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Lymphocytic Leukemia, Chronic Phase 3 Time-to-Event Analysis NCT01010061

CLL11: A Study of Obinutuzumab (RO5072759 [GA101]) With Chlorambucil in Patients With Previously Untreated Chronic Lymphocytic Leukemia (Stage 1a): Complete Statistical Analysis

This page examines the registry results for the randomized CLL11 comparison of obinutuzumab plus chlorambucil with chlorambucil alone. It focuses on investigator-assessed progression-free survival, the reported hazard ratio, and the interpretation limits of the posted results.

Trial start: 2009-12-21  ·  Enrollment: 787  ·  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 CLL11: A Study of Obinutuzumab (RO5072759 [GA101]) With Chlorambucil in Patients With Previously Untreated Chronic Lymphocytic Leukemia (Stage 1a) (NCT01010061), a randomized phase 3 study. The primary outcome is Progression-free Survival (PFS).

787
Enrollment
Phase 3
2
Arms
In the primary outcome
0.21
Hazard ratio
Obinutuzumab + Chlorambucil (GClb) vs Ch
0.16–0.28
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT01010061
PhasePhase 3
ConditionLymphocytic Leukemia, Chronic
AllocationRandomized
Design modelParallel
MaskingNone (open label)
Enrollment787
Arms in the primary outcome2
Lead sponsorHoffmann-La Roche
Results postedYes

2. Clinical Question

Population

The study enrolled patients with previously untreated chronic lymphocytic leukemia and comorbidities. The primary analysis population was the intent-to-treat population: all randomized participants. The registry record reports 787 participants enrolled across the three-arm study.

Intervention

The intervention of interest was obinutuzumab plus chlorambucil, abbreviated GClb. Participants could receive up to six 28-day cycles. Obinutuzumab was given intravenously and chlorambucil orally, according to the treatment schedule recorded for the study.

Comparator

The primary posted comparison is GClb versus chlorambucil alone, abbreviated Clb. The trial also randomized participants to rituximab plus chlorambucil, abbreviated RClb, but results for that arm are not included in the primary comparison. Participants assigned to Clb could cross over to GClb under the conditions described in the registry record.

Primary question

The primary endpoint asks how long participants remained alive without progression or relapse, as assessed by the investigator. The registry reports median progression-free survival and a hazard ratio for GClb versus Clb. These summaries describe the posted comparison; they do not establish what would happen for every participant or in other populations.

3. Trial Design

This was a completed, phase 3, randomized, open-label, parallel-group, three-arm study. It enrolled 787 participants and compared obinutuzumab plus chlorambucil, rituximab plus chlorambucil, and chlorambucil alone in previously untreated chronic lymphocytic leukemia with comorbidities. The registry describes randomization in a 2:2:1 allocation. Masking was none, so treatment assignment was not concealed from participants and study personnel.

The treatment period allowed a maximum of six 28-day cycles. In the GClb arm, obinutuzumab was administered by intravenous infusion on days 1, 8, and 15 of cycle 1 and on day 1 of cycles 2 through 6; chlorambucil was given orally on days 1 and 15 of cycles 1 through 6. The arm description notes that the first obinutuzumab infusion was split between day 1 and day 2 according to a protocol amendment. In the RClb arm, rituximab was given intravenously on day 1 of each cycle, with different recorded doses in cycle 1 and cycles 2 through 6, alongside chlorambucil. The Clb arm received chlorambucil on days 1 and 15 of each cycle.

Participants assigned to chlorambucil alone could cross over to GClb after progressive disease or within 6 months of follow-up. This crossover is relevant when considering outcomes after treatment assignment, especially outcomes measured over longer follow-up. The primary comparison is GClb versus Clb, not a three-way comparison and not a comparison with RClb.

The primary endpoint was investigator-assessed progression-free survival, measured from randomization to progression, relapse, or death from any cause. The registry record gives a clinical cutoff date of 10 Oct 2017 and median observation of 62.5 months from randomization. The trial's original sample-size justification and detailed protocol-level 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: 589 patients were randomized to 1 of 3 treatment groups in 2:2:1 ratio: GClb (n=238), RClb (n=233) or Clb (n=118) in Stage 1 and an additional 192 randomized to GClb or RClb in Stage 2 \[NCT02053610\]. Stage 1 was divided for analysis into: Stage 1a (GClb vs Clb) n=356 reported here and Stage 1b (RClb vs Clb) \[NCT01998880\] reported separately.

