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 Study of Durvalumab + Tremelimumab, Durvalumab, and Placebo in Limited Stage Small-Cell Lung Cancer in Patients Who Have Not Progressed Following Concurrent Chemoradiation Therapy (NCT03703297), a randomized phase 3 study. The primary outcome is Durvalumab Versus Placebo: Progression-Free Survival (PFS) Assessed by Blinded Independent Central Review (BICR) Per Response Evaluation Criteria in Solid Tumors Version 1.1.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT03703297 |
| Phase | Phase 3 |
| Condition | Small Cell Lung Cancer |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Triple |
| Enrollment | 730 |
| Arms in the primary outcome | 2 |
| Lead sponsor | AstraZeneca |
| Results posted | Yes |
2. Clinical Question
Population
Participants with limited-stage small-cell lung cancer who had not progressed following concurrent chemoradiation therapy. The primary endpoint population was the full analysis set, defined in the registry record as all randomized participants.
Intervention
Durvalumab as consolidation treatment. The trial also included a durvalumab-plus-tremelimumab group, but that combination is not the intervention in the primary comparison described in the posted result.
Comparator
Placebo as consolidation treatment. The primary result compares the durvalumab group with the placebo group.
Primary question
How did progression-free survival, assessed by blinded independent central review using RECIST version 1.1, compare between participants assigned to durvalumab and those assigned to placebo after concurrent chemoradiation?
The clinical question is about the time until disease progression or death, not simply whether a participant had a response at a particular assessment. The registry defines progression-free survival from randomization to objective disease progression or death from any cause in the absence of progression. The result therefore combines these events into a time-to-event outcome.
The primary comparison concerns consolidation treatment after participants had completed concurrent chemoradiation without progression. It does not address durvalumab as a replacement for chemoradiation, nor does the primary result compare the combination with tremelimumab against durvalumab alone. Although the trial included a combination group, a numerical primary outcome for that group is not reported in the registry record. The posted primary result is specifically durvalumab versus placebo.
3. Trial Design
The registry describes a Phase III, randomized, placebo-controlled, parallel-group study in limited-stage small-cell lung cancer. The official title identifies it as double-blind, while the registry’s masking classification is triple. The study is also described as multi-center and international. Details of which people were masked are not reported in the registry record.
The trial enrolled 730 participants. The study status is active, not recruiting, and the recorded primary completion date is 2024-01-15. These record details do not, on their own, establish that every outcome has been fully reported or that follow-up has ended for all participants.
The registry lists three groups: durvalumab, durvalumab plus tremelimumab, and placebo. In the durvalumab group, the listed regimen began with durvalumab 1500 mg intravenously every 4 weeks, with placebo saline solution, for up to 4 doses or cycles each, followed by durvalumab 1500 mg every 4 weeks. The combination group used durvalumab 1500 mg and tremelimumab 75 mg intravenously every 4 weeks for up to 4 doses or cycles each, followed by durvalumab 1500 mg every 4 weeks. The placebo group received placebo solutions on a corresponding schedule. The full schedule descriptions are truncated in the registry record, so further dosing details are not reported there.
The primary comparison reported is between durvalumab and placebo. The registry describes the primary endpoint as progression-free survival assessed by blinded independent central review. It lists 264 participants in the durvalumab primary analysis group and 266 in the placebo group. How the trial’s original sample size was justified, and the original design assumptions for its primary comparison, are not reported in the registry record.
4. Participant Flow and Accounting
The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.
Before assignment: Based on the results of the secondary objectives at the interim analysis (reviewed by an unblinded independent data monitoring committee \[IDMC\]), data for the D+T arm were to remain blinded to the Sponsor as pre-specified in the study's unblinding plan. Since the D+T arm was blinded at the time of posting the results from this interim analysis, results for that arm will be posted at the time of final analysis.
Overall Study
| Stage | Durvalumab | Durvalumab Plus Tremelimumab | Placebo |
|---|---|---|---|
| STARTED | 264 | 200 | 266 |
| Safety Population | 262 | 0 | 265 |
| COMPLETED | 0 | 0 | 0 |
| NOT COMPLETED | 264 | 200 | 266 |
Reasons for not completing this period:
| Reason | Durvalumab | Durvalumab Plus Tremelimumab | Placebo |
|---|---|---|---|
| Death | 115 | 0 | 144 |
| Withdrawal by Subject | 9 | 0 | 11 |
| Ongoing at the time of DCO | 140 | 200 | 111 |
Analysis population for the primary outcome, as defined in the registry: The FAS included 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.
