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Multiple Myeloma Phase 3 Time-to-Event Analysis NCT01734928

Safety and Efficacy of Pomalidomide, Bortezomib and Low-dose Dexamethasone in Subjects With Relapsed or Refractory Multiple Myeloma: Complete Statistical Analysis

This analysis examines a randomized Phase 3 trial comparing pomalidomide, bortezomib and low-dose dexamethasone with bortezomib and low-dose dexamethasone for relapsed or refractory multiple myeloma. The primary outcome was progression-free survival, with overall survival and duration of response among the secondary outcomes.

Trial start: 2013-01-07  ·  Enrollment: 559  ·  Sponsor: Celgene
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 Safety and Efficacy of Pomalidomide, Bortezomib and Low-dose Dexamethasone in Subjects With Relapsed or Refractory Multiple Myeloma (NCT01734928), a randomized phase 3 study. The primary outcome is Progression Free Survival by Independent Response Adjudication Committee (IRAC).

559
Enrollment
Phase 3
2
Arms
In the primary outcome
0.61
Hazard ratio
Treatment 1: POM+BTZ+LD-DEX vs Treatment
0.49–0.77
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT01734928
PhasePhase 3
ConditionMultiple Myeloma
AllocationRandomized
Design modelParallel
MaskingNone (open label)
Enrollment559
Arms in the primary outcome2
Lead sponsorCelgene
Results postedYes

2. Clinical Question

Population

Participants with relapsed or refractory multiple myeloma were eligible for the trial. The primary endpoint population is described as all randomized participants. The registry record lists 559 participants enrolled; 281 were included in the primary outcome group for Treatment 1 and 278 for Treatment 2.

Intervention

Treatment 1 combined pomalidomide, bortezomib and low-dose dexamethasone. The registry describes pomalidomide as an oral drug and bortezomib as administered subcutaneously. The full dosing description for this arm is incomplete in the registry record.

Comparator

Treatment 2 combined bortezomib and low-dose dexamethasone. The registry describes bortezomib as administered subcutaneously. Its dosing description is also incomplete in the registry record.

Primary question

Did progression-free survival, assessed by the Independent Response Adjudication Committee, differ between the combination containing pomalidomide and the combination without it? The registry reports medians, a hazard ratio from a Cox proportional hazards model, a 95% confidence interval and a p-value for this comparison.

The trial also assessed safety and included secondary outcomes such as overall survival, response rate, duration of response and treatment-emergent adverse events. The posted results include estimates for overall survival and duration of response, but detailed estimates for some other listed secondary outcomes are not reported in the registry record. The primary comparison therefore answers a focused time-to-event question; it does not by itself describe every benefit or risk measured in the trial.

3. Trial Design

This was a Phase 3, multicenter, randomized, open-label, parallel-group study sponsored by Celgene. The registry lists 559 participants as enrolled. Participants were assigned to one of two treatment groups: pomalidomide, bortezomib and low-dose dexamethasone, or bortezomib and low-dose dexamethasone. The primary outcome includes 281 participants in Treatment 1 and 278 in Treatment 2. The study is marked completed.

The trial began on 2013-01-07, and primary completion is recorded as 2022-05-09. These dates describe the registry record; they do not establish when every participant entered or completed follow-up. The primary endpoint was progression-free survival assessed by the Independent Response Adjudication Committee. Its stated observation period was from randomization to progressive disease or death during the assessment period, up to approximately 42 months.

Open-label means the study was not masked according to the registry. The endpoint was nevertheless assessed by an independent response adjudication committee. The registry identifies the study as randomized and parallel-group, but details of the randomization procedure, allocation concealment, stratification factors and operational procedures are not reported in the registry record. The original sample-size justification and the trial’s own design assumptions are also not reported in the registry record.

