← Clinical Trials
Non-Small-Cell Lung Carcinoma NSCLC Phase 3 Time-to-Event Analysis NCT02453282

Phase III Open Label First Line Therapy Study of MEDI 4736 (Durvalumab) With or Without Tremelimumab Versus SOC in Non Small-Cell Lung Cancer (NSCLC): Complete Statistical Analysis

This analysis examines overall survival in the PD-L1 tumor-cell expression at least 25% subgroup of the MYSTIC trial, comparing durvalumab alone and durvalumab plus tremelimumab with standard-of-care chemotherapy. It explains the reported hazard ratios, uncertainty, planning illustrations, and limits of the registry record.

Trial start: 2015-07-21  ·  Enrollment: 1118  ·  Sponsor: AstraZeneca
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 Phase III Open Label First Line Therapy Study of MEDI 4736 (Durvalumab) With or Without Tremelimumab Versus SOC in Non Small-Cell Lung Cancer (NSCLC) (NCT02453282), a randomized phase 3 study. The primary outcome is Overall Survival (OS); PD-L1 (TC >=25%) Analysis Set Population, Durvalumab Monotherapy Vs SoC Chemotherapy and Durvalumab + Tremelimumab Vs SoC Chemotherapy.

1118
Enrollment
Phase 3
3
Arms
In the primary outcome
0.76
Hazard ratio
Durvalumab Monotherapy vs SoC Chemothera
0.56–1.02
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT02453282
PhasePhase 3
ConditionNon-Small-Cell Lung Carcinoma NSCLC
AllocationRandomized
Design modelParallel
MaskingNone (open label)
Enrollment1118
Arms in the primary outcome3
Lead sponsorAstraZeneca
Results postedYes

2. Clinical Question

Population

Adults with locally advanced or metastatic non-small-cell lung cancer (NSCLC) whose tumors were EGFR and ALK wild-type were studied in a first-line treatment setting. The primary analysis concerns the subset of the full analysis set (FAS) whose tumor-cell PD-L1 expression was at least 25%, defined using the Ventana PD-L1 (SP263) assay. The registry description does not provide further eligibility details.

Intervention

The experimental treatments were durvalumab monotherapy and durvalumab combined with tremelimumab. The registry describes durvalumab as a PD-L1 monoclonal antibody and the combination as PD-L1 plus tremelimumab therapy. Details of dosing and treatment duration are not reported in the registry record.

Comparator

The comparator was standard-of-care platinum-based chemotherapy. Listed regimens included paclitaxel with carboplatin, gemcitabine with cisplatin or carboplatin, and pemetrexed with cisplatin or carboplatin. The registry does not report how the choice among these regimens was made.

Primary question

Among participants in the PD-L1 tumor-cell expression at least 25% analysis set, how did overall survival with each immunotherapy strategy compare with standard-of-care chemotherapy? Overall survival is time from randomization until death from any cause. The reported comparisons use hazard ratios, with values interpreted relative to the chemotherapy group, alongside Kaplan-Meier median estimates and confidence intervals.

This was a randomized, open-label, Phase III study with parallel treatment groups. The registry lists enrollment of 1118 for the trial, while the primary endpoint is reported for the PD-L1-defined subgroup. The subgroup results therefore address a narrower population than the trial-wide enrollment figure. They should not be read as estimates for every person with NSCLC, or for people whose tumor PD-L1 status differs from the analysis definition.

The statistical question is comparative: whether the observed time-to-death patterns differ between each investigational group and the chemotherapy comparator. A hazard ratio summarizes relative event rates over follow-up under the model and analysis used; it is not a direct comparison of median survival times. The results describe the registry-reported analyses, not a recommendation about treatment choice.

3. Trial Design

MYSTIC is described in the registry as a randomized, open-label, multicenter, global Phase III study. Its stated purpose was to assess the efficacy and safety of durvalumab plus tremelimumab and durvalumab alone against platinum-based standard-of-care chemotherapy as first-line treatment for people with locally advanced or metastatic NSCLC that was EGFR and ALK wild-type. The registry lists a parallel-group model and no masking.

The three treatment groups were durvalumab monotherapy, durvalumab plus tremelimumab, and standard-of-care chemotherapy. Chemotherapy options listed in the record were paclitaxel with carboplatin, gemcitabine with cisplatin or carboplatin, and pemetrexed with cisplatin or carboplatin. The registry does not report the assignment ratio, the method used to generate or conceal allocation, or which chemotherapy regimen each participant received.

