← Clinical Trials
Amyloidosis Phase 3 Binary Endpoint NCT03201965

A Study to Evaluate the Efficacy and Safety of Daratumumab in Combination With Cyclophosphamide, Bortezomib and Dexamethasone (CyBorD) Compared to CyBorD Alone in Newly Diagnosed Systemic Amyloid Light-chain (AL) Amyloidosis: Complete Statistical Analysis

This analysis examines a randomized, open-label phase 3 trial comparing daratumumab plus CyBorD with CyBorD alone in newly diagnosed systemic AL amyloidosis. It focuses on overall complete hematologic response and the precision, interpretation, and limitations of the posted results.

Trial start: 2017-10-05  ·  Enrollment: 416  ·  Sponsor: Janssen Research & Development, LLC
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 to Evaluate the Efficacy and Safety of Daratumumab in Combination With Cyclophosphamide, Bortezomib and Dexamethasone (CyBorD) Compared to CyBorD Alone in Newly Diagnosed Systemic Amyloid Light-chain (AL) Amyloidosis (NCT03201965), a randomized phase 3 study. The primary outcome is Percentage of Participants With Overall Complete Hematologic Response (CHR).

416
Enrollment
Phase 3
2
Arms
In the primary outcome
+35.2 pts
Risk difference
Daratumumab Plus CyBorD
26.3 to 44.1 pts
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT03201965
PhasePhase 3
ConditionAmyloidosis
AllocationRandomized
Design modelParallel
MaskingNone (open label)
Enrollment416
Arms in the primary outcome2
Lead sponsorJanssen Research & Development, LLC
Results postedYes

2. Clinical Question

Population

The study concerned participants with newly diagnosed systemic amyloid light-chain (AL) amyloidosis. The primary outcome population is described as the intent-to-treat analysis set: participants who were randomized and received at least one dose of study treatment. The registry record says outcome data were planned for specified arms only.

Intervention

Daratumumab was given in combination with cyclophosphamide, bortezomib and dexamethasone, a regimen referred to as CyBorD. The registry lists the combination as Daratumumab Plus CyBorD.

Comparator

The comparison group received cyclophosphamide, bortezomib and dexamethasone without daratumumab, referred to as CyBorD alone.

Primary question

The primary question was whether the percentage of participants achieving overall complete hematologic response differed between the two treatment groups. The response definition followed the International Amyloidosis Consensus Criteria and was assessed up to 2.4 years.

This is a comparison of a treatment combination with its CyBorD backbone alone. It does not isolate the effects of the individual drugs within either regimen. The primary endpoint concerns hematologic response, rather than a direct measure of survival or organ response. The record also lists secondary outcomes covering organ response and other clinical measures, but the central result is the overall complete hematologic response rate.

3. Trial Design

The registry describes a completed, randomized, phase 3 study with a parallel-group model and no masking. Its purpose was to evaluate efficacy and safety of daratumumab plus CyBorD compared with CyBorD alone in newly diagnosed AL amyloidosis. The registry lists enrollment as 416. This enrollment figure is distinct from the group sizes used in the posted primary outcome results, which are reported for the analysis population.

The posted primary endpoint results include 193 participants in the CyBorD group and 195 in the Daratumumab Plus CyBorD group. The primary outcome description defines its analysis set as randomized participants who received at least one dose of study treatment. The record does not give further detail about the reasons participants might be excluded from a particular outcome analysis or how any such cases were handled.

The comparison was open-label: masking is listed as none. That design feature is relevant when considering outcomes involving assessment or decisions, although the record does not establish whether knowledge of treatment assignment affected outcome assessment. Random allocation supports a comparative interpretation, but the registry record does not report the allocation method or describe any stratification factors.

The recorded start date is 2017-10-05 and the primary completion date is 2020-02-14. These dates describe the study record, not the duration of follow-up for every participant. The primary outcome timeframe is stated as up to 2.4 years. The record does not report the original sample-size justification, the allocation ratio planned in the protocol, or the full schedule of study treatment. The arm descriptions available in the registry are incomplete, so treatment details beyond the named drugs and the stated comparison should not be inferred.

4. Participant Flow and Accounting

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

Before assignment: Participants with newly diagnosed Amyloid Light-chain (AL) amyloidosis with measurable disease and at least one organ involvement, and Mayo cardiac stage I - IIIA, who had not received prior therapy for AL amyloidosis or multiple myeloma were enrolled.