Overall Study

StageObinutuzumab + Chlorambucil (GClb)Chlorambucil (Clb)
STARTED238118
Received Study Drug236116
COMPLETED19078
NOT COMPLETED4840

Reasons for not completing this period:

ReasonObinutuzumab + Chlorambucil (GClb)Chlorambucil (Clb)
Adverse Events or Intercurrent Illness3316
Disease Progression28
Withdrew Consent51
Death36
Administrative/Other01
Refused Treatment/Did Not Cooperate20
Insufficient Therapeutic Response15
Violation of Selection Criteria01
Did Not Receive Treatment22

Analysis population for the primary outcome, as defined in the registry: Intent-to-treat population included all randomized participants. Patients without PFS events were censored.

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: Baseline measures are based on the participants who were included in the Stage 1a analysis.

CharacteristicUnitObinutuzumab + Chlorambucil (GClb)Chlorambucil (Clb)Total
Participants analysed238118356
Age, Customized: <65 yearsparticipants422668
Age, Customized: >=65 yearsparticipants19692288
Sex: Female, Male: FemaleParticipants9843141
Sex: Female, Male: MaleParticipants14075215

6. Primary Endpoint

The registry lists the primary outcome as Progression-free Survival (PFS), measured over Randomization to clinical cutoff date of 10 Oct 2017 (median observation 62.5 months from randomization).

ElementRegistry entry
Result typeMedian
Measure of spread95% Confidence Interval
UnitMonths
Endpoint classificationTime-to-Event Analysis

Progression-free survival (PFS) measures the time from randomization until the first recorded occurrence of disease progression, relapse, or death from any cause. Participants without a PFS event were censored, as stated in the registry record. This endpoint combines disease control and survival into a time-to-event outcome: an event can be recorded because of progression or relapse even when the participant is alive.

Progression was assessed by the investigator. The registry definition includes changes in lymphocyte counts, new or enlarging lymph nodes or other lesions, enlargement of the liver or spleen, transformation to a more aggressive histology, and specified worsening in blood-cell counts after treatment. The criteria therefore use clinical and laboratory observations rather than a single measurement.

Time-to-event endpoints are useful when the timing of an event matters and participants may have different lengths of follow-up. In general, censoring allows participants who have not had an event by their last observed time to contribute information up to that point; it does not mean that they are known to remain event-free afterward. The registry reports the median PFS for each arm and a hazard ratio for the comparison. The median describes the time by which half of the relevant survival distribution has had an event, while the hazard ratio summarizes the relative event rate over follow-up under the analysis used. Neither summary gives an individual participant's expected outcome.

7. Results Posted in the Registry

Hazard ratio: Obinutuzumab + Chlorambucil (GClb) vs Chlorambucil (Clb)

0.21

95% CI: 0.16 to 0.28

As reported in the registry

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Obinutuzumab + Chlorambucil (…0.140.210.320.490.761.16hazard ratio (as reported) 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
Progression Free Survival Based on Independent Review Committee (IRC) DataTime-to-Event AnalysisHazard ratio0.19 (0.14 to 0.27)12 events
Percentage of Participants With Progression Free Survival Events Based on Independent Review Committee (IRC) DataBinary EndpointRisk difference+38.9 pts (29.0 to 48.7)25 per arm
Event Free SurvivalTime-to-Event AnalysisHazard ratio0.19 (0.15 to 0.26)12 events

Progression Free Survival Based on Independent Review Committee (IRC) Data

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Obinutuzumab + Chlorambucil (…0.120.190.300.470.741.17hazard ratio (as reported) vs control (95% CI)

Percentage of Participants With Progression Free Survival Events Based on Independent Review Committee (IRC) Data

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Chlorambucil (Clb)-3.907.4019304153risk difference (percentage points) vs control (95% CI)

Event Free Survival

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Obinutuzumab + Chlorambucil (…0.130.200.310.480.751.16hazard ratio (as reported) vs control (95% CI)

The posted secondary results include an independent review committee assessment of PFS, the percentage with PFS events based on that review, and event-free survival. The registry also lists other outcomes, including overall survival, duration of response, response measures, and molecular remission. Taken as a set, the available time-to-event summaries broadly point in the same direction as the primary investigator-assessed PFS comparison: the reported GClb estimates are more favorable on the posted time-to-event scales than the Clb estimates. This overall consistency can be informative, while remaining distinct from the primary endpoint result.

Independent review of PFS addresses the outcome using a different assessment source from the investigator assessment used for the primary endpoint. Agreement in direction can help readers see whether the broad pattern depends only on one assessment. It does not erase differences between endpoint definitions, follow-up cutoffs, or assessment procedures. The registry's early IRC PFS results have a different cutoff and median observation time from the primary result, so their numerical estimates should not be treated as if they came from the same analysis occasion.

The record lists 14 outcome measures and reports that 12 secondary outcomes were posted. The details do not include numeric results for every listed secondary outcome. Those outcomes should not be assumed to confirm or contradict the primary finding when their results are not reported in the registry record.