Population: The full analysis set (FAS) included all randomized participants.
| Characteristic | Unit | Durvalumab | Durvalumab Plus Tremelimumab | Placebo | Total |
|---|---|---|---|---|---|
| Participants analysed | 264 | 200 | 266 | 730 | |
| Age, Customized: <65 years | Participants | 160 | NA | 162 | NA |
| Age, Customized: >=65 years | Participants | 104 | NA | 104 | NA |
| Sex: Female, Male: Female | Participants | 86 | NA | 78 | NA |
| Sex: Female, Male: Male | Participants | 178 | NA | 188 | NA |
| Race/Ethnicity, Customized: White | Participants | 130 | NA | 137 | NA |
| Race/Ethnicity, Customized: Black or African American | Participants | 1 | NA | 3 | NA |
| Race/Ethnicity, Customized: Asian | Participants | 131 | NA | 121 | NA |
| Race/Ethnicity, Customized: Other | Participants | 2 | NA | 5 | NA |
| Race/Ethnicity, Customized: Hispanic or Latino | Participants | 8 | NA | 14 | NA |
| Race/Ethnicity, Customized: Not Hispanic or Latino | Participants | 255 | NA | 249 | NA |
| Race/Ethnicity, Customized: Missing | Participants | 1 | NA | 3 | NA |
6. Primary Endpoint
The registry lists the primary outcome as Durvalumab Versus Placebo: Progression-Free Survival (PFS) Assessed by Blinded Independent Central Review (BICR) Per Response Evaluation Criteria in Solid Tumors Version 1.1, measured over Response evaluations performed every 8 weeks (q8w) ± 1 week up to 72 weeks, then every 12 weeks (q12w) ± 1 week up to 96 weeks, and then every 24 weeks (q24w) thereafter until PD, up to DCO date 15 January 2024 (a maximum of approximately 1936 days).
| Element | Registry entry |
|---|---|
| Result type | Median |
| Measure of spread | 95% Confidence Interval |
| Unit | months |
| Endpoint classification | Time-to-Event Analysis |
The primary endpoint is progression-free survival, measured in months from randomization until objective disease progression or death from any cause when progression has not occurred. The registry specifies that the outcome was assessed by blinded independent central review using RECIST version 1.1. This central review approach applies a defined assessment framework rather than relying only on an investigator’s judgment.
Progression was defined using changes in the sum of diameters of target lesions. The registry definition requires at least a 20% increase from the smallest previous sum, with an absolute increase of at least 5 millimeters. The assessment schedule was every 8 weeks, with a 1-week allowance, up to 72 weeks; every 12 weeks, with a 1-week allowance, up to 96 weeks; and every 24 weeks thereafter until progression or the data cut-off date of 15 January 2024.
As a time-to-event outcome, progression-free survival uses both whether an event occurred and when it occurred. The median is the time by which half of the estimated population has experienced progression or death. It is useful for describing the central timing of events, while a hazard ratio summarizes the relative event rate over follow-up under the analysis method. Neither measure alone describes every participant’s course or the duration of benefit for a particular individual.
The registry states that the median was estimated with the Kaplan-Meier method and its confidence interval with the Brookmeyer-Crowley method. The primary endpoint population was the full analysis set, comprising all randomized participants.
7. Results Posted in the Registry
- Durvalumab vs Placebo: hazard ratio 0.76 (95% CI 0.61–0.95), reported p = 0.016 (as reported in the registry).
Hazard ratio: Durvalumab vs Placebo
95% CI: 0.61 to 0.95
As reported in the registry
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 outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Durvalumab Versus Placebo: Objective Response Rate (ORR) Assessed by Blinded Independent Central Review Per Response Evaluation Criteria in Solid Tumors Version 1.1 | Binary Endpoint | Risk difference | -1.7 pts (-11.5 to 8.1) | 12,109 per arm |
| Durvalumab Versus Placebo: Percentage of Participants Progression-Free at 18 Months Following Randomization (PFS18) Assessed by Blinded Independent Central Review Per Response Evaluation Criteria in Solid Tumors Version 1.1 | Binary Endpoint | Risk difference | +12.8 pts (4.4 to 21.1) | 234 per arm |
| Durvalumab Versus Placebo: Percentage of Participants Progression-Free at 24 Months Following Randomization (PFS24) Assessed by Blinded Independent Central Review Per Response Evaluation Criteria in Solid Tumors Version 1.1 | Binary Endpoint | Risk difference | +12.0 pts (3.7 to 20.3) | 261 per arm |
Durvalumab Versus Placebo: Objective Response Rate (ORR) Assessed by Blinded Independent Central Review Per Response Evaluation Criteria in Solid Tumors Version 1.1
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Durvalumab: 30.3% (53/175) versus 32.0% (54/169) on control; risk difference -1.7 percentage points (95% CI -11.5 to 8.1), risk ratio 0.95 (0.69–1.30); unadjusted two-proportion z-test p = 0.738.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Durvalumab and the control. The interval gives the range of effects that remain compatible with the data.
