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Multiple Myeloma Phase 2 Binary Endpoint NCT02316106

A Study to Evaluate 3 Dose Schedules of Daratumumab in Participants With Smoldering Multiple Myeloma: Complete Statistical Analysis

A randomized phase 2 trial compared three daratumumab dose schedules in participants with smoldering multiple myeloma. The main reported result is the percentage achieving a complete response by IMWG criteria, with additional posted results describing response and safety outcomes.

Trial start: 2015-05-20  ·  Enrollment: 123  ·  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 3 Dose Schedules of Daratumumab in Participants With Smoldering Multiple Myeloma (NCT02316106), a randomized phase 2 study. The primary outcome is Percentage of Participants Who Achieved a Complete Response (CR) by International Myeloma Working Group (IMWG) Criteria.

123
Enrollment
Phase 2
3
Arms
In the primary outcome
+7.3 pts
Risk difference
Arm B (Intermediate)
-4.7 to 19.3 pts
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT02316106
PhasePhase 2
ConditionMultiple Myeloma
AllocationRandomized
Design modelParallel
MaskingNone (open label)
Enrollment123
Arms in the primary outcome3
Lead sponsorJanssen Research & Development, LLC
Results postedYes

2. Clinical Question

Population

Participants with smoldering multiple myeloma were enrolled. The primary endpoint was assessed in a response-evaluable analysis set: participants had measurable disease at baseline under IMWG criteria, received at least one dose of daratumumab, and had at least one post-baseline disease assessment.

Intervention

Daratumumab was given using three dose schedules. The registry labels the groups Long Intense, Intermediate, and Short Intense. It does not report the detailed dosing instructions in the arm descriptions, so the schedules cannot be compared by dose amount, frequency, or duration from this record.

Comparator

The three daratumumab schedules were compared with one another. Arm A (Long Intense) is the reference group for the posted pairwise comparisons with Arm B (Intermediate) and Arm C (Short Intense). There was no non-daratumumab comparison group in the listed arms.

Primary question

The primary question was what percentage of response-evaluable participants achieved complete response, including stringent complete response, by IMWG criteria. The comparison asks whether the reported percentage differed across the three schedules during the stated primary endpoint timeframe, from Cycle 1 Day 1 up to 1.58 years.

The study also recorded secondary outcomes concerning minimal residual disease, time to next treatment for active myeloma, response categories, progression-free survival, symptomatic myeloma with adverse prognostic features, response to the first subsequent multiple myeloma treatment, and overall survival. Numeric results are available for some, but not all, of these outcomes. The registry record does not report a primary hypothesis or a rationale for choosing this endpoint over the other response and disease-course outcomes.

3. Trial Design

This was a randomized, open-label, parallel-group phase 2 trial comparing three daratumumab schedules in participants with smoldering multiple myeloma. The registry lists enrollment of 123 participants and identifies the groups as Arm A (Long Intense), Arm B (Intermediate), and Arm C (Short Intense). All three listed interventions are daratumumab. Because the arm descriptions are empty, the actual dose amounts, timing, and schedule-specific treatment duration are not reported in the registry record.

The trial began on 2015-05-20, had a primary completion date of 2023-06-02, and is listed as completed. The primary endpoint timeframe extends from Cycle 1 Day 1 up to 1.58 years. A secondary response outcome has a longer stated observation window, up to 7.89 years, with follow-up ending at the earliest of the listed disease, treatment, consent, follow-up, or study-ending events. Those outcome-specific windows should not be treated as interchangeable: they describe different measures and follow-up rules.

The primary endpoint population was not simply every enrolled participant. It was the response-evaluable analysis set, defined by measurable baseline disease under IMWG criteria, receipt of at least one daratumumab dose, and at least one post-baseline disease assessment. The reported arm denominators for the primary endpoint are 41, 41, and 40. The registry record does not explain how these endpoint denominators relate to the enrollment figure or provide a full account of exclusions and missing assessments.