Overall Study

StageRun-In: Daratumumab Plus CyBorDCyBorDDaratumumab Plus CyBorD
STARTED28193195
Treated28188193
COMPLETED000
NOT COMPLETED28193195

Reasons for not completing this period:

ReasonRun-In: Daratumumab Plus CyBorDCyBorDDaratumumab Plus CyBorD
Death56547
Lost to Follow-up060
Withdrawal by Subject3238
Sponsor's Decision2099140

Analysis population for the primary outcome, as defined in the registry: The intent to treat analysis set included all the participants who were randomized and received at least one dose of study treatment in the study. Data for this outcome measure (OM) was planned to be collected and analyzed for specified arms only.

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.

CharacteristicUnitRun-In: Daratumumab Plus CyBorDCyBorDDaratumumab Plus CyBorDTotal
Participants analysed28193195416
Age, Continuousyears64.8 (SD 11.2)64 (SD 9.66)62.2 (SD 10.16)63.2 (SD 10.03)
Sex/Gender, Customized: FemaleParticipants117687174
Sex/Gender, Customized: MaleParticipants16117108241
Sex/Gender, Customized: Undifferentiated SexParticipants1001
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants113923
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants26176179381
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants14712
Race (NIH/OMB): American Indian or Alaska NativeParticipants0213
Race (NIH/OMB): AsianParticipants0343064
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants0101
Race (NIH/OMB): Black or African AmericanParticipants27615
Race (NIH/OMB): WhiteParticipants25143151319
Race (NIH/OMB): More than one raceParticipants0101
Race (NIH/OMB): Unknown or Not ReportedParticipants15713
Region of Enrollment: AUSTRALIAParticipants0151227
Region of Enrollment: BELGIUMParticipants0123
Region of Enrollment: BRAZILParticipants07411
Region of Enrollment: CANADAParticipants010919
Region of Enrollment: CHINAParticipants06612
Region of Enrollment: DENMARKParticipants0112
Region of Enrollment: FRANCEParticipants0221638
Region of Enrollment: GERMANYParticipants011819
Region of Enrollment: GREECEParticipants0111627
Region of Enrollment: HUNGARYParticipants0224
Weight group in Kilograms (Kg): <=65 kgParticipants57462141
Weight group in Kilograms (Kg): >65 to 85 kgParticipants127496182
Weight group in Kilograms (Kg): >85 kgParticipants11453793
Baseline Major Organ Involvement: Baseline Organ Involvement: HeartParticipants17137140294
Baseline Major Organ Involvement: Baseline Organ Involvement: KidneyParticipants19114115248
Baseline Major Organ Involvement: Baseline Organ Involvement: LiverParticipants4161535
Number of Organs Involvedorgans2.0 (SD 0.881)2.0 (SD 1.03)2.0 (SD 0.97)2.0 (SD 0.99)
Number of Organs Involved: 1 OrganParticipants96866143
Number of Organs Involved: 2 OrgansParticipants137776166
Number of Organs Involved: >=3 OrganParticipants64853107
Cardiac Stage Based on Mayo Clinic Cardiac Staging System: Class IParticipants6434796
Cardiac Stage Based on Mayo Clinic Cardiac Staging System: Class IIParticipants168076172
Cardiac Stage Based on Mayo Clinic Cardiac Staging System: Class IIIaParticipants56470139
Cardiac Stage Based on Mayo Clinic Cardiac Staging System: Class IIIbParticipants1629
New York Heart Association (NYHA) Class: Class IParticipants1794101212
New York Heart Association (NYHA) Class: Class IIParticipants108977176
New York Heart Association (NYHA) Class: Class IIIAParticipants1101728

6. Primary Endpoint

The registry lists the primary outcome as Percentage of Participants With Overall Complete Hematologic Response (CHR), measured over Up to 2.4 years.

ElementRegistry entry
Result typeNumber
Measure of spread95% Confidence Interval
Unitpercentage of participants
Endpoint classificationBinary Endpoint

The primary endpoint is the percentage of participants with overall complete hematologic response (CHR), assessed up to 2.4 years. It is a binary outcome: each participant either meets the response definition or does not. The registry defines CHR according to the International Amyloidosis Consensus Criteria, including normalization of free light chain levels and ratio and negative serum and urine immunofixation. It also specifies a condition under which normal uninvolved free light chain levels or a normal free light chain ratio are not required for complete response.

