An Open-label, Dose Escalation, Pharmacodynamic, Pharmacokinetic, and Effect of Food Phase 1 Study of E7820 to Determine the Maximum Tolerated Dose Following Twice Daily Oral Administration in Subjects With Unresectable Solid Tumors: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for An Open-label, Dose Escalation, Pharmacodynamic, Pharmacokinetic, and Effect of Food Phase 1 Study of E7820 to Determine the Maximum Tolerated Dose Following Twice Daily Oral Administration in Subjects With Unresectable Solid Tumors (NCT01773421), a randomized phase 1 study. The primary outcome is Treatment Phase Part A: AUC(0-inf): Area Under the Plasma Concentration-time Curve From Time 0 to Infinity for E7820.

2. Clinical Question

3. Trial Design

NCT01773421 was an open-label, randomized, crossover Phase 1 study of E7820 in people with advanced solid tumors. The registry lists 45 participants enrolled and a completed study status. The recorded study dates are 2011-06-30 for the start and 2014-04-30 for primary completion. These dates describe the registry record and do not provide a detailed account of the conduct of each study part.

The study had two parts. Part A was the food-effect study, comparing E7820 50 mg in fed and fasted conditions. Part B concerned determination of the maximum tolerated dose for twice-daily dosing. The registry summary states that Part A would begin first and that Part B would begin after the pharmacokinetic results of Part A had been evaluated. It does not report further sequencing or operational details. The primary endpoint results concern Part A, not the maximum tolerated dose question in Part B.

Randomization and crossover are both recorded, while masking is listed as none. The record does not describe the randomization procedure, the allocation sequence, the order of fed and fasted conditions, or any washout period. It also does not state how these design features were reflected in the analysis. Those details matter when interpreting a crossover comparison because observations from the same participant may be related, and the order or timing of conditions may affect interpretation.

The registry describes a pharmacokinetic analysis set based on availability of sufficient data to derive at least one pharmacokinetic parameter, with time-point eligibility for the endpoint. The number of participants contributing to every analysis is not reported in the registry record beyond the endpoint group counts. Results also include outcomes concerning response, response duration, disease progression or death, and adverse events, but the primary result addressed is the Part A exposure measure.

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: In Part A, a total of 18 participants were enrolled, out of which 15 participants were randomized and treated. In Part B, a total of 27 participants were enrolled, out of which 26 participants were treated.

Only the first 6 of 7 groups are shown.

Treatment Phase

Reasons for not completing this period:

Extension Phase

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: The pharmacokinetic (PK) analysis set included all participants who had sufficient PK data to derive at least 1 PK parameter. Participants who were evaluable at a particular time point for this endpoint were included in the assessment.

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.

6. Primary Endpoint

The registry lists the primary outcome as Treatment Phase Part A: AUC(0-inf): Area Under the Plasma Concentration-time Curve From Time 0 to Infinity for E7820, measured over Day 1 or 8: 0.5-48 hours.

The primary endpoint was AUC(0-inf), the area under the plasma concentration–time curve from time 0 to infinity for E7820, expressed in nanogram*hour per milliliter (ng*hr/mL). AUC is a pharmacokinetic summary of drug exposure over time: in general, it integrates measured plasma concentration across the specified period and extends the estimate to infinity. It is used to compare overall exposure between dosing conditions, rather than to describe a single concentration at one moment.

The registry gives the timeframe as Day 1 or 8, 0.5-48 hours. It reports the endpoint as a mean with standard deviation. The Part A group summaries are a mean of 12500.0 with standard deviation 3510.0 for the fed condition, based on 12 participants, and a mean of 11500.0 with standard deviation 3490.0 for the fasted condition, based on 14 participants. These are descriptive summaries of the endpoint values in the analysis groups.

AUC is suitable for a food-effect question because the comparison concerns exposure under fed and fasted conditions. The registry’s own analysis expresses the comparison as a geometric least-squares mean ratio, whereas the posted group summaries also permit a simple unadjusted comparison of arithmetic means. These are different summaries and should not be treated as interchangeable. The endpoint does not by itself measure tumor response, duration of response, or adverse effects.

7. Results Posted in the Registry

• Treatment Phase Part A: E7820 50 mg Fasted: mean 11,500 versus 12,500 on control; difference -1,000 (95% CI -3,699 to 1,699), standardized effect d = -0.29; z-test p = 0.468.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary endpoint is continuous: each evaluable participant has an AUC value measured in ng*hr/mL. The registry reports group means and standard deviations. A mean describes the average value in a group, while a standard deviation describes how spread out participant values are around that mean. A larger standard deviation indicates greater variability among observed values, but does not indicate whether the estimated difference between conditions is precise. Precision also depends on the amount of information available and the analysis design.