Overall survival and duration of response were among the secondary outcomes. Overall survival was followed from randomization to death, up to approximately 65 months. Duration of response was assessed during the same approximate 42-month period stated for the primary endpoint. The registry also lists response rate and adverse-event outcomes. Results for some of these listed measures 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: 548 participants treated

Randomization

StageTreatment 1: POM+BTZ+LD-DEXTreatment 2: BTZ+LD-DEX
STARTED281278
COMPLETED278270
NOT COMPLETED38

Reasons for not completing this period:

ReasonTreatment 1: POM+BTZ+LD-DEXTreatment 2: BTZ+LD-DEX
Physician Decision01
clinical progression01
progressive disease02
Withdrew informed consent04
Death10
Randomization error10
Lost to Follow-up10

Treatment Period

StageTreatment 1: POM+BTZ+LD-DEXTreatment 2: BTZ+LD-DEX
STARTED278270
COMPLETED00
NOT COMPLETED278270

Reasons for not completing this period:

ReasonTreatment 1: POM+BTZ+LD-DEXTreatment 2: BTZ+LD-DEX
Lost to Follow-up02
Progressive Disease167165
Adverse Event3952
Withdrawal of Consent2522
Death209
Other Reasons2719
Pregnancy01

Analysis population for the primary outcome, as defined in the registry: All randomized participants

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.

CharacteristicUnitTreatment 1: POM+BTZ+LD-DEXTreatment 2: BTZ+LD-DEXTotal
Participants analysed281278559
Age, ContinuousYears65.9 (SD 10.13)66.1 (SD 10.16)66.0 (SD 10.14)
Sex: Female, Male: FemaleParticipants126131257
Sex: Female, Male: MaleParticipants155147302
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants171431
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants244241485
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants202343
Race (NIH/OMB): American Indian or Alaska NativeParticipants000
Race (NIH/OMB): AsianParticipants14822
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants000
Race (NIH/OMB): Black or African AmericanParticipants81321
Race (NIH/OMB): WhiteParticipants237234471
Race (NIH/OMB): More than one raceParticipants000
Race (NIH/OMB): Unknown or Not ReportedParticipants222345

6. Primary Endpoint

The registry lists the primary outcome as Progression Free Survival by Independent Response Adjudication Committee (IRAC), measured over From randomization to progressive disease or death during the IRAC assessment period, up to approximately 42 months.

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

Progression-free survival measures the time from randomization until progressive disease or death, whichever occurs first. In this study, progression was assessed by the Independent Response Adjudication Committee. The registry describes progression criteria involving changes in measures of myeloma, development or enlargement of bone lesions or soft-tissue plasmacytomas, and hypercalcemia attributable to the plasma-cell disorder.

This is a time-to-event endpoint: it incorporates both whether an event occurred and the time until it occurred. Participants who have not had a recorded event by the end of their observed follow-up can contribute information up to that point, subject to the study’s censoring rules. The specific handling of censoring and any related analysis details are not reported in the registry record.

In general, progression-free survival is used to summarize the time until disease progression or death, rather than only the proportion of participants experiencing an event at a single time. That makes it useful for comparing the timing of events between randomized groups. It does not, by itself, capture every aspect of health, quality of life or safety. Nor does a difference in this endpoint automatically establish a difference in overall survival, which is a distinct outcome.

7. Results Posted in the Registry

Hazard ratio: Treatment 1: POM+BTZ+LD-DEX vs Treatment 2: BTZ+LD-DEX

0.61

95% CI: 0.49 to 0.77

As reported in the registry

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Treatment 1: POM+BTZ+LD-DEX v…0.460.550.640.760.901.06hazard 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
Overall Survival (OS)Time-to-Event AnalysisHazard ratio0.94 (0.77 to 1.15)8,201 events
Duration of Response by Independent Response Adjudication Committee (IRAC)Time-to-Event AnalysisHazard ratio0.76 (0.56 to 1.02)417 events

Overall Survival (OS)

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Treatment 1: POM+BTZ+LD-DEX v…0.750.820.900.991.081.19hazard ratio (as reported) vs control (95% CI)

Duration of Response by Independent Response Adjudication Committee (IRAC)

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Treatment 1: POM+BTZ+LD-DEX v…0.530.610.700.810.931.07hazard ratio (as reported) vs control (95% CI)

The secondary time-to-event results have a less definitive statistical pattern than the primary progression-free survival result. The overall-survival hazard-ratio interval includes 1 and its reported p-value is 0.571. The duration-of-response interval also includes 1 and its reported p-value is 0.064. These results do not meet the conventional 0.05 threshold in the reported analyses. They should not be read as establishing that there is no difference; their intervals retain uncertainty about the relative effects.

These secondary outcomes address distinct questions. Overall survival concerns time from randomization to death, while duration of response concerns the length of response under the registry’s endpoint description. Their findings do not overturn or duplicate the primary endpoint result. Rather, they add separate outcome information, and the difference in statistical evidence across outcomes may reflect the outcomes, their information content and their analysis populations.