The registry lists enrollment of 1118. The primary survival results are for the PD-L1 tumor-cell expression at least 25% analysis set, with reported group counts of 163 for durvalumab, 163 for durvalumab plus tremelimumab, and 162 for chemotherapy. Those subgroup counts are not interchangeable with the trial enrollment figure. The analysis set was drawn from the FAS and defined by PD-L1 status using the Ventana PD-L1 (SP263) assay.

The registry lists the study start as 2015-07-21 and primary completion as 2018-10-04; its status is active, not recruiting. The primary endpoint timeframe runs from baseline through death or censoring, with assessment up to the data cut-off and a maximum of approximately 3 years. The specific data cut-off date, planned follow-up schedule, treatment crossover rules, and trial-specific sample-size justification are not reported in the registry record.

Open-label means the treatment assignment was not masked according to the record. That is relevant when considering outcomes susceptible to expectations or differences in care, but death is a comparatively objective endpoint. The record does not describe procedures intended to mitigate potential open-label effects.

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: A total of 1118 participants were randomized in a 1:1:1 ratio in stratified manner as per programmed cell death ligand 1 (PD-L1) tumor expression status (PD-L1 \[tumor cell (TC) \>=25%\] versus (Vs) PD-L1 \[TC \<25%\]) and histology (squamous Vs non-squamous) to receive durvalumab alone, durvalumab + tremelimumab, or standard of care (SoC) chemotherapy.

Overall Study

StageDurvalumab MonotherapyDurvalumab + TremelimumabSoC Chemotherapy
STARTED374372372
Received Treatment369371352
COMPLETED000
NOT COMPLETED374372372

Reasons for not completing this period:

ReasonDurvalumab MonotherapyDurvalumab + TremelimumabSoC Chemotherapy
Death275277296
Lost to Follow-up102
Withdrawal by Subject121011
Participants ongoing at data cut-off858462
Other111

Analysis population for the primary outcome, as defined in the registry: The PD-L1 (TC \>=25%) analysis set included subset of participants in the FAS whose PD-L1 status was PD-L1 (TC \>=25%) as defined by Ventana PD-L1 (SP263) assay (ie, \>=25% TCs expressing PD-L1 on the membrane). Comparison of durvalumab monotherapy Vs SoC and durvalumab + tremelimumab Vs SoC reporting groups were analysed for primary outcome measure.

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: Full analysis set (FAS) included all randomized participants analyzed on an intent-to-treat (ITT) basis.

CharacteristicUnitDurvalumab MonotherapyDurvalumab + TremelimumabSoC ChemotherapyTotal
Participants analysed3743723721118
Age, Continuousyears63.2 (SD 10.30)64.3 (SD 9.52)63.6 (SD 9.36)63.7 (SD 9.74)
Sex: Female, Male: FemaleParticipants118106122346
Sex: Female, Male: MaleParticipants256266250772
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants1513634
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants3593583661083
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants0101
Race/Ethnicity, Customized: WhiteParticipants243249243735
Race/Ethnicity, Customized: Black or African AmericanParticipants33410
Race/Ethnicity, Customized: AsianParticipants125118120363
Race/Ethnicity, Customized: Native Hawaiian or other Pacific IslanderParticipants0022
Race/Ethnicity, Customized: OtherParticipants3137
Race/Ethnicity, Customized: MissingParticipants0101

6. Primary Endpoint

The registry lists the primary outcome as Overall Survival (OS); PD-L1 (TC >=25%) Analysis Set Population, Durvalumab Monotherapy Vs SoC Chemotherapy and Durvalumab + Tremelimumab Vs SoC Chemotherapy, measured over From baseline (Day 1, Week 0) until death due to any cause, assessed up to the data cut-off date (a maximum of approximately 3 years)..

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

The primary endpoint is overall survival (OS), defined as the time from randomization until death from any cause. If a participant was not known to have died at the time of analysis, the record says the participant was censored using the last recorded date they were known to be alive. The stated timeframe begins at baseline, Day 1, Week 0, and extends to the data cut-off, up to a maximum of approximately 3 years.

OS is used in clinical trials because it captures a consequential, objectively defined event and does not require judging whether a tumor has changed enough to count as progression or response. It also incorporates deaths from any cause, rather than only deaths attributed to the cancer. That broad definition makes the endpoint straightforward to describe, although interpretation still depends on follow-up, censoring, and the analysis population.

The registry says median OS was estimated with the Kaplan-Meier technique. The median is the time by which the estimated survival curve reaches the halfway point; it describes the middle of the estimated time-to-event distribution, not the experience of every participant. A confidence interval conveys uncertainty around that estimate.

The comparisons are also reported as hazard ratios from log-rank analyses. A hazard ratio compares the event rates over follow-up between groups, as represented by the reported analysis. It is not a ratio of median survival times and does not state how many months an individual may live. The registry record does not describe proportional-hazards checks, the handling of competing events, or additional model diagnostics.