A percentage makes the outcome interpretable as the share of the analysis group meeting the defined response criteria. Comparing the group percentages describes the observed difference in response rates between the treatment strategies. Because the endpoint is defined by laboratory and immunofixation criteria, it captures hematologic response as specified by the registry; it should not be treated as interchangeable with organ response, survival, or a broader measure of health.

For a binary endpoint, uncertainty in each group percentage and in the between-group comparison matters alongside the point estimates. Confidence intervals describe a range of values compatible with the observed data under the method used; they do not guarantee that the underlying effect lies within the interval. The registry lists 95% confidence intervals for the group percentages. It also reports a sponsor analysis of the between-group comparison using an odds ratio. These statistics express different aspects of the data and should be read according to their respective scales.

7. Results Posted in the Registry

Risk difference: Daratumumab Plus CyBorD

+35.2

95% CI: 26.3 to 44.1 percentage points

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals8.719.931.142.453.664.9CyBorD (n=193)Daratumumab Plus CyBorD (n=195)% of participants (95% CI)
Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Daratumumab Plus CyBorD-3.536.7017273748risk difference (percentage points) vs control (95% CI)

8. Secondary Efficacy Endpoints

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

Secondary outcomeTypeEffect measureEstimate (95% CI)Planning size, 80% power
Organ Response Rate (OrRR) at 6 Months: Cardiac ResponseBinary EndpointRisk difference+19.3 pts (7.6 to 31.0)91 per arm
Organ Response Rate (OrRR) at 6 Months: Renal ResponseBinary EndpointRisk difference+26.4 pts (14.2 to 38.6)54 per arm
Organ Response Rate (OrRR) at 6 Months: Liver ResponseBinary EndpointRisk difference+32.9 pts (-0.4 to 66.1)25 per arm

Organ Response Rate (OrRR) at 6 Months: Cardiac Response

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Daratumumab Plus CyBorD-2.484.7112192633risk difference (percentage points) vs control (95% CI)

Organ Response Rate (OrRR) at 6 Months: Renal Response

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Daratumumab Plus CyBorD-3.095.8715243342risk difference (percentage points) vs control (95% CI)

Organ Response Rate (OrRR) at 6 Months: Liver Response

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Daratumumab Plus CyBorD-5.689.7325415671risk difference (percentage points) vs control (95% CI)

The secondary outcomes cover organ response, survival, progression-free outcomes, and additional hematologic response measures. Taken broadly, the posted organ response estimates tend in the same direction as the primary hematologic response comparison, but their precision varies across outcomes. The liver response estimate is particularly uncertain in relation to the cardiac and renal outcomes, as its analysis groups are much smaller and its interval includes no difference. These patterns are descriptive and do not establish that all secondary outcomes have the same evidential strength.

Secondary outcomes address questions related to, but distinct from, the primary endpoint. A hematologic response result does not guarantee an organ response, and an organ response result does not establish an effect on survival or progression-free survival. Each outcome has its own definition, analysis population, timeframe, and uncertainty. The registry lists 16 secondary outcomes as posted, but detailed results are available only for some of them in the record summarized for this analysis.

Unadjusted secondary results carry less weight because multiple outcomes create multiple opportunities for a chance finding. If many hypotheses are tested without an appropriate plan for multiplicity, nominal p-values can overstate the strength of evidence across the collection of outcomes. The registry record does not report whether multiplicity was controlled, which outcomes were prespecified in a hierarchy, or whether any secondary analysis was intended to be confirmatory.

For that reason, secondary findings are best treated as supportive or exploratory unless the analysis plan establishes otherwise. Their direction can help describe consistency across domains, but isolated statistical significance should not be interpreted as definitive evidence. The record does not report a comprehensive secondary analysis plan or adjustment strategy, so the relative priority of individual secondary results is not established.

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

9. Statistical Interpretation

Clinical Biostats interpretation

For overall CHR, the posted rate was 18.1% in the CyBorD group and 53.3% in the Daratumumab Plus CyBorD group. The corresponding 95% confidence intervals were 13.0% to 24.3% and 46.1% to 60.5%. These estimates describe the analyzed groups; the intervals convey uncertainty around the group rates.

The unadjusted recalculation of the risk difference is 0.352, with a 95% confidence interval from 0.263 to 0.441 and p < 0.001. A risk difference is an absolute contrast on the probability scale, represented as a proportion. Its positive direction reflects a higher observed response rate in the Daratumumab Plus CyBorD group. This recalculation uses posted summary statistics and is not the sponsor's reported analysis.