Randomization supports a planned comparison among schedules, but the record does not state the randomization method, allocation ratio, concealment procedures, or stratification factors. Masking is listed as none. The record also does not report the original sample-size justification, planned statistical analysis methods, or interim-analysis plan. These omissions limit what can be inferred about the design beyond the listed randomized, open-label, parallel structure.

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

StageArm A (Long Intense)Arm B (Intermediate)Arm C (Short Intense)
STARTED414141
Participants Who Entered Extension Phase21150
Participants Switched: Daratumumab IV to SC16100
Treated414140
COMPLETED100
NOT COMPLETED404141

Reasons for not completing this period:

ReasonArm A (Long Intense)Arm B (Intermediate)Arm C (Short Intense)
Withdrawal by Subject349
Other111
Death754
End of data collection293127

Analysis population for the primary outcome, as defined in the registry: Response evaluable analysis set included participants who had measurable disease at baseline as per IMWG criteria (serum and urine, serum only, urine only, FLC) and received at least 1 dose of daratumumab treatment and had at least 1 post-baseline disease assessment.

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.

CharacteristicUnitArm A (Long Intense)Arm B (Intermediate)Arm C (Short Intense)Total
Participants analysed414141123
Age, Continuousyears62.4 (SD 9.86)61.5 (SD 8.76)59.0 (SD 10.55)61 (SD 9.78)
Sex: Female, Male: FemaleParticipants24242068
Sex: Female, Male: MaleParticipants17172155
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants0202
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants403839117
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants1124
Race (NIH/OMB): American Indian or Alaska NativeParticipants1001
Race (NIH/OMB): AsianParticipants2114
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants0000
Race (NIH/OMB): Black or African AmericanParticipants2125
Race (NIH/OMB): WhiteParticipants353735107
Race (NIH/OMB): More than one raceParticipants0000
Race (NIH/OMB): Unknown or Not ReportedParticipants1236
Region of Enrollment: AustraliaParticipants23510
Region of Enrollment: CanadaParticipants2619
Region of Enrollment: FranceParticipants1146
Region of Enrollment: GermanyParticipants0156
Region of Enrollment: IsraelParticipants66113
Region of Enrollment: ItalyParticipants3249
Region of Enrollment: NetherlandsParticipants2136
Region of Enrollment: Russian FederationParticipants2237
Region of Enrollment: TurkeyParticipants5139
Region of Enrollment: United KingdomParticipants27110
Stage of Disease (ISS): Stage IParticipants30343498
Stage of Disease (ISS): Stage IIParticipants87722
Stage of Disease (ISS): Stage IIIParticipants3003
WeightKilograms (Kg)81.11 (SD 17.434)78.87 (SD 18.471)80.04 (SD 13.481)80.01 (SD 16.491)

6. Primary Endpoint

The registry lists the primary outcome as Percentage of Participants Who Achieved a Complete Response (CR) by International Myeloma Working Group (IMWG) Criteria, measured over From Cycle 1 Day 1 up to 1.58 years.

ElementRegistry entry
Result typeNumber
Measure of spreadnot applicable
Unitpercentage of participants
Endpoint classificationBinary Endpoint

The primary endpoint is the percentage of participants who achieved a complete response by International Myeloma Working Group criteria. The registry defines the reported category as complete response plus stringent complete response. Complete response requires negative serum and urine immunofixation and less than 5% plasma cells in bone marrow. Stringent complete response additionally requires a normal free light chain ratio and no clonal plasma cells by the listed laboratory methods.

In general, a response endpoint describes whether participants reach a prespecified disease-response category. Complete response is a more stringent category than partial response, so it captures a different aspect of response than a measure that combines partial response and better categories. These categories can help characterize the depth of response, but a response percentage does not by itself describe how long a response lasts or what happens after the observation window.

The registry specifies the primary timeframe as Cycle 1 Day 1 up to 1.58 years and defines a response-evaluable population requiring measurable disease at baseline, at least one daratumumab dose, and at least one post-baseline assessment. Those criteria matter when interpreting the percentages: they describe participants meeting the endpoint population definition, rather than necessarily every randomized participant. The record does not provide the complete endpoint assessment schedule or explain how an absent or unevaluable response assessment was handled.