The registry also lists overall response rate and grade 3-4 and grade 5 treatment-emergent adverse events among secondary outcomes. Detailed comparative estimates for these measures are not reported in the registry record. Their absence from the posted numerical results means that the secondary outcome picture is incomplete.

In general, unadjusted secondary analyses carry less confirmatory weight when multiple outcomes are tested because the chance of at least one apparently notable result can increase across tests. Whether multiplicity adjustments were planned or applied is not reported in the registry record. Secondary results can therefore be useful for context, but should be interpreted with caution and alongside the primary result, endpoint definitions and confidence intervals.

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

9. Statistical Interpretation

Clinical Biostats interpretation

The registry reports median progression-free survival of 11.2 months for Treatment 1, with a 95% confidence interval from 9.66 to 13.73 months. For Treatment 2, the reported median is 7.1 months, with a 95% confidence interval from 5.88 to 8.48 months. These are group-level median estimates; they do not describe the experience of every participant.

For the primary comparison, the sponsor-reported hazard ratio is 0.61, with a 95% confidence interval from 0.49 to 0.77 and p = 0.001. In general, a hazard ratio compares the instantaneous event rates between groups over follow-up under the fitted model. With Treatment 1 compared with Treatment 2, a value below 1 indicates a lower estimated event hazard in Treatment 1 under that model. The confidence interval is entirely below 1, and the reported p-value is 0.001. These statistics describe evidence for a group difference in progression-free survival; they do not determine the magnitude or certainty of effects for any individual participant.

Overall survival is a separate secondary endpoint. Its reported medians are 35.58 months for Treatment 1 and 31.61 months for Treatment 2. The reported hazard ratio is 0.94, with a 95% confidence interval from 0.77 to 1.15 and p = 0.571. This interval includes 1, and the posted result does not provide evidence of a statistically significant difference under the reported analysis. The estimates are compatible with a range of relative effects, so the result should not be read as proof that the groups are identical.

For duration of response, the registry reports medians of 13.7 months for Treatment 1 and 10.94 months for Treatment 2. The hazard ratio is 0.76, with a 95% confidence interval from 0.56 to 1.02 and p = 0.064. The confidence interval includes 1, and the reported p-value is above 0.05. This secondary result is less conclusive than the primary result and should be interpreted with the limitations of secondary analyses in mind.

Together, the posted estimates show a statistically significant primary comparison for progression-free survival, while the reported secondary time-to-event comparisons do not meet the conventional 0.05 threshold. These outcomes address different questions and should not be treated as interchangeable. No medical conclusion for an individual follows from these group-level estimates.

10. Statistical Methods Explained

The primary outcome is a time-to-event measure, so the analysis must account for both event occurrence and the time participants remain under observation. The registry reports median progression-free survival for each group and a hazard ratio for the comparison. The medians give the time by which half of the group’s estimated event-time distribution has experienced progression or death, subject to the analysis and follow-up. They do not represent the time every participant remained progression-free.

The reported primary comparison is based on a Cox proportional hazards model. In general, a Cox model compares event hazards between groups while allowing the underlying hazard to vary over time. The hazard ratio is the model’s relative comparison. Its conventional interpretation as a single summary over follow-up relies on a proportional hazards assumption: broadly, the relative hazards should be sufficiently stable over time. Whether this assumption was assessed, and how it was assessed, is not reported in the registry record. The model’s covariate adjustment details are also not reported in the registry record.

The reported hazard ratio for progression-free survival is 0.61, with a 95% confidence interval from 0.49 to 0.77. The comparison is Treatment 1 relative to Treatment 2. In general, a hazard ratio of 1 represents equal estimated hazards between the groups; a value below 1 indicates a lower estimated hazard in the first group under the model. This interpretation concerns event rates over time, not the ratio of the two medians or the proportion of participants who benefit.

The primary p-value is 0.001. In general, a p-value describes how unusual data at least as incompatible with a specified null hypothesis would be if that null hypothesis and the test assumptions were true. It is not the probability that the null hypothesis is true, and it does not measure the size or clinical importance of a difference. The confidence interval adds an estimate of precision and a range of values compatible with the analysis and its assumptions.