The sponsor's reported analysis used a Cochran-Mantel-Haenszel method and expressed the comparison as an odds ratio of 5.13, with a 95% confidence interval from 3.22 to 8.16 and p < 0.001. An odds ratio compares odds, whereas the recalculated risk difference compares probabilities. They are not the same measure, so their numerical magnitudes should not be compared as though they shared a scale. The registry does not report further details about the adjustment structure used in the sponsor analysis.

Both the reported analysis and the unadjusted recalculation indicate a clear separation in the observed primary outcome rates, with uncertainty intervals that do not include the null value for their respective measures. A small p-value describes how unusual data at least as incompatible with a null comparison would be under the test assumptions; it does not measure the probability that the null hypothesis is true, the size of a clinical benefit, or the likelihood that the result will reproduce.

The endpoint is a hematologic response measure. Its result does not by itself establish the size or timing of an organ response, a survival effect, or a safety trade-off. Those questions involve different outcomes and require their own estimates and uncertainty. The registry lists secondary outcomes for these areas, but their multiplicity and analysis details are not reported in the registry record. Accordingly, the primary result is the strongest basis for describing the trial's central statistical finding, while interpretation of the other outcomes requires more caution.

10. Statistical Methods Explained

What does a binary response rate represent?

Complete hematologic response is recorded as a yes-or-no outcome for each participant under the stated criteria. A group response rate is the percentage of participants in that group meeting those criteria. For this endpoint, the posted rates are 18.1% for CyBorD and 53.3% for Daratumumab Plus CyBorD. The group-level percentages provide a direct description of the observed data, but they do not show how much individual responses varied or whether the endpoint captures every clinically relevant aspect of the condition.

For a binary outcome, several measures can describe the comparison. A risk difference subtracts one group's probability from the other's and uses the probability scale. A risk ratio divides one probability by the other. An odds ratio compares the odds of the event between groups. These measures answer related but distinct questions; the odds ratio can appear numerically further from its null value than a risk ratio when the outcome is common. General statistical interpretation therefore requires naming the measure and its scale rather than treating all relative or absolute comparisons as interchangeable.

Why are confidence intervals reported?

A confidence interval describes the uncertainty associated with an estimate under a specified statistical procedure. In repeated applications of a method under its assumptions, intervals constructed at a stated confidence level would cover the target parameter at that level in the long run. That general interpretation is not a statement that an individual interval has a probability of containing the fixed true value. The registry reports 95% confidence intervals for each primary group rate and for the sponsor's odds ratio.

The width of an interval is affected by the amount of information in the data and by the variability of the outcome. A wider interval indicates less precision than a narrower one on the same scale. The interval should be considered along with the point estimate, the endpoint definition, and the analysis population. A confidence interval is not a range of individual participant outcomes, nor does it account automatically for bias from missing data, unblinded assessment, or a misspecified analysis.

What is the role of the p-value?

A p-value is calculated under a specified null hypothesis and statistical model. It expresses how compatible the observed data, or more extreme data, are with that null model. It does not quantify the probability that the observed difference arose by chance in an everyday sense, and it does not tell readers whether an effect is important. The registry reports p < 0.001 for the sponsor's primary comparison. The unadjusted recalculation reports p < 0.001. These are results from different stated analyses and should not be substituted for one another.

Statistical significance does not remove uncertainty about the effect's size or generalizability. The estimates and their confidence intervals carry information about magnitude and precision, while the endpoint and design determine what the comparison can address. A favorable direction for a hematologic response rate should not be extended automatically to other outcomes.

What distinguishes the sponsor analysis from the recalculation?

The registry's reported primary analysis uses the Cochran-Mantel-Haenszel method and reports an odds ratio. This method is commonly used to estimate a group comparison while accounting for strata, but the registry record does not describe which strata or adjustment details were used in this case. The reported estimate is 5.13, with a 95% confidence interval from 3.22 to 8.16.

The recalculated result is an unadjusted risk difference based on posted group summary statistics. It is a simple comparison of the observed group rates rather than a reproduction of the sponsor's analysis. The recalculated confidence interval and p-value depend on the unadjusted method used for that calculation. Differences between estimates, if any, can reflect the measure, adjustment, and method; they do not alone establish an error. The registry record does not flag a discrepancy between the sponsor analysis and the recalculation.

Why can over-dispersion matter in other settings?

