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Biliary Tract Neoplasms Phase 3 Time-to-Event Analysis NCT03875235

Durvalumab or Placebo in Combination With Gemcitabine/Cisplatin in Patients With 1st Line Advanced Biliary Tract Cancer (TOPAZ-1): Complete Statistical Analysis

The registry record describes TOPAZ-1, a randomized comparison of durvalumab plus gemcitabine and cisplatin with placebo plus gemcitabine and cisplatin in first-line advanced biliary tract cancer. The primary result is overall survival, with progression-free survival and other outcomes recorded as secondary endpoints.

Trial start: 2019-04-16  ·  Enrollment: 810  ·  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 Durvalumab or Placebo in Combination With Gemcitabine/Cisplatin in Patients With 1st Line Advanced Biliary Tract Cancer (TOPAZ-1) (NCT03875235), a randomized phase 3 study. The primary outcome is Overall Survival (OS).

810
Enrollment
Phase 3
2
Arms
In the primary outcome
0.80
Hazard ratio
Durvalumab + Gemcitabine + Cisplatin vs
0.64–0.99
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT03875235
PhasePhase 3
ConditionBiliary Tract Neoplasms
AllocationRandomized
Design modelParallel
MaskingQuadruple
Enrollment810
Arms in the primary outcome2
Lead sponsorAstraZeneca
Results postedYes

2. Clinical Question

Population

Patients with first-line advanced biliary tract cancer, described in the registry under biliary tract neoplasms. The primary outcome analysis population is the full analysis set. The registry record does not report further eligibility characteristics in the registry record.

Intervention

Durvalumab given in combination with gemcitabine and cisplatin. The registry identifies durvalumab as a drug and names the combination as the treatment arm.

Comparator

Placebo given in combination with gemcitabine and cisplatin. The chemotherapy combination is therefore present in both randomized groups; the assigned difference is durvalumab versus placebo.

Primary question

How did overall survival, measured from randomization until death from any cause, compare between the two assigned combinations? The registry reports median overall survival and a hazard ratio from a Log Rank analysis.

The clinical question is framed around the addition of durvalumab to gemcitabine and cisplatin, rather than a comparison of chemotherapy with no treatment. Randomization assigns participants to the durvalumab combination or the placebo combination, and the quadruple-masked design is intended to keep group assignment concealed from multiple groups involved in the trial. The record lists 810 participants enrolled.

The primary endpoint focuses on time until death from any cause. Secondary outcomes include progression-free survival, progression-free survival rates at specified time points, objective response rate, duration of response, and disease control rate. The outcomes address different aspects of the clinical course and should not be treated as interchangeable measures. The primary question remains the comparison in overall survival; secondary findings offer additional context but do not replace that endpoint.

3. Trial Design

TOPAZ-1 is registered as a Phase III, randomized, parallel-group study with quadruple masking. It compares durvalumab plus gemcitabine plus cisplatin with placebo plus gemcitabine plus cisplatin in patients with first-line advanced biliary tract cancer. The registry lists AstraZeneca as the sponsor and 810 as the enrollment.

The study start date is 2019-04-16, and the primary completion date is 2021-08-11. The registry status is active, not recruiting. These are registry record details; they do not by themselves describe the complete conduct history or establish when every analysis was finalized.

The primary outcome is overall survival in the full analysis set. It is defined as time from randomization until death due to any cause. A participant not known to have died by the analysis is censored at the last recorded date known alive. The stated assessment period extends to a maximum of approximately 27 months, from randomization to the primary analysis data cut-off. The registry describes a second interim analysis as pre-specified after approximately 397 overall-survival events in both arms, corresponding to 59% maturity.

The registered arms include 341 participants in the durvalumab combination and 344 in the placebo combination for the posted primary outcome. Those outcome-group counts are not the same thing as the registry's total enrollment. The record names the full analysis set as the primary analysis population but does not report further details about the population definition in the registry record.

The registry record does not report the original sample-size justification, the planned allocation ratio, or the complete statistical analysis plan. The planning illustrations associated with the posted results are separate calculations based on observed effects and should not be read as the trial's original design calculations.

