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 Efficacy Evaluation of TheraSphere in Patients With Inoperable Liver Cancer (NCT01556490), a randomized na study. The primary outcome is Overall Survival (OS) Results Are Based on the Modified Intent-to-treat (mITT).
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT01556490 |
| Phase | NA |
| Condition | Unresectable Hepatocellular Carcinoma |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | None (open label) |
| Enrollment | 526 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Boston Scientific Corporation |
| Results posted | Yes |
2. Clinical Question
Population
People with unresectable hepatocellular carcinoma (HCC) for whom treatment with standard-of-care sorafenib was planned. The primary endpoint is described as analyzed in a modified intent-to-treat population. The record does not give further eligibility details in the information reported for this analysis.
Intervention
TheraSphere, an intra-arterial device, added to standard-of-care sorafenib. The registry describes the trial as evaluating the safety and effectiveness of this combination.
Comparator
Standard-of-care sorafenib without added therapy. Both groups therefore received sorafenib; the randomized contrast concerns the addition of TheraSphere.
Primary question
Does adding TheraSphere to sorafenib change overall survival, measured from randomization until death from any cause, compared with sorafenib alone? The primary endpoint counts deaths, while the sponsor's reported analysis uses a time-to-event comparison.
3. Trial Design
The registry describes a completed, randomized, parallel-group trial with no masking. It enrolled 526 participants and compared standard-of-care sorafenib alone with sorafenib plus TheraSphere. The condition listed is unresectable hepatocellular carcinoma. The phase is not reported in the registry record: the phase field is listed as NA.
The trial began in 2012-03, and primary completion is recorded as 2022-04-30. The overall survival follow-up timeframe is described as running from randomization to death or the last date known to be alive, with data cut-off 30Apr2022 and an average of 16.3 months. The sponsor is Boston Scientific Corporation.
For the primary outcome, the registry identifies a modified intent-to-treat analysis and reports death counts of 200 among 241 in the sorafenib group and 206 among 240 in the combination group. These are the outcome-specific denominators and event counts shown in the record; they should not be treated as a complete description of every analysis population. The reason the safety analysis uses different denominators is not reported in the registry record.
Random allocation is intended to make treatment groups comparable, on average, at the start of a trial. No masking means participants and study personnel were not blinded to group assignment. That feature is particularly relevant to outcomes requiring judgment, while death is a comparatively objective endpoint. The allocation method, concealment procedures, stratification factors, and further details of the original design are not reported in the registry record.
4. Participant Flow and Accounting
The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.
Before assignment: The Overall Survival (OS) efficacy endpoints analyzed on the modified Intent-To-Treat (mITT) population, comprising 481/526 randomized patients who met eligibility criteria.
Randomized Patients Summary
| Stage | Sorafenib + Standard of Care | TheraSphere + Sorafenib + Standard of Care |
|---|---|---|
| STARTED | 263 | 263 |
| COMPLETED | 241 | 240 |
| NOT COMPLETED | 22 | 23 |
Reasons for not completing this period:
| Reason | Sorafenib + Standard of Care | TheraSphere + Sorafenib + Standard of Care |
|---|---|---|
| Protocol Violation | 22 | 23 |
Overall Survival (OS)
| Stage | Sorafenib + Standard of Care | TheraSphere + Sorafenib + Standard of Care |
|---|---|---|
| STARTED | 241 | 240 |
| COMPLETED | 229 | 222 |
| NOT COMPLETED | 12 | 18 |
Reasons for not completing this period:
| Reason | Sorafenib + Standard of Care | TheraSphere + Sorafenib + Standard of Care |
|---|---|---|
| Untreated Patients who Discontinued/Completed from Study | 12 | 18 |
Analysis population for the primary outcome, as defined in the registry: All participants were analyzed, and the count of participants is reporting the number of events (deaths).
