who were taking inhaled corticosteroids and a second controller medication. The registry describes standard-of-care therapy as continuing alongside study treatment. The overall enrollment was 346.

Participants were assigned to lebrikizumab at a high or low dose, or placebo. The brief summary states that assignment was in a 1:1:1 ratio. During the 52-week placebo-controlled period, study treatment was administered subcutaneously every 4 weeks. The primary endpoint timeframe was baseline up to Week 52. The reported primary analysis used the ITT population.

The study description includes an optional 52-week double-blind active-treatment extension, with anticipated time on study treatment up to 104 weeks. Participants completing the study to Week 104, stopping early, or not entering the optional extension were to transition to a 20-week safety follow-up period. These are features described in the study summary; the posted primary outcome concerns the placebo-controlled period rather than the optional extension.

The registry lists a start date of 2013-08-13, a primary completion date of 2016-12-28, and a terminated status. The reason for termination, the timing of termination relative to the analyses, and whether the status changed the outcome collection are not reported in the registry record. The registry record also does not report the original sample-size justification, the detailed randomization procedure, or the full statistical analysis plan. The allocation ratio and design labels describe the recorded study design, but do not supply these missing operational details.

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: A total of 579 participants were screened for the study of which 346 were randomized and received at least one dose of study drug.

Overall Study

StagePlaceboLebrikizumab 37.5 mgLebrikizumab 125 mgPlacebo/Lebrikizumab 37.5 mgPlacebo/Lebrikizumab 125 mg
STARTED561131163031
COMPLETED030311614
NOT COMPLETED5683851417

Reasons for not completing this period:

ReasonPlaceboLebrikizumab 37.5 mgLebrikizumab 125 mgPlacebo/Lebrikizumab 37.5 mgPlacebo/Lebrikizumab 125 mg
Study Terminated by Sponsor356166913
Withdrawal by Subject1613541
Lost to Follow-up40100
Adverse Event12200
Physician Decision02100
Missing04912
Other01100
Pregnancy00001

Analysis population for the primary outcome, as defined in the registry: Adjusted exacerbation rate estimated from a Poisson regression model was reported. Analysis was performed on ITT population.

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: The intent-to-treat (ITT) population included all randomized participants who received at least one dose of study medication or have any post-baseline efficacy data.

CharacteristicUnitPlaceboLebrikizumab 37.5 mgLebrikizumab 125 mgTotal
Participants analysed117113116346
Age, Continuousyears14.1 (SD 1.7)14.2 (SD 1.5)14.2 (SD 1.6)14.2 (SD 1.6)
Sex: Female, Male: FemaleParticipants494359151
Sex: Female, Male: MaleParticipants687057195
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants394233114
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants777181229
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants1023
Race (NIH/OMB): American Indian or Alaska NativeParticipants3115
Race (NIH/OMB): AsianParticipants3339
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants0000
Race (NIH/OMB): Black or African AmericanParticipants9131335
Race (NIH/OMB): WhiteParticipants847574233
Race (NIH/OMB): More than one raceParticipants0112
Race (NIH/OMB): Unknown or Not ReportedParticipants18202462
Age group (years): 12 to 14Participants716467202
Age group (years): 15 to 17Participants464949144
Baseline Use of Inhaled Corticosteroid (ICS) and Long-Acting Beta-Agonist (LABA): ICS < 1000 µg/day or no LABAParticipants878888263
Baseline Use of Inhaled Corticosteroid (ICS) and Long-Acting Beta-Agonist (LABA): ICS >= 1000 µg/day and LABAParticipants30252883
Number of Asthma Exacerbations in Last 12 MonthsAsthma Exacerbations1.6 (SD 2.1)1.4 (SD 1.9)1.7 (SD 1.9)1.6 (SD 1.9)

6. Primary Endpoint

The registry lists the primary outcome as Rate of Asthma Exacerbations During 52-Week Placebo Controlled Period, measured over Baseline up to Week 52.

ElementRegistry entry
Result typeNumber
Measure of spreadnot applicable
Unitevents per patient year
Endpoint classificationEvent-Rate Endpoint

The primary endpoint was the rate of asthma exacerbations during the 52-week placebo-controlled period, expressed as events per patient year. The registry defines an exacerbation as new or increased asthma symptoms, including wheeze, cough, dyspnea, chest tightness, or night-time awakening due to these symptoms, that lead to systemic corticosteroid treatment or hospitalization. Systemic corticosteroid treatment included oral, intravenous, or intramuscular corticosteroids for at least 3 days, or an emergency department visit with at least 1 dose of intravenous or intramuscular corticosteroids.