Secondary outcomes generally carry less inferential weight than a prespecified primary endpoint, particularly when many outcomes are examined. Unless multiplicity is addressed, repeated testing can increase the chance of findings that appear persuasive by chance alone. The registry does not report a multiplicity adjustment or a testing hierarchy. Accordingly, the secondary results add context to the primary analysis, but they should not be presented as independent confirmation with the same evidential standing.

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

9. Statistical Interpretation

Clinical Biostats interpretation

The posted primary results compare GClb with Clb in the intent-to-treat population. Median PFS was 31.1 months for GClb, with a 95% confidence interval from 26.5 to 35.6 months, and 11.1 months for Clb, with a 95% confidence interval from 10.7 to 11.3 months. The reported hazard ratio was 0.21, with a 95% confidence interval from 0.16 to 0.28; the reported p-value was < 0.001. The analysis method was a stratified log-rank test.

In general, a hazard ratio below 1 indicates a lower estimated event hazard in the first named group relative to the comparator, under the analysis that produced the estimate. It is a relative time-to-event summary, not a direct estimate of how many months an individual gains and not a probability that a participant will experience progression. The reported confidence interval lies below 1, indicating that the estimate is not close to the no-difference value on the hazard-ratio scale. The p-value gives evidence against the null hypothesis used for the reported test, but it does not measure the size or clinical importance of an effect.

The medians and hazard ratio describe different aspects of the event-time distributions. The medians locate a point in each arm's estimated distribution, while the hazard ratio summarizes the comparison across event times according to the analysis. They should be read together rather than treated as interchangeable measures. The registry does not report the full survival curves or enough detail to assess how the relative event pattern varied over time.

The primary analysis used all randomized participants, and participants without PFS events were censored. That definition is important: the posted medians and hazard ratio depend on the recorded events, follow-up, and censoring information. The registry record does not provide additional detail on the amount or reasons for missing follow-up data. Nor does it give the original analysis plan's complete specification beyond the endpoint description and the reported stratified log-rank method.

These are findings for the stated GClb-versus-Clb comparison in this trial. The trial had a third randomized group, RClb, but the primary results do not establish how GClb compares with that group. Crossover from Clb to GClb was allowed under specified conditions, which is also relevant to interpreting longer-term outcomes. The posted result should therefore be understood as a registry-reported comparison with its stated endpoint and analysis, not as a universal conclusion about all treatment choices or all patients.

10. Statistical Methods Explained

The primary result is a time-to-event analysis. The registry defines PFS as time from randomization to the first occurrence of progression, relapse, or death from any cause, assessed by the investigator. The reported summary includes arm-specific medians and a hazard ratio, with a stratified log-rank method noted for the comparison.

What does a median time-to-event value describe?

In general, the median time-to-event value is the point at which the estimated event-free proportion reaches one half. It is not an average, and it does not imply that every participant experiences an event at that time. Participants may have events earlier or later, and those without an event by their last observation are censored. Censoring means their event time is not fully observed; their available follow-up still contributes information up to the censoring time under the analysis approach.

The registry reports median PFS of 31.1 months for GClb and 11.1 months for Clb. Each median has a 95% confidence interval, which expresses uncertainty around that estimated median. The interval is not a range containing the event times of most participants. It describes uncertainty in the estimate, conditional on the data and analysis assumptions.

How should the hazard ratio be read?

In general, a hazard is the event rate at a given time among participants who have not yet had the event. A hazard ratio compares the hazards between groups as summarized by the analysis. The reported estimate of 0.21 compares GClb with Clb. It is not a risk ratio, a difference in medians, or a statement that each participant's chance of an event is multiplied by that value.

A single hazard ratio is most straightforward to interpret when the relative hazards are reasonably stable over time. The registry record does not report a diagnostic or analysis of that assumption, so this page cannot determine whether it held. The reported confidence interval and p-value describe statistical uncertainty and evidence under the specified method, but they do not address every possible source of bias or model limitation.

What does the stratified log-rank method do?

In general, the log-rank test compares event-time patterns between groups while accounting for the timing of events and censoring. A stratified version performs the comparison within strata and combines information across them. The registry names the method as Log Rank, Stratified, but the stratification factors are not reported in the registry record. The corresponding hazard ratio is the sponsor-reported comparative estimate; the method label alone does not disclose every detail of how that estimate was calculated.

The reported p-value is < 0.001. In general, a p-value measures how unusual data at least as incompatible with a specified null hypothesis would be if that hypothesis and the analysis assumptions were correct. It is not the probability that the null hypothesis is true, nor is it a measure of the probability that the result will be reproduced. It also does not substitute for the effect estimate or its confidence interval.