Over-dispersion is a general statistical issue that arises when observed variability is greater than a model assumes. If a model underestimates variability, standard errors can be too small and confidence intervals too narrow. It is relevant to count or rate outcomes and some clustered data structures, but the primary endpoint is a binary response rate. The registry does not report a model-based over-dispersion assessment for this endpoint, so there is no basis to claim that it was present or that a correction was applied.

What does randomization contribute?

Randomization is intended to make treatment assignment independent of participant characteristics on average, supporting a fair comparison between assigned groups. It does not guarantee that every characteristic is balanced in a particular trial, and it cannot remove bias introduced after randomization through missing outcomes, nonadherence, or outcome assessment. The registry identifies the study as randomized but does not describe its sequence generation, concealment procedures, stratification, or detailed analysis plan.

The described primary analysis population includes randomized participants who received at least one dose of study treatment. This definition is not equivalent to a statement that every randomized participant was included regardless of treatment receipt. The number randomized but not treated, the handling of their outcomes, and any sensitivity analyses are not reported in the registry record. These details matter when judging how closely the analyzed groups preserve the protection intended by random allocation.

11. Confidence Intervals and Precision

The primary group estimates have 95% confidence intervals of 13.0% to 24.3% for CyBorD and 46.1% to 60.5% for Daratumumab Plus CyBorD. Those ranges express uncertainty in the response rate for each analyzed group. They are not bounds on the response of every participant, and they do not summarize uncertainty about all possible differences between the treatment strategies.

The recalculated unadjusted risk difference is 0.352, with a 95% confidence interval from 0.263 to 0.441. The interval lies on the positive side of the null value for a difference, indicating that the observed direction is not explained by an interval that includes no difference under this calculation. The precision statement remains conditional on the calculation's unadjusted method and the available summary data.

The sponsor's odds ratio estimate has a 95% confidence interval from 3.22 to 8.16. This interval is on the odds-ratio scale and has a different null value and interpretation from the risk-difference interval. Its width communicates uncertainty for that analysis, not a range of plausible risk differences. The two interval types should not be compared by their raw numerical widths.

Confidence intervals address sampling uncertainty under the method's assumptions. They do not account automatically for every potential source of uncertainty, including missing outcome data, departures from the analysis plan, multiplicity across outcomes, or limitations associated with open-label assessment. Those matters require information about methods and conduct, some of which is not reported in the registry record. Precision should therefore be read as one part of the statistical evidence, not as a complete measure of reliability.

12. Planning a Similar Trial: Sample Size

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

Effect to detectParticipants per arm, 80% powerParticipants per arm, 90% power
100% of the observed effect2837
75% of the observed effect4863
50% of the observed effect99132
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect205010020040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, pooled-variance normal approximation for two proportions. Counts were reconstructed from the posted percentages and arm sizes, so small rounding differences are possible. Calculated for the comparison: Daratumumab Plus CyBorD.

The sample-size illustrations are expressed as participants per arm for the binary primary outcome. They are planning illustrations based on the observed effect, not counts of total events. The listed assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each planning scenario uses the stated fraction of the observed effect as the effect to detect. The trial's own original sample-size assumptions are not reported in the registry record.

The column for 80% power gives the illustrative number of participants per arm for a design with an 80% chance of detecting the specified effect under the stated assumptions, if that effect and assumptions were correct. The 90% power column gives the corresponding planning number for a higher chance of detection. These are design calculations, not forecasts of what any future study will find.

For example, planning for 100% of the observed effect gives 28 participants per arm for 80% power and 37 participants per arm for 90% power. Planning for 75% of the observed effect gives 48 participants per arm for 80% power and 63 participants per arm for 90% power. Planning for 50% of the observed effect gives 99 participants per arm for 80% power and 132 participants per arm for 90% power. The pattern illustrates that smaller effects need more participants to detect under otherwise fixed assumptions.

These figures are not observed power. They do not estimate the probability that the completed trial detected its actual effect, and they should not be used to judge the trial's success after seeing its results. The planning table and curve are best read as conditional illustrations of how sample size changes with the assumed effect and target 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

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

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

Worked calculation for this trial

  1. Control proportion p0 = 0.181; treatment proportion p1 = 0.533; average p̄ = 0.357.
  2. First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6777 = 1.3283.
  3. Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.6304 = 0.5305.
  4. n = (1.3283 + 0.5305)2 / (0.3520)2 = 27.9, rounded up to 28 participants per arm for 80% power.