What does the recalculated mean difference represent?

The recalculated contrast subtracts the fed-group mean from the fasted-group mean. Its estimate of -1000.0 ng*hr/mL therefore points toward a lower arithmetic mean in the fasted group in this simple comparison. The confidence interval ranges from -3699.0 to 1699.0 ng*hr/mL. Because zero lies within that interval, the summary-based estimate does not precisely distinguish a difference in one direction from no difference or a difference in the other direction. The unadjusted p-value is 0.468. A p-value describes how compatible the observed data are with a specified null model under the assumptions of a statistical test; it is not the probability that the null hypothesis is true.

This calculation is labelled a recalculation because it uses the posted group-level summaries rather than the sponsor’s analysis output. It is unadjusted and should not be mistaken for the full analysis of a crossover study. In a crossover design, participants may receive both conditions, and the paired comparison can account for the fact that measurements from one participant are related. A comparison that ignores pairing can give a different estimate of uncertainty. The registry does not report sufficient details to reconstruct the participant-level crossover analysis.

Why are the sponsor’s ratio and the recalculated difference distinct?

The sponsor reported a geometric least-squares mean ratio of 1.06 with a 90% confidence interval from 0.97 to 1.15 and identified the analysis as equivalence. A ratio compares values on a multiplicative scale, whereas a mean difference compares values on an additive scale. Geometric means are generally used when positive measurements are analyzed on a logarithmic scale or when relative changes are the scientific focus. Least-squares means may incorporate a model, but the registry record does not report the model or adjustments used for this analysis.

Equivalence is a specific statistical question: it asks whether the estimated difference is sufficiently bounded within prespecified acceptable limits. The confidence interval alone does not establish that conclusion without the equivalence margins and analysis details. Those details are not reported in the registry record. The sponsor’s designation can be accurately stated, but its full statistical basis cannot be independently evaluated from the available record.

What does a confidence interval convey?

In general, a confidence interval expresses uncertainty around an estimate under the assumptions of the analysis. A wider interval indicates less precision than a narrower interval on the same scale. It is not a range containing all participant values, nor does it assign a probability to the true effect after the data have been observed. The recalculated 95% interval quantifies uncertainty for the unadjusted arithmetic mean difference; the sponsor’s 90% interval quantifies uncertainty for the reported ratio. Because these are different estimands and confidence levels, they should not be compared as if they were the same analysis.

What is not available about the analysis?

The registry does not report the statistical model, transformation, treatment of period or sequence, handling of carryover, or method used to calculate the sponsor’s ratio. The original statistical plan, original sample-size justification, and interim-analysis plan are not reported in the registry record. The record describes the pharmacokinetic analysis set and time-point eligibility, but does not provide a complete account of missing measurements or all exclusions. These gaps limit independent assessment of whether the reported analysis matched the intended crossover design and how robust the result is to analytic choices.

These explanations of means, standard deviations, ratios, confidence intervals, and p-values are general statistical guidance. They do not add an unreported method or assumption to the trial record. The recalculated result is a simple unadjusted comparison from the available group summaries, while the sponsor’s reported ratio remains the registry’s own analysis.

10. Confidence Intervals and Precision

The unadjusted mean-difference estimate is -1000.0 ng*hr/mL, and its 95% confidence interval extends from -3699.0 to 1699.0 ng*hr/mL. This interval is broad relative to the point estimate and includes zero. It therefore reflects substantial uncertainty about the direction and size of the arithmetic mean difference in this summary-based comparison. It should not be read as evidence that the conditions are identical: the interval includes values on both sides of zero.

The sponsor’s reported result uses a different scale. The geometric least-squares mean ratio is 1.06, with a 90% confidence interval from 0.97 to 1.15. The registry labels this result as an equivalence analysis. Whether an interval supports equivalence depends on prespecified equivalence limits; those limits and the analysis method are not reported in the registry record. The interval can be reported as given, but its equivalence interpretation cannot be independently checked from the recorded details.

Precision is affected by variability, the amount of analyzable information, and the structure of the analysis. The group standard deviations are 3510.0 for the fed condition and 3490.0 for the fasted condition. The reported endpoint group counts are 12 and 14. Because the study is a crossover, participant-level pairing could be important to the precision of the contrast, but paired values and the sponsor’s model are not reported. The recalculated interval is therefore a measure of uncertainty for the simple unadjusted comparison, not necessarily the interval from the trial’s primary analysis.