7. Results Posted in the Registry

Hazard ratio: Durvalumab Monotherapy vs SoC Chemotherapy

0.76

95% CI: 0.56 to 1.02

As reported in the registry

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Durvalumab Monotherapy vs SoC…Durvalumab + Tremelimumab vs …0.530.630.750.891.051.24hazard ratio (as reported) vs control (95% CI)

8. Secondary Efficacy Endpoints

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

Secondary outcomeTypeEffect measureEstimate (95% CI)Planning size, 80% power
OS; PD-L1 (TC >=25%) Analysis Set Population, Durvalumab + Tremelimumab Vs Durvalumab MonotherapyTime-to-Event AnalysisHazard ratio1.09 (0.84 to 1.42)4,228 events
OS; PD-L1 (TC >=1%) Analysis Set PopulationTime-to-Event AnalysisHazard ratio0.88 (0.72 to 1.07)1,922 events
OS; FAS PopulationTime-to-Event AnalysisHazard ratio0.96 (0.81 to 1.13)18,840 events

OS; PD-L1 (TC >=25%) Analysis Set Population, Durvalumab + Tremelimumab Vs Durvalumab Monotherapy

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Durvalumab Monotherapy vs Dur…0.800.911.021.161.311.48hazard ratio (as reported) vs control (95% CI)

OS; PD-L1 (TC >=1%) Analysis Set Population

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Durvalumab Monotherapy vs SoC…Durvalumab + Tremelimumab vs …0.700.780.881.001.121.26hazard ratio (as reported) vs control (95% CI)

OS; FAS Population

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Durvalumab Monotherapy vs SoC…Durvalumab + Tremelimumab vs …0.770.840.910.991.071.16hazard ratio (as reported) vs control (95% CI)

The registry lists secondary outcomes covering overall survival (OS), progression-free survival (PFS), and objective response rate (ORR), with analyses in PD-L1-defined groups and the FAS. The posted secondary OS results span comparisons between the immunotherapy groups and chemotherapy, as well as a comparison of the two immunotherapy strategies. Across those OS analyses, the estimates do not form a uniform pattern of clear separation from chemotherapy: the reported hazard-ratio intervals include 1 and the corresponding reported p-values do not indicate small p-values.

This broad pattern is consistent with treating the primary subgroup result cautiously rather than as a finding that automatically extends across populations or endpoints. Secondary analyses address related but distinct questions. PFS and ORR are not equivalent to OS, and evidence for one endpoint cannot be assumed to establish a result for another. Numerical PFS and ORR results are not reported in the registry record available for this analysis, so their direction and precision cannot be characterized.

Secondary results generally carry less inferential weight than a primary result when many endpoints, populations, and comparisons are examined. Repeated testing increases the opportunity for chance findings, while subgroup definitions can further narrow the population to which an estimate applies. The registry lists numerous outcomes and analyses but does not report a multiplicity strategy or a hierarchy specifying which tests were confirmatory.

Accordingly, secondary analyses are best viewed as supporting context or as questions for further evaluation, rather than as independent confirmation of the primary comparison. The registry record does not report enough information to determine whether each secondary result was prespecified in the same way, adjusted for multiplicity, or intended as confirmatory.

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

9. Statistical Interpretation

Clinical Biostats interpretation

In the PD-L1 tumor-cell expression at least 25% analysis set, median OS was 16.3 months for durvalumab monotherapy, with a 95% confidence interval of 12.2 to 20.8 months. For durvalumab plus tremelimumab, the median was 11.9 months, with a 95% confidence interval of 9.0 to 17.7 months. The chemotherapy group median was 12.9 months, with a 95% confidence interval of 10.5 to 15.0 months. These are Kaplan-Meier median estimates; their confidence intervals overlap.

For durvalumab monotherapy versus chemotherapy, the registry reports a hazard ratio of 0.76 and p = 0.036. The reported hazard-ratio interval is 0.564 to 1.019 at 97.54% confidence. The point estimate is below 1, while the interval includes 1. The p-value and interval are reported at different inferential levels, so the p-value should not be read as if it were paired with an ordinary 95% interval. The record does not explain the choice of confidence level or how the comparisons were handled jointly.

For durvalumab plus tremelimumab versus chemotherapy, the reported hazard ratio is 0.85, with a 98.77% confidence interval of 0.611 to 1.173 and p = 0.202. The point estimate is below 1, but the interval includes 1. These estimates do not establish a precise difference from the comparator. The reported p-value is not evidence that the groups are identical; it indicates that the analysis did not produce a small p-value under its test assumptions.