Why do the endpoint definition and population matter?

The endpoint includes progression, relapse, and death from any cause, and progression was assessed by investigators. The study was open-label, so treatment assignment was known; this is relevant context when an endpoint includes investigator assessment. The record does not establish that this feature biased the assessment, but it is a design consideration when interpreting the result.

The primary population was intent-to-treat and included all randomized participants. This approach retains participants in their randomized groups for the primary comparison, regardless of later treatment changes as defined by the analysis. Participants without PFS events were censored. Additional details about missing observations, censoring rules, stratification factors, and the full statistical analysis plan are not reported in the registry record.

11. Confidence Intervals and Precision

The primary PFS estimates are accompanied by 95% confidence intervals. For GClb, the median was 31.1 months with an interval from 26.5 to 35.6 months. For Clb, the median was 11.1 months with an interval from 10.7 to 11.3 months. These intervals communicate uncertainty in the estimated medians; they are not ranges of individual participant outcomes.

The reported hazard ratio was 0.21, with a 95% confidence interval from 0.16 to 0.28. In general, a confidence interval describes a range of values compatible with the data under the analysis and its assumptions. It is not a guarantee that the true value lies within that particular interval, and its interpretation depends on the design and statistical method. Here, the interval is wholly below 1, the value corresponding to equal hazards on the hazard-ratio scale.

Precision is distinct from the size of an estimate. A relatively narrow interval indicates less statistical uncertainty than a wider interval on the same scale, but it does not address systematic error, endpoint assessment, missing data, or whether the estimate applies outside the trial population. The intervals also do not provide the complete distribution of PFS times. The registry record reports the median observation time as 62.5 months from randomization and the clinical cutoff date as 10 Oct 2017; those details describe follow-up context, not the precision of every participant's outcome.

The p-value of < 0.001 and the confidence interval are related ways of conveying evidence and uncertainty, but they answer different questions. The p-value is tied to a test of a null hypothesis, while the interval shows a range of estimated hazard-ratio values. Neither measure alone describes clinical importance or settles the limitations of the analysis.

12. Planning a Similar Trial: Sample Size

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

Effect to detect (log scale)Hazard ratioEvents, 80% powerEvents, 90% power
100% of the observed effect0.211318
75% of the observed effect0.312331
50% of the observed effect0.465270
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect10205010020040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: events required (total))
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, Schoenfeld approximation for the log-rank test or Cox model. The answer is the total number of events, not participants; the number of participants depends on how quickly events accrue. Calculated for the comparison: Obinutuzumab + Chlorambucil (GClb) vs Chlorambucil (Clb).

The sample-size display is a planning illustration based on the observed effect, not a reconstruction of the trial's original design. For time-to-event outcomes, its entries are total numbers of events, not participants per arm. The calculations use a two-sided significance level of 0.05, equal allocation between the two arms, a normal approximation, and an effect to detect set to the stated fraction of the observed effect. The original sample-size assumptions are not reported in the registry record.

The 80% power column gives the total event count that the illustration estimates would be needed for an 80% chance of detecting the specified effect under those assumptions, if that effect and the assumptions applied. The 90% power column gives the corresponding event count for a 90% chance. These are planning probabilities under a hypothetical calculation, not probabilities that the trial's result is correct.

The rows show planning for 100%, 75%, and 50% of the observed effect. A smaller target effect generally requires more information to detect, so the table's smaller-effect rows call for more total events. The number of events is not interchangeable with the number of enrolled participants: how many participants are needed to accumulate those events depends on event occurrence and follow-up. These figures are not observed power.

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

d = 4 (z1−α/2 + z1−β)2 / [ln(HR)]2

d is the total number of events needed (Schoenfeld's formula) with 1:1 allocation and proportional hazards.

Worked calculation for this trial

  1. Hazard ratio HR = 0.210, so ln(HR) = -1.5606.
  2. d = 4 × (1.96 + 0.842)2 / [ln(0.210)]2 = 12.9, rounded up to 13 events in total 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
hr <- 0.21                              # observed hazard ratio
events_needed <- function(power, frac = 1) ceiling(round(4 * (z_a + qnorm(power))^2 / log(hr^frac)^2, 6))   # Schoenfeld, 1:1 allocation
for (f in c(1, 0.75, 0.5))
  cat(sprintf("%3.0f%% of observed effect: events = %s (80%% power), %s (90%% power)\n", 100 * f,
              format(events_needed(0.80, f), big.mark = ","), format(events_needed(0.90, f), big.mark = ",")))