Durvalumab Versus Placebo: Percentage of Participants Progression-Free at 18 Months Following Randomization (PFS18) Assessed by Blinded Independent Central Review Per Response Evaluation Criteria in Solid Tumors Version 1.1
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Durvalumab: 48.9% (129/264) versus 36.1% (96/266) on control; risk difference 12.8 percentage points (95% CI 4.4 to 21.1), risk ratio 1.35 (1.11–1.66); unadjusted two-proportion z-test p = 0.003.
- Interpretation:
- The 95% confidence interval excludes no difference, so the proportion with the event is statistically higher for Durvalumab than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Durvalumab Versus Placebo: Percentage of Participants Progression-Free at 24 Months Following Randomization (PFS24) Assessed by Blinded Independent Central Review Per Response Evaluation Criteria in Solid Tumors Version 1.1
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Durvalumab: 46.2% (122/264) versus 34.2% (91/266) on control; risk difference 12.0 percentage points (95% CI 3.7 to 20.3), risk ratio 1.35 (1.09–1.67); unadjusted two-proportion z-test p = 0.005.
- Interpretation:
- The 95% confidence interval excludes no difference, so the proportion with the event is statistically higher for Durvalumab than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The secondary outcomes address several related but distinct questions, including objective response and the proportion of participants progression-free at later time points. In broad terms, the posted landmark progression-free results follow the same direction as the primary time-to-event comparison, whereas the response outcome does not show the same directional pattern. That difference is not inherently contradictory: a response measure and a time-to-event measure capture different aspects of disease course.
These endpoints provide context rather than a replacement for the primary result. Landmark percentages describe progression-free status at a specified follow-up time; objective response describes whether the defined response criteria were met. Neither has the same interpretation as the time-to-event hazard ratio, and neither by itself confirms or refutes the primary comparison.
Many secondary outcomes are listed, including outcomes involving the durvalumab-plus-tremelimumab group. Numerical results for all listed outcomes are not reported in the registry record. The posted secondary estimates should therefore be interpreted only for the outcomes with results available, without assuming that unreported outcomes had a particular direction.
Unadjusted secondary results carry less inferential weight when many outcomes are examined. General explanation: testing multiple outcomes increases the chance that some results will appear notable by chance, even when no corresponding underlying effect exists. The registry record does not report a multiplicity strategy for these secondary analyses. Their findings are best treated as supportive or exploratory rather than as independent confirmatory evidence.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Durvalumab Plus Tremelimumab Combination Versus Placebo: Progression-Free Survival Assessed by Blinded Independent Central Review Per Response Evaluation Criteria in Solid Tumors Version 1.1
- Durvalumab Plus Tremelimumab Combination Versus Placebo: Overall Survival
- Durvalumab Versus Placebo: Objective Response Rate (ORR) Assessed by Blinded Independent Central Review Per Response Evaluation Criteria in Solid Tumors Version 1.1
- Durvalumab Plus Tremelimumab Combination Versus Placebo: Objective Response Rate Assessed by Blinded Independent Central Review Per Response Evaluation Criteria in Solid Tumors Version 1.1
- Durvalumab Versus Placebo: Percentage of Participants Progression-Free at 18 Months Following Randomization (PFS18) Assessed by Blinded Independent Central Review Per Response Evaluation Criteria in Solid Tumors Version 1.1
- Durvalumab Plus Tremelimumab Combination Versus Placebo: Percentage of Participants Progression-Free at 18 Months Following Randomization Assessed by Blinded Independent Central Review Per Response Evaluation Criteria in Solid Tumors Version 1.1
- Durvalumab Versus Placebo: Percentage of Participants Progression-Free at 24 Months Following Randomization (PFS24) Assessed by Blinded Independent Central Review Per Response Evaluation Criteria in Solid Tumors Version 1.1
- Durvalumab Plus Tremelimumab Combination Versus Placebo: Percentage of Participants Progression-Free at 24 Months Following Randomization Assessed by Blinded Independent Central Review Per Response Evaluation Criteria in Solid Tumors Version 1.1
9. Statistical Interpretation
The registry reports a median progression-free survival of 16.6 months for durvalumab, with a 95% confidence interval from 10.2 to 28.2 months. The placebo group’s median was 9.2 months, with a 95% confidence interval from 7.4 to 12.9 months. These are Kaplan-Meier median estimates, not averages of each participant’s observed time.