7. Results Posted in the Registry

Risk difference: Arm B (Intermediate)

+7.3

95% CI: -4.7 to 19.3 percentage points

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals0.05.611.216.922.528.1Arm A (Long Intense) (n=41)Arm B (Intermediate) (n=41)Arm C (Short Intense) (n=40)% of participants (95% CI)
Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Arm B (Intermediate)Arm C (Short Intense)-14-6.790.357.491522risk 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
Percentage of Participants Who Achieved Partial Response or Better Response (Stringent Complete Response [sCR] Plus Complete Response [CR] Plus Very Good Partial Response [VGPR] or a Partial Response [PR])Binary EndpointRisk difference+0.0 pts (-21.5 to 21.5)n/a
Number of Participants With Response to First Subsequent Multiple Myeloma TreatmentBinary EndpointRisk difference+10.6 pts (-26.7 to 47.9)317 per arm

Percentage of Participants Who Achieved Partial Response or Better Response (Stringent Complete Response [sCR] Plus Complete Response [CR] Plus Very Good Partial Response [VGPR] or a Partial Response [PR])

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Arm B (Intermediate)Arm C (Short Intense)-45-31-16-2.111226risk difference (percentage points) vs control (95% CI)

Number of Participants With Response to First Subsequent Multiple Myeloma Treatment

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Arm B (Intermediate)Arm C (Short Intense)-37-19-0.62183654risk difference (percentage points) vs control (95% CI)

The secondary outcomes cover several distinct questions: depth of response, disease progression and subsequent treatment, later response, symptomatic disease features, and survival. They do not all measure the same aspect of disease course, and their stated follow-up windows differ. The posted numeric results concern partial response or better and response to the first subsequent multiple myeloma treatment. Numeric results for the other listed secondary outcomes are not reported in the registry record.

The broader response measure gives context alongside the primary complete-response measure because it includes less stringent response categories. Its pattern need not match the primary endpoint, and it should not be treated as a replication of the complete-response result. Response to the first subsequent treatment is further removed from the initial schedule comparison: it describes a later treatment outcome among participants with a recorded subsequent-treatment response denominator. It therefore complements, rather than directly confirms or contradicts, the primary response measure.

Secondary results generally carry less weight than a prespecified primary result when the analysis plan and multiplicity handling are not reported. Examining several outcomes and contrasts creates more opportunities for chance patterns, and the registry record does not state whether adjustments or a hierarchy of hypotheses were used. The secondary estimates are useful as descriptive evidence, but their p-values should not be interpreted as if they were independent confirmatory tests.

The differing denominators and observation periods also matter. An outcome measured over longer follow-up, or among participants who proceeded to another treatment, represents a different analysis population and opportunity for events than the primary response-evaluable endpoint. Without details on missing data, subsequent therapy, and analysis methods, these outcomes cannot be combined into a single overall claim about comparative schedule performance.

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

9. Statistical Interpretation

Clinical Biostats interpretation

For the primary endpoint, complete response including stringent complete response was reported in 4.9% of Arm A, 12.2% of Arm B, and 0.0% of Arm C. The posted unadjusted comparison of Arm B with Arm A gives a risk difference of 0.073, with a confidence interval from -0.047 to 0.193 and p = 0.236. The comparison of Arm C with Arm A gives a risk difference of -0.049, with a confidence interval from -0.115 to 0.017 and p = 0.157. Both intervals include no difference, and the p-values do not provide strong evidence against equal response percentages under the unadjusted comparisons. The estimates remain compatible with a range of differences in either direction.

The primary percentages are based on small arm denominators: 41 participants in Arm A, 41 in Arm B, and 40 in Arm C. In that setting, a few observed responses can materially affect a percentage. The zero in Arm C means that no participant in its listed primary endpoint denominator met the response definition; it does not establish that the underlying chance of response is exactly zero. The arm-level endpoint percentages are posted without confidence intervals, while the pairwise risk-difference intervals express uncertainty for the comparisons.