The rate is defined in the registry as the total number of exacerbation events divided by total follow-up time in patient years. Using exposure time matters because participants may contribute different amounts of follow-up. A rate therefore incorporates both the number of events and the time over which those events could be observed. It is not the same quantity as the risk or percentage of participants with at least one exacerbation: one participant may have more than one event, and the denominator is follow-up time rather than simply the number of participants.

The registry reports adjusted exacerbation rates estimated from a Poisson regression model, with analysis performed on the ITT population. The primary comparison is summarized as a rate ratio against placebo for each lebrikizumab dose. A rate ratio below 1 indicates a lower estimated event rate in the lebrikizumab group relative to placebo within that comparison. This statistical description does not by itself establish the reason for any difference or whether the result should guide an individual treatment decision.

7. Results Posted in the Registry

Rate ratio: Lebrikizumab 37.5 mg

0.60

95% CI: 0.38 to 0.95

Recalculated from the posted summary statistics

Treatment effect versus the control arm
Forest plot of rate ratio vs control (95% CI)Lebrikizumab 37.5 mgLebrikizumab 125 mg0.270.360.480.630.831.10rate ratio 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
Percent Change From Baseline in Pre-Bronchodilator Forced Expiratory Volume in 1 Second (FEV1) at Week 52Continuous EndpointMean difference6.00 (5.02 to 6.98)4 per arm
Absolute Change From Baseline in Pre-Bronchodilator FEV1 at Week 52Continuous EndpointMean difference198.00 (49.70 to 346.30)84 per arm
Time to First Asthma ExacerbationTime-to-Event AnalysisHazard ratio0.40 (0.22 to 0.73)38 events

Percent Change From Baseline in Pre-Bronchodilator Forced Expiratory Volume in 1 Second (FEV1) at Week 52

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Lebrikizumab 37.5 mgLebrikizumab 125 mg-0.561.062.684.305.927.54mean difference vs control (95% CI)

Absolute Change From Baseline in Pre-Bronchodilator FEV1 at Week 52

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Lebrikizumab 37.5 mgLebrikizumab 125 mg-132-2973176279382mean difference vs control (95% CI)

Time to First Asthma Exacerbation

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Placebo vs Lebrikizumab 37.5 …Placebo vs Lebrikizumab 125 mg0.190.270.380.550.791.13hazard ratio (as reported) vs control (95% CI)

The secondary endpoints broaden the assessment beyond the primary exacerbation rate. They include pre-bronchodilator FEV1 changes, time to first asthma exacerbation, FeNO, asthma-related quality of life, rescue medication use, urgent health-care utilization, and injection acceptability. The registry reports results for some of these measures, while not all listed secondary outcomes have posted results in the record.

Across the reported secondary outcomes, the pattern is not uniform across dose groups or outcome types. Some posted comparisons have intervals that do not include the relevant null value, while others include it. Continuous measures and time-to-event outcomes also use different scales and statistical summaries, so their estimates cannot be combined into one overall treatment effect. They provide supporting context for the primary endpoint rather than a direct replication of it.

For time to first exacerbation, the registry posts hazard ratios of 0.40 for placebo versus lebrikizumab 37.5 mg and 0.37 for placebo versus lebrikizumab 125 mg, each with a reported 95% confidence interval. Group-specific median times are not reported. FEV1 comparisons include sponsor-reported adjusted mean differences as well as simple recalculations from posted summary values. The adjusted and unadjusted results are different types of analysis and should not be conflated.

Secondary outcomes usually involve several endpoints, doses, and analyses. When many comparisons are considered, the chance of at least one apparently notable result arising by chance can increase unless the analysis addresses multiplicity. Whether and how multiplicity was handled is not reported in the registry record. For that reason, unadjusted secondary results carry less weight than a prespecified primary result and should be treated as exploratory or supportive unless the trial’s analysis plan establishes otherwise. That plan is not reported in the registry record. Missing outcome values and differing analysis populations may also affect comparability; the registry does not fully report these details for all secondary measures.