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.
| Characteristic | Unit | Sorafenib + Standard of Care | TheraSphere + Sorafenib + Standard of Care | Total |
|---|---|---|---|---|
| Participants analysed | 241 | 240 | 481 | |
| Age, Categorical: <=18 years | Participants | 0 | 0 | 0 |
| Age, Categorical: Between 18 and 65 years | Participants | 130 | 120 | 250 |
| Age, Categorical: >=65 years | Participants | 111 | 120 | 231 |
| Sex: Female, Male: Female | Participants | 26 | 30 | 56 |
| Sex: Female, Male: Male | Participants | 215 | 210 | 425 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 6 | 4 | 10 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 144 | 136 | 280 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 91 | 100 | 191 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 4 | 2 | 6 |
| Race (NIH/OMB): Asian | Participants | 55 | 52 | 107 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 0 | 1 | 1 |
| Race (NIH/OMB): Black or African American | Participants | 2 | 9 | 11 |
| Race (NIH/OMB): White | Participants | 95 | 79 | 174 |
| Race (NIH/OMB): More than one race | Participants | 0 | 0 | 0 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 85 | 97 | 182 |
| Region of Enrollment: Canada | participants | 22 | 21 | 43 |
| Region of Enrollment: South Korea | participants | 47 | 43 | 90 |
| Region of Enrollment: Belgium | participants | 2 | 1 | 3 |
| Region of Enrollment: United States | participants | 26 | 34 | 60 |
| Region of Enrollment: Netherlands | participants | 4 | 4 | 8 |
| Region of Enrollment: United Kingdom | participants | 28 | 22 | 50 |
| Region of Enrollment: France | participants | 80 | 94 | 174 |
| Region of Enrollment: Germany | participants | 1 | 3 | 4 |
| Region of Enrollment: Spain | participants | 28 | 15 | 43 |
| Region of Enrollment: Hong Kong | participants | 2 | 0 | 2 |
6. Primary Endpoint
The registry lists the primary outcome as Overall Survival (OS) Results Are Based on the Modified Intent-to-treat (mITT), measured over From time of randomization up to date of death or last date known to be alive (data cut-off 30Apr2022), an average of 16.3 months.
| Element | Registry entry |
|---|---|
| Result type | Count Of Participants |
| Measure of spread | not applicable |
| Unit | Participants |
| Endpoint classification | Binary Endpoint |
Overall survival is the time from randomization until death from any cause, as reported by the study site. The registry describes its primary result as a count of participants with the event, where the event is death. It gives the timeframe as extending to death or the last date known to be alive, with a data cut-off of 30Apr2022 and an average of 16.3 months.
Overall survival is used in clinical trials because it captures a direct outcome that is important to participants and does not depend on an investigator's interpretation of tumor imaging or progression criteria. Counting deaths gives a straightforward description of how many participants had the event by the reported follow-up. A time-to-event analysis adds information about when events occurred and about follow-up time, rather than reducing the comparison to event counts alone.
Those two presentations answer related but not identical statistical questions. The event counts support a simple unadjusted comparison of observed proportions; the sponsor's reported log-rank analysis compares survival experience over follow-up using a hazard ratio. Interpretation therefore needs to consider both the number of deaths and the reported time-to-event estimate and its confidence interval. The registry does not report additional detail about censoring or how missing survival status was handled.
7. Results Posted in the Registry
- TheraSphere + Sorafenib + Standard of Care: 85.8% (206/240) versus 83.0% (200/241) on control; risk difference 2.8 percentage points (95% CI -3.6 to 9.3), risk ratio 1.03 (0.96–1.12); unadjusted two-proportion z-test p = 0.390.
Risk difference: TheraSphere + Sorafenib + Standard of Care
95% CI: -3.6 to 9.3 percentage points
Recalculated from the posted summary statistics
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 |
|---|---|---|---|---|
| Time to Progression (TTP) From Time of Randomization Based on Investigator, According RECIST Criteria. | Time-to-Event Analysis | Hazard ratio | 0.76 (0.59 to 0.96) | 417 events |
| Time to Untreatable Progression (TTUP) From the Time of Randomization Based One or More of the Following: Investigator Assessment According to RECIST Criteria | Time-to-Event Analysis | Hazard ratio | 0.68 (0.52 to 0.89) | 212 events |
| Tumor Response | Binary Endpoint | Risk difference | +15.5 pts (9.0 to 21.9) | 88 per arm |
Time to Progression (TTP) From Time of Randomization Based on Investigator, According RECIST Criteria.
- Endpoint type: Time to event: compared as a hazard ratio.
- Test: Hazard ratio as reported by the sponsor (Log Rank); it was not recalculated.