Confidence intervals describe uncertainty under an analysis and its assumptions; they do not show the range of individual AUC values or guarantee that the true value lies within the displayed endpoints. Read together, the posted summaries indicate that the arithmetic mean comparison is imprecise, while the sponsor’s ratio is the reported analysis for the registry’s equivalence question. The two intervals answer different statistical questions.

11. 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.

The planning figures are illustrations based on the observed recalculated effect, not the trial’s original design assumptions. The stated assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. The effect to detect is set to the stated fraction of the observed effect. The original trial’s sample-size justification is not reported in the registry record.

For this continuous endpoint, the figures are participants per arm, not total events. The 80% power column describes the planning number per arm under the stated assumptions for a design with an 80% chance of detecting the chosen effect if that effect is the true one, subject to the model assumptions. The 90% power column applies the corresponding higher target chance of detection. These are planning scenarios, not descriptions of the study’s actual power or of the probability that the result is correct.

The entries illustrate how the required number per arm increases as the target effect becomes smaller relative to the observed effect: the rows consider planning for 100%, 75%, and 50% of the observed effect. At the full observed effect, the figures are 193 participants per arm for 80% power and 258 participants per arm for 90% power. For planning at 75% of the observed effect, they are 342 and 458 participants per arm, respectively. For planning at 50% of the observed effect, they are 769 and 1,030 participants per arm, respectively. Smaller effects are harder to distinguish from random variation, so they require more participants under these assumptions.

These are hypothetical planning illustrations calculated from a simple observed contrast. They do not account for details that may matter to a crossover design, and the registry does not report the trial’s own planning method. They are not observed power.

12. 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 z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = -1000.000; pooled standard deviation σ = 3499.181.
2. n = 2 × (1.96 + 0.842)² × 3499.181² / -1000.000² = 192.2, rounded up to 193 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
delta <- -1000                      # observed difference in means
sigma <- 3499.18085652438                     # pooled standard deviation
n_per_arm <- function(power, frac = 1) {
  ceiling(round(2 * (z_a + qnorm(power))^2 * sigma^2 / (delta * frac)^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 (t-based, so very slightly larger)
cat("power.t.test:", round(power.t.test(delta = delta, sd = sigma, power = 0.80)$n, 1), "\n")

# Simulation: exact two-sample t-test using simulated means and variances
set.seed(1773421)
n    <- n_per_arm(0.80)
reps <- 20000
m_diff <- rnorm(reps, delta, sigma * sqrt(2 / n))             # difference in sample means
s2     <- sigma^2 * rchisq(reps, 2 * (n - 1)) / (2 * (n - 1))   # pooled sample variance
tstat  <- m_diff / sqrt(s2 * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(tstat) > qt(0.975, 2 * (n - 1))), reps))

Output from running the code

100% of observed effect: n per arm = 193 (80% power), 258 (90% power)
 75% of observed effect: n per arm = 342 (80% power), 458 (90% power)
 50% of observed effect: n per arm = 769 (80% power), 1,030 (90% power)
power.t.test: 193.2 
Simulated power at n = 193 per arm: 0.801 (20000 replicates)

The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-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.

13. Analyses Reported by the Sponsor

The sponsor’s own reported analysis is a geometric least-squares mean ratio of 1.06, with a 90% confidence interval from 0.97 to 1.15. The registry classifies it as an equivalence analysis. This is the sponsor’s analysis as posted in the registry and is distinct from the simple unadjusted recalculation based on the arithmetic group means.

The recalculation gives a fasted-minus-fed arithmetic mean difference of -1000.0 ng*hr/mL, with a 95% confidence interval from -3699.0 to 1699.0 and an unadjusted p-value of 0.468. It uses a different effect measure, confidence level, and summary-statistic approach. It is useful as a transparent descriptive check, but it does not replace or reproduce the sponsor’s analysis. The registry record does not report the model, equivalence bounds, or other analytic details needed to reproduce the sponsor’s result.

The recorded discrepancy flag is false, but that does not make the two results interchangeable: they answer the comparison on different scales. Where a sponsor analysis and a recalculation differ, the sponsor’s own analysis takes precedence as the trial’s reported analysis. The recalculation should be read as supplementary and unadjusted, particularly because the study is recorded as a crossover and participant-level paired data are not reported.

