This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.
1. Trial at a Glance
This page covers the registry results for Study of Durvalumab and Tremelimumab as First-line Treatment in Patients With Advanced Hepatocellular Carcinoma (NCT03298451), a randomized phase 3 study. The primary outcome is Overall Survival (OS) - Treme 300 mg x1 Dose + Durva 1500 mg vs Sora 400 mg.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT03298451 |
| Phase | Phase 3 |
| Condition | Hepatocellular Carcinoma |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | None (open label) |
| Enrollment | 1324 |
| Arms in the primary outcome | 4 |
| Lead sponsor | AstraZeneca |
| Results posted | Yes |
2. Clinical Question
Population
Patients with unresectable hepatocellular carcinoma who had received no prior systemic therapy and were not eligible for locoregional therapy. The primary analysis population was the Full Analysis Set, defined as all randomized participants.
Intervention
The primary comparison concerns tremelimumab 300 mg as a single dose plus durvalumab 1500 mg. The study also included durvalumab alone and a regimen of tremelimumab 75 mg for four doses plus durvalumab 1500 mg.
Comparator
Sorafenib 400 mg was the comparator for the primary overall-survival analysis.
Primary question
How did overall survival from randomization compare between the single-dose tremelimumab plus durvalumab regimen and sorafenib, through the final analysis data cut-off?
This was a comparison among randomized treatment groups in a Phase III study. Overall survival is a time-to-event outcome: it tracks the time from randomization until death from any cause. The registry defines the primary endpoint without restricting the analysis to participants who stayed on randomized treatment or avoided subsequent anticancer therapy. That definition matters because it describes the outcome after assignment, rather than only outcomes while participants were receiving the assigned regimen.
The primary result is one part of a larger study question. The registry also lists a comparison of durvalumab alone with sorafenib, another tremelimumab plus durvalumab regimen, and outcomes including progression-free survival, response, and time to progression. The primary question addressed is narrower: the registry's designated overall-survival comparison of tremelimumab 300 mg as a single dose plus durvalumab against sorafenib. Results from other arms or outcomes should not be treated as though they were the same comparison.
3. Trial Design
The registry describes a randomized, open-label, multicenter, global, parallel-group Phase III study. Its stated enrollment is 1324. The study began on 2017-10-11, and primary completion is recorded as 2021-08-27. The registry status is active, not recruiting. The overall-survival analysis uses a data cut-off of 27Aug2021, with follow-up assessed to a maximum of approximately 46 months.
Four treatment groups are described: durvalumab 1500 mg; tremelimumab 300 mg as a single dose plus durvalumab 1500 mg; tremelimumab 75 mg for four doses plus durvalumab 1500 mg; and sorafenib 400 mg. The primary outcome title compares the single-dose combination with sorafenib. The registry also identifies a durvalumab-alone comparison with sorafenib as a secondary outcome. The primary analysis reports group sizes of 393 for the single-dose combination and 389 for sorafenib; the durvalumab-alone group is also reported with 389 participants. The four-dose combination group is reported with 153 participants in the primary outcome results.
The Full Analysis Set is defined as all participants randomized. The record notes that the tremelimumab 75 mg plus durvalumab arm was closed during the study, but does not report the reason for closure. Allocation was randomized and masking was none, so the study was open-label. The registry record does not report further details of the allocation procedure, treatment adherence, or the original sample-size justification. The planning illustrations associated with the posted outcomes are not the trial's original design assumptions.
The primary outcome is overall survival from randomization until death from any cause, with censoring for participants not known to have died by the cut-off. The record describes censoring at the last known date alive, or at the data cut-off when the last known alive date or death date was after the cut-off. This definition and the stated analysis population provide context for interpreting the reported time-to-event estimates.
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: Of 1,950 participants screened in the study, 1,324 were randomized across 4 arms, out of which 1,302 participants received treatment.
Overall Study
| Stage | Durva 1500 mg | Treme 300 mg x1 Dose + Durva 1500 mg | Treme 75 mg x4 Doses + Durva 1500 mg | Sora 400 mg |
|---|---|---|---|---|
| STARTED | 389 | 393 | 153 | 389 |
| Received Treatment | 386 | 389 | 153 | 374 |
| COMPLETED | 104 | 125 | 30 | 82 |
| NOT COMPLETED | 285 | 268 | 123 | 307 |
Reasons for not completing this period:
| Reason | Durva 1500 mg | Treme 300 mg x1 Dose + Durva 1500 mg | Treme 75 mg x4 Doses + Durva 1500 mg | Sora 400 mg |
|---|---|---|---|---|
| Death | 275 | 260 | 122 | 280 |
| Lost to Follow-up | 1 | 1 | 0 | 7 |
| Withdrawal by Subject | 9 | 7 | 1 | 20 |
Analysis population for the primary outcome, as defined in the registry: The FAS included all participants who were randomized. T75+D arm was closed during study.
5. Baseline Characteristics
The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.