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

9. Statistical Interpretation

Clinical Biostats interpretation

For the primary endpoint, the posted adjusted rates were 0.43 events per patient year for placebo, 0.26 for lebrikizumab 37.5 mg, and 0.21 for lebrikizumab 125 mg. These are the registry’s arm-level adjusted rate estimates. The sponsor-reported adjusted rate ratio was 0.60 for lebrikizumab 37.5 mg versus placebo, with a 95% confidence interval from 0.35 to 1.03. For lebrikizumab 125 mg versus placebo, the adjusted rate ratio was 0.49, with a 95% confidence interval from 0.28 to 0.83. The registry does not provide a p-value for either sponsor-reported primary comparison.

The interval for the 37.5 mg comparison includes 1, so the posted interval is compatible with values on both sides of no rate ratio difference. The interval for the 125 mg comparison lies below 1. An interval describes uncertainty around an estimate; it is not a guarantee that the true effect lies within it, nor does it indicate the probability that a hypothesis is true. The registry lists both analyses as superiority comparisons, but the statistical plan and any decision rules are not reported in the registry record.

Simple unadjusted recalculations from the posted arm-level rates give rate ratios of 0.605 for 37.5 mg versus placebo and 0.488 for 125 mg versus placebo. Their recalculated intervals are 0.383 to 0.954 and 0.301 to 0.793, respectively. These are not the sponsor’s adjusted estimates or intervals. The recalculated unadjusted p-values are 0.031 and 0.004, respectively; they should not be substituted for missing sponsor-reported p-values, or treated as the trial’s original inferential analysis. The registry reports no discrepancy flag, and the sponsor-reported adjusted analyses remain the relevant posted trial analyses.

The endpoint’s exposure-time denominator and regression adjustment distinguish these results from a raw comparison of participant counts. The registry does not report the covariates used for adjustment, the model diagnostics, or how recurrent events were handled beyond identifying the adjusted Poisson regression model. Those omissions limit independent assessment of the analysis. Also, the trial status is terminated, but the reason and its implications for the results are not reported in the registry record.

Secondary outcome results include measures of lung function, time to first exacerbation, and other asthma-related measures. They provide additional context, but multiple outcomes and comparisons make isolated secondary findings less conclusive, particularly when the registry does not report the multiplicity plan. The primary result should therefore be read alongside its confidence intervals, the specific outcome definition, the reported analysis population, and the missing details about the statistical plan. These trial results describe group-level estimates; they do not establish what an individual participant would experience.

10. Statistical Methods Explained

The primary outcome is an event rate, rather than a continuous measurement or a simple event/no-event outcome. The registry defines the rate as total exacerbation events divided by total follow-up time in patient years. This structure is useful when participants contribute varying follow-up time and when the endpoint can include recurrent events. The rate ratio compares the estimated event rate in a lebrikizumab group with the estimated rate in placebo. A rate ratio of 1 represents equal estimated rates; a value below 1 represents a lower estimated rate in the numerator group relative to the comparator.

Why use a rate model?

Poisson regression is a general method for modeling event counts in relation to exposure time and explanatory variables. In a rate analysis, follow-up time can be incorporated so that participants who are observed for different durations are not treated as though they had identical time at risk. The registry says that the adjusted exacerbation rate was estimated using a Poisson regression model. It does not report the model’s covariates, link function details, assumptions checks, or the approach used to address any over-dispersion.

Over-dispersion is a general concern when event counts vary more than a simple Poisson model expects. If present and not addressed, uncertainty estimates can be too small. This is a general statistical consideration, not a claim that over-dispersion occurred in this trial. Whether it was assessed or accommodated is not reported in the registry record.

What does adjustment mean?

In general, an adjusted model estimates a treatment contrast while accounting for other variables included in the model. Adjustment can affect both the estimate and its uncertainty. The term “adjusted” appears in the registry’s primary outcome description and sponsor-reported rate ratios, but the variables and details of the adjustment are not reported in the registry record. The posted adjusted results therefore cannot be fully reconstructed from the arm-level rates alone.

Unadjusted recalculations are separate, simple comparisons based on posted summary statistics. For the primary endpoint, the recalculated rate ratios are 0.605 and 0.488, with recalculated confidence intervals of 0.383 to 0.954 and 0.301 to 0.793. Those calculations do not reproduce the sponsor’s adjustment, and they should be viewed as an independent descriptive check rather than a replacement for the registry’s reported analysis. The sponsor-reported adjusted estimates are 0.60 and 0.49.