The partial-response-or-better outcome has a different pattern and a broader response definition. Arm A and Arm B each have a reported percentage of 56.1%, and Arm C has 37.5%. The Arm B versus Arm A risk difference is 0.0, with a confidence interval from -0.215 to 0.215 and p = 1.0. For Arm C versus Arm A, the risk difference is -0.186, with an interval from -0.400 to 0.028 and p = 0.094. These results are not a substitute for the primary complete-response endpoint: combining response categories can yield a different pattern from counting only complete and stringent complete responses.

For response to the first subsequent multiple myeloma treatment, the reported counts are 6 of 10, 12 of 17, and 15 of 23 for Arms A, B, and C. The comparison intervals are broad, consistent with the small and unequal denominators for this outcome. This endpoint concerns a later treatment, not the initial daratumumab schedule itself, and the record does not provide further detail about the treatments or the circumstances leading to them.

These results describe the posted outcomes and their precision, not a definitive ranking of schedules. The record does not include reported analyses beyond the posted arm results and unadjusted comparisons, and it does not state whether any multiplicity procedure was planned. The values therefore need to be read as limited comparisons among several outcomes, rather than as a fully documented confirmatory analysis.

10. Statistical Methods Explained

What does a percentage measure?

A percentage of participants with an event is a binary outcome: each participant either meets the stated response definition within the specified assessment framework or does not. The percentage is calculated from the number meeting the definition relative to the relevant endpoint denominator. Here, the primary endpoint applies to the response-evaluable analysis set, not automatically to the full enrollment. The endpoint definition, observation timeframe, and population criteria are essential parts of the measure; percentages should not be compared as though they came from identical populations or follow-up rules when they do not.

For the primary endpoint, response is classified using IMWG criteria. The registry defines complete response as negative serum and urine immunofixation and less than 5% plasma cells in bone marrow. It defines stringent complete response as complete response plus a normal free light chain ratio and absence of clonal plasma cells by the listed methods. The reported primary category combines complete response and stringent complete response. A participant counted in this category must therefore meet the defined response criteria, while the endpoint does not quantify duration of response.

How should a risk difference be read?

A risk difference expresses the absolute difference between the event percentages in two groups. A positive value means the event percentage is higher in the comparison group than in the reference group; a negative value means it is lower. A value of zero represents equal observed percentages. For the primary endpoint, the comparison of Arm B with Arm A has a positive estimated risk difference, while the comparison of Arm C with Arm A has a negative estimated risk difference. These are unadjusted comparisons based on the posted counts and denominators. They do not adjust for other characteristics or for the presence of multiple comparisons.

The risk-difference confidence interval describes a range of values compatible with the data under the interval method. When an interval includes zero, the results are compatible with no difference as well as with differences in either direction covered by the interval. The interval is not a guarantee that the true difference lies within its bounds, nor does it measure the probability that one schedule is better. The primary pairwise intervals both include zero, so the estimates do not sharply distinguish the groups.

What do p-values and relative measures add?

An unadjusted p-value describes how unusual a result at least as far from the no-difference value would be under a statistical model that assumes no group difference. It is not the probability that the null hypothesis is true, and it does not describe the size or clinical importance of a difference. Interpretation should consider the effect estimate and its interval as well as the p-value. The record reports p-values for unadjusted pairwise comparisons but does not report a multiplicity adjustment or a complete sponsor analysis plan.

Risk ratios and odds ratios are relative measures. A risk ratio compares event probabilities, while an odds ratio compares event odds. Their interpretation can be less direct than an absolute risk difference, particularly when events are uncommon. The posted primary comparison of Arm B with Arm A includes a risk ratio of 2.5, with an interval from 0.514 to 12.16, and an odds ratio of 2.708, with an interval from 0.494 to 14.84. The wide intervals indicate substantial uncertainty in these relative estimates. Neither measure removes the underlying limitations of small event counts.

Why do small event counts matter?