The medians and hazard ratios describe different features of survival. Medians summarize a point on the survival curve, whereas the hazard ratio summarizes relative event rates across the analysis period. They need not move in lockstep, and a comparison of median values alone is not a substitute for the reported time-to-event comparison.

These are subgroup findings based on the PD-L1 assay-defined analysis set, not the entire trial population. They do not by themselves establish that the treatment effect differs by PD-L1 status; that conclusion would require a relevant interaction analysis, which is not reported in the registry record. The results also do not identify why the observed survival curves or estimates differ. Their interpretation should account for statistical uncertainty, the open-label design, the subgroup definition, the two primary comparisons, and the unreported details of the analysis plan.

10. Statistical Methods Explained

The primary outcome is time-to-event data: each participant contributes information about the time from randomization to death, or to the last date they were known to be alive if no death had been recorded by analysis. Censoring means the exact event time is not observed for that participant during the available follow-up. Kaplan-Meier estimation accounts for this incomplete follow-up by updating the estimated survival curve as events and censoring occur. It relies on assumptions about censoring, and the registry record does not report diagnostic checks or further details about those assumptions.

What does the median OS estimate describe?

The median is the time at which the estimated proportion surviving reaches one half. It is a summary of the Kaplan-Meier curve, not an average and not a prediction for a particular participant. Its confidence interval reflects uncertainty in locating that point on the curve. If follow-up is limited or many observations are censored, the tail of the curve can be less informative; the record does not provide enough detail to characterize that issue for these results.

The posted medians are 16.3 months for durvalumab monotherapy, 11.9 months for the combination, and 12.9 months for chemotherapy in the primary analysis set. Each has a 95% confidence interval. These descriptive estimates should be considered alongside the comparative analysis rather than treated as standalone proof of a treatment difference.

How should the hazard ratio be read?

The hazard ratio compares the event rate in one treatment group with that in the reference group over follow-up, according to the reported analysis. A value of 1 is the conventional no-relative-difference reference; a value below 1 indicates a lower estimated event rate in the numerator group, and a value above 1 indicates a higher estimated rate. This interpretation is conditional on the analysis and its assumptions. A hazard ratio is not an absolute risk, a percentage change in survival, or a difference in median months.

The registry reports hazard ratios using log-rank analyses. For durvalumab monotherapy versus chemotherapy, the reported estimate is 0.76; for the combination versus chemotherapy, it is 0.85. The accompanying p-values and confidence intervals express uncertainty in different ways. The confidence intervals include the value 1 for both reported primary comparisons. The first reported p-value is 0.036, and the second is 0.202. Their confidence intervals are reported at 97.54% and 98.77%, respectively, rather than the 95% level used for the medians. A p-value is calculated under a null hypothesis and analysis procedure; it is not the probability that the null hypothesis is true, nor does it measure the size or clinical importance of an effect.

Why do confidence levels matter?

A confidence interval is a range generated by a statistical procedure that, under repeated use of the procedure and its assumptions, would contain the underlying parameter at the stated rate. A higher confidence level generally produces a wider interval than a lower level using the same data and method. Comparisons require attention to the confidence level, endpoint, and analysis method. Here, median OS intervals and hazard-ratio intervals describe different estimands and are not interchangeable.

The confidence interval for a hazard ratio that contains 1 is compatible with no relative difference as well as with effects in either direction within the interval. It does not prove there is no effect. Conversely, a point estimate below 1 does not establish a reliable advantage on its own. The width of the interval indicates how much uncertainty remains, and its position indicates which values are compatible with the analysis.

What does randomization contribute?

Random allocation is intended to support comparisons by making treatment assignment independent of participants' measured and unmeasured characteristics on average. It does not guarantee that every subgroup is balanced, and the registry record does not describe the allocation procedure or balance checks. The primary results are restricted to a biomarker-defined subgroup, so the whole-trial enrollment should not be treated as the size of this specific analysis set.

The study was open label, with no masking reported. Randomization and masking address different sources of bias: randomization governs treatment assignment, while masking can limit knowledge of assignment during care or outcome assessment. Death is less subjective than many outcomes, but an open-label design may still affect aspects of treatment and follow-up. The registry record does not detail how such influences were assessed.

What analysis details are not available?

The registry describes the endpoint definition, Kaplan-Meier estimation, and log-rank comparison, but it does not report the trial's complete statistical analysis plan, proportional-hazards assessment, stratification factors, missing-data procedures beyond censoring, interim analysis plan, or multiplicity adjustment. These omissions limit how fully the reported p-values and confidence levels can be reconstructed or placed in the planned testing hierarchy. No alternative analysis should be inferred from the registry record.