- Result:
- Sorafenib + Standard of Care vs TheraSphere + Sorafenib + Standard of Care: hazard ratio 0.76 (95% CI 0.59–0.96), reported p = 0.023 (as reported in the registry).
- Interpretation:
- The 95% confidence interval excludes no difference (a ratio of 1), so the hazard of the event is statistically lower for Sorafenib + Standard of Care vs TheraSphere + Sorafenib + Standard of Care than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Time to Untreatable Progression (TTUP) From the Time of Randomization Based One or More of the Following: Investigator Assessment According to RECIST Criteria
- Endpoint type: Time to event: compared as a hazard ratio.
- Test: Hazard ratio as reported by the sponsor (Log Rank); it was not recalculated.
- Result:
- Sorafenib + Standard of Care vs TheraSphere + Sorafenib + Standard of Care: hazard ratio 0.68 (95% CI 0.52–0.89), reported p = 0.004 (as reported in the registry).
- Interpretation:
- The 95% confidence interval excludes no difference (a ratio of 1), so the hazard of the event is statistically lower for Sorafenib + Standard of Care vs TheraSphere + Sorafenib + Standard of Care than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Tumor Response
- 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:
- TheraSphere + Sorafenib + Standard of Care: 23.8% (57/240) versus 8.3% (20/241) on control; risk difference 15.5 percentage points (95% CI 9.0 to 21.9), risk ratio 2.86 (1.78–4.61); unadjusted two-proportion z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the proportion with the event is statistically higher for TheraSphere + Sorafenib + Standard of Care than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The secondary outcomes present a generally favorable pattern for the TheraSphere group on progression and tumor response measures: the registry-reported time-to-event hazard ratios are below 1, and more tumor responses are recorded in the combination group. This pattern is distinct from the primary overall survival result, which does not show a clear difference in the sponsor's reported analysis. Progression and response outcomes can provide information about disease course, but they do not establish an overall survival effect.
Time to progression and time to untreatable progression are related but not identical endpoints. The registry defines the former using investigator assessment according to RECIST criteria and describes the latter as based on one or more criteria including investigator assessment according to RECIST. The specific full definition of the untreatable-progression endpoint is not reported in the registry record. Tumor response is reported as a participant count, with the sponsor also reporting a final-values mean difference.
These secondary results carry less weight than the primary endpoint for confirmatory interpretation. Multiple outcomes create more opportunities for apparently notable results to arise by chance when each is tested separately. The record reports several secondary analyses but does not report whether p-values were adjusted, whether a testing hierarchy was used, or how secondary outcomes were designated for formal inference. Their p-values should therefore be read as reported, unadjusted evidence rather than as proof that the overall family of outcomes has been controlled for false-positive findings.
The secondary outcomes can be informative about the treatment comparison and help characterize the pattern of observed results. Their consistency does not remove uncertainty in the primary endpoint, and their statistical significance does not establish that a secondary effect necessarily translates into a meaningful difference in survival or in other outcomes. Interpretation should keep the endpoint definitions, analysis methods, and uncertainty in view without treating the results as interchangeable.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Time to Progression (TTP) From Time of Randomization Based on Investigator, According RECIST Criteria.
- Time to Untreatable Progression (TTUP) From the Time of Randomization Based One or More of the Following: Investigator Assessment According to RECIST Criteria
- Tumor Response
9. Statistical Interpretation
For overall survival, the record reports 200 deaths among 241 participants receiving sorafenib and 206 among 240 receiving sorafenib plus TheraSphere. The simple unadjusted comparison gives a small positive absolute difference in the death proportion for the combination group, but its confidence interval spans no difference. Its unadjusted p-value is 0.39. This comparison does not provide clear evidence of a difference in the event proportions, and the interval indicates uncertainty about the direction and size of the difference.
The sponsor's primary time-to-event analysis reports a hazard ratio of 1.08, with a 95% confidence interval from 0.89 to 1.31. Because the interval includes 1, the data are compatible with no hazard difference as well as with differences in either direction. The reported p-value is 0.455. The event-count comparison and the log-rank analysis use different summaries of survival data, but both present a primary result that is uncertain rather than a precise demonstration of a survival advantage.