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

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
p0 <- 0.181347150259067                          # control proportion
p1 <- 0.533333333333333                          # treatment proportion
n_per_arm <- function(power, frac = 1) {
  q1 <- p0 + (p1 - p0) * frac               # smaller effect = fraction of the observed difference
  pbar <- (p0 + q1) / 2
  z_b <- qnorm(power)
  ceiling(round((z_a * sqrt(2 * pbar * (1 - pbar)) + z_b * sqrt(p0 * (1 - p0) + q1 * (1 - q1)))^2 / (q1 - p0)^2, 6))
}
for (f in c(1, 0.75, 0.5))
  cat(sprintf("%3.0f%% of observed effect: n per arm = %s (80%% power), %s (90%% power)\n", 100 * f,
              format(n_per_arm(0.80, f), big.mark = ","), format(n_per_arm(0.90, f), big.mark = ",")))

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

# Simulation: how often does the z-test reject at the 80%-power sample size?
set.seed(3201965)
n    <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z  <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))

Output from running the code

100% of observed effect: n per arm = 28 (80% power), 37 (90% power)
 75% of observed effect: n per arm = 48 (80% power), 63 (90% power)
 50% of observed effect: n per arm = 99 (80% power), 132 (90% power)
power.prop.test: 27.9 
Simulated power at n = 28 per arm: 0.809 (20000 replicates)

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

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

14. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
Cochran-Mantel-HaenszelOdds Ratio (OR) 5.133.22 to 8.16< 0.001

The sponsor's reported primary analysis used a Cochran-Mantel-Haenszel method and reported an odds ratio of 5.13, with a 95% confidence interval from 3.22 to 8.16 and p < 0.001. This is the registry's own analysis of the primary comparison. The registry does not report the details of any strata or other adjustments used in that method.

The recalculated comparison is an unadjusted risk difference of 0.352, with a 95% confidence interval from 0.263 to 0.441 and p < 0.001. It is calculated from the posted group summary statistics, rather than reproducing the sponsor's analysis. Odds ratios and risk differences use different scales, and the sponsor method and unadjusted recalculation also differ in their approach. Their numerical values are therefore not direct alternatives for the same estimand.

The registry record does not flag a discrepancy. The sponsor result should be read as the trial's reported analysis, while the recalculation offers a transparent unadjusted contrast based on the posted summaries. Neither result changes the endpoint definition or resolves limitations that are not described in the registry record.

15. Multiplicity, Missing Data and Analysis Populations

The registry lists a primary outcome and multiple secondary outcomes. Testing several outcomes can increase the chance of at least one apparently unusual result even if none reflects a real effect. Statistical approaches to multiplicity can adjust significance thresholds, control error rates, or define a sequence for testing outcomes. Which approach is appropriate depends on the study's aims and prespecified plan.

The registry record does not report a multiplicity adjustment, an outcome hierarchy, or whether secondary analyses were confirmatory or exploratory. Consequently, the posted secondary p-values should not be interpreted as though a family-wide error rate has necessarily been controlled. This limitation does not alter the reported primary endpoint estimate, but it affects how much weight to assign to additional outcomes when considered collectively.

The primary outcome population is described as randomized participants who received at least one dose of study treatment. This is the population definition recorded for the primary measure. The registry does not state how participants without an evaluable outcome were handled, whether missing values were imputed, or whether sensitivity analyses tested alternative assumptions about missingness. The numbers excluded from specific outcome analyses and reasons for exclusion are not reported in the registry record.

Missing data can affect a response rate if outcome availability differs between groups or is related to participants' response status. The direction and size of any resulting bias cannot be determined without information about the missingness pattern and analysis methods. The record also does not report whether the sponsor conducted analyses using a broader randomized population or other analysis sets.