How should the confidence interval be read?

A confidence interval communicates uncertainty in an estimate under the statistical method used. In general, a wider interval indicates less precision, while a narrower interval indicates greater precision. For a rate ratio, the null comparison is 1. If an interval includes 1, its range includes no rate ratio difference; if it lies entirely below 1, its range is consistent with a lower estimated rate in the treatment group across the interval. The sponsor-reported 95% interval for 37.5 mg is 0.35 to 1.03, and for 125 mg it is 0.28 to 0.83. These intervals should be interpreted with the adjustment and analysis details in mind, which are not fully reported.

A confidence interval is not a range that captures every possible value, and it is not a statement that the treatment effect has a particular probability of being within the interval. It summarizes the variability expected from repeated use of the method under its assumptions. The registry does not provide a primary p-value, so no sponsor-reported p-value should be inferred from the listed intervals.

What other statistical summaries are posted?

Secondary outcomes use different types of summaries. The registry posts mean changes for FEV1 outcomes and hazard ratios for time to first asthma exacerbation. A mean difference compares average values, while a hazard ratio compares event hazards over time under the survival-analysis framework. These are not interchangeable with the primary rate ratio. Their interpretation depends on their outcome definitions, analysis models, and reported uncertainty.

Some secondary analyses are available as arm-level values and sponsor-reported adjusted comparisons. The re-calculated mean differences are unadjusted calculations from the posted summaries, whereas sponsor-reported differences are adjusted means. A median time outcome may be unreported for the individual groups even when a hazard ratio comparison is posted. The registry’s reported values should be kept distinct from derived summaries, and the registry record does not report enough methodological detail to reproduce all adjusted secondary analyses.

The reported primary analysis population is ITT. In general, an intention-to-treat population retains participants according to their randomized assignment for analysis, but the exact population definition, exclusions, and handling of missing observations are not reported in the registry record. The outcome-specific analysis populations may also differ; the registry identifies the primary analysis population but does not give a complete account of analysis populations for every posted outcome.

11. Confidence Intervals and Precision

The sponsor-reported adjusted rate ratio for lebrikizumab 37.5 mg versus placebo is 0.60, with a 95% confidence interval from 0.35 to 1.03. For lebrikizumab 125 mg versus placebo, the estimate is 0.49, with a 95% confidence interval from 0.28 to 0.83. These intervals show the range of effect estimates compatible with the posted analysis at the stated confidence level under its statistical assumptions. The interval for 37.5 mg includes the null rate ratio of 1; the interval for 125 mg does not.

Precision is distinct from the point estimate. The point estimate gives one summary value, while the interval communicates uncertainty around that value. Neither interval establishes that the estimate is exact, and neither describes the range of outcomes for individual participants. The registry does not report p-values for the sponsor’s primary comparisons, nor does it provide enough model detail to assess all sources of uncertainty independently.

The recalculated unadjusted intervals are 0.383 to 0.954 for 37.5 mg and 0.301 to 0.793 for 125 mg. They differ from the sponsor-reported adjusted intervals, as expected when calculations use posted arm-level rates rather than the adjusted analysis. These recalculations are not the sponsor’s primary inference. The sponsor-reported estimates and intervals should be used to describe the registered adjusted analyses.

Precision also depends on the amount of information contributing to an outcome. The primary arm counts listed are 117 for placebo, 113 for lebrikizumab 37.5 mg, and 116 for lebrikizumab 125 mg. These are not necessarily the number of participants with complete data for every secondary outcome. The secondary FEV1 summaries use smaller listed analysis groups, and the registry record does not report the reasons for outcome-specific availability or the effects of missing observations.

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 effect193258
75% of the observed effect317424
50% of the observed effect662886
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)
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, Poisson model with equal follow-up (from the outcome time frame: 1.00 years per participant). Real event counts are usually over-dispersed, so a negative binomial model would need more participants than shown; treat these figures as a lower bound. Calculated for the comparison: Lebrikizumab 37.5 mg.