For overall survival, the registry reports a hazard ratio of 0.94 from a log-rank analysis, with a 95% confidence interval from 0.77 to 1.15 and p = 0.571. For duration of response, it reports a hazard ratio of 0.76 from an unstratified log-rank test, with a 95% confidence interval from 0.56 to 1.02 and p = 0.064. In general, the log-rank test compares time-to-event experience between groups while accounting for event timing and censoring. The registry does not report further implementation details for these analyses.

What does randomization contribute? In general, random assignment aims to make the treatment groups comparable at baseline, including for factors that were not measured. It supports an interpretation of between-group differences as associated with assignment to the trial regimens, while other design, conduct and analysis issues still matter. The record identifies the trial as randomized, but procedural details beyond that designation are not reported in the registry record.

What does an open-label design mean? In general, open-label means participants and study personnel are not masked to assigned treatment. Knowledge of assignment can affect some aspects of care or outcome assessment. Here, the primary outcome is described as assessed by an Independent Response Adjudication Committee, but the registry record does not give further details about committee procedures or masking.

How should medians and hazard ratios be read together? The median is a time-point summary of each group’s estimated event-time distribution. The hazard ratio is a relative comparison over follow-up under a model or test. They answer related but distinct questions and need not convey the same numerical contrast. Neither should be reconstructed from the other. The registry reports both, and the sponsor-reported hazard ratios are the comparison statistics for the posted analyses.

The registry’s primary endpoint population is described as all randomized participants. The analysis population definitions for the secondary outcomes, the handling of missing outcome information, censoring rules, sensitivity analyses and any interim analyses are not reported in the registry record. These omissions limit what can be said about the full analysis strategy.

11. Confidence Intervals and Precision

A 95% confidence interval expresses uncertainty around an estimated quantity under the statistical method and its assumptions. In general, intervals that are narrower indicate greater precision, while wider intervals indicate more uncertainty. A confidence interval is not a guarantee that the true value lies inside it, nor does it describe the range of individual participant outcomes.

For progression-free survival, the median estimate is 11.2 months in Treatment 1, with a 95% confidence interval from 9.66 to 13.73 months. The Treatment 2 median is 7.1 months, with a 95% confidence interval from 5.88 to 8.48 months. The hazard-ratio interval, 0.49 to 0.77, lies below 1. In combination with p = 0.001, this indicates that the posted primary analysis estimates a lower event hazard for Treatment 1 under the Cox model, with uncertainty that does not include equal hazards.

The secondary intervals are less decisive. The overall-survival hazard-ratio interval extends from 0.77 to 1.15, and the duration-of-response interval extends from 0.56 to 1.02. Both include 1, so the posted estimates allow values on either side of equal hazards. The corresponding medians also have confidence intervals: 28.55 to 41.2 months and 26.05 to 37.16 months for overall survival; 10.94 to 18.1 months and 8.11 to 14.78 months for duration of response.

Precision depends on the amount and timing of observed information, among other factors. The registry record does not provide enough detail to assess the impact of censoring, missing outcome information or specific analysis choices on these intervals. The intervals should therefore be read as uncertainty summaries for the reported analyses, not as a complete account of all sources of uncertainty.

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 effect0.61129173
75% of the observed effect0.69229306
50% of the observed effect0.78514689
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect1002005001,0002,00040%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: Treatment 1: POM+BTZ+LD-DEX vs Treatment 2: BTZ+LD-DEX.

The sample-size figures are planning illustrations based on the observed effect, not the trial’s original design assumptions. For these time-to-event outcomes, the figures refer to the total number of events, not participants per arm. The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, a normal approximation and an effect to detect equal to the stated fraction of the observed effect. The original design assumptions are not reported in the registry record.

The 80% power column gives the planned event count associated with an 80% chance of detecting the specified effect under those assumptions if that effect is real. The 90% power column uses a higher target chance of detection and therefore generally calls for more events. For the primary endpoint, the event-count illustrations are 129 and 173 for planning at 100% of the observed effect, 229 and 306 for planning at 75% of the observed effect, and 514 and 689 for planning at 50% of the observed effect, respectively for 80% and 90% power.

As the assumed effect becomes smaller, it is harder to distinguish it from chance variation, so more events are needed under the same planning assumptions. Similar illustrations are listed for the secondary time-to-event outcomes. These are not observed power calculations and do not describe the actual power of the completed trial. The event counts are planning targets under specified assumptions, not a claim about how many events occurred in the trial.