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: Eligible patients previously untreated for unresectable locally advanced or metastatic Biliary Tract Cancer (BTC) were randomized in a 1:1 ratio with either Durvalumab in combination with Gemcitabine/Cisplatin or Placebo in combination with Gemcitabine/Cisplatin. Randomization was stratified by disease status (initially unresectable versus recurrent) and primary tumor site (IHCC versus EHCC versus GBC).

Overall Study

StageDurvalumab + Gemcitabine + CisplatinPlacebo + Gemcitabine + Cisplatin
STARTED341344
Treated338342
COMPLETED00
NOT COMPLETED341344

Reasons for not completing this period:

ReasonDurvalumab + Gemcitabine + CisplatinPlacebo + Gemcitabine + Cisplatin
Ongoing study treatment70
Off treatment178
Withdrawal by Subject68
Death308326
Lost to Follow-up31
Re-consent refusal01

Analysis population for the primary outcome, as defined in the registry: Full analysis set

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: Baseline analysis was based on all patients in the full analysis set (FAS), which comprised all patients randomized prior to or on 18 December 2020. Patients were included in the analysis in the treatment arm to which they were randomized, regardless of the treatment they received.

CharacteristicUnitDurvalumab + Gemcitabine + CisplatinPlacebo + Gemcitabine + CisplatinTotal
Participants analysed341344685
Age, ContinuousYears62.2 (SD 10.49)62.6 (SD 10.66)62.4 (SD 10.57)
Age, Customized: Age group (years) – < 65 yearsParticipants181184365
Age, Customized: Age group (years) – >=65 - < 75 yearsParticipants122114236
Age, Customized: Age group (years) – >= 75 yearsParticipants384684
Sex: Female, Male: FemaleParticipants172168340
Sex: Female, Male: MaleParticipants169176345
Race/Ethnicity, Customized: Race – American Indian of Alaska NativeParticipants011
Race/Ethnicity, Customized: Race – AsianParticipants185201386
Race/Ethnicity, Customized: Race – Black or African AmericanParticipants8614
Race/Ethnicity, Customized: Race – WhiteParticipants131124255
Race/Ethnicity, Customized: Race – OtherParticipants171229

6. Primary Endpoint

The registry lists the primary outcome as Overall Survival (OS), measured over From date of randomization until death due to any cause. Assessed up to maximum of approximately 27 months (from date of randomization to primary analysis data cut-off).

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

Overall survival measures the time from randomization until death from any cause. It is a time-to-event outcome: each participant contributes information about how long they were followed and whether the event occurred during that period. Participants not known to have died by the analysis are censored at their last recorded date known alive, rather than being treated as if they had died or as if they could be followed indefinitely.

The registry reports median overall survival, with confidence intervals for each arm, and a hazard ratio comparing the randomized groups. The median summarizes the time by which the estimated survival curve reaches the halfway point. Kaplan-Meier estimation is used to account for participants whose event time is not observed during the analysis period through censoring. The hazard ratio summarizes the relative event rate over follow-up under the model and assumptions used for the analysis; it is not a difference between the two medians.

Overall survival is used because it directly captures time until death from any cause and does not require a judgment about whether a particular cause of death is related to the cancer or treatment. It is still influenced by follow-up duration, censoring, and the number and timing of observed events. The stated primary assessment period was up to approximately 27 months. The registry does not provide additional detail about follow-up completeness or later overall-survival analyses in the registry record.

7. Results Posted in the Registry

Hazard ratio: Durvalumab + Gemcitabine + Cisplatin vs Placebo + Gemcitabine + Cisplatin

0.80

95% CI: 0.64 to 0.99

As reported in the registry

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Durvalumab + Gemcitabine + Ci…0.620.680.760.840.931.04hazard 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
Progression-free Survival (PFS)Time-to-Event AnalysisHazard ratio0.75 (0.63 to 0.89)380 events
Progression-free Survival (PFS) Rate at 9 MonthsBinary EndpointRisk difference+10.2 pts (3.4 to 17.0)316 per arm
Progression-free Survival (PFS) Rate at 12 MonthsBinary EndpointRisk difference+9.4 pts (4.7 to 14.2)177 per arm

Progression-free Survival (PFS)

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Durvalumab + Gemcitabine + Ci…0.610.680.750.840.931.04hazard ratio (as reported) vs control (95% CI)