The record lists many secondary outcome measures and analyses. Multiple comparisons create more opportunities for apparently notable results, particularly when no adjustment strategy is specified. Secondary results should therefore be read in the context of the planned endpoint hierarchy and analysis plan; those details are not reported in the registry record.

11. Confidence Intervals and Precision

Precision concerns how narrowly the data locate an estimate. The median OS estimates have 95% confidence intervals: 12.2 to 20.8 months for durvalumab monotherapy, 9.0 to 17.7 months for durvalumab plus tremelimumab, and 10.5 to 15.0 months for chemotherapy. The intervals indicate uncertainty around each estimated median; they are not ranges containing a specified proportion of individual survival times.

The hazard-ratio intervals for the primary comparisons are reported at different confidence levels. For durvalumab monotherapy versus chemotherapy, the estimate is 0.76 with a 97.54% confidence interval of 0.564 to 1.019. For durvalumab plus tremelimumab versus chemotherapy, the estimate is 0.85 with a 98.77% confidence interval of 0.611 to 1.173. Both intervals include 1, the reference value for no relative difference. Their breadth leaves room for a range of possible relative effects, including values on either side of 1.

Confidence intervals are not guarantees about the true value, nor are they measures of clinical importance. A broad interval indicates less precision than a narrow interval, but the practical importance of any value also depends on the outcome and clinical context. The registry record does not specify a threshold for a clinically important survival difference.

Intervals for separate groups should not be used as a formal test of the difference between those groups. The reported hazard-ratio comparisons are the relevant comparative estimates. Their confidence levels differ from the median confidence intervals and from each other, so readers should avoid treating all intervals as if they represented the same inferential procedure.

Uncertainty also reflects the analysis population and follow-up. The primary results concern the PD-L1-defined subgroup, and the timeframe extends up to approximately 3 years. The registry record does not report numbers at risk over time or the distribution of follow-up, which would help characterize how much information supports later portions of the survival curves.

12. Planning a Similar Trial: Sample Size

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

Effect to detect (log scale)Hazard ratioEvents, 80% powerEvents, 90% power
100% of the observed effect0.76417559
75% of the observed effect0.81742993
50% of the observed effect0.871,6682,233
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect5001,0002,0005,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: events required (total))
Treat these figures cautiously. The observed difference is imprecise: its confidence interval includes no difference at all. A sample size built on a noisy estimate can be far too small or too large, so the smaller-effect rows are the more cautious guide.
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, Schoenfeld approximation for the log-rank test or Cox model. The answer is the total number of events, not participants; the number of participants depends on how quickly events accrue. Calculated for the comparison: Durvalumab Monotherapy vs SoC Chemotherapy.

The planning illustration is based on the observed effect, not on the original trial design. Because the outcome is time-to-event, its planning figures are total event counts, not participants per arm. The registry record's original sample-size assumptions and justification are not reported in the registry record.

The illustration assumes a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. It considers the full observed effect and smaller fractions of that effect, including planning for 75% and 50% of the observed effect. The event requirement is shown for both 80% and 90% power. In plain language, a power target is the probability, under the assumed effect and analysis conditions, of detecting an effect at the stated significance level. The 90% target is a higher chance of detection than the 80% target, and generally requires more events under otherwise similar assumptions.

Smaller effects are harder to distinguish from random variation, so planning to detect a smaller effect requires more information and usually more events. The illustration makes this relationship visible across the listed effect assumptions. It is not observed power: it does not describe the probability that the completed trial detected its true effect, and it does not revise the trial's original design.

These figures are hypothetical planning quantities derived from the observed estimate. They should not be read as actual participant counts or as a claim that the trial had a particular prespecified event target. The registry record does not report its original power target, target event count, allocation ratio, or sample-size calculation 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

d = 4 (z1−α/2 + z1−β)2 / [ln(HR)]2

d is the total number of events needed (Schoenfeld's formula) with 1:1 allocation and proportional hazards.

Worked calculation for this trial

  1. Hazard ratio HR = 0.760, so ln(HR) = -0.2744.
  2. 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(2453282)
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 738 participants in total, with the boundaries below.

AnalysisCalendar time (months)EventsEfficacy boundary (z)Nominal one-sided pCumulative alpha spent
Look 119.01883.7100.00010.0001
Look 230.33762.5110.00600.0060
Look 360.05631.9930.02310.0250
01234z = 3.7119 mo188 eventsz = 2.5130 mo376 eventsz = 1.9960 mo563 eventsUpper efficacy boundary (z)

Fixed design versus group-sequential alternatives

DesignPowerEvents at final analysisParticipantsStudy length (months)
Fixed design, one analysis80%41654460.0
Two looks, O'Brien-Fleming80%41754660.0
Three looks, O'Brien-Fleming80%42155160.0
Three looks, Pocock80%48663760.0
Fixed design, one analysis90%55772960.0
Two looks, O'Brien-Fleming90%55973160.0
Three looks, O'Brien-Fleming90%56373860.0
Three looks, Pocock90%64384160.0

Group-sequential designs cost a small increase in maximum sample size and events compared with the fixed design, in exchange for the chance to stop early for overwhelming efficacy. O'Brien-Fleming spending keeps early boundaries very conservative and the final boundary close to the fixed-design value, whereas Pocock spending spends more alpha early.