# Simulation: given d total events under proportional hazards, events in the treatment arm are Binomial(d, hr / (1 + hr)).
# The score (log-rank type) statistic is (D1 - d / 2) / sqrt(d / 4).
set.seed(1010061)
d    <- events_needed(0.80)
reps <- 20000
D1 <- rbinom(reps, d, hr / (1 + hr))
z  <- (D1 - d / 2) / sqrt(d / 4)
cat(sprintf("Simulated power with %s events: %.3f (%d replicates)\n", format(d, big.mark = ","), mean(abs(z) > z_a), reps))

Output from running the code

100% of observed effect: events = 13 (80% power), 18 (90% power)
 75% of observed effect: events = 23 (80% power), 31 (90% power)
 50% of observed effect: events = 52 (80% power), 70 (90% power)
Simulated power with 13 events: 0.601 (20000 replicates)

The simulation uses the fact that, with d events in total and proportional hazards, the number of events in the treatment arm is binomial. It is an approximation that conditions on the total number of events, and it should land close to the target power.

Very small required sample. The formula gives a very small requirement because the observed effect is very large relative to the variability. Normal-approximation formulas are unreliable at such sizes, and the simulation above shows the power actually achieved. An exact or simulation-based design would be needed in practice.

14. Group-Sequential Design Analysis

Many time-to-event trials, especially in oncology, stop or report early when interim data are overwhelming, so a single fixed-sample number understates the real design problem. The calculation below is an illustrative group-sequential design built from this trial's posted control median and hazard ratio. The registry record does not state the planned number of looks or the spending function, so the design is a planning illustration, not a reconstruction of the protocol. Assumed: one-sided α = 0.025, 90% power, three equally spaced looks on information, Lan-DeMets O'Brien-Fleming spending, 24 months of accrual, 60 months in total and a 1% monthly dropout hazard.

Under these assumptions the design needs about 29 participants in total, with the boundaries below.

AnalysisCalendar time (months)EventsEfficacy boundary (z)Nominal one-sided pCumulative alpha spent
Look 119.263.7100.00010.0001
Look 230.8112.5110.00600.0060
Look 360.0171.9930.02310.0250
01234z = 3.7119 mo6 eventsz = 2.5131 mo11 eventsz = 1.9960 mo17 eventsUpper efficacy boundary (z)

Fixed design versus group-sequential alternatives

DesignPowerEvents at final analysisParticipantsStudy length (months)
Fixed design, one analysis80%122160.0
Two looks, O'Brien-Fleming80%122160.0
Three looks, O'Brien-Fleming80%122160.0
Three looks, Pocock80%142460.0
Fixed design, one analysis90%172860.0
Two looks, O'Brien-Fleming90%172860.0
Three looks, O'Brien-Fleming90%172960.0
Three looks, Pocock90%193360.0

Group-sequential designs cost a small increase in maximum sample size and events compared with the fixed design, in exchange for the chance to stop early for overwhelming efficacy. O'Brien-Fleming spending keeps early boundaries very conservative and the final boundary close to the fixed-design value, whereas Pocock spending spends more alpha early.

Sensitivity to a smaller true effect

Planning for exactly the observed effect is optimistic, because observed effects in published trials tend to be somewhat larger than the true effect. The table repeats the main design (three looks, O'Brien-Fleming spending, 90% power) for smaller true hazard ratios.

True effect assumedHazard ratioEvents at final analysisParticipants
100% of the observed effect0.2101729
75% of the observed effect0.3103046
50% of the observed effect0.4586995

For context, this trial enrolled 787 participants.

Cross-check, upper boundaries: gsDesign 3.71, 2.511, 1.993 | rpact 3.71, 2.511, 1.993. Agreement between the two packages confirms the boundary calculation.

R code and output

suppressWarnings(suppressMessages({ library(gsDesign); library(rpact) }))
med_control <- 11.1          # control-arm median, months (converted from the posted unit)
hr          <- 0.21          # hazard ratio used for planning
lambdaC     <- log(2) / med_control
eta         <- 0.01               # dropout hazard per month (assumption)
acc_months  <- 24                 # accrual duration (assumption)
study_months<- 60                 # total study duration (assumption)

design <- function(k, sfu, beta, h = hr) gsSurv(k = k, test.type = 1, alpha = 0.025, beta = beta, sfu = sfu,
  lambdaC = lambdaC, hr = h, hr0 = 1, eta = eta, gamma = 1, R = acc_months, T = study_months, minfup = study_months - acc_months)