Progression-free Survival (PFS) Rate at 9 Months

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Durvalumab + Gemcitabine + Ci…-1.362.586.53101418risk difference (percentage points) vs control (95% CI)

Progression-free Survival (PFS) Rate at 12 Months

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Durvalumab + Gemcitabine + Ci…-1.132.155.448.721215risk difference (percentage points) vs control (95% CI)

The secondary outcomes address disease progression, response, and disease control in addition to overall survival. The posted progression-free survival summaries and rates generally have a direction consistent with the primary overall-survival comparison: the estimates for the durvalumab combination are more favorable on these recorded time-to-event measures. This broad pattern provides context for the primary finding but does not make each secondary measure equivalent to overall survival.

Progression-free survival is defined through radiological progression or death, with tumor assessments every 6 weeks after randomization for the first 24 weeks and every 8 weeks thereafter. The registry also lists progression-free survival rates at 9 and 12 months, objective response rate, duration of response, duration-of-response rates at specified times, and disease control rate. Although 14 outcome measures and 3 analyses are listed in the record, individual posted results for every listed secondary outcome are not reported in the registry record.

The secondary outcomes add different perspectives: a time-to-event measure, a rate at a defined time point, or a response-related outcome. Differences in outcome definitions, assessment timing, and censoring mean that their estimates should not be combined into a single summary without an appropriate method. The registry does not provide enough information to determine how all secondary outcomes were prioritized relative to one another.

Unadjusted secondary comparisons carry less inferential weight when multiple outcomes are examined. General explanation: testing many outcomes increases the chance that at least one nominally notable result arises by chance, unless the analysis plan accounts for multiplicity. The registry record does not report a multiplicity adjustment strategy for the secondary outcomes. Accordingly, secondary estimates are best interpreted as supporting or exploratory context rather than as independent confirmation of the primary endpoint.

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

9. Statistical Interpretation

Clinical Biostats interpretation

The posted primary outcome gives median overall survival of 12.8 months for durvalumab plus gemcitabine and cisplatin, with a 95% confidence interval from 11.1 to 14.0 months. For placebo plus gemcitabine and cisplatin, median overall survival is 11.5 months, with a 95% confidence interval from 10.1 to 12.5 months. These are Kaplan-Meier median estimates, not the survival times of every participant in either group.

The sponsor-reported comparison is a hazard ratio of 0.80, with an interval from 0.64 to 0.99 and p = 0.021, using a Log Rank method. The sponsor's analysis labels this interval as 97%. A hazard ratio below 1 indicates that the estimated event rate over follow-up was lower in the durvalumab-combination group under this analysis. The interval reaches close to 1, so the estimate retains uncertainty about the size of the between-group difference. The p-value is evidence against the statistical null used for this comparison, not a measure of the probability that the null is true or the probability that the result will recur.

The primary result should be read in conjunction with the study design and outcome definition. Randomization supports a comparison of assigned groups, while the use of overall survival includes deaths from any cause. Censoring means that participants who were still alive or not known to have died at analysis contribute follow-up only through their last known-alive date. The registry notes a pre-specified second interim analysis after approximately 397 events, or 59% maturity; the available record does not describe any additional interim-analysis procedures or decision boundaries.

The secondary endpoint estimates generally point in a direction consistent with the primary comparison, with the posted progression-free survival summaries favoring the durvalumab combination. These measures assess disease progression or response-related outcomes rather than death from any cause. They provide supporting context, but they do not establish the same claim as the primary endpoint. The registry lists additional response and disease-control outcomes, while the registry entries do not give individual results for all of them.

Some secondary comparison statistics are unadjusted recalculations from posted summaries rather than sponsor-reported analyses. Such estimates can describe the posted data, but their inferential weight is more limited when many outcomes are examined and no multiplicity adjustment is reported. A nominal p-value for one secondary outcome should not be interpreted as if that endpoint had been the sole pre-specified question. The registry record does not report a multiplicity strategy for the secondary outcomes.

These results describe the registered randomized groups and analysis presented in the record. They do not, by themselves, establish how well the estimates apply to people outside the trial population, nor do they resolve questions about other outcomes, subgroups, or longer follow-up not documented in the registry record.

