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Multiple Myeloma Phase 3 Time-to-Event Analysis NCT01302392

A Study of Carfilzomib vs Best Supportive Care in Subjects With Relapsed and Refractory Multiple Myeloma: Complete Statistical Analysis

This analysis examines a randomized, open-label Phase 3 comparison of carfilzomib with best supportive care in people with relapsed and refractory multiple myeloma. The primary outcome was overall survival, with several additional outcomes and safety counts also reported in the registry record.

Trial start: 2010-09  ·  Enrollment: 315  ·  Sponsor: Amgen
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 Carfilzomib vs Best Supportive Care in Subjects With Relapsed and Refractory Multiple Myeloma (NCT01302392), a randomized phase 3 study. The primary outcome is Overall Survival.

315
Enrollment
Phase 3
2
Arms
In the primary outcome
0.97
Hazard ratio
Best Supportive Care vs Carfilzomib
0.76–1.25
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT01302392
PhasePhase 3
ConditionMultiple Myeloma
AllocationRandomized
Design modelParallel
MaskingNone (open label)
Enrollment315
Arms in the primary outcome2
Lead sponsorAmgen
Results postedYes

2. Clinical Question

Population

Participants with multiple myeloma who had received all available approved treatment options and could therefore be considered candidates for palliative care. The primary analysis population was the intent-to-treat group, comprising all randomized participants.

Intervention

Carfilzomib, as named in the registry record. Further details of the treatment regimen are not reported in the registry record.

Comparator

Best supportive care. The registry record does not give a fuller description of what supportive care included.

Primary question

How did overall survival, measured from randomization until death, compare between participants assigned to carfilzomib and those assigned to best supportive care? Participants still alive were censored at the date they were last known alive or the data cutoff, whichever occurred earlier.

The registry describes a randomized comparison in people with relapsed and refractory multiple myeloma after all available approved treatment options. Its primary focus is the time-to-event outcome overall survival. The posted arm results give median survival estimates and confidence intervals, while the sponsor's comparison is expressed as a hazard ratio with a confidence interval and a log-rank p-value.

The question is not simply whether the two reported medians differ. Survival analysis uses the timing of deaths and accounts for participants whose survival time was not observed through death by censoring their follow-up. This allows the analysis to use information from participants who were alive at their last observation, while recognizing that their later survival status is unknown within the analysis.

The registry also lists outcomes covering response and disease control, including progression-free survival, duration of response, clinical benefit response, duration of clinical benefit, disease control, and duration of disease control. The values available for some of these outcomes are described separately; results for the other listed outcomes are not reported in the registry record.

3. Trial Design

The study is identified as a Phase 3, randomized, open-label, multicenter, parallel-group trial comparing carfilzomib with best supportive care in participants with multiple myeloma. The registry reports enrollment of 315 participants. The trial status is completed; the recorded start is 2010-09 and primary completion is 2014-07.

Random allocation is intended to create groups that are comparable, on average, at the start of a trial. The parallel design means that participants were assigned to one of the two groups rather than crossing between treatments as part of the stated design. The groups included 157 participants in the carfilzomib arm and 158 in the best supportive care arm. The primary analysis population was the intent-to-treat set, defined in the registry as all randomized participants.

The study was open-label, with masking listed as none. Participants and study personnel therefore were not masked to the assigned group, according to the registry design fields. This is relevant context when considering outcomes that may involve judgment or reporting; overall survival is a death-based endpoint, although follow-up and censoring procedures still matter.

The brief summary describes participants who had received all available approved treatment options and who might be candidates for palliative care. The registry names the two interventions but does not give arm-specific regimen descriptions. Details such as the protocol's original sample-size justification, planned allocation ratio, eligibility criteria beyond the summary, and statistical analysis plan are not reported in the registry record. The planning assumptions accompanying the sample-size illustrations are not a substitute for those original protocol 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.

Overall Study

StageBest Supportive CareCarfilzomib
STARTED158157
Treated153157
COMPLETED151156
NOT COMPLETED71

Reasons for not completing this period:

ReasonBest Supportive CareCarfilzomib
Lost to Follow-up10
Withdrawal by Subject61

Analysis population for the primary outcome, as defined in the registry: The intent to treat (ITT) analysis set comprised 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.