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 = 0.610, so ln(HR) = -0.4943.
  2. d = 4 × (1.96 + 0.842)2 / [ln(0.610)]2 = 128.5, rounded up to 129 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 <- 0.61                              # 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(1734928)
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 = 129 (80% power), 173 (90% power)
 75% of observed effect: events = 229 (80% power), 306 (90% power)
 50% of observed effect: events = 514 (80% power), 689 (90% power)
Simulated power with 129 events: 0.797 (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.

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 201 participants in total, with the boundaries below.

AnalysisCalendar time (months)EventsEfficacy boundary (z)Nominal one-sided pCumulative alpha spent
Look 116.6583.7100.00010.0001
Look 226.21152.5110.00600.0060
Look 360.01731.9930.02310.0250
01234z = 3.7117 mo58 eventsz = 2.5126 mo115 eventsz = 1.9960 mo173 eventsUpper efficacy boundary (z)

Fixed design versus group-sequential alternatives

DesignPowerEvents at final analysisParticipantsStudy length (months)
Fixed design, one analysis80%12714960.0
Two looks, O'Brien-Fleming80%12814960.0
Three looks, O'Brien-Fleming80%12915060.0
Three looks, Pocock80%14917460.0
Fixed design, one analysis90%17119960.0
Two looks, O'Brien-Fleming90%17120060.0
Three looks, O'Brien-Fleming90%17320160.0
Three looks, Pocock90%19723060.0

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 effect0.610173201
75% of the observed effect0.690308354
50% of the observed effect0.781695787

For context, this trial enrolled 559 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 <- 7.1          # control-arm median, months (converted from the posted unit)
hr          <- 0.61          # 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: 140         p (1-sided)   0.0001
  Events: 58        ~HR at bound   0.3763
   Month: 17    P(Cross) if HR=1   0.0001
             P(Cross) if HR=0.61   0.0338
   IA 2: 67%                   Z   2.5114
      N: 202         p (1-sided)   0.0060
 Events: 116        ~HR at bound   0.6264
   Month: 26    P(Cross) if HR=1   0.0060
             P(Cross) if HR=0.61   0.5603
       Final                   Z   1.9930
      N: 202         p (1-sided)   0.0231
 Events: 173        ~HR at bound   0.7385
   Month: 60    P(Cross) if HR=1   0.0250
             P(Cross) if HR=0.61   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
Based on Cox proportional hazards modelHazard Ratio (HR) 0.610.49 to 0.770.001

The registry reports the sponsor’s primary comparison as a hazard ratio of 0.61, with a 95% confidence interval from 0.49 to 0.77 and p = 0.001, based on a Cox proportional hazards model. The corresponding sponsor-reported results for overall survival and duration of response use the methods identified for those outcomes and are reported separately.

Recalculated values, when shown, are simple unadjusted calculations from posted summary statistics. Such calculations do not reproduce a time-to-event model and should not replace the sponsor’s reported analysis. The registry record does not flag a discrepancy between the reported and recalculated results. Accordingly, interpretation of the primary finding should be anchored to the sponsor-reported model and its stated confidence interval and p-value, rather than to a different analysis reconstructed from summary data.

The registry does not report enough detail to reproduce the full model specification, including covariate adjustment or all analysis procedures. A close-looking recalculation would not demonstrate that those choices were identical. The sponsor’s reported analysis therefore remains the relevant result for interpreting the posted primary comparison.

16. Multiplicity, Missing Data and Analysis Populations

The registry lists multiple outcomes: progression-free survival as the primary endpoint, along with secondary outcomes including overall survival, response rate, duration of response and adverse-event measures. When several outcomes are examined, multiplicity becomes relevant because repeated testing can increase the chance of a false-positive finding across the set of tests. In general, a prespecified strategy may control that risk by defining an order for testing or adjusting significance thresholds. Whether this trial used such a strategy is not reported in the registry record.

The posted p-values for the primary and secondary time-to-event outcomes are reported individually. The registry record does not state whether they were adjusted for multiple comparisons, whether secondary analyses were considered confirmatory or exploratory, or whether a hierarchy governed their interpretation. The secondary findings should therefore not be treated as if the record established a multiplicity-controlled sequence of tests.