For the primary comparison, the sponsor reports a hazard ratio of 0.76, with a 95% confidence interval from 0.606 to 0.950, using a log-rank analysis. A hazard ratio below 1 indicates a lower estimated rate of progression or death in the durvalumab group relative to placebo over the analysis period, according to this comparison. The confidence interval describes uncertainty around that relative estimate; it does not mean that every participant had a lower risk or that the effect was constant for every participant.
The sponsor’s reported analysis classifies the result as superiority. That is the sponsor’s statistical conclusion for the prespecified primary comparison as represented in the registry. The result should be read together with the endpoint definition, the follow-up and assessment schedule, and the confidence intervals around the estimates. The median estimates and hazard ratio are different summaries of the same time-to-event outcome, so they should not be treated as interchangeable quantities.
The primary outcome is specific to durvalumab versus placebo. It does not establish the effect of durvalumab plus tremelimumab relative to placebo or the added effect of tremelimumab. A numerical primary result for that combination comparison is not reported in the registry record.
Posted secondary results cover response and progression-free status at later assessment times. Their pattern is not uniform across outcome types: the landmark progression-free percentages are directionally consistent with the primary time-to-event result, while the objective response percentages do not show the same direction. These secondary outcomes address different questions and do not replace the primary endpoint. Their inferential weight also depends on how multiple comparisons were handled, which is not reported in the registry record.
These estimates describe group-level results in the registry. They do not establish an individual participant’s likely course, and the registry record does not provide enough information to interpret every aspect of missing outcome data, protocol adherence, or the full analysis plan.
10. Statistical Methods Explained
What does the median describe?
For a time-to-event endpoint, some participants may not have experienced progression or death by the end of their observed follow-up. Kaplan-Meier estimation allows those participants to contribute information for the period during which they were followed, without treating their last observed time as if it were an event. The estimated median is the point at which the estimated proportion remaining free of the event reaches one half. It is not a simple arithmetic average, and it does not state that every participant experienced the event at that time.
The registry says that Kaplan-Meier estimation was used for the median progression-free survival. It reports medians of 16.6 months for durvalumab and 9.2 months for placebo. The confidence intervals around these medians reflect uncertainty in their estimated locations. The median summarizes one point on the estimated time-to-event distribution; participants’ actual event times can vary around it.
What does a hazard ratio summarize?
A hazard is the event rate at a given point in follow-up among participants who have not yet experienced the event. A hazard ratio compares the event rates between groups over the analysis. General interpretation: a ratio below 1 favors the group in the numerator in the sense of a lower estimated event rate, while a ratio above 1 indicates a higher estimated event rate. This interpretation is about the relative rate, not the proportion of participants who ever experience an event.
The sponsor’s reported hazard ratio is 0.76, with a 95% confidence interval from 0.606 to 0.950, and the registry identifies the method as log-rank. The hazard ratio is a distinct summary from the difference between medians. It should not be translated into a number of additional months, nor should it be interpreted as a direct percentage change in the probability of remaining progression-free at every time point.
Why use central review and RECIST?
General explanation: central review can apply assessment criteria independently of the local clinical team, and a common response framework can make progression assessments more consistent across participants and sites. RECIST version 1.1 supplies the criteria used for the registry’s definition of objective progression. The record specifies blinded independent central review, but details of how disagreements were resolved or how assessments were operationalized are not reported in the registry record.
The progression definition uses both a relative change and an absolute change in target-lesion measurements. General explanation: requiring both types of change can help distinguish a meaningful increase from a small change that appears large only because the original measurements were small. The registry also includes death in the endpoint, so a participant can have a progression-free survival event without a recorded radiographic progression.
What does the log-rank analysis contribute?
The log-rank method compares the observed timing of events between groups across follow-up. It uses the event and censoring information rather than comparing only the two median estimates. The registry reports a sponsor hazard ratio from a log-rank analysis and classifies the analysis as superiority. The exact test specification, stratification factors, and any covariate adjustment are not reported in the registry record.
General explanation: time-to-event analyses rely on assumptions about how censoring relates to the outcome and how the groups’ event patterns are summarized. If the relative event rate changes substantially over time, a single hazard ratio may not capture that variation fully. The registry record does not report an assessment of proportional hazards or other diagnostics, so those assumptions cannot be evaluated from the posted result alone.
Why do confidence intervals matter?
A confidence interval conveys the uncertainty associated with an estimate, rather than presenting the point estimate as exact. In repeated use of a method under its assumptions, a 95% confidence interval is designed to cover the underlying quantity in 95% of such intervals. It is not a statement that there is a 95% probability that the specific interval contains the true value. The reported interval is also not a range containing 95% of individual participants’ outcomes.