10. Statistical Methods Explained

Overall survival and progression-free survival are time-to-event outcomes. Their analysis differs from a simple comparison of the number of participants who experienced an event by a single date, because participants may have different lengths of follow-up and some may not have an observed event by the analysis cut-off.

What does Kaplan-Meier estimation do?

General explanation: Kaplan-Meier estimation constructs an estimate of the probability of remaining event-free over time while accounting for censoring. A participant who has not had the event by the last known follow-up contributes information up to that point. Censoring is not counted as an event, and it does not establish what happened after the participant's last observed follow-up.

For the primary endpoint, the event is death from any cause. The registry says that participants not known to have died are censored at the last recorded date known alive and that median overall survival was calculated using the Kaplan-Meier technique. The median is the time at which the estimated survival probability reaches the midpoint of the distribution. It summarizes the estimated curve; it does not mean that every participant lived for that duration.

How should the hazard ratio be understood?

General explanation: A hazard ratio compares event rates between groups over follow-up. It is not an absolute difference in months and should not be interpreted as a direct transformation of the two reported medians. Its meaning depends on the analysis and assumptions, including how the relative event rate behaves over time. The registry reports a Log Rank comparison and a hazard ratio for overall survival and progression-free survival. The detailed model specification and diagnostics are not reported in the registry record.

The primary sponsor-reported hazard ratio is 0.80, with a reported interval from 0.64 to 0.99 and p = 0.021. The reported analysis identifies the interval as 97%. The median survival confidence intervals are separately listed as 95% confidence intervals. These intervals answer different questions: arm-specific median intervals describe uncertainty in each median, whereas the hazard-ratio interval describes uncertainty in the relative comparison. The reported p-value is tied to the sponsor's comparison method and should be read alongside its effect estimate and interval.

Why do event counts matter?

General explanation: For time-to-event comparisons, information depends substantially on how many events have occurred, not just on how many participants entered the study. More observed events typically make an estimate more informative, while censoring and unequal follow-up can affect the information available. The registry states that the second interim analysis was pre-specified after approximately 397 overall-survival events in both arms, representing 59% maturity. Further details about the interim process are not reported in the registry record.

For a binary outcome measured at a fixed time, the analysis instead concerns the proportion or estimated rate meeting the outcome definition at that time. The posted progression-free survival rates at 9 and 12 months are calculated using the Kaplan-Meier technique, so they are estimates at specific follow-up times rather than raw proportions that necessarily treat every participant as having complete follow-up to that time. The registry gives confidence intervals for these rates.

What does a confidence interval communicate?

General explanation: A confidence interval gives a range of values compatible with the estimate under the analysis procedure. A narrower interval generally indicates greater precision, while a wider interval indicates more uncertainty. It is not a guarantee that the true value lies inside a particular calculated interval, and the interpretation depends on the method and assumptions used. Confidence intervals should be read with the point estimate and the outcome scale, rather than as a stand-alone judgment.

For a hazard ratio, the value 1 represents equal relative event rates. An interval spanning 1 is compatible with a range that includes no relative difference under the usual interpretation; an interval not spanning 1 indicates that this particular interval excludes that null value. This general description does not replace the sponsor's analysis or account for any unreported multiplicity procedure. For medians and rates, the null value and scale differ from those for a hazard ratio.

What do the recalculated statistics represent?

Some posted binary-outcome comparisons include unadjusted recalculations based on summary statistics. General explanation: Such calculations use aggregate counts or estimates and do not reproduce a participant-level analysis with covariate adjustment, censoring details, or a full trial analysis model. They are useful for describing a simple comparison, but they may not match a sponsor analysis that uses a different method. The record does not list sponsor-reported analyses for the posted 9-month and 12-month rate comparisons.

For the time-to-event outcomes, the registry includes sponsor-reported hazard ratios and Log Rank comparisons. Those are the appropriate posted comparisons to cite for those endpoints. The simple sample-size illustrations use observed effect estimates and stated planning assumptions; they do not establish the power achieved in the completed trial. The original trial design assumptions are not reported in the registry record.