CharacteristicUnitBest Supportive CareCarfilzomibTotal
Participants analysed158157315
Age, Continuousyears65.5 (SD 8.02)63.3 (SD 10.71)64.4 (SD 9.50)
Sex: Female, Male: FemaleParticipants6275137
Sex: Female, Male: MaleParticipants9682178
Race/Ethnicity, Customized: American Indian or Alaska Nativeparticipants000
Race/Ethnicity, Customized: Asianparticipants415
Race/Ethnicity, Customized: Native Hawaiian or Other Pacific Islanderparticipants000
Race/Ethnicity, Customized: Black or African Americanparticipants112
Race/Ethnicity, Customized: Whiteparticipants148151299
Race/Ethnicity, Customized: Otherparticipants549
Region: Europeparticipants138140278
Region: Non-Europeparticipants201737
Number of Prior Regimens to Treat Multiple Myeloma: 3participants191736
Number of Prior Regimens to Treat Multiple Myeloma: 4participants353469
Number of Prior Regimens to Treat Multiple Myeloma: ≥5participants104106210

6. Primary Endpoint

The registry lists the primary outcome as Overall Survival, measured over From randomization through the final analysis data cutoff with longest follow-up time of approximately 45 months. Median follow up times were 27.8 months and 29.8 months for Carfilzomib and Best Supportive Care groups, respectively..

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

Overall survival measures the time from randomization to death. In this trial, participants who remained alive were censored at the date they were last known alive or at the data cutoff, whichever occurred earlier. The registry reports the median as the arm-level summary and a hazard ratio for the sponsor's comparison.

Overall survival is commonly used in clinical trials because it is a direct time-to-event outcome: the event is death, and the analysis uses both whether and when that event occurred. Censoring allows participants whose deaths were not observed during the available follow-up to contribute the time during which they were known to be alive. It does not establish what happened after their last known-alive date or after the cutoff.

The registry's primary timeframe runs from randomization through the final analysis cutoff, with longest follow-up of approximately 45 months. Median follow-up times were 27.8 months for carfilzomib and 29.8 months for best supportive care. Those follow-up summaries describe observation time, not median survival. The endpoint is therefore interpreted alongside the censoring definition, follow-up period, arm estimates, and sponsor-reported comparison rather than from a median alone.

7. Results Posted in the Registry

Hazard ratio: Best Supportive Care vs Carfilzomib

0.97

95% CI: 0.76 to 1.25

As reported in the registry

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Best Supportive Care vs Carfi…0.730.820.921.031.161.30hazard 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 ResponseBinary EndpointRisk difference+7.7 pts (-0.2 to 15.6)340 per arm
Clinical Benefit ResponseBinary EndpointRisk difference+10.3 pts (0.7 to 20.0)283 per arm
Disease ControlBinary EndpointRisk difference+8.1 pts (-1.8 to 18.0)487 per arm

Overall Response

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Carfilzomib-1.442.225.889.551317risk difference (percentage points) vs control (95% CI)

Clinical Benefit Response

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Carfilzomib-1.603.037.66121722risk difference (percentage points) vs control (95% CI)

Disease Control

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Carfilzomib-3.411.185.78101520risk difference (percentage points) vs control (95% CI)

The registry lists secondary outcomes spanning response, clinical benefit, disease control, and time-to-event measures. The posted binary results show more participants counted for carfilzomib than best supportive care for overall response, clinical benefit response, and disease control. The uncertainty around these unadjusted comparisons is not uniform: some recalculated intervals include no risk difference, while the clinical benefit response interval does not.

This pattern offers additional descriptive context, but it does not overturn or replace the primary overall-survival result. The outcomes answer different questions: a response or disease-control count is not the same as survival time, and a difference in a secondary endpoint does not establish a difference in the primary endpoint. Nor does the primary survival finding determine what the secondary outcomes must show.

Unadjusted secondary findings carry less weight because several outcomes are considered. When multiple comparisons are examined, the chance of observing a result that appears notable by chance can increase. A multiplicity procedure can address that issue, but whether one was prespecified or used is not reported in the registry record. The recalculated p-values should therefore be treated as exploratory descriptions rather than as evidence adjusted for the full set of secondary questions.

The record lists other secondary measures, including progression-free survival and durations of response, clinical benefit, and disease control. Their detailed results are not reported in the registry record. The available secondary data are thus incomplete as a picture of all listed outcomes, and conclusions should stay within the outcomes with posted results. Differences in follow-up windows also matter: the binary outcomes have a stated longest follow-up of approximately 31 months, whereas the primary endpoint has a longer stated follow-up period.