The sample-size illustrations use the observed effect as a starting point and show planning values for detecting the full observed effect, 75% of the observed effect, or 50% of the observed effect. For the primary rate endpoint and continuous outcomes, the entries are participants per arm. For time-to-event comparisons, the entries are total events, not participants per arm. The distinction matters: an event target does not state how many participants must be enrolled, because the number of events depends on follow-up and event occurrence.

The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The time-to-event illustrations use the Schoenfeld approach. These calculations are planning illustrations based on observed effects, not the original trial’s design assumptions; those original assumptions are not reported in the registry record.

The 80% power column gives the illustrative number of participants per arm, or total events for time-to-event analyses, associated with an 80% chance of detecting the specified effect under the stated assumptions if that effect were the true effect. The 90% column expresses the corresponding planning target for a higher chance of detection. These percentages describe hypothetical design properties, not the probability that a result is correct or that a treatment effect exists.

Smaller effects require more information to distinguish them from random variation. Accordingly, planning for 75% or 50% of the observed effect generally requires more participants per arm or more total events than planning for the full observed effect. The displayed values are not observed power; they are illustrations of sample-size or event requirements under the stated assumptions. They should not be read as proof that the terminated trial was adequately or inadequately sized, because the registry does not report the original sample-size justification.

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 + z1−β)2 (1/λ0 + 1/λ1) / ( T · [ln(λ1/λ0)]2 )

n is the number of participants in each arm, λ0 and λ1 are event rates per patient-year, and T is follow-up per participant in years. This assumes Poisson counts and equal follow-up.

Worked calculation for this trial

  1. Control rate λ0 = 0.4300; treatment rate λ1 = 0.2600 events per patient-year; follow-up T = 1.00 years.
  2. n = (1.96 + 0.842)2 × (1/0.4300 + 1/0.2600) / (1.00 × [ln(0.605)]2) = 192.0, rounded up to 193 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
lambda0 <- 0.43                      # control rate, events per patient-year
lambda1 <- 0.26                      # treatment rate
tt      <- 0.996550402453047                       # follow-up per participant, years
n_per_arm <- function(power, frac = 1) {
  l1 <- lambda0 * (lambda1 / lambda0)^frac   # smaller effect = fraction of the observed log rate ratio
  ceiling(round((z_a + qnorm(power))^2 * (1 / lambda0 + 1 / l1) / (tt * log(l1 / lambda0)^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 = ",")))

# Simulation 1: Poisson counts. Simulation 2: over-dispersed counts (variance = 1.5 x mean), analysed with the matching variance.
set.seed(1875003)
n    <- n_per_arm(0.80)
reps <- 20000
m0 <- lambda0 * n * tt; m1 <- lambda1 * n * tt
x0 <- rpois(reps, m0); x1 <- rpois(reps, m1)
z  <- log(x1 / x0) / sqrt(1 / x0 + 1 / x1)
cat(sprintf("Simulated power, Poisson counts, n = %s per arm: %.3f\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE)))
phi <- 1.5
y0 <- rnbinom(reps, mu = m0, size = m0 / (phi - 1)); y1 <- rnbinom(reps, mu = m1, size = m1 / (phi - 1))
z2 <- log(y1 / y0) / sqrt(phi * (1 / y0 + 1 / y1))
cat(sprintf("Simulated power, over-dispersed counts (phi = 1.5), same n: %.3f\n", mean(abs(z2) > z_a, na.rm = TRUE)))

Output from running the code

100% of observed effect: n per arm = 193 (80% power), 258 (90% power)
 75% of observed effect: n per arm = 317 (80% power), 424 (90% power)
 50% of observed effect: n per arm = 662 (80% power), 886 (90% power)
Simulated power, Poisson counts, n = 193 per arm: 0.812
Simulated power, over-dispersed counts (phi = 1.5), same n: 0.641

The first simulation draws Poisson counts and should land close to the target power. The second allows extra variability (variance 1.5 times the mean, a purely illustrative value), which lowers the power at the same sample size, so rate trials usually need more participants than the Poisson formula suggests.

14. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
not statedAdjusted Rate Ratio 0.600.35 to 1.03not reported
not statedAdjusted Rate Ratio 0.490.28 to 0.83not reported

The registry’s sponsor-reported primary analyses are adjusted rate ratios: 0.60 for lebrikizumab 37.5 mg versus placebo, with a 95% confidence interval of 0.35 to 1.03; and 0.49 for lebrikizumab 125 mg versus placebo, with a 95% confidence interval of 0.28 to 0.83. The sponsor-reported analyses do not include p-values in the registry record.