# Main design: 3 looks, Lan-DeMets O'Brien-Fleming spending, one-sided alpha 0.025, 90% power
x <- design(3, sfLDOF, 0.10)
cat(sprintf("N_TOTAL|%s\n", format(ceiling(sum(x$gamma * x$R)), big.mark = ",")))
for (i in 1:3) cat(sprintf("GS|%d|%.1f|%.0f|%.3f|%.5f|%.5f\n", i, x$T[i], x$n.I[i], x$upper$bound[i], pnorm(-x$upper$bound[i]), cumsum(x$upper$spend)[i]))
cat("\n"); print(gsBoundSummary(x))

# Comparison of designs
cmp <- list(list("Fixed design, one analysis", 1, sfLDOF), list("Two looks, O'Brien-Fleming", 2, sfLDOF),
            list("Three looks, O'Brien-Fleming", 3, sfLDOF), list("Three looks, Pocock", 3, sfLDPocock))
cat("\n")
for (b in c(0.20, 0.10)) for (d in cmp) {
  y <- design(d[[2]], d[[3]], b)
  cat(sprintf("DES|%s|%d|%.0f|%s|%.1f\n", d[[1]], round(100 * (1 - b)), tail(y$n.I, 1), format(ceiling(sum(y$gamma * y$R)), big.mark = ","), tail(y$T, 1)))
}

# Sensitivity: what if the true effect is smaller than the observed one? (3 looks, O'Brien-Fleming, 90% power)
cat("\n")
for (fr in c(1, 0.75, 0.5)) {
  y <- design(3, sfLDOF, 0.10, exp(log(hr) * fr))
  cat(sprintf("SENS|%.2f|%.3f|%.0f|%s\n", fr, exp(log(hr) * fr), tail(y$n.I, 1), format(ceiling(sum(y$gamma * y$R)), big.mark = ",")))
}

# Independent cross-check of the boundaries with rpact
r <- getDesignGroupSequential(kMax = 3, alpha = 0.025, beta = 0.10, sided = 1, typeOfDesign = "asOF", informationRates = x$timing)
cat(sprintf("\nCross-check, upper boundaries: gsDesign %s | rpact %s\n", paste(round(x$upper$bound, 3), collapse = ", "), paste(round(r$criticalValues, 3), collapse = ", ")))

Method: LachinFoulkes 
   Analysis               Value Efficacy
  IA 1: 33%                   Z   3.7103
      N: 24         p (1-sided)   0.0001
  Events: 6        ~HR at bound   0.0442
  Month: 19    P(Cross) if HR=1   0.0001
            P(Cross) if HR=0.21   0.0338
  IA 2: 67%                   Z   2.5114
      N: 30         p (1-sided)   0.0060
 Events: 12        ~HR at bound   0.2247
  Month: 31    P(Cross) if HR=1   0.0060
            P(Cross) if HR=0.21   0.5603
      Final                   Z   1.9930
      N: 30         p (1-sided)   0.0231
 Events: 17        ~HR at bound   0.3801
  Month: 60    P(Cross) if HR=1   0.0250
            P(Cross) if HR=0.21   0.9000



Cross-check, upper boundaries: gsDesign 3.71, 2.511, 1.993 | rpact 3.71, 2.511, 1.993

15. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
Log Rank, StratifiedHazard Ratio (HR) 0.210.16 to 0.28< 0.001

The registry reports the sponsor's primary comparison as a hazard ratio of 0.21, with a 95% confidence interval from 0.16 to 0.28 and p < 0.001, using a stratified log-rank method. These are the sponsor-reported results for GClb versus Clb. They are the main inferential results to use when describing this analysis.

Any simple unadjusted re-calculation from posted summary statistics is supplementary: it does not reproduce the sponsor's full time-to-event analysis, which uses event timing, censoring, and the stated method. No discrepancy is flagged in the registry record. The sponsor-reported result and any derived planning illustration should therefore be kept distinct; the latter does not replace the reported analysis or establish the trial's original design assumptions.

The registry record does not report every detail needed to independently reproduce the stratification or the full analysis. In particular, it does not state the stratification factors in the information. The reported estimate can be interpreted alongside its interval and p-value, while recognizing that a summary statistic does not expose all of the underlying analysis decisions.

16. Multiplicity, Missing Data and Analysis Populations

The registry identifies PFS as the primary endpoint and lists multiple secondary outcomes, including other time-to-event, response, and molecular outcomes. When many outcomes are assessed, multiplicity matters: in general, the more statistical tests performed, the greater the opportunity for at least one apparently unusual result to arise by chance. Adjustment procedures or a prespecified testing sequence can control how results are interpreted across a family of tests.

A multiplicity adjustment, testing hierarchy, or other family-wise error strategy is not reported in the registry record. The reported primary p-value can be read as the result for the stated primary comparison and test, but the record does not establish how confirmatory claims across the secondary outcomes were controlled. Secondary p-values or effect estimates should therefore be interpreted with that uncertainty in mind.