The primary endpoint population is identified as all randomized participants. The record does not provide a fuller account of analysis populations for every endpoint, including whether all randomized participants were included in each secondary analysis or how participants with missing data were handled. It also does not report details about censoring beyond the endpoint definitions, methods for handling protocol deviations, sensitivity analyses or interim analyses.

In general, missing outcome information and censoring can affect time-to-event estimates if the circumstances associated with loss of observation are related to event risk. Appropriate methods depend on the study’s data and analysis plan. Without the relevant details, it is not possible to assess the effect of missingness or censoring on these estimates from the registry record alone. These omissions do not alter the posted numbers, but they limit assessment of their robustness and of how the full analysis was planned.

17. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Treatment 1: POM + BTZ + LD-DEX17727863.7%
Treatment 2: BTZ + LD-DEX11927044.1%
Participants with at least one serious adverse event
Serious adverse events by armTreatment 1: POM + BTZ + LD-D…63.7%Treatment 2: BTZ + LD-DEX44.1%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
Treatment 1: POM + BTZ + LD-DEX197 of 281
Treatment 2: BTZ + LD-DEX193 of 278

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
Treatment 1: POM + BTZ + LD-DEX276 of 278
Treatment 2: BTZ + LD-DEX260 of 270

Most frequent serious adverse event terms

Event termOrgan systemTreatment 1: POM + BTZ + LD-DEXTreatment 2: BTZ + LD-DEX
PneumoniaInfections and infestations34 of 27817 of 270
PyrexiaGeneral disorders12 of 2785 of 270
Lower respiratory tract infectionInfections and infestations10 of 2785 of 270
General physical health deteriorationGeneral disorders5 of 2789 of 270
InfluenzaInfections and infestations10 of 2784 of 270
Acute kidney injuryRenal and urinary disorders8 of 2786 of 270
Atrial fibrillationCardiac disorders9 of 2782 of 270
DiarrhoeaGastrointestinal disorders5 of 2786 of 270
SyncopeNervous system disorders6 of 2785 of 270
Pulmonary embolismRespiratory, thoracic and mediastinal disorders9 of 2781 of 270

Most frequent non-serious adverse event terms

Event termOrgan systemTreatment 1: POM + BTZ + LD-DEXTreatment 2: BTZ + LD-DEX
Peripheral sensory neuropathyNervous system disorders134 of 278103 of 270
ThrombocytopeniaBlood and lymphatic system disorders110 of 278105 of 270
DiarrhoeaGastrointestinal disorders102 of 27882 of 270
NeutropeniaBlood and lymphatic system disorders150 of 27829 of 270
FatigueGeneral disorders107 of 27872 of 270
ConstipationGastrointestinal disorders106 of 27865 of 270
AnaemiaBlood and lymphatic system disorders87 of 27872 of 270
Oedema peripheralGeneral disorders101 of 27854 of 270
Upper respiratory tract infectionInfections and infestations71 of 27851 of 270
CoughRespiratory, thoracic and mediastinal disorders66 of 27845 of 270

Serious events with the highest arm-level rate: pneumonia (12.2%), pyrexia (4.3%), influenza (3.6%), lower respiratory tract infection (3.6%), general physical health deterioration (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 reports that 177 of 278 participants in Treatment 1 and 119 of 270 participants in Treatment 2 were affected by serious adverse events, using the listed at-risk counts for each group. These are participant counts, not event counts; a participant may have experienced more than one event. The record does not provide a comparative statistical analysis of these serious adverse-event figures in the material.

The most frequently listed serious-event terms include pneumonia, reported as 12.2%; pyrexia, 4.3%; influenza, 3.6%; lower respiratory tract infection, 3.6%; general physical health deterioration, 3.3%; and atrial fibrillation, 3.2%. These percentages are reported for the listed terms; their denominators and detailed event-level counting rules are not described in the registry record.

Safety counts are descriptive and should be read alongside the trial’s follow-up, event definitions and population. The registry also lists deaths of 197 participants in Treatment 1 and 193 in Treatment 2, but the record does not provide context sufficient to interpret those counts as treatment-related deaths. These data do not, on their own, establish the cause of an event or a causal difference between groups.

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

The posted primary result indicates a difference in progression-free survival between the randomized groups under the sponsor-reported analysis. The estimated median was 11.2 months for Treatment 1 and 7.1 months for Treatment 2, and the reported hazard ratio was 0.61, with a 95% confidence interval from 0.49 to 0.77 and p = 0.001. These statistics describe group-level outcomes during the trial’s observation period and the relative event hazard under the stated model.