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

9. Statistical Interpretation

Clinical Biostats interpretation

The reported median overall survival was 10.2 months for carfilzomib, with a 95% confidence interval from 8.4 to 14.4 months, and 10.0 months for best supportive care, with a 95% confidence interval from 7.7 to 12.0 months. The sponsor-reported hazard ratio for best supportive care versus carfilzomib was 0.975, with a 95% confidence interval from 0.760 to 1.249 and a log-rank p-value of 0.417.

The confidence interval for the hazard ratio includes 1, the value corresponding to equal hazards in the compared groups. The p-value is not small by conventional reference standards. Together, these reported statistics do not establish a clear difference in overall survival between the randomized groups. They also do not prove that the groups have identical survival; the interval includes a range of values on either side of 1, so the estimate remains uncertain.

The hazard ratio is the registry's reported relative time-to-event measure, and its direction should be read with the stated comparison order, best supportive care versus carfilzomib. It is not a ratio of the median survival times. The two medians are arm-specific summaries, whereas the hazard ratio uses event timing over follow-up. Neither statistic alone describes every feature of the survival curves.

The secondary outcome results give additional descriptive information. For overall response, the registry lists 18 participants in the best supportive care group and 30 in the carfilzomib group; the recalculated unadjusted risk-difference confidence interval includes zero. For clinical benefit response, the corresponding counts are 33 and 49, with the recalculated confidence interval for the risk difference above zero. For disease control, the counts are 107 and 119, and the recalculated interval includes zero. These are unadjusted secondary comparisons, not the sponsor's reported primary survival analysis.

The registry lists median follow-up times of 26.6 months for carfilzomib and 23.1 months for best supportive care for the reported binary secondary outcomes, with a longest follow-up of approximately 31 months. Their observation window therefore differs from the primary endpoint's stated timeframe. The secondary results should be read as supporting context, not as replacements for the primary endpoint or as a set of independent confirmations. The registry does not report a multiplicity adjustment for these comparisons.

The posted results describe what was observed under this trial's design and follow-up. They do not by themselves establish a causal explanation for any difference in a secondary outcome, nor do they resolve questions not addressed by the reported analyses. Interpretation also depends on the trial's open-label design, the details available about the interventions, the outcome definitions, and the extent of missing or censored data.

10. Statistical Methods Explained

The primary outcome is time-to-event data. Each participant contributes a time from randomization until death or, if death was not observed, until censoring at the last date known alive or the data cutoff, whichever occurred earlier. A participant censored while alive has incomplete event-time information: the analysis knows the person survived at least until the censoring time, but not the later time to death.

What does the median describe?

A median survival estimate is the time by which the estimated survival distribution has reached its midpoint. It summarizes the survival experience without assuming that every participant had a death observed. The registry gives median overall survival separately for each arm and reports a confidence interval for each estimate. A comparison of the two medians is not the same as the sponsor's time-to-event test, because the comparison uses more of the event-time information than a pair of median summaries alone.

What does the hazard ratio describe?

A hazard is the instantaneous event rate among participants still at risk at a given time, under the analysis framework. A hazard ratio compares hazards between groups over follow-up. A value of 1 corresponds to equal hazards; values on either side represent different relative hazards according to the order of the comparison. The registry labels the sponsor's result as best supportive care versus carfilzomib, so that ordering should accompany interpretation of the reported estimate.

A hazard ratio is not an absolute difference in survival time, a ratio of medians, or the probability that a participant will die. Its interpretation as one relative summary across the follow-up relies on the model or test's assumptions. The statistical plan and any assessment of those assumptions are not reported in the registry record.

How does the log-rank method fit?

The sponsor reports a log-rank comparison and a hazard ratio. The log-rank method compares the observed and expected event patterns between groups over the event times, while accounting for censoring. It uses information across follow-up rather than comparing only the two median estimates. The registry reports the resulting p-value and confidence interval; detailed modeling choices, including whether any covariates were included, are not reported in the registry record.

A p-value measures how compatible the observed data are with a specified null model under the assumptions of the analysis. It is not the probability that the null hypothesis is true, nor is it a measure of clinical importance. The confidence interval provides a range of values compatible with the data and analysis at the stated confidence level. If an interval includes the null value, the results do not rule out that value at the corresponding confidence level.