Simple recalculations from the posted arm-level rates produce unadjusted rate ratios of 0.605 and 0.488. Their intervals are 0.383 to 0.954 and 0.301 to 0.793. These estimates are close to the sponsor’s rounded point estimates, but their intervals are not identical. This is not an inconsistency to resolve by choosing the more favorable result: the recalculations use a simple unadjusted approach, while the registry identifies the sponsor’s outcome as adjusted and based on Poisson regression.

The recalculated p-values, 0.031 for 37.5 mg and 0.004 for 125 mg, are not sponsor-reported p-values and should not be presented as such. The registry’s sponsor-reported analysis is the appropriate source for describing the trial’s adjusted primary result. The adjustment variables and detailed model specification are not reported in the registry record, so the posted adjusted estimates cannot be independently reproduced from the summaries alone.

15. Multiplicity, Missing Data and Analysis Populations

The registry lists 10 outcome measures and 16 analyses. The primary outcome has two dose-versus-placebo comparisons, and the secondary outcomes include multiple measurements and comparisons. Examining several outcomes creates a multiplicity issue: the more statistical comparisons made, the greater the chance that some results appear unusual through random variation alone. General approaches include defining a primary comparison in advance, adjusting significance thresholds, or treating secondary analyses as exploratory. Which approach was planned or applied in this trial is not reported in the registry record.

The registry labels the primary comparisons as superiority analyses and reports 95% confidence intervals, but it does not report the full statistical analysis plan, a hierarchy of endpoints, adjustment for multiple comparisons, interim analyses, or stopping rules. Their presence or absence should not be inferred from the posted results. The sponsor-reported primary p-values are also not reported in the registry record. Recalculated p-values from posted summary rates are unadjusted and do not reveal whether the sponsor’s analysis accounted for multiplicity.

The primary outcome description identifies the ITT population. The exact ITT definition, any exclusions, and handling of participants without endpoint data are not reported in the registry record. The registry also does not provide a complete outcome-by-outcome account of analysis populations, missingness, or imputation. Secondary FEV1 summaries have listed analysis counts that differ from the primary arm counts, but the reasons for that availability are not reported. A group-level summary cannot establish whether missing observations were balanced or whether missingness affected the estimates.

These omissions matter because confidence intervals and p-values depend on the analysis population and model. The adjusted model covariates, detailed handling of recurrent events, sensitivity analyses, and diagnostics are not reported. The study is listed as terminated, but the reason for termination and whether it influenced follow-up, data collection, or analytic decisions are not reported in the registry record. These gaps limit assessment of how robust the findings 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
Placebo3565.4%
Lebrikizumab 37.5 mg61135.3%
Lebrikizumab 125 mg81166.9%
Placebo/ Lebrikizumab 37.5 mg33010.0%
Placebo/ Lebrikizumab 125 mg43112.9%
Participants with at least one serious adverse event
Serious adverse events by armPlacebo5.4%Lebrikizumab 37.5 mg5.3%Lebrikizumab 125 mg6.9%Placebo/ Lebrikizumab 37.5 mg10.0%Placebo/ Lebrikizumab 125 mg12.9%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
Placebo0 of 56
Lebrikizumab 37.5 mg0 of 113
Lebrikizumab 125 mg0 of 116
Placebo/ Lebrikizumab 37.5 mg0 of 30
Placebo/ Lebrikizumab 125 mg0 of 31

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
Placebo23 of 56
Lebrikizumab 37.5 mg67 of 113
Lebrikizumab 125 mg72 of 116
Placebo/ Lebrikizumab 37.5 mg23 of 30
Placebo/ Lebrikizumab 125 mg24 of 31