For the primary result, the interval around the hazard ratio lies below 1, and the sponsor reports superiority. The median intervals are wider descriptions of uncertainty around each group’s median. Confidence intervals do not address every source of uncertainty, such as incomplete reporting of analysis decisions or possible systematic differences between observed and unobserved outcomes.
11. Confidence Intervals and Precision
The primary medians are reported as 16.6 months for durvalumab, with a 95% confidence interval from 10.2 to 28.2 months, and 9.2 months for placebo, with a 95% confidence interval from 7.4 to 12.9 months. The interval around the durvalumab median extends across a broader range of times than the point estimate alone suggests. These intervals describe uncertainty in the estimated medians, not individual variation in progression-free survival.
The sponsor’s hazard ratio is 0.76, with a 95% confidence interval from 0.606 to 0.950. The interval gives a range of relative hazard values compatible with the analysis under its assumptions. Its position below 1 is consistent with the sponsor’s reported superiority conclusion for the primary comparison. The interval is not a guarantee that the true effect lies within its endpoints, nor does it show the probability of benefit for any individual.
Precision depends on the amount and timing of outcome information, not only the number of participants. In time-to-event analyses, the number of observed events is particularly relevant, as are follow-up and censoring. The event count for this primary analysis is not reported in the registry record. The median and hazard-ratio intervals therefore offer useful information about statistical uncertainty, but the record does not provide every detail needed to assess how much information supports the analysis.
Confidence intervals also do not account for every design or reporting issue. They reflect statistical uncertainty under the analysis method; they do not resolve questions about missing data, multiplicity, protocol deviations, or the generalizability of the study population.
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 ratio | Events, 80% power | Events, 90% power |
|---|---|---|---|
| 100% of the observed effect | 0.76 | 417 | 559 |
| 75% of the observed effect | 0.81 | 742 | 993 |
| 50% of the observed effect | 0.87 | 1,668 | 2,233 |
The sample-size figures are planning illustrations based on the observed effect, not the trial’s original design calculation. The planning assumptions listed are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set to the stated fraction of the observed effect. The original trial’s sample-size assumptions are not reported in the registry record.
For time-to-event planning, figures refer to the total number of events required, not participants per arm. For other outcomes, figures refer to participants per arm. The 80% power column gives an illustrative number of events or participants that would yield an 80% chance of detecting the assumed effect under the listed assumptions, if that effect were real. The 90% power column describes the corresponding planning target for a 90% chance. These are design concepts, not probabilities that the observed finding is correct.
The rows consider planning for 100%, 75%, and 50% of the observed effect. As the assumed effect becomes smaller, more event information or more participants are needed to detect it with the same target power. The figures are sensitive to the observed effect used as their starting point, so they should not be treated as a universal recommendation for a future study.
This is not observed power. It is a forward-looking planning illustration under explicit assumptions, not a retrospective measure of the trial’s success or of the probability that its result is true.
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 is the total number of events needed (Schoenfeld's formula) with 1:1 allocation and proportional hazards.
Worked calculation for this trial
- Hazard ratio HR = 0.760, so ln(HR) = -0.2744.
- d = 4 × (1.96 + 0.842)2 / [ln(0.760)]2 = 416.9, rounded up to 417 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 <- 0.76 # 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(3703297)
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 = 417 (80% power), 559 (90% power)
75% of observed effect: events = 742 (80% power), 993 (90% power)
50% of observed effect: events = 1,668 (80% power), 2,233 (90% power)
Simulated power with 417 events: 0.797 (20000 replicates)
The simulation uses the fact that, with d events in total and proportional hazards, the number of events in the treatment arm is binomial. It is an approximation that conditions on the total number of events, and it should land close to the target power.
14. Group-Sequential Design Analysis
Many time-to-event trials, especially in oncology, stop or report early when interim data are overwhelming, so a single fixed-sample number understates the real design problem. The calculation below is an illustrative group-sequential design built from this trial's posted control median and hazard ratio. The registry record does not state the planned number of looks or the spending function, so the design is a planning illustration, not a reconstruction of the protocol. Assumed: one-sided α = 0.025, 90% power, three equally spaced looks on information, Lan-DeMets O'Brien-Fleming spending, 24 months of accrual, 60 months in total and a 1% monthly dropout hazard.