What are the recalculated secondary comparisons?

The binary secondary outcomes are reported as participant counts by arm. The accompanying recalculated comparisons use an unadjusted risk difference: the difference between the observed proportions in the two groups, with carfilzomib treated as the group of interest and best supportive care as the comparator. The confidence interval gives a range of values compatible with that simple, unadjusted comparison. It is not an adjusted estimate from the sponsor's statistical analysis plan.

These recalculations are based on posted summary counts, not participant-level records. They cannot account for covariates, time-to-event structure, stratification, or missing-outcome methods unless those features are explicitly part of the calculation; such details are not reported for these recalculated comparisons. The registry has no sponsor-reported analysis listed for the binary secondary outcomes in the record.

The reported response and disease-control counts are endpoint totals, while the arm denominators are the listed group sizes. These counts should not be interpreted as time-to-event measures. The registry also lists secondary time-to-event outcomes, but the detailed values for those outcomes are not reported in the registry record.

Why does over-dispersion matter in general?

General statistical explanation: over-dispersion occurs when variation in the data is greater than a model assumes. If a model underestimates that variation, its standard errors can be too small and its confidence intervals too narrow. The posted primary analysis is described as a log-rank analysis, and the registry does not report an over-dispersion assessment or a model-based dispersion adjustment. This general issue should not be read as evidence that over-dispersion occurred in this trial.

Likewise, analyses of time-to-event outcomes depend on the censoring process and the definition of the analysis population. The primary population is stated to be all randomized participants, and the censoring rule is given. The registry does not report further sensitivity analyses or detailed missing-data procedures. The results should therefore be interpreted within the methods explicitly described rather than assuming additional adjustments or checks.

11. Confidence Intervals and Precision

The primary hazard-ratio estimate is 0.975, with a 95% confidence interval from 0.760 to 1.249. The interval includes 1, so the reported data are compatible with equal hazards as well as values indicating a relative difference in either direction under the comparison's stated ordering. Its breadth reflects uncertainty in the estimate; it does not identify one exact underlying effect.

The arm-specific median estimates are 10.2 months for carfilzomib, with a 95% confidence interval from 8.4 to 14.4 months, and 10.0 months for best supportive care, with a 95% confidence interval from 7.7 to 12.0 months. These intervals overlap. Overlap alone is not a formal test of the difference between medians, and the sponsor's reported comparison is the log-rank hazard-ratio analysis.

A confidence interval is a measure of statistical uncertainty under the method used. It is not a guarantee that the true value lies within the particular calculated interval, and it does not account for limitations such as unreported analysis choices or missing-data procedures. Greater precision would generally mean a narrower interval, all else being equal. The available interval still allows a range of effects, so the estimate should not be described as proving equivalence or ruling out every potentially relevant difference.

The secondary risk-difference intervals also convey uncertainty. The intervals for overall response and disease control include zero, while the interval for clinical benefit response is above zero. Because these are recalculated, unadjusted secondary comparisons and are among multiple outcomes, they warrant more cautious interpretation than a single prespecified primary comparison. The registry does not report multiplicity-adjusted intervals for them.

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 effect0.9748,98065,570
75% of the observed effect0.9887,075116,569
50% of the observed effect0.99195,919262,280
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect50,000100,000200,000500,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: events required (total))
Treat these figures cautiously. The observed difference is imprecise: its confidence interval includes no difference at all. A sample size built on a noisy estimate can be far too small or too large, so the smaller-effect rows are the more cautious guide.
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, 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: Best Supportive Care vs Carfilzomib.

The sample-size figures are planning illustrations based on the observed effect, not the trial's original design justification. For the binary outcomes, the figures are participants per arm for 80% power and participants per arm for 90% power. For the time-to-event outcome, figures are total events across the comparison, not participants per arm.

The stated illustration assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each scenario asks what planning size would be needed to detect the stated fraction of the observed effect under those assumptions. The original trial's sample-size assumptions and justification are not reported in the registry record.

The 80% power column represents the planning size associated with an 80% chance of detecting the specified effect under the stated assumptions, if that effect were the true effect. The 90% power column represents the corresponding planning size for a 90% chance. These are design calculations, not statements about the probability that the trial's findings are true. The figures do not establish the power actually achieved by this completed trial.