The secondary results show a different pattern. The reported time-to-progression hazard ratio is 0.76, with a 95% confidence interval from 0.59 to 0.96, and the time-to-untreatable-progression hazard ratio is 0.68, with a 95% confidence interval from 0.52 to 0.89. Both registry-reported p-values are below the 0.05 planning significance level. The tumor-response outcome also has more reported events in the combination group, and its unadjusted p-value is <0.001. These results concern secondary outcomes and do not replace the primary overall survival result.
A hazard ratio is a relative comparison of event rates over follow-up under the model and analysis used; it is not a difference in median time or a probability that an individual will experience an event. A value below 1 for the listed secondary comparisons indicates a lower estimated hazard in the TheraSphere group, given the stated group ordering. The primary hazard ratio is reported for the groups in the opposite direction only as an unordered group listing, so its direction should not be inferred from that listing alone.
These findings are statistical descriptions of the posted results, not proof that an intervention will have the same effect in every setting or for every participant. The primary estimate is imprecise enough to include no difference, and the secondary outcomes require caution because multiple outcomes were reported. The registry does not report whether multiplicity adjustments or a hierarchical testing plan were used.
10. Statistical Methods Explained
The registry presents two kinds of comparisons: binary event summaries and time-to-event analyses. They describe different features of the trial data and should not be treated as interchangeable. The primary outcome is reported as a count of deaths, while the sponsor's primary analysis is a log-rank comparison expressed as a hazard ratio.
What does a risk difference describe?
For a binary endpoint, the risk difference is the difference between the observed event proportions in two groups. In this record, death counts are the events for the primary outcome, while tumor response is another binary outcome. A risk difference is expressed on an absolute scale: it describes how far apart the event proportions are, rather than comparing them as a ratio. A positive or negative sign depends on which group is subtracted from which, so the group ordering matters.
The posted binary comparisons include confidence intervals and unadjusted p-values. The simple recalculation uses the posted counts and denominators and is not the same thing as the sponsor's selected analysis. For overall survival, the sponsor reports a log-rank result rather than a risk-difference analysis. For tumor response, the registry's own analysis is reported as a mean difference in final values, which is a different statistical summary from the binary event-count comparison. These outputs address related data but are not numerically interchangeable.
What does a hazard ratio describe?
General statistical context: a hazard is an event rate among participants who have not yet had the event, at a given point in follow-up. A hazard ratio compares those rates between groups over time. It is not a direct comparison of the proportion of participants who have an event, and it is not an absolute change in months. A hazard ratio of 1 represents equal estimated hazards; a value below or above 1 represents a lower or higher estimated hazard for the numerator group, depending on the analysis ordering.
The registry reports log-rank analyses for overall survival, time to progression, and time to untreatable progression. The log-rank test compares event-time patterns between groups, accounting for the timing of events and censoring. The registry gives the hazard ratio and confidence interval alongside the test result. Details of the hazard-ratio estimation model and its assumptions are not reported in the registry record.
Why do confidence intervals matter?
General statistical context: a confidence interval describes the uncertainty around an estimate under the statistical method used. A narrower interval indicates greater precision; a wider interval indicates that a broader range of effects remains compatible with the data. For a risk difference, an interval spanning zero includes no difference. For a hazard ratio, an interval spanning 1 includes equal hazards. Neither an interval nor a p-value establishes that an effect is important in clinical practice.
The primary survival confidence interval includes 1, while the secondary time-to-event confidence intervals reported in the registry do not. The inference from the secondary outcomes remains qualified by their status as secondary endpoints and by the absence of registry-reported multiplicity procedures. The width of each interval also matters: the bounds indicate a range of effect sizes compatible with the data, not a guarantee that the true effect lies within a particular range in this trial.
What is an unadjusted recalculation?
General statistical context: an unadjusted comparison is calculated from the observed summaries without controlling for other covariates or applying a stated adjustment. It can be useful for understanding the posted event proportions, but it does not necessarily reproduce the sponsor's analysis, which may use a different endpoint definition, time-to-event method, or analysis population. The registry does not report covariate-adjusted estimates for these results.
The binary comparisons include unadjusted risk differences, relative risks, odds ratios, and p-values. Those measures emphasize different scales: absolute difference, relative probability, relative odds, and evidence against a null hypothesis, respectively. These recalculations are descriptive aids and should not be substituted for the sponsor's reported result. In particular, the sponsor's overall survival analysis is the log-rank hazard-ratio analysis, and the sponsor's tumor-response result is reported using a different summary than the posted event-count comparison.