11. Confidence Intervals and Precision

The primary arm-specific median estimates have 95% confidence intervals of 11.1 to 14.0 months for the durvalumab combination and 10.1 to 12.5 months for the placebo combination. The intervals overlap. Overlap between two separate arm-specific intervals is not itself a formal test of the between-group comparison; the sponsor-reported hazard ratio and its interval address that comparison using the registered Log Rank analysis.

The reported primary hazard ratio is 0.80, with an interval from 0.64 to 0.99. The registry's sponsor analysis labels this as a 97% confidence interval. Its upper limit is close to 1, so the estimate is compatible with a range of relative effects that includes values close to no difference, while excluding 1 under that reported interval. The interval also includes values farther below 1, reflecting uncertainty in the magnitude of the relative comparison.

Confidence intervals for the secondary time-to-event and fixed-time outcomes also convey uncertainty. For rates, the intervals describe uncertainty in the estimated rate at the stated follow-up point; they are not interchangeable with the interval for a risk difference or the hazard ratio. The secondary binary comparisons include unadjusted recalculated estimates, so their intervals should be understood as describing those particular calculations, not as a substitute for a sponsor-reported analysis.

General explanation: Precision depends on the amount and distribution of information, including observed events, follow-up, censoring, and the analysis method. A point estimate alone does not show how much uncertainty surrounds it. Conversely, an interval does not convey clinical importance by itself. The registry record does not report all details needed to independently assess the assumptions behind every interval or the degree of missing follow-up.

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 effect0.80631845
75% of the observed effect0.851,1211,501
50% of the observed effect0.892,5233,377
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect5001,0002,0005,00010,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: events required (total))
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 + Gemcitabine + Cisplatin vs Placebo + Gemcitabine + Cisplatin.

The planning figures are illustrations based on observed effects, not the trial's original design justification. For time-to-event endpoints, the values are total events required across the comparison, not participants per arm. For the other outcomes, the values are participants per arm. For example, planning around 100% of the observed overall-survival effect gives 631 total events for 80% power; the 9-month progression-free survival rate illustration at the same stated effect fraction gives 316 participants per arm for 80% power. These are different endpoints and different units.

The stated assumptions 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 time-to-event calculations use the Schoenfeld method for total events. The original design assumptions for TOPAZ-1 are not reported in the registry record.

The 80% power column represents the planning size associated with an 80% chance of detecting the specified effect under the stated assumptions if that effect is real. The 90% power column applies a higher target probability of detection under the same general planning framework. These are design probabilities, not probabilities that a particular observed result is correct. A smaller target effect is harder to distinguish from random variation, so the planning figures increase as the assumed effect is reduced from 100% to 75% to 50% of the observed effect.

A plotted planning curve should be read as a visual display of this relationship between the effect size chosen for planning and the required events or participants. The displayed values are planning illustrations, not observed enrollment targets or a retrospective measure of the trial's achieved power. This is not observed power.

13. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z1−α/2 = 1.960) and the desired power (z1−β = 0.842 for 80% and 1.282 for 90%).

Formula

d = 4 (z1−α/2 + z1−β)2 / [ln(HR)]2

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

Worked calculation for this trial

  1. Hazard ratio HR = 0.800, so ln(HR) = -0.2231.
  2. d = 4 × (1.96 + 0.842)2 / [ln(0.800)]2 = 630.5, rounded up to 631 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 <- 0.8                              # 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(3875235)
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 = 631 (80% power), 845 (90% power)
 75% of observed effect: events = 1,121 (80% power), 1,501 (90% power)
 50% of observed effect: events = 2,523 (80% power), 3,377 (90% power)
Simulated power with 631 events: 0.791 (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 1,068 participants in total, with the boundaries below.

AnalysisCalendar time (months)EventsEfficacy boundary (z)Nominal one-sided pCumulative alpha spent
Look 118.42843.7100.00010.0001
Look 229.15682.5110.00600.0060
Look 360.08531.9930.02310.0250
01234z = 3.7118 mo284 eventsz = 2.5129 mo568 eventsz = 1.9960 mo853 eventsUpper efficacy boundary (z)