Most frequent serious adverse event terms

Event termOrgan systemPlaceboLebrikizumab 37.5 mgLebrikizumab 125 mgPlacebo/ Lebrikizumab 37.5 mgPlacebo/ Lebrikizumab 125 mg
AsthmaRespiratory, thoracic and mediastinal disorders1 of 562 of 1132 of 1161 of 302 of 31
DehydrationMetabolism and nutrition disorders1 of 560 of 1131 of 1160 of 300 of 31
EosinophiliaBlood and lymphatic system disorders0 of 561 of 1130 of 1160 of 300 of 31
Abdominal painGastrointestinal disorders0 of 560 of 1130 of 1160 of 301 of 31
DiarrhoeaGastrointestinal disorders1 of 560 of 1130 of 1160 of 300 of 31
VomitingGastrointestinal disorders1 of 560 of 1130 of 1160 of 300 of 31
Anaphylactic reactionImmune system disorders0 of 560 of 1131 of 1160 of 300 of 31
Anaphylactic shockImmune system disorders0 of 560 of 1131 of 1160 of 300 of 31
AppendicitisInfections and infestations0 of 561 of 1130 of 1160 of 300 of 31
GastroenteritisInfections and infestations0 of 560 of 1131 of 1160 of 300 of 31

Most frequent non-serious adverse event terms

Event termOrgan systemPlaceboLebrikizumab 37.5 mgLebrikizumab 125 mgPlacebo/ Lebrikizumab 37.5 mgPlacebo/ Lebrikizumab 125 mg
AsthmaRespiratory, thoracic and mediastinal disorders12 of 5625 of 11331 of 11611 of 3015 of 31
PharyngitisInfections and infestations5 of 5610 of 11318 of 1168 of 304 of 31
NasopharyngitisInfections and infestations4 of 5614 of 11313 of 1166 of 307 of 31
Upper respiratory tract infectionInfections and infestations3 of 5616 of 11311 of 1162 of 302 of 31
HeadacheNervous system disorders2 of 568 of 11311 of 1163 of 306 of 31
BronchitisInfections and infestations2 of 5610 of 1136 of 1164 of 304 of 31
TonsillitisInfections and infestations2 of 569 of 1138 of 1162 of 303 of 31
RhinitisInfections and infestations1 of 565 of 1136 of 1163 of 303 of 31
Rhinitis allergicRespiratory, thoracic and mediastinal disorders1 of 563 of 1136 of 1162 of 302 of 31
InfluenzaInfections and infestations0 of 565 of 1136 of 1161 of 301 of 31

Serious events with the highest arm-level rate: asthma (6.5%), sinusitis (3.3%), type 1 diabetes mellitus (3.3%), headache (3.3%), abdominal pain (3.2%).

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 and other adverse events for several treatment periods or group labels. For the placebo group, serious adverse events affected 3 participants among 56 at risk; other adverse events affected 23 among 56 at risk. For lebrikizumab 37.5 mg, the corresponding figures are 6 among 113 for serious adverse events and 67 among 113 for other adverse events. For lebrikizumab 125 mg, they are 8 among 116 and 72 among 116.

The record also lists placebo/ lebrikizumab extension groups: serious adverse events affected 3 among 30 and 4 among 31, and other adverse events affected 23 among 30 and 24 among 31, respectively. These group labels reflect different treatment periods in the registry and should not be combined with the placebo-controlled groups. The registry lists 0 deaths for each adverse-event group.

These are counts of participants affected, not event rates or measures of severity across all events. The placebo serious-event group has 56 at risk, unlike the 117 listed for the primary endpoint placebo group; the reason for that difference is not reported in the registry record. The record lists serious-event terms including asthma, sinusitis, type 1 diabetes mellitus, headache, abdominal pain, and abortion spontaneous, with percentages attached to those terms. The registry summaries do not establish whether an event was caused by study treatment. Comparisons should be interpreted cautiously because exposure periods and analysis denominators may differ.

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

The posted primary results describe adjusted exacerbation-rate comparisons during the 52-week placebo-controlled period in a randomized study of adolescents with uncontrolled asthma on inhaled corticosteroids and a second controller medication. The adjusted rate ratios are below 1 for both lebrikizumab dose groups relative to placebo, with sponsor-reported estimates of 0.60 for 37.5 mg and 0.49 for 125 mg. Their confidence intervals indicate different degrees of precision: the 37.5 mg interval extends across 1, while the 125 mg interval is below 1.

These estimates do not mean that every participant experienced a lower event rate, or that an individual’s outcome can be predicted from a group-level average. The primary measure counts exacerbation events relative to follow-up time, rather than counting only whether each person had any event. The result also applies to the endpoint definition and period recorded in the trial; it is not a claim about every asthma outcome, longer-term effects, or other populations.