The primary population is reported as intent-to-treat and includes all randomized participants. Participants without PFS events were censored. The registry record does not provide further details about the number of censored participants, reasons for censoring, missing assessments, or sensitivity analyses for missing data. In general, time-to-event methods rely on assumptions about the relationship between censoring and future event risk; the record does not report enough information to assess those assumptions fully.

Other analysis-plan details are also not reported in the registry record, including the original sample-size justification, the stratification factors for the log-rank analysis, and any planned interim analyses. These omissions should not be filled in by assumption. They limit how completely a reader can reconstruct the trial's statistical decision process, while leaving the posted endpoint definitions and sponsor-reported estimates available for interpretation.

17. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Obinutuzumab + Chlorambucil (GClb)11324146.9%
Chlorambucil (Clb)4511638.8%
Crossover Subjects: Obinutuzumab + Chlorambucil (GClb)83026.7%
Participants with at least one serious adverse event
Serious adverse events by armObinutuzumab + Chlorambucil (…46.9%Chlorambucil (Clb)38.8%Crossover Subjects: Obinutuzu…26.7%% 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
Obinutuzumab + Chlorambucil (GClb)215 of 241
Chlorambucil (Clb)89 of 116
Crossover Subjects: Obinutuzumab + Chlorambucil (GClb)23 of 30

Most frequent serious adverse event terms

Event termOrgan systemObinutuzumab + Chlorambucil (GClb)Chlorambucil (Clb)Crossover Subjects: Obinutuzumab + Chlorambucil (GClb)
Infusion related reactionInjury, poisoning and procedural complications27 of 2410 of 1160 of 30
PneumoniaInfections and infestations10 of 2414 of 1161 of 30
Basal cell carcinomaNeoplasms benign, malignant and unspecified (incl cysts and polyps)7 of 2410 of 1161 of 30
Febrile neutropeniaBlood and lymphatic system disorders2 of 2415 of 1161 of 30
Squamous cell carcinoma of skinNeoplasms benign, malignant and unspecified (incl cysts and polyps)6 of 2410 of 1160 of 30
Myocardial infarctionCardiac disorders4 of 2412 of 1160 of 30
Respiratory tract infectionInfections and infestations2 of 2413 of 1160 of 30
SepsisInfections and infestations0 of 2414 of 1161 of 30
Cardiac failureCardiac disorders3 of 2412 of 1160 of 30
Septic shockInfections and infestations2 of 2412 of 1160 of 30

Most frequent non-serious adverse event terms

Event termOrgan systemObinutuzumab + Chlorambucil (GClb)Chlorambucil (Clb)Crossover Subjects: Obinutuzumab + Chlorambucil (GClb)
Infusion related reactionInjury, poisoning and procedural complications147 of 2410 of 11615 of 30
NeutropeniaBlood and lymphatic system disorders99 of 24121 of 11612 of 30
NauseaGastrointestinal disorders32 of 24129 of 1163 of 30
ThrombocytopeniaBlood and lymphatic system disorders36 of 2419 of 1167 of 30
AnaemiaBlood and lymphatic system disorders27 of 24112 of 1163 of 30
DiarrhoeaGastrointestinal disorders23 of 24113 of 1163 of 30
PyrexiaGeneral disorders25 of 2418 of 1162 of 30
CoughRespiratory, thoracic and mediastinal disorders22 of 2418 of 1164 of 30
ConstipationGastrointestinal disorders17 of 24112 of 1162 of 30
FatigueGeneral disorders16 of 24112 of 1161 of 30

Serious events with the highest arm-level rate: infusion related reaction (11.2%), febrile neutropenia (4.3%), pneumonia (4.1%), sepsis (3.4%), basal cell carcinoma (3.3%).

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 for three groups: the GClb safety group, the Clb safety group, and participants who crossed over to GClb. Serious adverse events affected 113 of 241 participants in the GClb group, 45 of 116 in the Clb group, and 8 of 30 crossover participants. These are counts within the recorded groups, not the intent-to-treat denominators used for the primary PFS results.

The listed serious adverse event terms include infusion related reaction at 11.2%, febrile neutropenia at 4.3%, pneumonia at 4.1%, sepsis at 3.4%, basal cell carcinoma at 3.3%, and ileus at 3.3%. The registry labels these among the top serious terms. The figures should be read as the recorded adverse-event summaries, not as a complete account of every possible event or a direct comparison of causation between groups.

The record also gives counts for participants with other adverse events, but does not include deaths in the posted safety summary. Death counts are not reported in the registry record. Differences in safety-group sizes and the crossover group should be kept in view; these figures alone do not establish comparative risk or explain the clinical circumstances of any event.