Population: The full analysis set (FAS) included all participants who were randomized.
| Characteristic | Unit | Durva 1500 mg | Treme 300 mg x1 Dose + Durva 1500 mg | Treme 75 mg x4 Doses + Durva 1500 mg | Sora 400 mg | Total |
|---|---|---|---|---|---|---|
| Participants analysed | 389 | 393 | 153 | 389 | 1324 | |
| Age, Continuous | years | 62.6 (SD 11.47) | 63.0 (SD 11.65) | 63.4 (SD 12.03) | 63.5 (SD 11.12) | 63.1 (SD 11.48) |
| Age, Customized: <65 | Participants | 203 | 195 | 74 | 195 | 667 |
| Age, Customized: >=65-<75 | Participants | 130 | 145 | 55 | 137 | 467 |
| Age, Customized: >=75 | Participants | 56 | 53 | 24 | 57 | 190 |
| Sex: Female, Male: Female | Participants | 66 | 66 | 32 | 52 | 216 |
| Sex: Female, Male: Male | Participants | 323 | 327 | 121 | 337 | 1108 |
| Race/Ethnicity, Customized: White | Participants | 160 | 182 | 70 | 179 | 591 |
| Race/Ethnicity, Customized: Black or African American | Participants | 2 | 7 | 4 | 10 | 23 |
| Race/Ethnicity, Customized: Asian | Participants | 212 | 195 | 75 | 189 | 671 |
| Race/Ethnicity, Customized: Native Hawaiian or other Pacific Islander | Participants | 0 | 1 | 0 | 0 | 1 |
| Race/Ethnicity, Customized: American Indian or Alaska Native | Participants | 0 | 0 | 0 | 0 | 0 |
| Race/Ethnicity, Customized: Other | Participants | 15 | 7 | 4 | 5 | 31 |
| Race/Ethnicity, Customized: Missing | Participants | 0 | 1 | 0 | 6 | 7 |
| Race/Ethnicity, Customized: Hispanic or Latino | Participants | 13 | 21 | 11 | 21 | 66 |
| Race/Ethnicity, Customized: Not Hispanic or Latino | Participants | 376 | 372 | 142 | 362 | 1252 |
| Race/Ethnicity, Customized: Missing | Participants | 0 | 0 | 0 | 6 | 6 |
| Region group: Asia (except Japan) | Participants | 167 | 156 | 60 | 156 | 539 |
| Region group: Rest of World (includes Japan) | Participants | 222 | 237 | 93 | 233 | 785 |
6. Primary Endpoint
The registry lists the primary outcome as Overall Survival (OS) - Treme 300 mg x1 Dose + Durva 1500 mg vs Sora 400 mg, measured over From the date of randomization until death due to any cause, assessed up to the data cut-off date (27Aug2021, to a maximum of approximately 46 months)..
| Element | Registry entry |
|---|---|
| Result type | Median |
| Measure of spread | 95% Confidence Interval |
| Unit | months |
| Endpoint classification | Time-to-Event Analysis |
Overall survival measures the time from randomization until death due to any cause. It is a time-to-event outcome, so the analysis uses both the timing of events and information from participants whose follow-up ends before death is observed. The registry says that a participant not known to have died by the data cut-off was censored at the last recorded date known alive. When the last known date alive or a death date fell after the cut-off, censoring was at the cut-off.
This endpoint is used to describe how long participants lived after randomization, regardless of whether they stopped randomized treatment or received another anticancer therapy. That feature makes the outcome distinct from measures tied to tumor shrinkage or progression, and it means the analysis concerns survival after assignment rather than survival only during treatment. The registry reports median overall survival for each group and a hazard ratio for the primary comparison.
In general, the median is the point in the estimated survival distribution at which half the population has experienced the event and half has not yet experienced it. A median does not describe every participant's course, nor does it by itself capture the full pattern of survival over follow-up. The hazard ratio provides a relative comparison over the observed time-to-event data under the model used. Both measures need their uncertainty intervals and analysis context to be interpreted; neither alone establishes why a difference arose or how it applies to an individual.
7. Results Posted in the Registry
- Treme 300 mg x1 Dose + Durva 1500 mg vs Sora 400 mg: hazard ratio 0.78 (95% CI 0.66–0.92) (as reported in the registry).
Hazard ratio: Treme 300 mg x1 Dose + Durva 1500 mg vs Sora 400 mg
95% CI: 0.66 to 0.92
As reported in the registry
8. Secondary Efficacy Endpoints
The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.
| Secondary outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Overall Survival (OS) - Durva 1500 mg vs Sora 400 mg | Time-to-Event Analysis | Hazard ratio | 0.86 (0.73 to 1.03) | 1,381 events |
| Objective Response Rate (ORR) | Binary Endpoint | Risk difference | +3.1 pts (-2.3 to 8.6) | 2,411 per arm |
Overall Survival (OS) - Durva 1500 mg vs Sora 400 mg
- Endpoint type: Time to event: compared as a hazard ratio.
- Test: Hazard ratio as reported by the sponsor (Regression, Cox); it was not recalculated.
- Result:
- Durva 1500 mg vs Sora 400 mg: hazard ratio 0.86 (95% CI 0.73–1.03) (as reported in the registry).