General statistical context: over-dispersion matters when the observed variability is greater than a model assumes; ignoring it can make standard errors too small and intervals too narrow. The registry record does not identify a count model for these outcomes or report an over-dispersion analysis, so that issue cannot be evaluated from the reported summaries. Likewise, the record does not provide enough detail to assess proportional-hazards assumptions or other model diagnostics.
11. Confidence Intervals and Precision
The primary endpoint's sponsor-reported hazard ratio is 1.08, with a 95% confidence interval from 0.89 to 1.31. The interval crosses 1, so equal hazards remain compatible with the data. It also permits values on either side of 1, reflecting uncertainty about the direction and size of any difference. The reported p-value is 0.455, which is consistent with the interval's lack of clear evidence against equal hazards under the reported analysis.
The unadjusted event-count comparison for overall survival likewise has an interval that spans no difference. Together, these summaries do not precisely establish a survival difference. They also do not prove that the groups have identical survival; a nonsignificant result can reflect uncertainty rather than equivalence. The registry does not report a prespecified equivalence margin or noninferiority margin.
For the secondary time-to-event outcomes, the reported hazard-ratio intervals lie below 1, but they still cover a range of possible effect sizes. The time-to-progression interval ranges from 0.59 to 0.96, and the time-to-untreatable-progression interval ranges from 0.52 to 0.89. Tumor response has an unadjusted risk-difference interval from 0.090 to 0.219. These intervals convey precision for their respective estimates, but their interpretation should account for the secondary status of the outcomes and the unreported multiplicity plan.
General statistical context: a confidence interval is not a range that contains every participant's outcome, nor does its width alone determine clinical importance. It reflects sampling uncertainty under the analysis method. The registry does not report all details needed to independently assess how censoring, missing data, or analysis assumptions affect the intervals.
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 | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 2,550 | 3,413 |
| 75% of the observed effect | 4,618 | 6,181 |
| 50% of the observed effect | 10,578 | 14,160 |
The planning illustrations use the observed effect as a reference and then consider detecting the full observed effect, 75% of the observed effect, or 50% of the observed effect. For binary outcomes, the figures are participants per arm. For time-to-event outcomes, the figures are total events, not participants per arm. The planning assumptions stated in the registry are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation; the target effect is the stated fraction of the observed effect.
The column for 80% power describes the planned sample size or event count that would give an 80% chance of detecting the specified effect under those assumptions if that effect were true. The 90% power column describes the corresponding planning target for a 90% chance. These are design illustrations, not an assessment of the chance that the trial's result is true. The trial's own original design assumptions and sample-size justification are not reported in the registry record.
Smaller effects require more information to detect reliably. That is why the planning requirements increase when the target is reduced from the full observed effect to 75% or 50% of it. The binary-outcome illustrations are shown in participants per arm, while the time-to-event illustrations are expressed in total events. Those units must not be confused when reading the figures.
These calculations are planning illustrations based on observed results, not observed power. Observed power is not a useful substitute for interpreting the estimate and its confidence interval; precision and the range of effects compatible with the data are more informative about what the results establish.
13. How the Sample Size Is Derived
Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z1−α/2 = 1.960) and the desired power (z1−β = 0.842 for 80% and 1.282 for 90%).
Formula
n is the number of participants in each arm, p0 and p1 are the control and treatment proportions, and p̄ is their average.
Worked calculation for this trial
- Control proportion p0 = 0.830; treatment proportion p1 = 0.858; average p̄ = 0.844.
- First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.5130 = 1.0055.
- Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.5126 = 0.4314.
- n = (1.0055 + 0.4314)2 / (0.0285)2 = 2,549.6, rounded up to 2,550 participants per arm for 80% power.
The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).