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

The result describes a randomized comparison of GClb with Clb in participants with previously untreated chronic lymphocytic leukemia and comorbidities. For investigator-assessed PFS, the registry reports a median of 31.1 months for GClb and 11.1 months for Clb, along with a hazard ratio of 0.21 and a 95% confidence interval from 0.16 to 0.28. These findings summarize the observed trial data under the stated endpoint and analysis.

They do not mean that every participant in one group remained progression-free longer than every participant in the other group. A median is a group-level summary, and a hazard ratio is a relative time-to-event summary. Neither provides an individual prediction. The confidence interval expresses uncertainty in the hazard-ratio estimate under the analysis; it does not account for every possible source of bias or establish how the results apply to people outside the study.

The comparison is specifically GClb versus Clb. Although the study included an RClb arm, the primary result does not compare GClb with RClb. Crossover from Clb to GClb was permitted under the recorded conditions, which may matter when considering longer-term outcomes and interpretation by original treatment assignment. The study was open-label, and progression was assessed by investigators; these are design features to keep in context, not proof that assessments were biased.

The registry record does not report the original sample-size justification, multiplicity strategy, or several details needed to reconstruct the full analysis plan. The posted data therefore support a careful description of the reported comparison, but not conclusions beyond its population, endpoint, groups, and analysis. This page describes statistical evidence and uncertainty; it does not make treatment recommendations.

19. Why This Trial Matters Statistically

This trial illustrates why a clinical result should be read through its endpoint, population, and analysis rather than through a single headline number. PFS is a time-to-event endpoint that includes progression, relapse, or death, and the registry reports both arm-specific medians and a comparative hazard ratio. Those summaries answer related but different questions and are best considered together.

The record also provides useful context for interpreting a randomized comparison: the study was open-label, used three arms, and allowed crossover from Clb to GClb under specified conditions. The primary result is only one of the possible pairwise comparisons. Recognizing that distinction prevents the GClb-versus-Clb result from being generalized to the RClb arm without evidence in the posted comparison.

Statistically, the confidence interval helps distinguish the estimated effect from its uncertainty, while the p-value addresses compatibility with a null hypothesis under the reported test. Neither resolves questions about multiplicity, missing data, outcome assessment, or assumptions behind time-to-event analysis. The registry record leaves several of those details unreported, making transparent qualification important.

The sample-size illustration is another useful teaching point: event-based planning for time-to-event outcomes is not the same as counting participants, and planning calculations based on an observed effect do not describe the trial's original design or its observed power. Keeping these concepts separate supports a more accurate reading of registry results.

20. Limitations

Several limitations specific to this record affect interpretation. The study was open-label, and the primary endpoint included investigator-assessed progression. This does not establish that assessment was biased, but the lack of masking is relevant when considering an outcome that involves clinical judgments.

The primary comparison presented is GClb versus Clb, while the randomized design also included RClb. The result therefore does not answer the comparative question between GClb and RClb. In addition, participants assigned to Clb could cross over to GClb under the registry's stated conditions. Crossover can complicate interpretation of outcomes measured over extended follow-up; the available record does not provide enough detail to quantify its influence on the primary estimate.

The primary endpoint analysis included the intent-to-treat population, and participants without events were censored. Further information about censoring, missing assessments, and sensitivity analyses is not reported in the registry record. The stratified log-rank method is named, but the factors used for stratification are not reported. The original sample-size rationale, interim analysis plan, and multiplicity approach are also not reported.

The primary result uses an investigator assessment and a clinical cutoff date of 10 Oct 2017, with median observation of 62.5 months. The secondary IRC PFS result uses a different cutoff date and observation period. These should not be combined as though they were the same analysis. Finally, not every listed secondary outcome has numeric results in the information, limiting conclusions across the full outcome set.

21. Related Tutorials

22. Related Statistical Calculators

23. Sources

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24. Record Summary

NCT01010061 is a completed, phase 3, randomized, open-label, parallel-group study of treatment in previously untreated chronic lymphocytic leukemia with comorbidities. The three arms were obinutuzumab plus chlorambucil, rituximab plus chlorambucil, and chlorambucil alone. The primary result is the intent-to-treat comparison of obinutuzumab plus chlorambucil with chlorambucil alone.

The primary endpoint was investigator-assessed PFS from randomization to progression, relapse, or death from any cause. The registry reports median PFS of 31.1 months and 11.1 months in the two groups, respectively, and a hazard ratio of 0.21 with a 95% confidence interval from 0.16 to 0.28 and p < 0.001. The comparison used a stratified log-rank method. Interpretation should account for the open-label design, permitted crossover, censoring, and statistical-plan details not reported in the registry record.

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