When an outcome is uncommon, the number of participants who meet the endpoint can be low even when the group denominator is larger. The primary endpoint has few recorded complete responses, including no recorded responses in Arm C. Such sparse outcomes lead to imprecise comparisons and can make relative estimates especially sensitive to individual observations. A zero observed count is a description of this sample, not proof that the event cannot occur in a broader population.

In general, statistical methods for binary outcomes must account for the discrete nature of counts and the uncertainty that comes from limited observations. Different interval or testing methods can produce different estimates, particularly with sparse data. The registry record does not identify the methods used for the sponsor's own endpoint analyses. The posted comparisons are therefore best treated as unadjusted calculations based on the reported summary counts, rather than as a complete account of the sponsor's statistical analysis.

Why distinguish the endpoint population and timeframes?

The response-evaluable definition excludes participants who do not meet one or more listed criteria, such as having no post-baseline disease assessment. This can make the endpoint denominator differ from the number enrolled or randomized. Such exclusions may affect interpretation if evaluability is related to outcome, but the record does not report the number or characteristics of participants excluded from the primary analysis set or how missing assessments were handled.

The primary endpoint timeframe ends at 1.58 years, whereas the partial-response-or-better outcome has a stated follow-up period up to 7.89 years and event-based stopping conditions. The outcomes thus do not necessarily cover the same observation period. In general, longer follow-up provides more opportunity to observe response or later events, but differences in endpoint definitions and follow-up rules prevent a simple direct comparison of the percentages across measures.

Finally, three treatment schedules and several outcomes create multiple possible comparisons. General statistical practice treats multiplicity as relevant because examining many outcomes or group contrasts increases the chance of finding an apparently notable result by chance. No multiplicity strategy is reported in the registry record. That absence, together with small denominators and incomplete analysis details, supports a cautious, descriptive reading of the posted estimates.

11. Confidence Intervals and Precision

Precision concerns how much uncertainty surrounds an estimate. A confidence interval presents a range of values compatible with the observed data under the method used. A narrow interval indicates greater precision than a wide interval; it does not establish clinical importance, eliminate bias, or guarantee that the true value is inside the interval.

For the primary endpoint, the registry posts arm percentages but no arm-level confidence intervals. The unadjusted risk-difference interval for Arm B compared with Arm A ranges from -0.047 to 0.193. The interval for Arm C compared with Arm A ranges from -0.115 to 0.017. Each includes zero, so the primary comparisons do not precisely establish a nonzero difference. The breadth of the intervals also means that differences in either direction remain compatible with the observed data.

The secondary partial-response-or-better percentages have reported 90% confidence intervals. For Arm A and Arm B, each interval runs from 42.1% to 69.4%; for Arm C it runs from 24.7% to 51.7%. The pairwise risk-difference intervals are also broad: -0.215 to 0.215 for Arm B versus Arm A and -0.400 to 0.028 for Arm C versus Arm A. The latter includes zero despite a negative point estimate.

In general, estimates based on few events or modest denominators tend to be uncertain. This is particularly relevant to the primary outcome, where the posted number of complete responses is small, and to response to the first subsequent treatment, whose group denominators are 10, 17, and 23. The registry record does not report confidence intervals for every outcome. Absence of an interval should not be read as absence of uncertainty.

12. Planning a Similar Trial: Sample Size

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

Effect to detectParticipants per arm, 80% powerParticipants per arm, 90% power
100% of the observed effect228305
75% of the observed effect366490
50% of the observed effect733981
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect2005001,0002,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
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, 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: Arm B (Intermediate).

The sample-size figures are planning illustrations based on the observed effect, not the trial's original design assumptions. The planning assumptions are a two-sided significance level of 0.05, equal allocation between the two compared arms, and a normal approximation. Each planning row considers detecting a stated fraction of the observed effect. The columns describe participants per arm for 80% power and participants per arm for 90% power; they are not totals across both arms. These are not observed power.

In plain language, a power target describes the chance that a planned study would detect an effect of the specified size under the planning assumptions, if that effect were present. The 90% target requires more participants per arm than the 80% target for the same effect size. Planning for 75% or 50% of the observed effect means planning to detect a smaller effect than the full observed difference. Smaller effects need more participants, so those rows require larger per-arm sample sizes.