- Interpretation:
- The 95% confidence interval includes no difference (a ratio of 1), so these data do not show a statistically significant difference between Durva 1500 mg vs Sora 400 mg and the control. The interval gives the range of effects that remain compatible with the data.
Objective Response Rate (ORR)
- Endpoint type: Binary: the number of participants with the event, compared as proportions.
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Treme 300 mg x1 Dose + Durva 1500 mg: 20.1% (79/393) versus 17.0% (66/389) on control; risk difference 3.1 percentage points (95% CI -2.3 to 8.6), risk ratio 1.18 (0.88–1.59); unadjusted two-proportion z-test p = 0.259.
- Treme 75 mg x4 Doses + Durva 1500 mg: 17.0% (26/153) versus 17.0% (66/389) on control; risk difference 0.0 percentage points (95% CI -7.0 to 7.1), risk ratio 1.00 (0.66–1.51); unadjusted two-proportion z-test p = 0.994.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Treme 300 mg x1 Dose + Durva 1500 mg and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Treme 75 mg x4 Doses + Durva 1500 mg and the control. The interval gives the range of effects that remain compatible with the data.
The registry's secondary outcomes broaden the scope beyond the primary overall-survival comparison. They include a durvalumab-alone comparison with sorafenib, survival at specified follow-up times, progression-free survival, time to progression, objective response, disease control, duration of response, and survival by PD-L1. These outcomes address different questions and have different data structures, so they should be interpreted on their own terms rather than combined into a single claim.
The posted durvalumab-alone overall-survival analysis reports a Cox estimate and a log-rank test, but the confidence interval for the Cox estimate includes 1 and the log-rank p-value is 0.067. The registry also posts objective-response counts and unadjusted recalculations. Those results do not provide a complete, multiplicity-adjusted account of the full set of secondary outcomes. Results for the other listed endpoints are not reported in the registry record in the material available for this analysis.
Secondary outcomes can help describe whether patterns in survival, tumor response, and disease progression align, but alignment cannot be established from endpoint names alone. Different outcome definitions, follow-up, missingness, and statistical methods may lead to different estimates. The primary overall-survival result remains the designated primary comparison; secondary analyses provide context rather than independent confirmation of it.
Multiplicity is relevant because the more outcomes and comparisons examined, the more opportunity there is for a nominally notable result to occur by chance. Unadjusted secondary p-values or re-calculated estimates therefore carry less inferential weight than a prespecified primary analysis unless the analysis plan and multiplicity procedure support stronger claims. The registry record does not report the full multiplicity strategy, so the secondary findings should be treated as exploratory context rather than a definitive ranking of treatments across outcomes.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Overall Survival (OS) - Durva 1500 mg vs Sora 400 mg
- Overall Survival (OS) at 18, 24, and 36 Months After Randomization
- Progression Free Survival (PFS)
- Time To Progression (TTP)
- Objective Response Rate (ORR)
- Disease Control Rate (DCR)
- Duration of Objective Response (DoR)
- Overall Survival (OS) by PD-L1
9. Statistical Interpretation
For the primary comparison, the registry reports median overall survival of 16.43 months for tremelimumab 300 mg as a single dose plus durvalumab 1500 mg, with a 95% confidence interval of 14.16 to 19.58 months. For sorafenib 400 mg, the median is 13.77 months, with a 95% confidence interval of 12.25 to 16.13 months. The reported Cox hazard ratio is 0.78, with a 95% confidence interval of 0.66 to 0.92. The registry's log-rank analysis reports p = 0.004 and labels the comparison as a superiority analysis.
These are estimates from the registry's final-analysis data cut-off, not a guarantee that every participant was followed for the maximum stated period. The median values describe the estimated time-to-event distributions. The hazard ratio summarizes the relative event rate over follow-up in the Cox analysis; it is not a ratio of the medians and should not be read as a direct difference in months. Its interval lies below 1, while the log-rank result is reported as statistically significant under the analysis as recorded. These statistical features describe the posted comparison, not a treatment recommendation or a conclusion about an individual patient's outcome.
For context, the durvalumab-alone comparison with sorafenib is reported separately as a secondary overall-survival analysis. Its Cox hazard ratio is 0.86, with a 95% confidence interval of 0.73 to 1.03, and its log-rank p-value is 0.067. The registry identifies a non-inferiority analysis for the Cox result and a superiority analysis for the log-rank result. These analyses address a different treatment comparison and should not be substituted for the primary combination-versus-sorafenib result.
The registry also records response counts and lists other secondary outcomes, but the available results do not provide a complete inferential account for every listed endpoint. Secondary outcomes may help characterize the study, but their interpretation depends on their analysis methods, uncertainty, and the number of comparisons considered. A statistically notable result on one outcome does not establish a consistent pattern across all outcomes. The primary overall-survival result is most directly interpreted within its own defined population, endpoint, and comparison.
Overall, the posted primary analysis estimates longer median survival in the combination group and reports a hazard ratio below 1 with an interval that does not include 1. The result is accompanied by uncertainty and is bounded by the registry's follow-up and analysis details. It does not establish the size of benefit for every participant, explain the biological cause of the observed pattern, or resolve questions not addressed in the record, such as subgroup effects or comparative quality of life.