Each row uses a different fraction of the observed effect as the effect to detect. Smaller effects require more information, which is why the planning figures increase as the target effect becomes smaller. The displayed values should be read as hypothetical planning requirements under the listed assumptions, not as observed participant counts or as proof that the trial was designed around the effect seen in its results. This is 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 = 0.975, so ln(HR) = -0.0253.
  2. d = 4 × (1.96 + 0.842)2 / [ln(0.975)]2 = 48,979.6, rounded up to 48,980 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 <- 0.975                              # 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(1302392)
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 = 48,980 (80% power), 65,570 (90% power)
 75% of observed effect: events = 87,075 (80% power), 116,569 (90% power)
 50% of observed effect: events = 195,919 (80% power), 262,280 (90% power)
Simulated power with 48,980 events: 0.802 (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 78,127 participants in total, with the boundaries below.

AnalysisCalendar time (months)EventsEfficacy boundary (z)Nominal one-sided pCumulative alpha spent
Look 117.222,1143.7100.00010.0001
Look 227.244,2282.5110.00600.0060
Look 360.066,3431.9930.02310.0250
01234z = 3.7117 mo22114 eventsz = 2.5127 mo44228 eventsz = 1.9960 mo66343 eventsUpper efficacy boundary (z)

Fixed design versus group-sequential alternatives

DesignPowerEvents at final analysisParticipantsStudy length (months)
Fixed design, one analysis80%48,97857,67860.0
Two looks, O'Brien-Fleming80%49,16157,89360.0
Three looks, O'Brien-Fleming80%49,60358,41360.0
Three looks, Pocock80%57,32567,50860.0
Fixed design, one analysis90%65,56977,21560.0
Two looks, O'Brien-Fleming90%65,79377,47960.0
Three looks, O'Brien-Fleming90%66,34378,12760.0
Three looks, Pocock90%75,68189,12360.0

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 effect0.97566,34378,127
75% of the observed effect0.981117,943138,799
50% of the observed effect0.987265,374312,090

For context, this trial enrolled 315 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 <- 10          # control-arm median, months (converted from the posted unit)
hr          <- 0.975          # 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: 56108         p (1-sided)   0.0001
 Events: 22115        ~HR at bound   0.9513
     Month: 17    P(Cross) if HR=1   0.0001
               P(Cross) if HR=0.98   0.0338
     IA 2: 67%                   Z   2.5114
      N: 78128         p (1-sided)   0.0060
 Events: 44229        ~HR at bound   0.9764
     Month: 27    P(Cross) if HR=1   0.0060
               P(Cross) if HR=0.98   0.5603
         Final                   Z   1.9930
      N: 78128         p (1-sided)   0.0231
 Events: 66343        ~HR at bound   0.9846
     Month: 60    P(Cross) if HR=1   0.0250
               P(Cross) if HR=0.98   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 RankHazard Ratio (HR) 0.9750.760 to 1.2490.417

For overall survival, the registry reports the sponsor's own analysis: a log-rank comparison with a hazard ratio of 0.975 for best supportive care versus carfilzomib, a 95% confidence interval from 0.760 to 1.249, and p = 0.417. This is the primary inferential result to use when describing the trial's sponsor-reported comparison.

The recalculated material does not replace that analysis. The registry's posted arm-level medians are useful descriptive summaries, but they do not reproduce the log-rank analysis. The sponsor's result uses the reported time-to-event comparison and should take precedence over any simple, unadjusted re-calculation from arm summaries. There is no discrepancy flagged between the posted values and the sponsor-reported result.

For the binary secondary outcomes, the listed risk differences, confidence intervals, and p-values are unadjusted recalculations from posted counts; the registry does not list sponsor-reported analyses for those comparisons. They therefore should not be presented as the sponsor's prespecified inferential findings. The record does not report the full statistical analysis plan, so the extent to which those recalculations match planned methods is unknown.

16. Multiplicity, Missing Data and Analysis Populations

The registry identifies overall survival as the primary outcome and lists several secondary outcomes. It does not report whether the trial used a multiplicity adjustment, a hierarchical testing sequence, or another strategy to control the chance of false-positive findings across multiple endpoints. Those features are not reported in the registry record and should not be inferred from the number or ordering of outcomes.

The primary analysis population is described as the intent-to-treat set, comprising all randomized participants. This helps define who was included in the primary analysis, but it does not by itself specify how every outcome with unavailable information was handled. For overall survival, the record states that participants still alive were censored at the date last known alive or the data cutoff, whichever occurred earlier. Other missing-data procedures, including methods for missing secondary outcome assessments, are not reported in the registry record.