Under these assumptions the design needs about 671 participants in total, with the boundaries below.
| Analysis | Calendar time (months) | Events | Efficacy boundary (z) | Nominal one-sided p | Cumulative alpha spent |
|---|---|---|---|---|---|
| Look 1 | 17.4 | 188 | 3.710 | 0.0001 | 0.0001 |
| Look 2 | 27.4 | 376 | 2.511 | 0.0060 | 0.0060 |
| Look 3 | 60.0 | 563 | 1.993 | 0.0231 | 0.0250 |
Fixed design versus group-sequential alternatives
| Design | Power | Events at final analysis | Participants | Study length (months) |
|---|---|---|---|---|
| Fixed design, one analysis | 80% | 416 | 496 | 60.0 |
| Two looks, O'Brien-Fleming | 80% | 417 | 497 | 60.0 |
| Three looks, O'Brien-Fleming | 80% | 421 | 502 | 60.0 |
| Three looks, Pocock | 80% | 487 | 580 | 60.0 |
| Fixed design, one analysis | 90% | 557 | 664 | 60.0 |
| Two looks, O'Brien-Fleming | 90% | 559 | 666 | 60.0 |
| Three looks, O'Brien-Fleming | 90% | 563 | 671 | 60.0 |
| Three looks, Pocock | 90% | 643 | 766 | 60.0 |
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 assumed | Hazard ratio | Events at final analysis | Participants |
|---|---|---|---|
| 100% of the observed effect | 0.760 | 563 | 671 |
| 75% of the observed effect | 0.814 | 1,003 | 1,184 |
| 50% of the observed effect | 0.872 | 2,257 | 2,645 |
For context, this trial enrolled 730 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 <- 9.2 # control-arm median, months (converted from the posted unit)
hr <- 0.76 # 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: 488 p (1-sided) 0.0001
Events: 188 ~HR at bound 0.5819
Month: 17 P(Cross) if HR=1 0.0001
P(Cross) if HR=0.76 0.0338
IA 2: 67% Z 2.5114
N: 672 p (1-sided) 0.0060
Events: 376 ~HR at bound 0.7717
Month: 27 P(Cross) if HR=1 0.0060
P(Cross) if HR=0.76 0.5603
Final Z 1.9930
N: 672 p (1-sided) 0.0231
Events: 564 ~HR at bound 0.8454
Month: 60 P(Cross) if HR=1 0.0250
P(Cross) if HR=0.76 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
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| Log Rank | Hazard Ratio (HR) 0.76 | 0.606 to 0.950 | 0.016 |
The primary result in the registry is the sponsor’s reported analysis: a hazard ratio of 0.76, with a 95% confidence interval from 0.606 to 0.950, from a log-rank analysis. The sponsor classifies the result as superiority. For a time-to-event primary outcome, the posted interpretation uses the sponsor’s hazard ratio rather than attempting to reconstruct one from the group medians.
The medians and their confidence intervals provide useful descriptive context, but they are not sufficient to reproduce the hazard ratio or the log-rank analysis. A re-calculation from summary medians would not capture event timing, censoring, or the full analysis data. The registry record indicates no discrepancy for this primary result, and the sponsor’s own analysis is the reported basis for the inferential conclusion.
The registry does not report all details of the primary analysis plan, such as stratification or covariate adjustment. The sponsor’s stated method and result can therefore be described, but the complete analysis cannot be independently reconstructed from the posted summary statistics.
16. Multiplicity, Missing Data and Analysis Populations
The registry identifies a primary comparison and lists a broad set of secondary outcomes, including progression-free survival, overall survival, objective response, and progression-free status at later time points. The posted record includes 25 outcome measures and 2 analyses. The number of posted secondary results is 23. These listings show that more than the primary endpoint was considered, but they do not fully specify how statistical testing across outcomes was controlled.
Multiplicity concerns arise when many hypotheses are tested. General explanation: without an adjustment or an ordered testing strategy, the chance of at least one apparently positive result can increase as the number of tests grows. A statistical plan may address this through procedures such as a hierarchy or adjusted significance thresholds, but the registry record does not report which approach, if any, was used for the secondary outcomes. It is therefore not possible to determine from the record whether the secondary results were confirmatory under a prespecified multiplicity procedure.
Missing-data handling is also important for interpreting time-to-event and binary outcomes. The primary endpoint population is defined as all randomized participants, but the record does not report a full account of censoring, missing assessments, or sensitivity analyses for the primary endpoint. For secondary outcomes, the analysis denominators differ by endpoint; reasons for those denominators and the handling of missing outcome data are not reported in the registry record.
The registry gives the primary endpoint definition and the assessment schedule, but detailed analysis-plan elements such as stratification factors, covariate adjustment, interim analyses, and the original sample-size justification are not reported in the registry record. These omissions limit a complete assessment of the planned inferential framework. They do not change the values reported, but they restrict what can be concluded about the handling of multiple testing and incomplete observations.
17. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Durvalumab | 78 | 262 | 29.8% |
| Placebo | 64 | 265 | 24.2% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Durvalumab | 115 of 264 |
| Durvalumab Plus Tremelimumab | 0 of 0 |
| Placebo | 146 of 266 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 5% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Durvalumab | 209 of 262 |
| Durvalumab Plus Tremelimumab | 0 of 0 |
| Placebo | 196 of 265 |
Most frequent serious adverse event terms
| Event term | Organ system | Durvalumab | Durvalumab Plus Tremelimumab | Placebo |
|---|---|---|---|---|
| Pneumonia | Infections and infestations | 12 of 262 | n/a of 0 | 10 of 265 |
| Radiation pneumonitis | Injury, poisoning and procedural complications | 13 of 262 | n/a of 0 | 7 of 265 |
| Pneumonitis | Respiratory, thoracic and mediastinal disorders | 8 of 262 | n/a of 0 | 6 of 265 |
| Interstitial lung disease | Respiratory, thoracic and mediastinal disorders | 6 of 262 | n/a of 0 | 0 of 265 |
| Chronic obstructive pulmonary disease | Respiratory, thoracic and mediastinal disorders | 1 of 262 | n/a of 0 | 4 of 265 |
| Immune-mediated lung disease | Respiratory, thoracic and mediastinal disorders | 4 of 262 | n/a of 0 | 0 of 265 |
| Asthenia | General disorders | 0 of 262 | n/a of 0 | 3 of 265 |
| Pneumonia bacterial | Infections and infestations | 3 of 262 | n/a of 0 | 0 of 265 |
| Pulmonary embolism | Respiratory, thoracic and mediastinal disorders | 2 of 262 | n/a of 0 | 1 of 265 |
| Diarrhoea | Gastrointestinal disorders | 2 of 262 | n/a of 0 | 1 of 265 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Durvalumab | Durvalumab Plus Tremelimumab | Placebo |
|---|---|---|---|---|
| Radiation pneumonitis | Injury, poisoning and procedural complications | 49 of 262 | n/a of 0 | 55 of 265 |
| Decreased appetite | Metabolism and nutrition disorders | 44 of 262 | n/a of 0 | 34 of 265 |
| Cough | Respiratory, thoracic and mediastinal disorders | 40 of 262 | n/a of 0 | 32 of 265 |
| Fatigue | General disorders | 31 of 262 | n/a of 0 | 33 of 265 |
| Nausea | Gastrointestinal disorders | 33 of 262 | n/a of 0 | 29 of 265 |
| Headache | Nervous system disorders | 24 of 262 | n/a of 0 | 35 of 265 |
| Pruritus | Skin and subcutaneous tissue disorders | 34 of 262 | n/a of 0 | 19 of 265 |
| Dizziness | Nervous system disorders | 32 of 262 | n/a of 0 | 20 of 265 |
| Hypothyroidism | Endocrine disorders | 42 of 262 | n/a of 0 | 10 of 265 |
| Constipation | Gastrointestinal disorders | 26 of 262 | n/a of 0 | 26 of 265 |
Serious events with the highest arm-level rate: radiation pneumonitis (5.0%), pneumonia (4.6%), pneumonitis (3.1%), interstitial lung disease (2.3%), immune-mediated lung disease (1.5%).
The posted safety counts are listed for the durvalumab and placebo groups. Serious adverse events were reported for 78 participants among 262 at risk in the durvalumab group and 64 among 265 at risk in the placebo group. Other adverse events were reported for 209 among 262 and 196 among 265, respectively. The registry also lists deaths for these groups. These are counts within the registry’s safety reporting, not estimates of a causal treatment effect.
The registry lists radiation pneumonitis, pneumonia, pneumonitis, interstitial lung disease, immune-mediated lung disease, and chronic obstructive pulmonary disease among the leading serious adverse event terms, with the reported percentages shown in the safety results. Those term percentages should be read as registry safety summaries; the record does not provide enough context to infer individual causality or compare the terms as treatment effects.
The combination group is listed with zero participants at risk and zero events in the displayed safety data. This provides no interpretable safety estimate for that group in this listing. Differences in safety counts should not be interpreted without considering follow-up, exposure, event definitions, and the way the safety population was assembled. Further safety-analysis details are not reported in the registry record.
18. What the Result Does, and Does Not, Mean
The primary result describes a group-level comparison of progression-free survival after concurrent chemoradiation among participants with limited-stage small-cell lung cancer who had not progressed. The sponsor reports a hazard ratio below 1 for durvalumab versus placebo and classifies the primary analysis as superiority. The reported medians and confidence intervals provide additional context about the timing of progression or death in each group.