10. Statistical Methods Explained
What does a median survival estimate describe?
Overall survival is analyzed as a time-to-event outcome. Participants contribute information from randomization until death or censoring. Censoring occurs when the event has not been observed by the end of the available follow-up; it does not mean that the participant died at that time. The registry describes censoring at the last date known alive, with censoring at the data cut-off for dates after the cut-off. In general, survival methods use such information without treating a censored participant as though the event had occurred.
The median is a summary of the estimated survival distribution. In general, it is the time by which half of the population is estimated to have experienced the event. It compresses a survival curve into one value, so it does not show the distribution of individual survival times or the shape of the curve across follow-up. Confidence intervals around the median communicate uncertainty in that estimate.
What does the Cox hazard ratio summarize?
The primary comparison uses a Cox regression hazard ratio as reported by the sponsor. In general, a hazard is the instantaneous event rate among participants still at risk at a given time. A hazard ratio compares those rates between groups over follow-up, subject to the model's assumptions. It is not a comparison of median survival times, an estimate of the number of months gained, or a probability that a particular participant will experience an event. The registry reports a hazard ratio of 0.78 with a 95% confidence interval of 0.66 to 0.92 for the primary comparison.
The Cox model commonly relies on a proportional-hazards assumption: the relative hazards are treated as sufficiently stable over time for a single summary hazard ratio to be meaningful. The registry record does not report whether that assumption was assessed, how it was assessed, or what diagnostics were used. A single hazard ratio can be less descriptive if relative event patterns change over time, so survival curves and other time-specific summaries can add context when available.
Why is a log-rank test also reported?
In general, the log-rank test compares survival experience across groups using the observed timing of events and the risk sets over follow-up. It provides a test of evidence for a difference in survival distributions, while the Cox hazard ratio provides an estimated relative effect with an interval. They are related approaches but answer different statistical questions: one is a test statistic summarized by a p-value, and the other is an effect estimate with uncertainty. The primary log-rank p-value is 0.004. The registry does not report a p-value for the primary Cox estimate.
A p-value describes how compatible the observed data are with a specified null hypothesis under the test's assumptions. It is not the probability that the null hypothesis is true, nor a measure of the size or clinical importance of an effect. The effect estimate and confidence interval are therefore important alongside the reported test result.
What does a confidence interval add?
In general, a confidence interval conveys sampling uncertainty in an estimate under the analysis method. It gives a range of values compatible with the data and method at the stated confidence level. It does not guarantee that the true value lies inside the interval, and it does not account automatically for bias, incomplete reporting, model misspecification, or multiplicity. For a hazard ratio, an interval that includes 1 is compatible with no relative difference under the model, while an interval entirely on one side of 1 indicates that the interval excludes that null value. This is a statistical description, not a standalone measure of clinical relevance.
The primary median estimates also have confidence intervals: 14.16 to 19.58 months for the combination and 12.25 to 16.13 months for sorafenib. Their overlap or separation should not be used as a replacement for the reported between-group analysis. A comparison of two separately estimated medians is not the same test as the Cox or log-rank analysis.
How should other outcome types be understood?
The registry lists objective response rate as a count of participants with a response and includes unadjusted re-calculations for risk differences and related measures. In general, a risk difference expresses the difference between group response proportions, while a confidence interval describes uncertainty around that difference. Re-calculations from summary counts do not incorporate any adjustment unless specifically stated. No sponsor-reported objective-response analysis is listed in the record.
The registry also lists progression-free survival, time to progression, disease control, duration of response, and survival at specified follow-up times. These outcomes address different aspects of disease course. Statistical evidence across them should not be assumed to be independent, and they do not replace the primary endpoint. Details of the statistical methods for every secondary analysis are not reported in the registry record.
Finally, over-dispersion is a general issue for count outcomes when variability exceeds what a simple model assumes; ignoring it can make uncertainty estimates too narrow. The registry's primary outcome is time-to-event rather than a count outcome, and the record does not indicate that over-dispersion is part of the primary model. This general concept should not be taken as a description of a method used in this analysis.
11. Confidence Intervals and Precision
The primary Cox estimate is a hazard ratio of 0.78, with a 95% confidence interval from 0.66 to 0.92. The interval is the main numerical description of precision for that relative estimate: it indicates that the point estimate is not exact and that a range of values remains compatible with the analysis. Because the interval lies below 1, it excludes the null hazard ratio of 1 under the reported model and interval method. It does not describe uncertainty from unreported sources such as model violations or incomplete registry detail.
The median overall-survival estimates also have 95% confidence intervals. The combination group's interval is 14.16 to 19.58 months, and the sorafenib group's interval is 12.25 to 16.13 months. These intervals express uncertainty in each group's median estimate. They are not a confidence interval for the difference between medians, and comparing their endpoints is not a substitute for the reported between-group analysis.