Sensitivity to a smaller true effect

Planning for exactly the observed effect is optimistic, because observed effects in published trials tend to be somewhat larger than the true effect. The table repeats the main design (three looks, O'Brien-Fleming spending, 90% power) for smaller true hazard ratios.

True effect assumedHazard ratioEvents at final analysisParticipants
100% of the observed effect0.760563738
75% of the observed effect0.8141,0021,296
50% of the observed effect0.8722,2572,884

For context, this trial enrolled 1,118 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 <- 12.9          # 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: 586         p (1-sided)   0.0001
 Events: 188        ~HR at bound   0.5818
   Month: 19    P(Cross) if HR=1   0.0001
             P(Cross) if HR=0.76   0.0338
   IA 2: 67%                   Z   2.5114
      N: 738         p (1-sided)   0.0060
 Events: 376        ~HR at bound   0.7717
   Month: 30    P(Cross) if HR=1   0.0060
             P(Cross) if HR=0.76   0.5603
       Final                   Z   1.9930
      N: 738         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

MethodEstimate95% CIP-value
Log RankHazard Ratio (HR) 0.760.564 to 1.0190.036
Log RankHazard Ratio (HR) 0.850.611 to 1.1730.202

The registry reports sponsor analyses for the primary OS comparisons, using log-rank methods and reporting hazard ratios, confidence intervals, and p-values. The hazard ratios and p-values discussed in the primary interpretation are those reported in the registry record. The record does not flag a discrepancy between a recalculation and the sponsor's analysis.

Planning illustrations based on the observed effect serve a different purpose from the sponsor's treatment comparison. They translate an observed estimate into hypothetical event requirements under stated planning assumptions; they do not replace or independently verify the trial's survival analysis. No independently recalculated hazard ratio is used in interpreting the primary result.

The sponsor's reported analysis is the relevant source for the posted comparative estimates. Its interpretation remains bounded by the reported analysis population, endpoint definition, confidence levels, and information missing from the registry record. The registry does not provide enough detail to reconstruct the full analysis plan or independently assess all modeling and testing decisions.

16. Multiplicity, Missing Data and Analysis Populations

The primary outcome includes two comparisons against the same chemotherapy group: durvalumab monotherapy and durvalumab plus tremelimumab. Testing more than one comparison raises a multiplicity question because the chance of at least one apparently notable result can increase when several hypotheses are tested. The registry record reports comparison-specific p-values and confidence levels but does not state whether a family-wise error strategy, a hierarchical testing plan, or another adjustment was used.

The two primary hazard-ratio intervals are reported at 97.54% and 98.77% confidence, rather than the 95% level used for the median OS estimates. The record does not explain how those confidence levels relate to the testing strategy. They should therefore be read as reported, without assuming a particular adjustment procedure. The p-values likewise should not be interpreted as a complete account of the trial's overall type I error control.

The record lists many secondary outcomes and analyses across OS, PFS, and ORR, with more than one analysis population. The full analysis plan, prespecified endpoint hierarchy, and multiplicity handling are not reported in the registry record. This matters because results from multiple endpoints or subgroups are not equivalent to a single prespecified primary test.

The primary analysis is restricted to the FAS subset defined by PD-L1 tumor-cell expression at least 25% using the Ventana SP263 assay. The record describes censoring for participants not known to have died at analysis, but does not provide further missing-data methods, numbers at risk over follow-up, or sensitivity analyses for censoring. Details on how incomplete biomarker measurements or unavailable status were handled are not reported in the registry record.

Without those details, it is not possible to determine from the registry record how robust the conclusions are to alternative missing-data assumptions or how the analysis population was finalized. These are limits on interpretation, not proof that the analyses were conducted inappropriately.

17. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Durvalumab Monotherapy13136935.5%
Durvalumab + Tremelimumab17837148.0%
SoC Chemotherapy11235231.8%
Participants with at least one serious adverse event
Serious adverse events by armDurvalumab Monotherapy35.5%Durvalumab + Tremelimumab48.0%SoC Chemotherapy31.8%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
Durvalumab Monotherapy278 of 374
Durvalumab + Tremelimumab278 of 372
SoC Chemotherapy297 of 372

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 0% reporting threshold.