For the primary comparison of Arm B with Arm A, the planning figures are 228 participants per arm for 80% power and 305 for 90% power when planning for 100% of the observed effect. For 75% of that effect, the figures are 366 and 490; for 50%, they are 733 and 981. These figures illustrate how the sample-size requirement changes with the assumed effect and power target. They are not evidence that the original trial was designed around these values, and the registry record does not report its original sample-size justification.

Planning figures are available only for comparisons with a listed planning illustration. They should be interpreted in light of the assumptions and the uncertainty of the observed effect, which comes from relatively small endpoint groups. They do not establish that an actual future study would achieve the stated power if its design, population, follow-up, or analysis differed from these assumptions.

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 = 0.049; treatment proportion p1 = 0.122; average p̄ = 0.085.
  2. First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.3952 = 0.7745.
  3. Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.3918 = 0.3297.
  4. n = (0.7745 + 0.3297)2 / (0.0732)2 = 227.7, rounded up to 228 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 <- 0.0487804878048781                          # control proportion
p1 <- 0.121951219512195                          # 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(2316106)
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 = 228 (80% power), 305 (90% power)
 75% of observed effect: n per arm = 366 (80% power), 490 (90% power)
 50% of observed effect: n per arm = 733 (80% power), 981 (90% power)
power.prop.test: 227.7 
Simulated power at n = 228 per arm: 0.817 (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.

14. Multiplicity, Missing Data and Analysis Populations

Multiplicity arises when a study assesses more than one outcome, compares several groups, or performs multiple statistical tests. Even when no true group differences exist, conducting many tests increases the chance that at least one result will appear noteworthy by chance. General approaches include prespecifying a primary hypothesis, ordering tests, or adjusting inference to account for multiple comparisons. The registry record lists several secondary outcomes and pairwise schedule comparisons, but does not report a multiplicity strategy or a hierarchy for interpreting them.

The record reports no analyses in its reported-analysis listing. It does post arm-level results and unadjusted comparisons, but it does not describe whether those comparisons reproduce a sponsor's prespecified analysis. No adjusted p-values or multiplicity-adjusted confidence intervals are reported. Accordingly, the unadjusted secondary p-values should be regarded as exploratory descriptions, not as a family of controlled confirmatory conclusions.

Missing-data handling is also not reported. For the primary outcome, the response-evaluable set requires measurable disease at baseline, at least one dose, and at least one post-baseline assessment. The record does not give the number excluded for each criterion, explain the handling of participants without an assessment, or state whether missing responses were treated as nonresponses. It also does not report whether the reasons for missingness differed by arm. These details are important because an evaluable-set result may not represent all randomized participants if inclusion in that set is related to prognosis or response.

The primary outcome population and the denominators for secondary outcomes are not necessarily the same. The subsequent-treatment response outcome, for example, uses denominators of 10, 17, and 23. The record does not specify the full selection process or missing-data rules for that outcome. The analysis populations and missing-data methods for the other listed secondary outcomes are not reported in the registry record.

Interim analyses, stopping rules, the randomization method, allocation concealment, and the original statistical analysis plan are also not reported in the registry record. Their absence does not establish that no such procedures existed; it means their use cannot be evaluated from this record. This limits assessment of how endpoint definitions, multiplicity, missing observations, and analysis choices were handled before the results were known.

15. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Arm A (Long Intense)204148.8%
Arm B (Intermediate)144134.1%
Arm C (Short Intense)44010.0%
Participants with at least one serious adverse event
Serious adverse events by armArm A (Long Intense)48.8%Arm B (Intermediate)34.1%Arm C (Short Intense)10.0%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
Arm A (Long Intense)7 of 41
Arm B (Intermediate)5 of 41
Arm C (Short Intense)4 of 41

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
Arm A (Long Intense)38 of 41
Arm B (Intermediate)41 of 41
Arm C (Short Intense)32 of 40