14. Multiplicity, Missing Data and Analysis Populations

The study includes a broad set of questions across two parts. The record identifies a Part A food-effect study and a Part B maximum tolerated dose study. It also lists outcomes concerning best overall response, duration of response, death and progressive disease, and treatment-emergent and serious adverse events. The registry record lists 8 outcome measures and 3 analyses, while 4 secondary outcomes are posted. These multiple outcomes and comparisons create the general possibility of multiplicity: when many statistical questions are tested, the chance of at least one apparently notable result can increase unless the analysis plan addresses that issue.

The registry record does not report a multiplicity adjustment, a hierarchy of hypotheses, or a complete statistical analysis plan. It is therefore not possible to determine from this record whether or how the study controlled the overall error rate across endpoints or comparisons. The unadjusted p-value of 0.468 for the simple recalculation should be understood as unadjusted, not as a result adjusted for the range of study questions.

The primary endpoint population is described as the pharmacokinetic analysis set, including participants with sufficient pharmacokinetic data to derive at least one parameter, with inclusion at a particular time point dependent on evaluability for that endpoint. The record reports group counts for the primary endpoint, but does not provide a complete flow of participants from enrollment through each analysis or explain every exclusion. Missing data amounts, reasons for missingness, and methods for handling missing values are not reported in the registry record.

For a crossover study, information about within-participant observations, period and sequence effects, and the treatment of incomplete pairs can affect analysis. Those details are not reported in the registry record. The record also does not report whether interim analyses were conducted. These omissions do not establish that a method was absent from the full study documents; they mean that the method cannot be evaluated from the registry record.

Consequently, the results should be interpreted as the analyses and outcome summaries that are posted, without assuming an unreported adjustment, imputation procedure, interim plan, or analysis population beyond the stated pharmacokinetic-set description.

15. Safety Results

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

Deaths

Other (non-serious) adverse events

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

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: nausea (28.6%), vomiting (28.6%), leukopenia (14.3%), neutropenia (14.3%), pericardial effusion (14.3%).

The registry posts serious adverse event counts by treatment group. In Treatment Phase Part A, the fed group had 0 serious adverse events among 15 at risk, and the fasted group had 1 among 15 at risk. In Extension Phase Part A at E7820 100 mg, the record reports 5 among 15 at risk. For Treatment and Extension Phase Part B, it reports 10 among 19 at risk for E7820 50 mg and 6 among 7 at risk for E7820 60 mg. These counts belong to different study phases and dose groups and should not be treated as a single direct comparison.

The registry also lists the most frequent serious adverse event terms as Nausea and Vomiting at 28.6% each, and Leukopenia, Neutropenia, Pericardial effusion, and Abdominal pain at 14.3% each. The record does not provide enough detail in these summaries to determine how terms relate to individuals or to compare risk across groups. The serious-event counts do not establish that an event was caused by treatment.

Deaths are listed as 11 in each Part A group, 11 in the Part A extension group, 14 in the Part B 50 mg group, and 5 in the Part B 60 mg group. The record does not provide a causal attribution for these counts in the summary. Serious adverse events, other adverse events, and deaths are distinct posted safety summaries and should be interpreted in their respective group and phase context.

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

The primary endpoint result describes pharmacokinetic exposure to E7820 under fed and fasted conditions in Part A. The posted arithmetic means were 12500.0 ng*hr/mL for fed dosing and 11500.0 ng*hr/mL for fasted dosing. The simple unadjusted recalculation estimates a fasted-minus-fed difference of -1000.0 ng*hr/mL, with a 95% confidence interval from -3699.0 to 1699.0 and an unadjusted p-value of 0.468. The wide interval includes zero and values in either direction, so the recalculation does not provide a precise estimate of the direction or size of the difference.

The sponsor’s reported geometric least-squares mean ratio was 1.06, with a 90% confidence interval from 0.97 to 1.15, and the registry labels it as equivalence. Since the equivalence limits and analysis details are not reported in the registry record, the statistical basis for that label cannot be fully assessed from this record. The ratio and the arithmetic mean difference are not interchangeable summaries.

These findings concern exposure, not whether E7820 changes tumor response, progression, survival, or quality of life. The record includes other outcomes, but the primary endpoint result alone cannot answer those clinical questions. Nor do the posted safety counts establish whether E7820 caused an adverse event or death. Those are separate questions requiring appropriate outcome definitions, comparisons, and analysis.