R code
alpha <- 0.05
z_a <- qnorm(1 - alpha / 2) # two-sided
p0 <- 0.829875518672199 # control proportion
p1 <- 0.858333333333333 # treatment proportion
n_per_arm <- function(power, frac = 1) {
q1 <- p0 + (p1 - p0) * frac # smaller effect = fraction of the observed difference
pbar <- (p0 + q1) / 2
z_b <- qnorm(power)
ceiling(round((z_a * sqrt(2 * pbar * (1 - pbar)) + z_b * sqrt(p0 * (1 - p0) + q1 * (1 - q1)))^2 / (q1 - p0)^2, 6))
}
for (f in c(1, 0.75, 0.5))
cat(sprintf("%3.0f%% of observed effect: n per arm = %s (80%% power), %s (90%% power)\n", 100 * f,
format(n_per_arm(0.80, f), big.mark = ","), format(n_per_arm(0.90, f), big.mark = ",")))
# Check against R's built-in function (unrounded n per arm)
cat("power.prop.test:", round(power.prop.test(p1 = p0, p2 = p1, power = 0.80)$n, 1), "\n")
# Simulation: how often does the z-test reject at the 80%-power sample size?
set.seed(1556490)
n <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))
Output from running the code
100% of observed effect: n per arm = 2,550 (80% power), 3,413 (90% power)
75% of observed effect: n per arm = 4,618 (80% power), 6,181 (90% power)
50% of observed effect: n per arm = 10,578 (80% power), 14,160 (90% power)
power.prop.test: 2549.6
Simulated power at n = 2,550 per arm: 0.802 (20000 replicates)
The simulation draws many pairs of event counts at the planned sample size and counts how often the two-proportion z-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.
14. Analyses Reported by the Sponsor
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| Log Rank | Hazard Ratio (HR) 1.08 | 0.89 to 1.31 | 0.455 |
The sponsor's primary analysis is a log-rank comparison of overall survival. It reports a hazard ratio of 1.08, a 95% confidence interval from 0.89 to 1.31, and a p-value of 0.455. The simple recalculation from posted death counts instead compares the observed event proportions and gives an interval that includes no difference. These are different summaries of the survival data: the sponsor's method uses event timing, whereas the unadjusted recalculation uses the counts and denominators.
The registry does not flag a discrepancy between the recalculation and the reported primary result. The sponsor's reported analysis should therefore be read as the trial's formal time-to-event result, while the recalculation is a supplementary, unadjusted description of the event counts. Neither summary shows a precise primary survival difference in the posted results.
For tumor response, the sponsor reports a mean difference in final values of 15.5, with a 95% confidence interval from 8.6 to 22.3 and a p-value of < 0.001. The event-count recalculation treats the outcome as binary. Because the registry presents these as different statistical summaries, they should not be combined or interpreted as estimates of exactly the same quantity. The record does not explain the sponsor's choice of the final-values analysis in further detail.
15. Multiplicity, Missing Data and Analysis Populations
The registry lists overall survival as the primary outcome and reports time to progression, time to untreatable progression, and tumor response as secondary outcomes. When several outcomes are analyzed, the chance of at least one apparently positive result can increase if each is assessed independently without adjustment. This is the general statistical concern known as multiplicity.
The registry record does not report whether the sponsor adjusted for multiple comparisons, used a prespecified testing hierarchy, or treated the secondary analyses as exploratory. It also does not report a multiplicity strategy for the different analysis measures presented for tumor response. Consequently, the reported secondary p-values should not be interpreted as though family-wise error control has been established. This does not invalidate the reported estimates; it limits the strength of confirmatory claims based on them.
The primary population is described as modified intent-to-treat, with the record stating that all participants were analyzed and that the count represents deaths. The exact modification to the intent-to-treat population and the inclusion rules are not reported in the registry record. The record also does not describe handling of missing outcome data, loss to follow-up, censoring rules, or sensitivity analyses for missingness.
For time-to-event outcomes, participants whose event is not observed by their last known follow-up may be censored. General statistical context: valid interpretation depends on appropriate censoring assumptions and on clear reporting of follow-up and event ascertainment. The registry provides a data cut-off and an average follow-up description for overall survival, but further censoring details are not reported. It is therefore not possible to assess from this record whether missing information could have affected the estimates.
Allocation is randomized and the trial is unmasked. The record does not provide the allocation concealment method, baseline balance details, or any subgroup-analysis plan. These omissions constrain assessment of the analysis and its robustness; they are not evidence that a particular procedure was or was not used.