Precision is affected by the amount and timing of observed follow-up and events, as well as by the statistical method. The registry's analysis window ends at the stated data cut-off, and participants without observed death by that point are censored according to the record's rules. The record does not report additional diagnostics or sensitivity analyses that would show how robust the estimates are to alternative assumptions.
For the separate durvalumab-alone comparison, the reported Cox hazard ratio is 0.86 with a 95% confidence interval of 0.73 to 1.03. This interval includes 1, so it does not exclude the null value at the stated confidence level. Its interpretation remains specific to that secondary comparison and its reported analysis. Confidence intervals describe statistical precision, not the certainty that a result will recur in another study or its importance for clinical decisions.
12. Planning a Similar Trial: Sample Size
This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.
| Effect to detect (log scale) | Hazard ratio | Events, 80% power | Events, 90% power |
|---|---|---|---|
| 100% of the observed effect | 0.78 | 509 | 681 |
| 75% of the observed effect | 0.83 | 905 | 1,211 |
| 50% of the observed effect | 0.88 | 2,035 | 2,724 |
The planning illustrations translate an observed effect into hypothetical future-study size requirements under stated assumptions. For the primary time-to-event comparison, the figures are total events, not participants per arm. For binary outcomes, the figures are participants per arm. The primary overall-survival illustrations list total events for 80% and 90% power at 100%, 75%, and 50% of the observed effect. The objective-response illustrations use participants per arm and present the same effect fractions.
The calculations use a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. For time-to-event outcomes, the method is identified as Schoenfeld, and the planning target is a total number of events. The effect to detect is the stated fraction of the observed effect. The trial's own original sample-size assumptions and justification are not reported in the registry record, so these planning illustrations should not be mistaken for the design rationale used when this study was planned.
The 80% power column describes the hypothetical number of events or participants per arm needed, under those assumptions, for an 80% chance of detecting the specified effect if it were present. The 90% power column describes the corresponding planning target for a 90% chance. These are design probabilities under a model, not probabilities that the treatment effect is true. Smaller effects require more participants or events to detect with the same planned power, which is why the listed requirements grow as the assumed fraction of the observed effect decreases.
These figures are not observed power. They are planning illustrations derived from the observed effect and specified calculation assumptions; they do not measure the probability that the completed study's finding is correct. Very large values in an illustration for a small observed binary difference also should not be read as a forecast of an actual trial's feasibility. Their role is to show how sensitive planning requirements can be to the effect size selected.
13. How the Sample Size Is Derived
Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z1−α/2 = 1.960) and the desired power (z1−β = 0.842 for 80% and 1.282 for 90%).
Formula
d is the total number of events needed (Schoenfeld's formula) with 1:1 allocation and proportional hazards.
Worked calculation for this trial
- Hazard ratio HR = 0.780, so ln(HR) = -0.2485.
- d = 4 × (1.96 + 0.842)2 / [ln(0.780)]2 = 508.6, rounded up to 509 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 <- 0.78 # 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(3298451)
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 = 509 (80% power), 681 (90% power)
75% of observed effect: events = 905 (80% power), 1,211 (90% power)
50% of observed effect: events = 2,035 (80% power), 2,724 (90% power)
Simulated power with 509 events: 0.802 (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 916 participants in total, with the boundaries below.
| Analysis | Calendar time (months) | Events | Efficacy boundary (z) | Nominal one-sided p | Cumulative alpha spent |
|---|---|---|---|---|---|
| Look 1 | 19.3 | 229 | 3.710 | 0.0001 | 0.0001 |
| Look 2 | 30.7 | 458 | 2.511 | 0.0060 | 0.0060 |
| Look 3 | 60.0 | 688 | 1.993 | 0.0231 | 0.0250 |
Fixed design versus group-sequential alternatives
| Design | Power | Events at final analysis | Participants | Study length (months) |
|---|---|---|---|---|
| Fixed design, one analysis | 80% | 507 | 676 | 60.0 |
| Two looks, O'Brien-Fleming | 80% | 509 | 679 | 60.0 |
| Three looks, O'Brien-Fleming | 80% | 514 | 685 | 60.0 |
| Three looks, Pocock | 80% | 594 | 791 | 60.0 |
| Fixed design, one analysis | 90% | 679 | 905 | 60.0 |
| Two looks, O'Brien-Fleming | 90% | 682 | 909 | 60.0 |
| Three looks, O'Brien-Fleming | 90% | 688 | 916 | 60.0 |
| Three looks, Pocock | 90% | 784 | 1,045 | 60.0 |
Group-sequential designs cost a small increase in maximum sample size and events compared with the fixed design, in exchange for the chance to stop early for overwhelming efficacy. O'Brien-Fleming spending keeps early boundaries very conservative and the final boundary close to the fixed-design value, whereas Pocock spending spends more alpha early.