This result does not mean that every participant assigned to durvalumab had a longer progression-free period than every participant assigned to placebo. Group summaries do not predict an individual participant’s outcome. The hazard ratio is not a direct measure of the chance that a particular person will benefit, and the median is not a promise about how long an individual will remain progression-free.
The result also does not establish the effect of durvalumab plus tremelimumab. Although that group was part of the study, a numerical primary result for the combination comparison is not reported in the registry record. Nor does this comparison answer questions about durvalumab used instead of concurrent chemoradiation, since the population had already received that treatment and had not progressed.
Secondary measures can add context, but they address different outcomes and are subject to the reporting and multiplicity limitations. The registry record does not provide all the information needed to evaluate missing data, the complete statistical plan, or every listed secondary outcome. Statistical evidence about the primary endpoint should therefore be distinguished from broader claims about treatment, safety, or applicability beyond the studied population.
19. Why This Trial Matters Statistically
This trial illustrates why a clinical result is not captured by a single number. The primary endpoint is time-to-event, so the analysis uses event timing and follow-up as well as whether progression or death occurred. The medians describe the estimated central timing in each group, while the hazard ratio summarizes a relative event rate across follow-up. Each measure has a different interpretation.
The registry’s use of blinded independent central review and RECIST version 1.1 gives the progression endpoint a defined assessment framework. The estimate is also accompanied by confidence intervals, which make uncertainty visible rather than presenting the point estimate as exact. Together, these features help readers distinguish the observed summary from the precision and scope of the inference.
The study also demonstrates the importance of keeping the primary comparison separate from combination and secondary comparisons. A positive primary result for durvalumab versus placebo does not automatically answer whether adding tremelimumab changes outcomes. Secondary endpoints can provide complementary information, but numerous outcomes and unreported multiplicity handling make them less suitable as stand-alone confirmatory evidence.
Finally, planning calculations based on an observed effect are not evidence about the trial’s original design or its retrospective power. Keeping planning illustrations distinct from observed results helps avoid treating a post hoc calculation as a feature of the trial protocol. The registry supports a focused statistical reading of the primary comparison, while leaving important design and analysis details unreported.
20. Limitations
- The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
- Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.
The registry record does not report the full primary analysis plan, including whether the analysis used stratification or covariate adjustment, nor does it report an assessment of proportional hazards. This limits evaluation of the assumptions and specifications behind the reported hazard ratio and log-rank analysis.
The event count supporting the primary time-to-event analysis is not reported in the registry record. Although the primary endpoint population is defined as all randomized participants, detailed information about censoring, missing assessments, and sensitivity analyses is not reported. These details matter for judging how incomplete follow-up and unavailable outcome assessments may affect the estimates.
The registry lists a combination group, but a numerical primary result for that group is not reported. The displayed safety group for durvalumab plus tremelimumab has zero participants at risk and zero events, so it does not permit a meaningful safety comparison for the combination in this listing. Numerical results are also not reported for every outcome listed among the secondary outcomes.
The registry does not report the original sample-size justification, interim-analysis plan, or multiplicity strategy for secondary outcomes. The planning illustrations based on observed effects should not be mistaken for those original design assumptions. In addition, the posted summary does not provide detailed reasons for the differing secondary-outcome denominators. These limits constrain independent reconstruction and broader interpretation, even though the sponsor’s primary result is reported with a confidence interval.
21. Related Tutorials
22. Related Statistical Calculators
23. Sources
- ClinicalTrials.gov: Study of Durvalumab + Tremelimumab, Durvalumab, and Placebo in Limited Stage Small-Cell Lung Cancer in Patients Who Have Not Progressed Following Concurrent Chemoradiation Therapy — NCT03703297.
- Registry record last updated 2025-11-21; status last verified 2025-11.
- Results first posted 2025-08-01.
- Data retrieved from ClinicalTrials.gov on 2026-11-09.
- Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.
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.
24. Record Summary
The registry describes a Phase III randomized, placebo-controlled study of consolidation treatment for limited-stage small-cell lung cancer in participants who had not progressed following concurrent chemoradiation. The primary comparison is durvalumab versus placebo, with progression-free survival assessed by blinded independent central review using RECIST version 1.1.
The reported medians are 16.6 months for durvalumab and 9.2 months for placebo. The sponsor reports a hazard ratio of 0.76, with a 95% confidence interval from 0.606 to 0.950, and classifies the primary comparison as superiority. The study also included durvalumab plus tremelimumab, but a numerical primary result for that comparison is not reported in the registry record.
Secondary outcomes and safety counts provide additional context, but multiplicity handling and several analysis details are not reported in the registry record. The findings should be interpreted as group-level results for the stated population and comparison.