16. 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 |
|---|---|---|---|
| Sorafenib + Standard of Care | 111 | 274 | 40.5% |
| TheraSphere + Sorafenib + Standard of Care | 94 | 207 | 45.4% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Sorafenib + Standard of Care | 239 of 274 |
| TheraSphere + Sorafenib + Standard of Care | 178 of 207 |
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 |
|---|---|
| Sorafenib + Standard of Care | 259 of 274 |
| TheraSphere + Sorafenib + Standard of Care | 189 of 207 |
Most frequent serious adverse event terms
| Event term | Organ system | Sorafenib + Standard of Care | TheraSphere + Sorafenib + Standard of Care |
|---|---|---|---|
| Disease progression | General disorders | 13 of 274 | 14 of 207 |
| Hepatic failure | Hepatobiliary disorders | 10 of 274 | 10 of 207 |
| Ascites | Gastrointestinal disorders | 5 of 274 | 10 of 207 |
| General physical health deterioration | General disorders | 6 of 274 | 5 of 207 |
| Hepatic encephalopathy | Nervous system disorders | 3 of 274 | 8 of 207 |
| Abdominal pain | Gastrointestinal disorders | 7 of 274 | 2 of 207 |
| Anaemia | Blood and lymphatic system disorders | 6 of 274 | 0 of 207 |
| Upper gastrointestinal haemorrhage | Gastrointestinal disorders | 5 of 274 | 1 of 207 |
| Renal failure acute | Renal and urinary disorders | 2 of 274 | 4 of 207 |
| Oesophageal varices haemorrhage | Gastrointestinal disorders | 4 of 274 | 1 of 207 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Sorafenib + Standard of Care | TheraSphere + Sorafenib + Standard of Care |
|---|---|---|---|
| Diarrhoea | Gastrointestinal disorders | 140 of 274 | 62 of 207 |
| Fatigue | General disorders | 84 of 274 | 69 of 207 |
| Decreased appetite | Metabolism and nutrition disorders | 87 of 274 | 64 of 207 |
| Abdominal pain | Gastrointestinal disorders | 54 of 274 | 42 of 207 |
| Nausea | Gastrointestinal disorders | 50 of 274 | 44 of 207 |
| Hypertension | Vascular disorders | 61 of 274 | 28 of 207 |
| Ascites | Gastrointestinal disorders | 38 of 274 | 42 of 207 |
| Weight decreased | Investigations | 43 of 274 | 30 of 207 |
| Asthenia | General disorders | 22 of 274 | 42 of 207 |
| Constipation | Gastrointestinal disorders | 36 of 274 | 26 of 207 |
Serious events with the highest arm-level rate: disease progression (6.8%), ascites (4.8%), hepatic failure (4.8%), hepatic encephalopathy (3.9%), abdominal pain (2.6%).
The safety record reports serious adverse events in 111 of 274 participants in the sorafenib group and 94 of 207 in the TheraSphere-plus-sorafenib group. Other adverse events are recorded for 259 of 274 and 189 of 207, respectively. The safety denominators differ from the primary outcome denominators, and the reason for that difference is not reported in the registry record. These counts should therefore be interpreted using their stated safety denominators, not the primary endpoint denominators.
The listed serious adverse event terms include disease progression at 6.8%, ascites at 4.8%, hepatic failure at 4.8%, hepatic encephalopathy at 3.9%, abdominal pain at 2.6%, and general physical health deterioration at 2.4%. The registry information presented does not assign these term-specific percentages to a particular group, so they should not be treated as group-specific comparisons.
Deaths recorded in the adverse-event information are 239 for the sorafenib group and 178 for the combination group. The record does not state the timing, causes, or relationship to treatment for these safety-section death counts. They are not interchangeable with the primary endpoint death counts, which use a different analysis population and outcome presentation. These summaries describe reported events and do not by themselves establish causation or comparative safety.
17. What the Result Does, and Does Not, Mean
The posted results support a measured conclusion: the registry's primary overall survival analysis does not show a clear difference between sorafenib alone and sorafenib plus TheraSphere. The sponsor-reported hazard ratio is 1.08 and its 95% confidence interval includes 1. The count-based comparison also has an interval spanning no difference. The estimates are uncertain; they do not establish that survival is identical between groups, nor do they demonstrate a survival advantage for either group.
The secondary outcomes show statistically notable differences in progression and tumor response summaries, with reported estimates favoring the combination group for the progression outcomes and a higher response count in that group. Those findings describe the endpoints reported in the registry. They cannot be substituted for overall survival, and the unreported multiplicity plan limits how strongly they can support confirmatory conclusions.