The registry reports secondary outcomes and adverse-event summaries, but the information does not establish a complete benefit-risk profile. Multiplicity handling, missing-data procedures, full model details, and the reason for trial termination are not reported in the registry record. The sponsor’s adjusted analyses should be distinguished from simple recalculations based on arm-level summaries, and secondary comparisons should not be treated as equally confirmatory when their multiplicity plan is unknown.

The results do not establish why the trial was terminated, why any participant experienced an exacerbation or adverse event, or whether a particular treatment is appropriate for an individual. They are statistical summaries of the outcomes reported for this trial. Their interpretation depends on the endpoint definition, analysis population, model assumptions, uncertainty intervals, and limitations of the registry record.

18. Why This Trial Matters Statistically

This trial offers a useful example of why endpoint scale matters. The primary outcome is an exacerbation rate per patient year, not a percentage of participants with an event. That distinction determines how the exposure time enters the analysis and why a rate ratio, rather than a risk difference, is the central comparative measure. The registry also identifies the adjusted Poisson regression analysis, making clear that the sponsor’s result is not simply a comparison of the three arm-level rates.

The record allows readers to distinguish adjusted sponsor estimates from unadjusted recalculations. The recalculated point estimates are close to the sponsor’s rounded rate ratios, but the recalculated intervals differ. This illustrates why agreement in rounded point estimates does not make analyses interchangeable: model adjustment and inferential procedures affect uncertainty as well as the estimate.

The secondary results further demonstrate that one trial can report several outcome types, including mean differences and hazard ratios, each with a different interpretation. Multiple endpoints increase the need for a prespecified analysis hierarchy and a clear multiplicity plan. Those details are not reported in the registry record, so secondary findings should be read as supporting context rather than as a collection of independent confirmatory tests.

Finally, the terminated status and the differences in listed outcome analysis groups highlight important reporting questions. The registry does not explain the termination or fully describe missing-data handling and analysis populations across outcomes. These omissions do not erase the reported estimates, but they affect how fully readers can evaluate precision, generalizability, and robustness.

19. Limitations

The registry record has important limitations for interpreting this trial. It lists a terminated status but does not report the reason for termination or whether termination affected recruitment, follow-up, endpoint collection, or analysis. Without that context, the status alone cannot explain the completeness or representativeness of the posted results.

The primary outcome description identifies an adjusted Poisson regression model and an ITT analysis population, but the model’s covariates and detailed specification are not reported. The record also does not describe model diagnostics, assessment or handling of over-dispersion, or the precise treatment of recurrent events beyond defining the event rate. These details are needed to reproduce or independently assess the adjusted estimates.

The sponsor-reported primary analyses include confidence intervals but no p-values. Recalculated unadjusted comparisons can be derived from posted rates, but they do not reproduce the adjusted analysis. The original sample-size justification, planned effect, and trial-specific design assumptions are not reported, so the planning illustrations cannot establish whether the study met its original design goals.

The registry record does not report multiplicity procedures, interim analyses, stopping rules, or the full statistical analysis plan. Missing-data methods and outcome-specific analysis populations are also not fully described. Several secondary outcomes are listed, but results are not posted for every listed measure. The reason for differing counts across outcomes is not reported.

Safety summaries use group-specific at-risk counts that differ across treatment labels and periods. The registry does not explain all denominator differences, and adverse-event counts alone do not establish causation. Finally, results from this adolescent population on background controller medication should not automatically be generalized to populations or treatment settings not described in the record.

20. Related Tutorials

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23. Record Summary

NCT01875003 is a Phase III, randomized, double-blind, parallel-group, placebo-controlled study sponsored by Hoffmann-La Roche. It enrolled adolescents with uncontrolled asthma despite inhaled corticosteroids and a second controller medication. Participants were assigned to lebrikizumab 37.5 mg, lebrikizumab 125 mg, or placebo; the primary endpoint was the adjusted asthma exacerbation rate during the 52-week placebo-controlled period.

The sponsor-reported adjusted rate ratios versus placebo were 0.60 for 37.5 mg and 0.49 for 125 mg. Their 95% confidence intervals were 0.35 to 1.03 and 0.28 to 0.83, respectively. The registry lists the study as terminated, with a start date of 2013-08-13 and primary completion date of 2016-12-28. The reason for termination and several key statistical details are not reported in the registry record.

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