The registry identifies the study as randomized and crossover, but does not describe the sequence, pairing, or analysis model. Thus, the summary-based recalculation is not a substitute for the sponsor’s crossover analysis. The most defensible reading is limited: the record presents an exposure comparison and a sponsor-reported ratio, while key details for reproducing and fully evaluating the analysis are absent. Neither a treatment recommendation nor a conclusion about clinical effectiveness follows from these pharmacokinetic summaries.

17. Why This Trial Matters Statistically

This study illustrates why the estimand and analysis scale matter in clinical biostatistics. The same fed-versus-fasted pharmacokinetic question can be expressed as an arithmetic mean difference or as a geometric least-squares mean ratio. A difference answers an additive question in the endpoint’s original units; a ratio expresses a relative comparison. Each has its own interpretation and uncertainty measure. Reporting both without distinguishing their roles could lead readers to treat unlike quantities as if they were directly comparable.

The crossover design also makes the analysis structure important. In general, when participants experience more than one condition, their responses may be correlated. An analysis that uses within-participant information can differ in precision from one that treats condition groups as independent. The registry records the crossover design, but does not provide enough detail to determine how the sponsor modeled pairing, sequence, or period. This is a useful example of why design labels alone do not permit reconstruction of an analysis.

The sponsor’s reported equivalence designation highlights another statistical distinction. Equivalence is not established merely by a point estimate close to a ratio of 1; interpretation depends on prespecified margins and a suitable confidence interval. The registry reports the ratio and interval but does not report the margins. The posted result can be accurately described while the underlying decision criteria remain unavailable.

Finally, the sample-size illustrations demonstrate how planning changes with the target effect and desired power. They are not evidence about the trial’s original design or the certainty of its observed result. Together, these issues make the study valuable as a case in reading pharmacokinetic summaries carefully: identify the population and endpoint, distinguish the sponsor’s analysis from a simple recalculation, and keep conclusions within what the registry record documents.

18. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.

The registry record does not report the equivalence margins used for the sponsor’s analysis, the model underlying the geometric least-squares mean ratio, or the method used to calculate its confidence interval. Without these details, the reported equivalence designation cannot be independently assessed. The record also does not provide participant-level pharmacokinetic values, so the sponsor analysis cannot be reproduced from the group summaries.

Although the study is identified as randomized and crossover, the sequence allocation, condition order, washout interval, and treatment of period or carryover effects are not reported in the registry record. The posted recalculation uses group-level summaries and is not a paired crossover reanalysis. It may therefore not capture the precision available from participant-level paired data or the model used in the sponsor’s analysis.

The endpoint population is described in terms of pharmacokinetic data availability and time-point evaluability, but complete participant flow and missing-data handling are not reported. The registry record does not describe the original sample-size calculation, interim analyses, or full statistical analysis plan. It also does not report a multiplicity strategy for the multiple outcomes and study parts.

The primary result addresses AUC in Part A. It should not be extended to Part B dose escalation or to clinical outcomes such as response or survival. The safety summaries include counts by phase and dose group, but do not establish causality or provide all context needed for between-group comparisons. These limitations reflect what the registry record reports, rather than proof that further information was absent from other study documents.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: An Open-label, Dose Escalation, Pharmacodynamic, Pharmacokinetic, and Effect of Food Phase 1 Study of E7820 to Determine the Maximum Tolerated Dose Following Twice Daily Oral Administration in Subjects With Unresectable Solid Tumors — NCT01773421.
• Registry record last updated 2023-06-22; status last verified 2018-02.
• Results first posted 2020-01-18.
• 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.

22. Record Summary

NCT01773421 is a completed, open-label, randomized crossover Phase 1 study of E7820 in people with advanced solid tumors. It included a Part A food-effect study and a Part B maximum tolerated dose study. The primary result discussed is Part A AUC(0-inf), a pharmacokinetic measure of exposure in fed and fasted conditions.

The posted group means were 12500.0 ng*hr/mL for fed dosing and 11500.0 ng*hr/mL for fasted dosing. The simple unadjusted recalculation gives a mean difference of -1000.0 ng*hr/mL, with a 95% confidence interval from -3699.0 to 1699.0. The sponsor reported a geometric least-squares mean ratio of 1.06 with a 90% confidence interval from 0.97 to 1.15 and identified the analysis as equivalence.

The record does not include the equivalence limits or sufficient crossover-analysis details to reproduce the sponsor’s result. The recalculation is supplementary, not a replacement for the sponsor analysis, and the endpoint concerns drug exposure rather than clinical effectiveness.