Fixed design versus group-sequential alternatives

DesignPowerEvents at final analysisParticipantsStudy length (months)
Fixed design, one analysis80%62978860.0
Two looks, O'Brien-Fleming80%63279160.0
Three looks, O'Brien-Fleming80%63779860.0
Three looks, Pocock80%73692260.0
Fixed design, one analysis90%8431,05560.0
Two looks, O'Brien-Fleming90%8461,05960.0
Three looks, O'Brien-Fleming90%8531,06860.0
Three looks, Pocock90%9731,21860.0

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 effect0.8008531,068
75% of the observed effect0.8461,5171,883
50% of the observed effect0.8943,4154,203

For context, this trial enrolled 810 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 <- 11.5          # control-arm median, months (converted from the posted unit)
hr          <- 0.8          # 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: 818        p (1-sided)   0.0001
 Events: 285       ~HR at bound   0.6439
   Month: 18   P(Cross) if HR=1   0.0001
             P(Cross) if HR=0.8   0.0338
   IA 2: 67%                  Z   2.5114
     N: 1068        p (1-sided)   0.0060
 Events: 569       ~HR at bound   0.8100
   Month: 29   P(Cross) if HR=1   0.0060
             P(Cross) if HR=0.8   0.5603
       Final                  Z   1.9930
     N: 1068        p (1-sided)   0.0231
 Events: 853       ~HR at bound   0.8724
   Month: 60   P(Cross) if HR=1   0.0250
             P(Cross) if HR=0.8   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) 0.800.64 to 0.990.021

For overall survival, the sponsor's own reported analysis is the Log Rank comparison with hazard ratio 0.80, interval 0.64 to 0.99, and p = 0.021. The sponsor identifies the interval as 97%. The posted arm-specific medians and their 95% confidence intervals describe the survival distributions, but they are not a recalculation of the sponsor's hazard-ratio analysis.

For progression-free survival, the registry also lists a sponsor-reported Log Rank hazard ratio of 0.75, with an interval from 0.63 to 0.89 and p = 0.001. The simple unadjusted calculations for fixed-time rates are separate from these sponsor analyses. The registry record does not list sponsor-reported comparisons for the 9-month and 12-month rate outcomes.

When sponsor-reported and recalculated statistics are available for the same analysis, the sponsor's own analysis takes precedence. Recalculations from posted summary statistics can be informative as a basic, unadjusted check, but they may use a different statistical approach and do not reproduce participant-level methods. The registry reports no discrepancy for the primary comparison. The absence of a reported sponsor analysis for a particular rate comparison should not be filled by treating an unadjusted calculation as the sponsor's prespecified result.

16. Multiplicity, Missing Data and Analysis Populations

The registry identifies overall survival as the primary outcome and lists multiple secondary outcomes, including progression-free survival, response, duration of response, and disease control. It also records 14 outcome measures and 3 analyses. The registry entries described in the registry record do not report a complete testing hierarchy, a family-wise error control procedure, or another multiplicity strategy for the secondary endpoints.

Multiplicity matters because repeated statistical tests can raise the probability of obtaining at least one apparently notable result when no true effect exists for any of the tested outcomes. General explanation: an analysis plan can address this through prespecified ordering, adjusted significance thresholds, or other methods. No such approach should be assumed when it is not described. The unadjusted recalculated p-values for the fixed-time secondary outcomes therefore do not carry the same weight as a result from a documented multiplicity-controlled plan.

The registry record states that the primary overall-survival analysis used the full analysis set. It describes censoring for participants not known to have died at the time of analysis, based on the last recorded date they were known alive. These details clarify the stated handling of the primary time-to-event outcome, but the record does not give a full account of missing data, withdrawal, loss to follow-up, or sensitivity analyses. The progression-free survival assessment schedule is described, but detailed missing-assessment rules are not reported in the registry record.

The second interim analysis was pre-specified after approximately 397 overall-survival events in both arms, or 59% maturity. The registry record does not report further details about interim monitoring, stopping boundaries, or adjustments to the statistical threshold across analyses. It would therefore be inappropriate to infer those procedures from the fact that an interim analysis was planned.

The available record also does not report the original sample-size justification or the trial's complete statistical analysis plan. These omissions limit independent assessment of how the final analyses relate to every original design decision. They do not change the interpretation of the statistics that are explicitly posted, but they constrain claims about unreported methods.