The primary timeframe extends through the final analysis cutoff, with longest follow-up of approximately 45 months. Median follow-up was 27.8 months for carfilzomib and 29.8 months for best supportive care. These summaries indicate that follow-up was not identical for every participant; they do not disclose the reasons for censoring or the amount of missing follow-up by itself.

The registry does not report interim analyses, stopping rules, detailed analysis-plan provisions, or sensitivity analyses for the primary endpoint. It also does not report the original sample-size justification. These omissions limit assessment of how closely the posted analysis follows the planned analysis and how robust conclusions are to alternative assumptions. They do not show that any particular procedure was absent from the original protocol; they mean the relevant details are not reported in the registry record.

Interpretation should therefore distinguish the sponsor-reported primary comparison from unadjusted recalculations for secondary outcomes, and should avoid treating nominal secondary results as if they were protected against multiplicity. The registry's stated intent-to-treat population and censoring rule are informative, but they do not resolve the unreported details of missing-data and multiplicity handling.

17. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Best Supportive Care7815351.0%
Carfilzomib9215758.6%
Participants with at least one serious adverse event
Serious adverse events by armBest Supportive Care51.0%Carfilzomib58.6%% 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
Best Supportive Care135 of 153
Carfilzomib141 of 157

Most frequent serious adverse event terms

Event termOrgan systemBest Supportive CareCarfilzomib
Disease progressionGeneral disorders19 of 15316 of 157
PneumoniaInfections and infestations18 of 15310 of 157
Renal failure acuteRenal and urinary disorders6 of 15315 of 157
AnaemiaBlood and lymphatic system disorders8 of 1534 of 157
BronchopneumoniaInfections and infestations5 of 1536 of 157
HypercalcaemiaMetabolism and nutrition disorders4 of 1537 of 157
Back painMusculoskeletal and connective tissue disorders3 of 1536 of 157
ThrombocytopeniaBlood and lymphatic system disorders5 of 1533 of 157
PyrexiaGeneral disorders2 of 1536 of 157
Cardiac failureCardiac disorders1 of 1534 of 157

Most frequent non-serious adverse event terms

Event termOrgan systemBest Supportive CareCarfilzomib
AnaemiaBlood and lymphatic system disorders72 of 15388 of 157
ThrombocytopeniaBlood and lymphatic system disorders43 of 15358 of 157
PyrexiaGeneral disorders28 of 15341 of 157
FatigueGeneral disorders28 of 15329 of 157
AstheniaGeneral disorders20 of 15326 of 157
NeutropeniaBlood and lymphatic system disorders23 of 15322 of 157
NauseaGastrointestinal disorders14 of 15331 of 157
DiarrhoeaGastrointestinal disorders18 of 15323 of 157
Bone painMusculoskeletal and connective tissue disorders16 of 15318 of 157
DyspnoeaRespiratory, thoracic and mediastinal disorders12 of 15321 of 157

Serious events with the highest arm-level rate: disease progression (12.4%), pneumonia (11.8%), renal failure acute (9.6%), anaemia (5.2%), hypercalcaemia (4.5%).

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 safety counts are reported separately by group. For serious adverse events, 78 of 153 participants at risk in the best supportive care group were affected, and 92 of 157 participants at risk in the carfilzomib group were affected. For other adverse events, 135 of 153 at risk in the best supportive care group and 141 of 157 at risk in the carfilzomib group were affected.

The registry's listed serious adverse event terms include disease progression at 12.4%, pneumonia at 11.8%, acute renal failure at 9.6%, anaemia at 5.2%, hypercalcaemia at 4.5%, and pyrexia at 3.8%. These are the posted term percentages; the registry entries do not provide corresponding counts for each term.

These figures describe affected participants in the reported safety groups. They do not, by themselves, establish that an event was caused by an assigned intervention, or allow a complete comparison of event severity, timing, duration, or exposure. Death counts are not reported in the safety information. The safety results should be read as descriptive registry counts alongside the trial's design and follow-up, not as a standalone causal analysis.

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

The registry reports similar median overall survival summaries for the two groups, alongside a sponsor-reported hazard ratio whose confidence interval includes 1 and a log-rank p-value of 0.417. This means the posted primary analysis does not establish a clear difference in overall survival between the randomized groups. It does not prove that the treatments have identical effects, and the confidence interval leaves uncertainty about the size and direction of a possible difference.