These results do not establish what would happen for an individual participant, nor do they determine the balance of benefits and harms for a particular person. The registry's outcome summaries do not include all information needed to interpret the clinical importance of each difference, such as prespecified thresholds for meaningful effects. They also do not resolve the impact of missing-data handling or other unreported analysis decisions.
General statistical context: a nonsignificant primary result is not proof of no effect, just as a statistically significant secondary result is not by itself proof of a clinically important effect. Estimates, confidence intervals, endpoint definitions, and the prespecified analysis plan all matter. The registry record is best read as a report of the observed comparisons and their uncertainty, not as a standalone basis for treatment decisions.
18. Why This Trial Matters Statistically
This trial is statistically informative because it compares an added device intervention against the same standard-of-care drug regimen, using random allocation. The design directly targets the incremental comparison: sorafenib plus TheraSphere versus sorafenib alone. That is a clearer contrast than comparing groups receiving entirely different treatment strategies, while still leaving the interpretation dependent on how outcomes were measured and analyzed.
The primary outcome also highlights why endpoint choice matters. Overall survival is a direct outcome, but its reported estimate is uncertain and does not show a clear difference. The progression and response results show a more favorable pattern for the combination group, yet they answer related but distinct questions and are secondary outcomes. The contrast between these findings illustrates why one should not infer a survival benefit solely from changes in intermediate or disease-response outcomes.
The record includes both the sponsor's time-to-event analysis and unadjusted summaries based on posted counts. Comparing these approaches helps readers distinguish a formal time-to-event estimate from a simple calculation using event proportions. It also makes clear that different analyses can summarize the same trial in different ways without being direct substitutes.
Finally, the registry's unreported information matters statistically. Details about multiplicity, missing data, censoring, analysis populations, and original sample-size assumptions would help readers judge how robustly the findings support broader claims. The trial's results are therefore useful not only for their estimates, but also as an example of why transparent reporting of methods is necessary for interpreting clinical evidence.
19. 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 trial-specific limits to interpretation follow from what the registry reports and does not report. The trial was unmasked, so knowledge of assignment could potentially affect conduct or assessment of outcomes that rely on judgment. Overall survival is less dependent on subjective assessment than tumor response or investigator-assessed progression, but the record does not describe safeguards for these assessments.
The registry identifies a modified intent-to-treat population but does not explain which participants were included or excluded under that definition. The primary outcome denominators are 241 and 240, while the safety denominators are 274 and 207. The reasons for those differences are not reported. The record also does not describe missing-data procedures, censoring rules, or sensitivity analyses, which limits independent appraisal of how incomplete follow-up may affect the estimates.
The record provides no multiplicity adjustment or hierarchy information for the secondary outcomes. This is important because the progression and tumor-response analyses are statistically notable while the primary survival result is not. Without a reported strategy for multiple outcomes, the secondary p-values should be treated cautiously.
Further details that would help assess the results—including allocation concealment, baseline characteristics, subgroup analyses, model diagnostics, and the original sample-size justification—are not reported in the registry record. The follow-up description gives an average of 16.3 months and a cut-off date, but additional detail about follow-up distribution is not provided. These reporting limits do not establish that procedures were inadequate; they restrict what can be concluded from the registry summary alone.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Efficacy Evaluation of TheraSphere in Patients With Inoperable Liver Cancer — NCT01556490.
- Registry record last updated 2023-11-08; status last verified 2023-08.
- Results first posted 2023-11-08.
- 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.
23. Record Summary
The registry describes a completed, randomized, unmasked, parallel-group trial in unresectable hepatocellular carcinoma. It compared standard-of-care sorafenib with the same regimen plus TheraSphere. Enrollment was 526; the trial began in 2012-03 and primary completion is recorded as 2022-04-30.
Overall survival was the primary endpoint. The sponsor's log-rank analysis reported a hazard ratio of 1.08 with a 95% confidence interval from 0.89 to 1.31 and p = 0.455. The posted secondary outcomes include time to progression, time to untreatable progression, and tumor response. The progression estimates and response counts favor the combination group in their reported comparisons, but multiplicity procedures are not reported.
The registry supplies limited detail about missing data, censoring, analysis-population rules, and the original design assumptions. Those omissions matter when judging precision and the strength of conclusions beyond the reported comparisons.