Sensitivity to a smaller true effect
Planning for exactly the observed effect is optimistic, because observed effects in published trials tend to be somewhat larger than the true effect. The table repeats the main design (three looks, O'Brien-Fleming spending, 90% power) for smaller true hazard ratios.
| True effect assumed | Hazard ratio | Events at final analysis | Participants |
|---|---|---|---|
| 100% of the observed effect | 0.780 | 688 | 916 |
| 75% of the observed effect | 0.830 | 1,223 | 1,611 |
| 50% of the observed effect | 0.883 | 2,754 | 3,586 |
For context, this trial enrolled 1,324 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 <- 13.77 # control-arm median, months (converted from the posted unit)
hr <- 0.78 # 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: 736 p (1-sided) 0.0001
Events: 230 ~HR at bound 0.6125
Month: 19 P(Cross) if HR=1 0.0001
P(Cross) if HR=0.78 0.0338
IA 2: 67% Z 2.5114
N: 916 p (1-sided) 0.0060
Events: 459 ~HR at bound 0.7909
Month: 31 P(Cross) if HR=1 0.0060
P(Cross) if HR=0.78 0.5603
Final Z 1.9930
N: 916 p (1-sided) 0.0231
Events: 688 ~HR at bound 0.8590
Month: 60 P(Cross) if HR=1 0.0250
P(Cross) if HR=0.78 0.9000
Cross-check, upper boundaries: gsDesign 3.71, 2.511, 1.993 | rpact 3.71, 2.511, 1.993
15. Analyses Reported by the Sponsor
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| Log Rank | not reported | 0.004 | |
| Regression, Cox | Hazard Ratio (HR) 0.78 | 0.66 to 0.92 | not reported |
The primary overall-survival result includes sponsor-reported analyses: a log-rank p-value of 0.004 and a Cox hazard ratio of 0.78 with a 95% confidence interval of 0.66 to 0.92. The registry labels the comparison as a superiority analysis. These sponsor analyses are the principal inferential results for the primary comparison, and the posted record does not indicate a discrepancy between them and a recalculation.
The Cox estimate is particularly useful as a relative effect summary, while the log-rank p-value gives a test result for the survival comparison. Neither should be detached from the endpoint definition, analysis population, censoring rules, and follow-up cut-off. The medians describe each group's estimated survival distribution, but the sponsor's reported hazard ratio and log-rank test address the comparison between groups.
Other calculations in the posted results, including unadjusted summaries for the response outcome, are not substitutes for sponsor-reported analyses. The registry lists no sponsor-reported objective-response analysis. Where an independently recalculated result differs from a sponsor analysis, the sponsor's own analysis takes precedence; no such discrepancy is flagged for the primary outcome. The record does not provide enough detail to independently reconstruct the full Cox model, including its covariates or diagnostic procedures.
16. Multiplicity, Missing Data and Analysis Populations
The registry identifies a primary overall-survival comparison and lists numerous secondary outcomes, but the multiplicity strategy for interpreting all these tests is not reported in the registry record. It is therefore not possible to determine from the record whether the secondary analyses were adjusted to control the chance of false-positive findings across multiple comparisons, or whether a hierarchical testing procedure was used. A nominal p-value from an individual secondary analysis should not be interpreted as though it were the only test conducted.
The primary outcome description defines the Full Analysis Set as all randomized participants. That gives a clear population definition for the primary analysis, but the record does not report detailed handling of missing covariates, incomplete outcome information, or sensitivity analyses for missingness. For overall survival, the stated censoring rules address participants not known to have died by the cut-off. Censoring is a standard way to use incomplete follow-up in time-to-event analysis, but it relies on assumptions about the relationship between censoring and the chance of the event. The record does not report diagnostics or analyses of those assumptions.
The registry states that the tremelimumab 75 mg plus durvalumab arm was closed during the study; the reason and implications for the planned analyses are not reported in the registry record. The record also does not provide the original sample-size justification, interim-analysis details, or the complete statistical analysis plan. These omissions limit assessment of whether all analyses followed prespecified procedures and how the study managed multiplicity, missing data, and changes over time.
Open-label allocation is another design feature relevant to outcomes that may depend on clinical assessment or participant and investigator decisions. Overall survival is an objective event, though follow-up and censoring still require operational choices. The registry does not describe additional procedures intended to reduce assessment or follow-up bias. These limitations do not invalidate the posted estimates, but they define what can and cannot be evaluated from the registry record.
17. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Durva 1500 mg | 115 | 388 | 29.6% |
| Treme 300 mg x1 Dose + Durva 1500 mg | 157 | 388 | 40.5% |
| Treme 75 mg x4 Doses + Durva 1500 mg | 52 | 152 | 34.2% |
| Sora 400 mg | 111 | 374 | 29.7% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Durva 1500 mg | 280 of 389 |
| Treme 300 mg x1 Dose + Durva 1500 mg | 262 of 393 |
| Treme 75 mg x4 Doses + Durva 1500 mg | 123 of 153 |
| Sora 400 mg | 293 of 389 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 5% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Durva 1500 mg | 299 of 388 |
| Treme 300 mg x1 Dose + Durva 1500 mg | 334 of 388 |
| Treme 75 mg x4 Doses + Durva 1500 mg | 133 of 152 |
| Sora 400 mg | 333 of 374 |
Most frequent serious adverse event terms
| Event term | Organ system | Durva 1500 mg | Treme 300 mg x1 Dose + Durva 1500 mg | Treme 75 mg x4 Doses + Durva 1500 mg | Sora 400 mg |
|---|---|---|---|---|---|
| Pneumonia | Infections and infestations | 3 of 388 | 7 of 388 | 6 of 152 | 8 of 374 |
| Death | General disorders | 8 of 388 | 4 of 388 | 5 of 152 | 5 of 374 |
| Diarrhoea | Gastrointestinal disorders | 2 of 388 | 9 of 388 | 4 of 152 | 6 of 374 |
| Gastrointestinal haemorrhage | Gastrointestinal disorders | 5 of 388 | 7 of 388 | 0 of 152 | 3 of 374 |
| Sepsis | Infections and infestations | 4 of 388 | 8 of 388 | 2 of 152 | 0 of 374 |
| Hepatic failure | Hepatobiliary disorders | 3 of 388 | 3 of 388 | 2 of 152 | 5 of 374 |
| Abdominal pain | Gastrointestinal disorders | 2 of 388 | 2 of 388 | 2 of 152 | 6 of 374 |
| Upper gastrointestinal haemorrhage | Gastrointestinal disorders | 1 of 388 | 7 of 388 | 0 of 152 | 4 of 374 |
| Pyrexia | General disorders | 6 of 388 | 4 of 388 | 0 of 152 | 2 of 374 |
| Anaemia | Blood and lymphatic system disorders | 1 of 388 | 5 of 388 | 3 of 152 | 2 of 374 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Durva 1500 mg | Treme 300 mg x1 Dose + Durva 1500 mg | Treme 75 mg x4 Doses + Durva 1500 mg | Sora 400 mg |
|---|---|---|---|---|---|
| Diarrhoea | Gastrointestinal disorders | 57 of 388 | 97 of 388 | 28 of 152 | 164 of 374 |
| Decreased appetite | Metabolism and nutrition disorders | 53 of 388 | 65 of 388 | 24 of 152 | 67 of 374 |
| Rash | Skin and subcutaneous tissue disorders | 39 of 388 | 84 of 388 | 27 of 152 | 50 of 374 |
| Fatigue | General disorders | 37 of 388 | 65 of 388 | 25 of 152 | 70 of 374 |
| Pruritus | Skin and subcutaneous tissue disorders | 56 of 388 | 89 of 388 | 27 of 152 | 24 of 374 |
| Palmar-plantar erythrodysaesthesia syndrome | Skin and subcutaneous tissue disorders | 1 of 388 | 3 of 388 | 3 of 152 | 173 of 374 |
| Abdominal pain | Gastrointestinal disorders | 35 of 388 | 44 of 388 | 24 of 152 | 59 of 374 |
| Asthenia | General disorders | 48 of 388 | 39 of 388 | 20 of 152 | 44 of 374 |
| Nausea | Gastrointestinal disorders | 37 of 388 | 46 of 388 | 13 of 152 | 52 of 374 |
| Aspartate aminotransferase increased | Investigations | 54 of 388 | 46 of 388 | 16 of 152 | 24 of 374 |
Serious events with the highest arm-level rate: pneumonia (3.9%), death (3.3%), diarrhoea (2.6%), hepatitis (2.6%), sepsis (2.1%).
The registry's safety results report serious adverse events among participants at risk in each group. For durvalumab alone, 115 of 388 participants at risk are listed as affected; for tremelimumab 300 mg as a single dose plus durvalumab, 157 of 388; for tremelimumab 75 mg for four doses plus durvalumab, 52 of 152; and for sorafenib, 111 of 374. The record separately reports deaths of 280, 262, 123, and 293 in those respective groups. These are distinct posted safety counts and should not be interpreted as evidence that each death was caused by treatment.
The registry lists pneumonia at 3.9%, death at 3.3%, diarrhoea at 2.6%, hepatitis at 2.6%, sepsis at 2.1%, and anaemia at 2.0% among the top serious-event terms. These percentages provide a limited view of selected serious event terms; they are not a complete safety profile. Serious adverse event counts and event-term percentages may reflect different reporting summaries, and the record does not provide enough detail to reconcile each term with the group-level counts.
Safety comparisons require attention to exposure time, definitions, attribution, and completeness of reporting. Those details are not reported in the registry record in the available results. The figures should therefore be read as descriptive registry counts, not as a direct causal comparison or a basis for individual treatment decisions.
18. What the Result Does, and Does Not, Mean
The posted primary analysis describes overall survival for randomized participants assigned to tremelimumab 300 mg as a single dose plus durvalumab 1500 mg compared with sorafenib 400 mg. It reports group medians, confidence intervals, a Cox hazard ratio, and a log-rank p-value. Together, these statistics characterize the observed comparison through the final-analysis cut-off: the estimated median is higher in the combination group, and the reported relative hazard estimate is below 1 with a confidence interval excluding 1.
That is a statement about the recorded study comparison and its analysis, not a guarantee of an outcome for any individual. The hazard ratio does not translate directly into additional months for a participant, and the median is not a prediction for every participant. The confidence intervals describe statistical uncertainty under the methods used; they do not cover every possible source of uncertainty, including unreported model diagnostics, missing-data concerns, or differences between this study population and another population.