The secondary results provide a mixed set of descriptive findings. The posted counts are higher in the carfilzomib group for the reported response and disease-control outcomes, but the unadjusted uncertainty intervals differ, and the registry does not report multiplicity handling for these comparisons. They should not be treated as independent confirmation of a primary survival effect or as a substitute for the sponsor's primary analysis.

The results apply to the participants and trial conditions described in the record: people with multiple myeloma who had received available approved treatment options, randomized to carfilzomib or best supportive care in an open-label study. The registry's brief summary describes participants as potentially candidates for palliative care. The treatment regimens and full content of supportive care are not described in detail, which limits interpretation of exactly what was compared.

These statistics do not provide an individual prediction, a complete account of benefits and harms, or a recommendation about treatment. The results also do not resolve questions outside the reported outcomes, populations, follow-up, and analyses. They describe the evidence recorded for this trial, with uncertainty and reporting limitations that should remain visible when drawing conclusions.

19. Why This Trial Matters Statistically

This trial illustrates why a time-to-event outcome should be interpreted through both an arm-level summary and a formal comparison. The medians give accessible summaries of overall survival, while the sponsor's log-rank hazard ratio uses event timing across follow-up and accounts for censoring. The two forms of information are related but not interchangeable.

It also shows the importance of reading an estimate together with its confidence interval. A point estimate gives one summary value; the interval communicates the range of values compatible with the data under the analysis. Here, the primary interval includes the null hazard-ratio value, and the reported p-value does not provide strong evidence against that null. The correct interpretation is uncertainty, rather than proof of no difference or proof of a difference.

The record distinguishes a sponsor-reported primary analysis from simple recalculations for binary secondary outcomes. That distinction matters: recalculations from summary counts can help readers understand the observed data, but they cannot be assumed to reproduce the planned analysis. Likewise, multiple unadjusted secondary comparisons require caution because each adds another opportunity for an apparently notable result.

Finally, the planning illustrations show how assumed effect size and target power shape planning requirements, but they are not evidence about the trial's design or its achieved power. Keeping design assumptions, observed estimates, and sponsor-reported analyses separate is central to sound interpretation of registry results.

20. Limitations

Several trial-specific reporting limitations constrain interpretation. The record names carfilzomib and best supportive care but does not describe the treatment regimen details or the components of supportive care. As a result, the interventions cannot be characterized more fully from the registry information.

The study was open-label, with masking listed as none. Awareness of assignment can affect treatment delivery, co-interventions, and subjective outcome assessment in general, although overall survival is a death-based outcome. The registry record does not provide enough detail to assess those possible influences for each endpoint.

The primary comparison is reported, but the complete statistical analysis plan is not. The original sample-size justification, interim analyses, multiplicity procedures, and sensitivity analyses are not reported in the registry record. The record also does not report detailed methods for handling missing secondary outcome data. The stated intent-to-treat population and primary censoring rule clarify important aspects, but not all analysis decisions.

Some secondary measures are named without detailed results, and the available binary comparisons are unadjusted recalculations rather than sponsor-reported analyses. The secondary follow-up window is shorter than the stated primary timeframe. The safety information provides affected-participant counts and selected serious-event terms, but death counts and detailed event-level timing or exposure are not reported in the safety data described.

These limitations do not establish that unreported methods were not used; they indicate that the registry record does not give the information needed to evaluate them. Conclusions should remain confined to the posted estimates and their stated analysis context.

21. Related Tutorials

22. Related Statistical Calculators

23. Sources

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24. Record Summary

The registry describes a completed, randomized, open-label, multicenter, parallel-group Phase 3 study of carfilzomib versus best supportive care in people with relapsed and refractory multiple myeloma. Enrollment was 315. The primary endpoint was overall survival in the intent-to-treat population, measured from randomization to death, with participants alive censored at their last-known-alive date or the data cutoff.

Median overall survival was 10.2 months for carfilzomib and 10.0 months for best supportive care. The sponsor-reported log-rank hazard ratio was 0.975, with a 95% confidence interval from 0.760 to 1.249 and p = 0.417. The primary result does not establish a clear difference between groups, while leaving uncertainty about the possible effect. Secondary and safety findings are descriptive and have the reporting limitations noted above.

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