ArmParticipants affected of at risk
Durvalumab Monotherapy335 of 369
Durvalumab + Tremelimumab328 of 371
SoC Chemotherapy332 of 352

Most frequent serious adverse event terms

Event termOrgan systemDurvalumab MonotherapyDurvalumab + TremelimumabSoC Chemotherapy
PneumoniaInfections and infestations20 of 36921 of 37119 of 352
DiarrhoeaGastrointestinal disorders2 of 36912 of 3716 of 352
AnaemiaBlood and lymphatic system disorders1 of 3694 of 37114 of 352
Pulmonary embolismRespiratory, thoracic and mediastinal disorders3 of 3696 of 3718 of 352
PneumonitisRespiratory, thoracic and mediastinal disorders5 of 3699 of 3711 of 352
DyspnoeaRespiratory, thoracic and mediastinal disorders6 of 3696 of 3712 of 352
Pleural effusionRespiratory, thoracic and mediastinal disorders6 of 3695 of 3711 of 352
PyrexiaGeneral disorders5 of 3694 of 3711 of 352
Chronic obstructive pulmonary diseaseRespiratory, thoracic and mediastinal disorders2 of 3697 of 3710 of 352
Interstitial lung diseaseRespiratory, thoracic and mediastinal disorders2 of 3697 of 3710 of 352

Most frequent non-serious adverse event terms

Event termOrgan systemDurvalumab MonotherapyDurvalumab + TremelimumabSoC Chemotherapy
NauseaGastrointestinal disorders46 of 36978 of 371143 of 352
Decreased appetiteMetabolism and nutrition disorders73 of 36989 of 37178 of 352
FatigueGeneral disorders65 of 36980 of 37180 of 352
AnaemiaBlood and lymphatic system disorders36 of 36933 of 371136 of 352
ConstipationGastrointestinal disorders62 of 36959 of 37183 of 352
DiarrhoeaGastrointestinal disorders51 of 36974 of 37141 of 352
AstheniaGeneral disorders48 of 36945 of 37148 of 352
RashSkin and subcutaneous tissue disorders39 of 36957 of 37140 of 352
VomitingGastrointestinal disorders28 of 36930 of 37174 of 352
PruritusSkin and subcutaneous tissue disorders42 of 36967 of 37117 of 352

Serious events with the highest arm-level rate: pneumonia (5.7%), anaemia (4.0%), diarrhoea (3.2%), pneumonitis (2.4%), pulmonary embolism (2.3%).

Do not overextend the safety comparison. Serious-adverse-event counts are safety observations, not efficacy outcomes, and should not be combined with the primary result into a single benefit-risk number.

The registry reports serious adverse events for each treatment group using counts of participants affected and counts at risk. Serious adverse events were reported for 131 of 369 at risk in the durvalumab monotherapy group, 178 of 371 in the durvalumab plus tremelimumab group, and 112 of 352 in the chemotherapy group. Other adverse events were reported for 335 of 369, 328 of 371, and 332 of 352 at risk, respectively. These are registry counts; they should not be combined or interpreted as event rates over a common exposure period without further information.

The listed serious adverse event terms include pneumonia at 5.7%, anaemia at 4.0%, diarrhoea at 3.2%, pneumonitis at 2.4%, pulmonary embolism at 2.3%, and chronic obstructive pulmonary disease at 1.9%. The registry information does not specify an arm attribution for these term percentages in the registry record. They should not be assigned to a particular group.

The record also lists deaths in the adverse-event group data, but does not provide the context needed to interpret those counts as treatment-related deaths. Definitions, event ascertainment periods, exposure-adjusted comparisons, and judgments of causality are not reported in the registry record. These summaries describe reported safety data and do not establish that a treatment caused or prevented an event.

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

The posted results describe overall survival in a specific biomarker-defined subgroup of a randomized Phase III study. They show Kaplan-Meier median estimates for each treatment group and sponsor-reported hazard ratios for comparisons with chemotherapy. The point estimates, intervals, and p-values are different summaries of the data and should be read together rather than reduced to a single label.

The durvalumab monotherapy comparison has a hazard-ratio point estimate below 1 and a reported p-value of 0.036, while its reported 97.54% interval includes 1. The combination comparison also has a point estimate below 1, but its reported interval includes 1 and its p-value is 0.202. These results do not establish a precise benefit or no benefit. In particular, a non-small p-value does not prove equality, and a point estimate alone does not establish a reliable difference.