The result also does not establish which component of the combination accounts for the observed pattern. The trial included multiple arms, but the primary comparison is the single-dose combination against sorafenib. A separate secondary analysis concerns durvalumab alone, and the other listed outcomes address response and disease progression. Those are different questions, not interchangeable confirmation of the primary comparison.
Open-label conduct, the registry's stated censoring approach, the data cut-off, and incomplete reporting of some analysis details all matter when assessing how broadly to interpret the result. The registry record does not report a complete account of multiplicity procedures, original sample-size assumptions, or all secondary endpoint results. Consequently, the primary estimate should be considered alongside its defined analysis population and limitations, without extending it to outcomes or comparisons that were not established by the posted results.
Statistical evidence is one component of evidence about a treatment comparison. It does not by itself determine clinical importance, net benefit, or an appropriate choice for an individual. Those questions require broader information than the registry's reported outcome statistics.
19. Why This Trial Matters Statistically
This trial illustrates how a randomized parallel-group design can compare an overall-survival outcome across several first-line treatment regimens. The primary endpoint is time to death from any cause, and the registry provides both group-specific median estimates and a relative hazard estimate for the main combination-versus-sorafenib comparison. Reading those measures together helps distinguish a summary of each group's survival distribution from a model-based comparison across follow-up.
The record also shows why analysis labels and endpoint roles matter. The primary comparison is accompanied by sponsor-reported superiority analyses, while the durvalumab-alone comparison appears as a secondary analysis with a different inferential label for its Cox result. These are not interchangeable claims. A registry can list many relevant outcomes, but their evidential weight depends on prespecification, multiplicity control, and completeness of reporting.
Sample-size illustrations provide another statistical lesson. Planning requirements depend strongly on the effect selected for detection and on assumptions about allocation, significance level, and analysis method. The event-based planning figures for survival should not be confused with participant-per-arm figures for binary outcomes, nor with the trial's original enrollment rationale. They are planning illustrations, not observed power.
Finally, the record separates efficacy summaries from safety descriptions. Overall-survival estimates and serious adverse-event counts answer different questions and have distinct limitations. Keeping those distinctions clear helps prevent a single statistic from being asked to support conclusions beyond what the trial analysis reports.
20. Limitations
- The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
- Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.
Several limitations are specific to this registry record. The study was open-label, with no masking. That feature may be particularly relevant to outcomes involving assessment or decisions during follow-up, although overall survival is defined as death from any cause. The registry does not report the procedures used to limit possible assessment or follow-up influences.
The primary outcome is bounded by the final-analysis data cut-off of 27Aug2021 and a maximum follow-up of approximately 46 months. Participants not known to have died by the cut-off were censored under the stated rules. The record does not provide additional sensitivity analyses or diagnostics for censoring assumptions. It also does not give detailed follow-up completeness by group.
The tremelimumab 75 mg for four doses plus durvalumab arm was closed during the study, but the reason is not reported in the registry record. Its smaller reported primary-outcome group size and its closure mean that its results should not be treated as though they had the same status as the designated primary comparison. The registry record does not explain whether or how closure affected the study's planned analyses.
Other important details are not reported in the registry record: the original sample-size justification, interim-analysis plan, full statistical analysis plan, multiplicity procedure, Cox model diagnostics, and complete missing-data sensitivity analyses. The record also does not provide detailed results for every listed secondary outcome in the material. These limits do not erase the posted primary estimate, but they restrict independent assessment of the analysis choices and the breadth of conclusions that can be drawn.
21. Related Tutorials
22. Related Statistical Calculators
23. Sources
- ClinicalTrials.gov: Study of Durvalumab and Tremelimumab as First-line Treatment in Patients With Advanced Hepatocellular Carcinoma — NCT03298451.
- Registry record last updated 2026-10-07; status last verified 2026-10.
- Results first posted 2023-06-18.
- Data retrieved from ClinicalTrials.gov on 2026-11-09.
- Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.
Continue through the Clinical Biostats statistical pathway
Use this trial's endpoint as a starting point for deeper study of effect measures, confidence intervals, and sample-size planning.
24. Record Summary
NCT03298451 is a randomized, open-label, multicenter Phase III study of first-line treatment for advanced hepatocellular carcinoma in patients with no prior systemic therapy who were not eligible for locoregional therapy. The primary registry outcome compares overall survival for tremelimumab 300 mg as a single dose plus durvalumab 1500 mg with sorafenib 400 mg.
The registry reports median overall survival of 16.43 months for the combination and 13.77 months for sorafenib. The sponsor-reported Cox hazard ratio is 0.78, with a 95% confidence interval of 0.66 to 0.92; the log-rank p-value is 0.004. The record also includes a separate durvalumab-alone comparison, additional listed outcomes, and descriptive safety results.
Interpretation is bounded by the defined analysis population, censoring and cut-off rules, open-label design, closure of one arm during the study, and statistical-plan details not reported in the registry record.