The result does not mean that every participant in one group had a longer progression-free interval than every participant in the other group. Medians are summaries of distributions, and the hazard ratio is a model-based comparison over follow-up. The result also does not establish an individual participant’s likely outcome or replace consideration of the full clinical context.

The primary finding should not be interpreted as proof of an overall-survival difference. The reported overall-survival hazard ratio is 0.94, with a 95% confidence interval from 0.77 to 1.15 and p = 0.571. Nor should the duration-of-response result be treated as definitive: its reported interval includes 1 and p = 0.064. These are distinct secondary endpoints with their own uncertainty.

The registry record does not report all details needed to assess the analysis plan, missing-data handling, multiplicity procedures or model assumptions. The numerical results therefore need to be understood within the limits of what is documented. They describe evidence from this randomized comparison, not a universal prediction, a guarantee of benefit or a substitute for medical advice.

19. Why This Trial Matters Statistically

Statistically, this trial illustrates why a primary endpoint and secondary endpoints should be read separately. The primary analysis uses a time-to-event outcome and a Cox proportional hazards model, reporting both group medians and a hazard ratio with a confidence interval. That combination communicates different features of the evidence: the medians describe the group distributions at a particular point, while the hazard ratio summarizes a relative comparison over follow-up under model assumptions.

The primary result is statistically distinct from the posted secondary results. The progression-free survival confidence interval for the hazard ratio does not include 1, whereas the overall-survival and duration-of-response intervals do. This contrast shows why one endpoint’s result cannot be carried over to another endpoint, even when they are measured in the same trial population.

The trial also offers a practical example of the limits of registry-level interpretation. The record identifies randomization, masking status, endpoint definitions and reported analyses, but does not document several elements needed to assess the complete analysis strategy. Multiplicity handling, detailed missing-data procedures and the original sample-size justification are not reported in the registry record. Those gaps matter when evaluating how confirmatory the secondary findings are and how robust the reported estimates may be.

Finally, the planning illustrations based on observed effects should not be confused with the actual trial design or its achieved power. They show how event requirements change when planning around different effect sizes under stated assumptions. Keeping the reported clinical analysis, the planning illustration and the limitations of the registry record distinct is essential for sound statistical interpretation.

20. Limitations

Several trial-specific limitations affect interpretation of the registry results. The study was open-label, and the registry does not describe further procedures intended to address the potential effects of treatment awareness. The primary outcome was assessed by an Independent Response Adjudication Committee, but details of committee procedures and masking are not reported in the registry record.

The primary result depends on a Cox proportional hazards model. The registry does not report whether the proportional hazards assumption was assessed, the model’s covariates, or the full analysis specification. The primary endpoint description identifies all randomized participants as the population, but the record does not provide complete analysis-population definitions for every outcome or details of missing-data and censoring procedures.

The registry record does not report the trial’s original sample-size assumptions, multiplicity procedures or interim-analysis plan. Those omissions limit interpretation of the confirmatory status of secondary results and prevent assessment of how the completed trial’s planning related to its final analyses. The planning illustrations based on observed effects are not a substitute for the original design justification.

Detailed numerical results are not reported for some listed secondary outcomes, including response rate and the grade-specific adverse-event measures. Safety figures are descriptive, and the record does not supply enough context to interpret the listed death counts as treatment-related. The incomplete dosing descriptions also mean that the full regimen cannot be reconstructed from the registry record alone. These limitations concern the information documented in the registry and do not establish that the omitted procedures or analyses were absent from the full study record.

21. Related Tutorials

22. Related Statistical Calculators

23. Sources

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24. Record Summary

This completed, randomized, open-label Phase 3 trial compared pomalidomide, bortezomib and low-dose dexamethasone with bortezomib and low-dose dexamethasone in participants with relapsed or refractory multiple myeloma. The registry lists 559 participants enrolled. The primary outcome was progression-free survival assessed by the Independent Response Adjudication Committee.

The sponsor-reported primary hazard ratio was 0.61, with a 95% confidence interval from 0.49 to 0.77 and p = 0.001. The posted secondary time-to-event results for overall survival and duration of response were less conclusive, with confidence intervals that include 1. Some additional listed secondary outcome estimates and important analysis-plan details are not reported in the registry record.

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