Randomization is an important design feature, but an analysis limited to participants who received treatment can differ from an analysis of everyone randomized. The registry's definition should be stated as written rather than assumed to be a conventional all-randomized intention-to-treat analysis. Further details on allocation, adherence, protocol deviations, and analysis populations are not reported in the registry record.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Run-In: Daratumumab Plus CyBorD122842.9%
CyBorD6818836.2%
Daratumumab Plus CyBorD9119347.2%
Participants with at least one serious adverse event
Serious adverse events by armRun-In: Daratumumab Plus CyBo…42.9%CyBorD36.2%Daratumumab Plus CyBorD47.2%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
Run-In: Daratumumab Plus CyBorD11 of 28
CyBorD67 of 193
Daratumumab Plus CyBorD47 of 195

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
Run-In: Daratumumab Plus CyBorD27 of 28
CyBorD181 of 188
Daratumumab Plus CyBorD184 of 193

Most frequent serious adverse event terms

Event termOrgan systemRun-In: Daratumumab Plus CyBorDCyBorDDaratumumab Plus CyBorD
PneumoniaInfections and infestations2 of 289 of 18814 of 193
Cardiac FailureCardiac disorders0 of 288 of 18814 of 193
Cardiac ArrestCardiac disorders0 of 283 of 1888 of 193
SyncopeNervous system disorders1 of 286 of 1884 of 193
Sudden DeathGeneral disorders0 of 283 of 1886 of 193
Atrial FibrillationCardiac disorders0 of 282 of 1886 of 193
DiarrhoeaGastrointestinal disorders1 of 284 of 1883 of 193
SepsisInfections and infestations0 of 280 of 1887 of 193
Acute Kidney InjuryRenal and urinary disorders3 of 281 of 1883 of 193
DyspnoeaRespiratory, thoracic and mediastinal disorders0 of 283 of 1884 of 193

Most frequent non-serious adverse event terms

Event termOrgan systemRun-In: Daratumumab Plus CyBorDCyBorDDaratumumab Plus CyBorD
Oedema PeripheralGeneral disorders14 of 2866 of 18871 of 193
DiarrhoeaGastrointestinal disorders19 of 2855 of 18869 of 193
ConstipationGastrointestinal disorders12 of 2854 of 18870 of 193
FatigueGeneral disorders16 of 2852 of 18855 of 193
NauseaGastrointestinal disorders12 of 2851 of 18855 of 193
Peripheral Sensory NeuropathyNervous system disorders5 of 2837 of 18865 of 193
AnaemiaBlood and lymphatic system disorders13 of 2844 of 18849 of 193
InsomniaPsychiatric disorders9 of 2847 of 18849 of 193
DyspnoeaRespiratory, thoracic and mediastinal disorders9 of 2829 of 18846 of 193
Upper Respiratory Tract InfectionInfections and infestations10 of 2821 of 18850 of 193

Serious events with the highest arm-level rate: fall (10.7%), acute kidney injury (10.7%), cardiac failure (7.3%), pneumonia (7.3%), cellulitis (7.1%).

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 adverse-event record separates a run-in group from the CyBorD and Daratumumab Plus CyBorD groups. For serious adverse events, it reports 12 affected among 28 at risk in the run-in group, 68 among 188 at risk in the CyBorD group, and 91 among 193 at risk in the Daratumumab Plus CyBorD group. These are group-specific counts, not a risk-adjusted comparison, and the run-in group should not be conflated with the randomized treatment groups.

The record also lists other adverse events as 27 among 28 at risk in the run-in group, 181 among 188 at risk in the CyBorD group, and 184 among 193 at risk in the Daratumumab Plus CyBorD group. Death counts are reported as 11, 67, and 47 for those respective groups. The record does not provide a comparative statistical analysis for these safety counts in the registry record.

Listed serious adverse-event terms include Fall and Acute Kidney Injury at 10.7% each, Cardiac Failure and Pneumonia at 7.3% each, Cellulitis at 7.1%, and Cardiac Arrest at 4.1%. These terms should be read as reported event information, not as proof that a particular treatment caused an event. A full safety assessment would require event definitions, exposure time, severity and relatedness assessments, follow-up, and a suitable comparison. Such details are not reported in the registry record.

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

The primary result describes a higher observed complete hematologic response rate in the Daratumumab Plus CyBorD group than in the CyBorD group, with the posted group estimates and confidence intervals indicating a clear separation. The sponsor's reported odds-ratio analysis and the unadjusted risk-difference recalculation both point in the same direction. The result is evidence about the specified hematologic endpoint in the analyzed trial population.

It does not establish that every participant responded, predict an individual participant's outcome, or show that the same pattern applies to every outcome. CHR is defined by laboratory and immunofixation criteria. Organ response, progression-free survival, overall survival, and safety are separate questions, with distinct outcome definitions and uncertainty. The primary response finding alone cannot answer those questions.