Most frequent serious adverse event terms

Event termOrgan systemArm A (Long Intense)Arm B (Intermediate)Arm C (Short Intense)
PneumoniaInfections and infestations4 of 411 of 411 of 40
ArthralgiaMusculoskeletal and connective tissue disorders1 of 412 of 410 of 40
SepsisInfections and infestations1 of 410 of 411 of 40
OsteoarthritisMusculoskeletal and connective tissue disorders0 of 412 of 410 of 40
LeukocytosisBlood and lymphatic system disorders1 of 410 of 410 of 40
Acute Coronary SyndromeCardiac disorders0 of 411 of 410 of 40
Angina PectorisCardiac disorders0 of 410 of 411 of 40
Angina UnstableCardiac disorders0 of 410 of 411 of 40
Atrial FibrillationCardiac disorders1 of 410 of 410 of 40
Atrioventricular BlockCardiac disorders0 of 411 of 410 of 40

Most frequent non-serious adverse event terms

Event termOrgan systemArm A (Long Intense)Arm B (Intermediate)Arm C (Short Intense)
FatigueGeneral disorders19 of 4125 of 419 of 40
CoughRespiratory, thoracic and mediastinal disorders18 of 4115 of 4111 of 40
Upper Respiratory Tract InfectionInfections and infestations20 of 4115 of 414 of 40
HeadacheNervous system disorders13 of 4110 of 4113 of 40
ArthralgiaMusculoskeletal and connective tissue disorders14 of 4119 of 411 of 40
InsomniaPsychiatric disorders13 of 4114 of 415 of 40
DiarrhoeaGastrointestinal disorders14 of 4113 of 414 of 40
Back PainMusculoskeletal and connective tissue disorders10 of 4112 of 414 of 40
NauseaGastrointestinal disorders10 of 4111 of 413 of 40
DyspnoeaRespiratory, thoracic and mediastinal disorders12 of 418 of 413 of 40

Serious events with the highest arm-level rate: pneumonia (9.8%), arthralgia (4.9%), osteoarthritis (4.9%), angina pectoris (2.5%), angina unstable (2.5%).

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 registry reports serious adverse events for each arm as participants with at least one serious adverse event relative to the listed number at risk: 20 of 41 in Arm A, 14 of 41 in Arm B, and 4 of 40 in Arm C. Other adverse events are reported for 38 of 41, 41 of 41, and 32 of 40, respectively. Death counts are 7, 5, and 4 for Arms A, B, and C. These are descriptive counts; the record does not provide an adjusted comparison or establish that events were caused by the study treatment.

The serious adverse event terms listed most often include pneumonia at 9.8%, arthralgia at 4.9%, osteoarthritis at 4.9%, angina pectoris at 2.5%, angina unstable at 2.5%, and sepsis at 2.5%. A term-level percentage does not convey event severity beyond its classification, timing, duration, recurrence, or relation to treatment. The registry record does not report those details or a complete account of safety analyses. Differences in counts across arms should therefore be read descriptively, with the group sizes and duration of observation in mind.

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

The posted results show that complete response including stringent complete response was reported in a small percentage of the response-evaluable population in each schedule group, with no such responses recorded in Arm C. The unadjusted pairwise estimates are uncertain: both primary risk-difference confidence intervals include zero. The data do not sharply distinguish the schedule groups on this endpoint. The observed percentages are a description of the participants assessed, not a direct estimate of what would occur in every person with smoldering multiple myeloma.

The broader partial-response-or-better measure gives a different view because it counts additional response categories. Its estimates are also uncertain, and its follow-up period differs from the primary endpoint timeframe. Later response to a subsequent treatment is yet another question, with smaller and differing denominators. These outcomes should be interpreted according to their own definitions rather than combined as if they measured one common endpoint.

In general, randomized comparisons can help assess differences between assigned groups, but interpretation depends on implementation and analysis details. The registry record does not report detailed dosing schedules, the randomization procedures, missing-data methods, the original statistical plan, or multiplicity handling. Those omissions prevent a full assessment of the trial's conduct and inferential framework. The results also do not establish whether any observed differences are clinically important; the record does not supply a threshold for that judgment.