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 + Gemcitabine + Cisplatin16833849.7%
Placebo + Gemcitabine + Cisplatin15234244.4%
Participants with at least one serious adverse event
Serious adverse events by armDurvalumab + Gemcitabine + Ci…49.7%Placebo + Gemcitabine + Cispl…44.4%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
Durvalumab + Gemcitabine + Cisplatin308 of 341
Placebo + Gemcitabine + Cisplatin326 of 344

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 5% reporting threshold.

ArmParticipants affected of at risk
Durvalumab + Gemcitabine + Cisplatin326 of 338
Placebo + Gemcitabine + Cisplatin330 of 342

Most frequent serious adverse event terms

Event termOrgan systemDurvalumab + Gemcitabine + CisplatinPlacebo + Gemcitabine + Cisplatin
CholangitisHepatobiliary disorders25 of 33817 of 342
PyrexiaGeneral disorders15 of 3388 of 342
SepsisInfections and infestations12 of 3389 of 342
AnaemiaBlood and lymphatic system disorders12 of 3384 of 342
PneumoniaInfections and infestations7 of 3388 of 342
Biliary obstructionHepatobiliary disorders8 of 3387 of 342
Acute kidney injuryRenal and urinary disorders8 of 3385 of 342
Biliary tract infectionInfections and infestations6 of 3387 of 342
Pulmonary embolismRespiratory, thoracic and mediastinal disorders6 of 3384 of 342
AscitesGastrointestinal disorders4 of 3386 of 342

Most frequent non-serious adverse event terms

Event termOrgan systemDurvalumab + Gemcitabine + CisplatinPlacebo + Gemcitabine + Cisplatin
AnaemiaBlood and lymphatic system disorders159 of 338150 of 342
NauseaGastrointestinal disorders139 of 338124 of 342
ConstipationGastrointestinal disorders110 of 338101 of 342
NeutropeniaBlood and lymphatic system disorders106 of 338101 of 342
Neutrophil count decreasedInvestigations89 of 338105 of 342
FatigueGeneral disorders90 of 33886 of 342
Decreased appetiteMetabolism and nutrition disorders86 of 33881 of 342
Platelet count decreasedInvestigations68 of 33878 of 342
VomitingGastrointestinal disorders61 of 33859 of 342
PyrexiaGeneral disorders62 of 33852 of 342

Serious events with the highest arm-level rate: cholangitis (7.4%), pyrexia (4.4%), sepsis (3.6%), anaemia (3.6%), acute kidney injury (2.4%).

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 serious adverse event figures use 338 participants at risk in the durvalumab combination group and 342 at risk in the placebo combination group. Serious adverse events affected 168 participants in the durvalumab group and 152 in the placebo group. Other adverse events affected 326 of 338 and 330 of 342, respectively. The recorded deaths are 308 and 326. These are separate registry counts and should not be treated as interchangeable endpoints.

The most frequently listed serious adverse event terms include cholangitis at 7.4%, pyrexia at 4.4%, sepsis at 3.6%, anaemia at 3.6%, acute kidney injury at 2.4%, and biliary obstruction at 2.4%. These figures describe terms recorded as serious adverse events; they do not show the cause, timing, duration, or relationship to treatment for every event. The record does not provide a detailed account of event attribution or exposure-adjusted rates in the registry record.

Group counts should be interpreted with their respective at-risk denominators and with attention to the registry's event definitions. The counts alone do not establish whether a difference is statistically meaningful or due to the assigned treatment. The registry data also do not support conclusions about the comparative severity of every adverse event or the cause of recorded deaths.

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

The registry reports a primary overall-survival comparison from a randomized, quadruple-masked trial of durvalumab plus gemcitabine and cisplatin versus placebo plus gemcitabine and cisplatin. The posted median estimates and sponsor-reported hazard ratio indicate a difference in the observed overall-survival distributions between the randomized groups, with the hazard-ratio estimate below 1. The reported interval and p-value describe the precision and statistical evidence for that comparison under the sponsor's analysis.

This result does not mean that every participant experienced the same survival time, or that the hazard ratio is a direct change in median survival. The median is a summary of an estimated time-to-event distribution, while the hazard ratio compares event rates over follow-up. Censoring and the event maturity at the analysis affect how much information the data contain. The registry notes a planned second interim analysis at approximately 397 events and 59% maturity, but does not provide the full interim-analysis plan.