The results do not show that the treatment effect is the same in all PD-L1 groups, because the primary comparison is limited to the subgroup with tumor-cell expression at least 25%. Nor do they establish a difference between the immunotherapy strategies: that question is distinct from comparing each strategy with chemotherapy, and any such interpretation requires its own reported comparison and uncertainty.

The registry record does not provide complete details about multiplicity, the full statistical analysis plan, or the original sample-size assumptions. Secondary outcomes are listed, but numerical results for PFS and ORR are not reported in the registry record. The results therefore do not answer every clinical or statistical question raised by the trial.

These findings are statistical summaries of a trial record, not individualized predictions or medical advice. They do not establish the best treatment for a particular person, and they do not by themselves determine the clinical importance of a difference. Clinical interpretation requires the broader evidence and context, which are beyond what the registry record reports.

19. Why This Trial Matters Statistically

This trial raises several important statistical issues common to randomized oncology studies. First, OS is a time-to-event endpoint with censoring, so interpretation depends on follow-up and survival analysis rather than a simple comparison of endpoint counts. The record defines death and censoring and identifies Kaplan-Meier estimation, allowing readers to distinguish the median summary from the hazard-ratio comparison.

Second, the primary result concerns a biomarker-defined subgroup. A precise subgroup definition matters for reproducibility: the record identifies tumor-cell PD-L1 expression at least 25% using the Ventana PD-L1 (SP263) assay. At the same time, a subgroup result is not automatically evidence that the treatment effect differs across biomarker groups. That requires an appropriate comparison of effects by subgroup, which is not reported in the registry record.

Third, there are two immunotherapy comparisons with the same chemotherapy comparator, along with many secondary outcomes and analyses. This makes multiplicity and prespecified testing strategy important. The registry record does not report how these issues were handled, so the reported p-values cannot be interpreted as a complete account of the testing family.

Finally, the contrast between median estimates, hazard ratios, confidence intervals, and p-values illustrates why no single statistic tells the whole story. Estimates describe magnitude, intervals describe uncertainty under a procedure, and p-values address compatibility with a null hypothesis under a specified test. The record's different confidence levels for the hazard-ratio comparisons make careful reading especially important. These considerations help separate what the randomized comparison estimates from what remains uncertain or undocumented.

20. Limitations

The registry record leaves important trial-specific statistical details unavailable. The original sample-size justification, target power, planned event count, and allocation ratio are not reported. The planning illustrations based on the observed effect cannot fill that gap or establish what assumptions governed the trial's design.

The primary analysis is restricted to the PD-L1 tumor-cell expression at least 25% subset, and the registry does not provide an interaction analysis establishing whether the treatment effects differ by PD-L1 status. The subgroup results should not be generalized automatically to the full FAS or to other biomarker groups. Although the assay and threshold are identified, further details about biomarker assessment and missing or indeterminate status are not reported.

The registry reports an open-label design. It does not describe allocation concealment, masking of outcome assessment, treatment adherence, treatment crossover, subsequent therapies, or sensitivity analyses. These omissions limit assessment of how care and follow-up may have influenced the observed outcome patterns.

For survival, the record specifies censoring at the last known date alive but does not report numbers at risk over time, follow-up distribution, proportional-hazards diagnostics, or alternative analyses. The data cut-off date is not stated in the registry record for this analysis. Those details would help assess how much information supports the survival estimates and whether the reported summary is an adequate description of changing relative event rates.

Finally, the registry lists secondary endpoints but does not provide numerical PFS and ORR findings in the record. Multiplicity methods and the full analysis plan are also not reported. These limitations constrain interpretation; they do not, on their own, show that the trial conduct or analyses were flawed.

21. Related Tutorials

22. Related Statistical Calculators

23. Sources

Continue through the Clinical Biostats statistical pathway

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

24. Record Summary

MYSTIC is a randomized, open-label, parallel-group Phase III study of durvalumab alone, durvalumab plus tremelimumab, and platinum-based standard-of-care chemotherapy for first-line treatment of locally advanced or metastatic EGFR and ALK wild-type NSCLC. The registry lists enrollment of 1118 and describes a primary OS analysis in the PD-L1 tumor-cell expression at least 25% subgroup.

Median OS was 16.3 months with durvalumab, 11.9 months with the combination, and 12.9 months with chemotherapy. The sponsor-reported hazard ratios versus chemotherapy were 0.76 and 0.85, respectively; both reported confidence intervals include 1. The record lists secondary OS, PFS, and ORR outcomes, but numerical PFS and ORR results are not reported in the registry record.

Important details, including the original sample-size justification, complete statistical analysis plan, and multiplicity strategy, are not reported in the registry record. The results should be interpreted as subgroup-specific estimates with uncertainty, rather than as definitive conclusions for all trial participants or all people with NSCLC.

Clinical Biostats