These findings do not establish that one schedule is superior or equivalent to another. A lack of a clear difference in these estimates is not proof that the schedules have identical effects, especially given the uncertainty and limited event counts. Nor do the response findings alone describe durability, progression, survival, or all aspects of safety. Several of those outcomes are listed, but their numeric results are not reported in the registry record.

The information is descriptive statistical evidence from a completed phase 2 randomized, open-label comparison. It should be understood within the stated population, endpoint definition, and follow-up windows, and not generalized beyond them without additional evidence and context.

17. Why This Trial Matters Statistically

Statistically, this trial is a useful example of the difference between a point estimate and the strength of evidence around it. Arm B has a higher observed primary response percentage than Arm A, while Arm C has a lower observed percentage. Yet the pairwise confidence intervals include no difference and span values on either side of zero. The direction of the estimates alone is therefore not enough to establish a reliable schedule contrast.

The endpoint also illustrates why outcome definitions matter. Complete response including stringent complete response is narrower than partial response or better. A pattern in a broad response category may not reproduce the pattern for a deeper response category. These endpoints answer related, but distinct, questions; their percentages should not be substituted for one another.

The record highlights how small event counts affect precision. A low number of primary responses, including a zero observed count in one group, produces substantial uncertainty in the comparative estimates. Relative effect measures can look large while their intervals remain wide. Absolute differences, confidence intervals, and the observed counts together give a more informative account than a single p-value or relative estimate alone.

Finally, a randomized design does not remove the need for transparent reporting of populations, analysis methods, missing data, multiplicity, and safety follow-up. Those details are not fully reported in the registry record. The example reinforces that statistical interpretation depends not only on the trial label and point estimates, but also on the definition of who was analyzed, how uncertainty was quantified, and how multiple outcomes were handled.

18. Limitations

Several limitations are specific to the information in this registry record. The arm labels identify three intensity schedules, but detailed dose amounts, timing, and duration are not reported in the arm descriptions. This prevents a reader from defining precisely what regimen differences the comparison represents.

The primary response percentages are based on response-evaluable denominators of 41, 41, and 40, and the record does not report how many randomized participants were excluded from that set or why. The handling of missing or unevaluable assessments is not stated. As a result, the relationship between the endpoint population and all enrolled participants cannot be fully assessed.

The record lists enrollment of 123, but the primary outcome arm denominators do not account for every enrolled participant in the posted endpoint population. No reconciliation is reported, so the reason for the difference should not be inferred. The record also does not provide a detailed account of loss to follow-up, treatment discontinuation, or adherence by group.

Although the study is randomized, details of sequence generation, allocation concealment, stratification, and the original sample-size justification are not reported in the registry record. Neither a complete statistical analysis plan nor a multiplicity procedure is reported. This matters because several outcomes and contrasts are listed, and unadjusted comparisons alone do not address the risk of chance findings across multiple analyses.

Some listed outcomes have no numeric results in this record, and the posted secondary outcomes use different definitions, denominators, and follow-up periods. Safety counts are descriptive, without reported adjusted comparisons or event-level detail such as timing and relatedness. These gaps constrain the completeness of interpretation; they do not, by themselves, show that any particular procedure was absent or that any result is invalid.

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22. Record Summary

NCT02316106 is a completed randomized, open-label, parallel phase 2 study of three daratumumab dose schedules in participants with smoldering multiple myeloma. The registry lists enrollment of 123 and identifies the groups as Long Intense, Intermediate, and Short Intense. The primary endpoint is the percentage achieving complete response, including stringent complete response, by IMWG criteria in the response-evaluable analysis set.

The primary endpoint percentages were 4.9% for Arm A, 12.2% for Arm B, and 0.0% for Arm C. The unadjusted pairwise risk-difference intervals include zero. Secondary numeric results are posted for partial response or better and response to the first subsequent multiple myeloma treatment; numeric results for other listed outcomes are not reported in the registry record. Detailed schedule descriptions, original design assumptions, analysis methods, multiplicity handling, and missing-data procedures are not reported.

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