The finding also does not resolve every question about progression, response, quality of life, long-term outcomes, or specific participant subgroups. The registry lists several secondary outcomes, but not all their results are included in the registry record. Secondary unadjusted comparisons warrant caution because the multiplicity strategy is not reported. Safety counts offer a description of recorded events, not proof of the cause or treatment relationship of each event.

These statistics describe the trial population and the analysis recorded for TOPAZ-1. They should not be extended automatically to populations or treatment settings not characterized in the registry record. The registry entries do not report enough detail to assess all eligibility criteria, follow-up patterns, analysis sensitivities, or later outcomes.

19. Why This Trial Matters Statistically

Statistically, TOPAZ-1 illustrates why randomized comparisons should be interpreted through both the effect estimate and its uncertainty. The primary outcome is time to death from any cause, and the sponsor's hazard ratio summarizes a between-group comparison over follow-up. The arm-specific medians are useful summaries, but they answer a different question from the hazard ratio and should not be substituted for it.

The record also illustrates the role of event maturity in survival analysis. The second interim analysis was pre-specified after approximately 397 overall-survival events in both arms, corresponding to 59% maturity. In time-to-event studies, the accumulation of events is central to the information available for estimating comparative effects; enrollment alone does not describe that information fully.

Another statistical issue is the distinction between confirmatory and secondary evidence. The primary endpoint has a sponsor-reported comparison, while some fixed-time secondary estimates are unadjusted recalculations and no sponsor comparison is listed for those rates. Since the multiplicity plan is not reported, the secondary results deserve more cautious interpretation than the primary analysis.

Finally, the planning illustrations make clear that sample-size requirements depend on the effect size selected for planning and on stated assumptions. They are not the original design justification, and they do not measure the power observed after the trial. Separating planning calculations from the sponsor's completed analysis helps avoid treating retrospective illustrations as evidence about how the original trial was designed or powered.

20. Limitations

The registry record gives the primary endpoint definition, the Kaplan-Meier approach, the censoring rule for participants not known to have died, and the stated analysis population. It does not report the complete statistical analysis plan, original sample-size justification, multiplicity strategy, or details of interim monitoring beyond the planned second interim analysis after approximately 397 events and 59% maturity. These omissions limit independent evaluation of whether every analysis followed the original plan.

The primary assessment period extends to a maximum of approximately 27 months from randomization to the primary analysis cut-off. The registry entries do not provide longer-term follow-up results or details sufficient to assess the completeness of follow-up. The outcome-group sample sizes differ from the overall enrollment figure, but the record details do not explain the participant flow between enrollment and the posted primary analysis groups.

The secondary outcomes include fixed-time rates estimated by Kaplan-Meier and other response-related measures, yet results are not reported for every listed measure. The sponsor does not list a reported analysis for the posted 9-month and 12-month rate comparisons in the registry record; the available comparisons are unadjusted recalculations. A complete interpretation of all secondary evidence is therefore not possible from these results alone.

The safety figures give counts and selected serious adverse event terms, but do not detail event attribution, exposure time, timing, or participant-level overlap among event categories. The registry record also does not provide further population characteristics in the registry record. These limits matter when considering how the estimates may relate to particular patient groups or when comparing event frequencies across groups.

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

TOPAZ-1 is a Phase III randomized, parallel-group, quadruple-masked study in first-line advanced biliary tract cancer. It compares durvalumab plus gemcitabine and cisplatin with placebo plus gemcitabine and cisplatin. The registry lists 810 enrolled participants, AstraZeneca as sponsor, a start date of 2019-04-16, a primary completion date of 2021-08-11, and a status of active, not recruiting.

The primary outcome is overall survival in the full analysis set, defined from randomization until death from any cause, with Kaplan-Meier estimation and censoring at the last recorded date known alive for participants not known to have died. Median overall survival is 12.8 months in the durvalumab combination group and 11.5 months in the placebo combination group. The sponsor-reported hazard ratio is 0.80, with an interval from 0.64 to 0.99 and p = 0.021.

The registry also lists progression-free survival and response-related secondary outcomes. The original sample-size justification, multiplicity strategy, and complete analysis plan are not reported in the registry record.

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