The result also does not show the reason for the observed group difference. Randomization supports comparison of assigned treatment strategies, but the registry record does not report enough detail to assess every potential influence on the analysis, including missing data handling, allocation procedures, or outcome assessment practices. The design is open-label, and the record does not state whether outcome assessment was blinded.

A confidence interval and p-value do not measure clinical importance. The interval represents uncertainty under a statistical method, while the p-value describes compatibility with a null model. Neither establishes the durability of response beyond the recorded timeframe, the balance of benefits and harms, or whether the outcome is meaningful to every patient. Those judgments require broader clinical evidence and context that are not reported in the registry record.

Accordingly, the defensible statistical conclusion is limited: the posted primary endpoint data show a higher observed CHR rate for the combination group, and the reported statistical comparison supports a difference on its stated scale. The finding should not be translated into an unqualified claim about treatment effectiveness across all outcomes or settings.

18. Why This Trial Matters Statistically

This trial provides a randomized comparison of a treatment combination against its CyBorD backbone alone, making the primary contrast directly relevant to the added daratumumab strategy as studied. The outcome is clearly defined in the record, and the group response percentages are accompanied by confidence intervals. Reporting both a sponsor analysis and a recalculation on another scale also illustrates why effect measures and analytic methods must be distinguished.

Statistically, the example demonstrates the value of reading an estimate together with its uncertainty and endpoint definition. The odds ratio from the sponsor's Cochran-Mantel-Haenszel analysis and the unadjusted risk difference answer related but not identical questions. A reader who focuses only on a p-value could miss these distinctions, as well as the difference between a hematologic response and outcomes such as organ response or survival.

The trial also illustrates that evidence across outcomes is not uniform in precision. The primary endpoint and some secondary outcomes have more informative group data than others. Secondary measures with limited information can have broad uncertainty, and multiple secondary comparisons create interpretive challenges when the multiplicity plan is not reported.

Finally, this record is useful for teaching the boundary between what a registry result can establish and what remains unknown. The design, endpoint, estimates, and safety counts are recorded, but details of the original sample-size justification, missing-data methods, multiplicity strategy, and several analysis procedures are not. Statistical interpretation therefore depends on both the numerical results and a careful account of what the record does not document.

19. Limitations

The trial is listed as open-label, with masking none. Knowledge of treatment assignment can potentially influence behavior, reporting, or assessment, depending on the outcome and study procedures. The primary endpoint uses laboratory and immunofixation criteria, but the registry record does not state whether endpoint assessment was blinded or how assessments were adjudicated.

The analysis population is described as randomized participants who received at least one dose of study treatment. The registry does not report how many randomized participants did not receive treatment, whether participants with missing outcomes were excluded, or how missing outcome data were handled. It also does not describe sensitivity analyses. These omissions limit assessment of the robustness of the primary comparison.

The registry reports an enrollment of 416, while the primary endpoint analysis groups are reported as 193 and 195. The record does not explain the relationship between enrollment and these analysis group sizes or provide a participant flow account in the registry record. No total or reason for the difference should be inferred from the available record.

The sponsor's primary method is named, but adjustment details are not reported. The original sample-size justification, interim analysis plan, multiplicity strategy, and full statistical analysis plan are also not reported in the registry record. The secondary results therefore require caution, particularly where group information is limited or confidence intervals are wide. Finally, the primary endpoint timeframe is up to 2.4 years; the record does not establish whether the observed response pattern persists beyond that stated timeframe.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

Continue through the Clinical Biostats statistical pathway

Use this trial's endpoint as a starting point for deeper study of effect measures, confidence intervals, and sample-size planning.

23. Record Summary

The registry record describes a completed randomized phase 3 parallel-group study with no masking, comparing Daratumumab Plus CyBorD with CyBorD in newly diagnosed systemic AL amyloidosis. The primary outcome was the percentage of participants with overall complete hematologic response, assessed up to 2.4 years and defined according to the International Amyloidosis Consensus Criteria.

The posted primary rates were 18.1% for CyBorD and 53.3% for Daratumumab Plus CyBorD. The sponsor reported a Cochran-Mantel-Haenszel odds ratio of 5.13, with a 95% confidence interval from 3.22 to 8.16 and p < 0.001. An unadjusted recalculation reported a risk difference of 0.352, with a 95% confidence interval from 0.263 to 0.441 and p < 0.001.

The record lists additional organ response, survival, progression-related, and safety outcomes. Details of the trial's original sample-size justification, missing-data handling, and multiplicity approach are not reported in the registry record.

Clinical Biostats