Calorie-restricted, Ketogenic Diet and Transient Fasting During Reirradiation for Patients With Recurrent Glioblastoma: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Calorie-restricted, Ketogenic Diet and Transient Fasting During Reirradiation for Patients With Recurrent Glioblastoma (NCT01754350), a randomized na study. The primary outcome is Progression-free-survival.

2. Clinical Question

The study rationale in the registry record is that glucose metabolism is important to tumor cells, and that restricting glucose availability had inhibited tumor growth in preclinical models. The clinical study was intended to evaluate whether the dietary intervention could enhance the efficacy of reirradiation. Those statements explain the rationale and question; they are not themselves clinical trial results.

The posted primary outcome is a group-level percentage at a specified follow-up point. It is not a direct measure of the duration of progression-free survival for each participant, and it should not be read as an estimate of overall survival. The record lists overall survival and other outcomes as secondary outcomes, but the primary result presented concerns progression-free survival at 6 months.

3. Trial Design

The registry describes a randomized, parallel-group study with no masking. It lists recurrent glioblastoma as the condition and identifies the sponsor as Johann Wolfgang Goethe University Hospital. The study phase is recorded as NA. Enrollment is listed as 50. The study start is recorded as 2013-05, primary completion as 2017-12, and status as completed.

Participants were assigned to one of two nutrition groups during reirradiation. The intervention arm is described as a calorie-restricted ketogenic diet and transient fasting. The comparator arm is described as standard nutrition, specifically nutrition according to recommendations of the German society for nutrition. The registry describes both interventions as dietary supplements, while the arm descriptions characterize the nutritional approaches used during reirradiation.

The primary outcome is progression-free survival expressed as a percentage of participants at 6 months after reirradiation, based on RANO criteria. The reported arm figures are 20.0 for ketogenic diet and transient fasting, with an arm size of 20, and 16.0 for standard nutrition, with an arm size of 22. The result entries also report 4 events in each group. These are the reported group summaries; the registry record does not provide further detail about how participants were assigned, how outcome assessments were masked, or how the analysis population was defined.

The registry lists 10 secondary outcomes, including feasibility, safety and tolerability, progression-free survival, overall survival, frequency of seizures, ketosis, quality of life, and depression. It lists 11 outcome measures overall and 0 analyses. A detailed statistical analysis plan, including any procedures used to handle missing outcomes or multiple comparisons, is 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.

Overall 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.

6. Primary Endpoint

The registry lists the primary outcome as Progression-free-survival, measured over 6 months.

The primary endpoint is progression-free survival at 6 months after reirradiation, reported as a percentage of participants and assessed using response assessment in neuro-oncology criteria (RANO). The outcome therefore asks whether participants meet the study’s progression-free survival definition at a particular follow-up point. The registry record does not provide a fuller operational definition of progression or explain the specific assessment schedule.

A fixed-time percentage can make the groups’ results easier to compare at a clinically specified follow-up point. It differs from a time-to-event summary, which uses information about when an event occurs and may account for different follow-up durations. The posted primary result is a binary percentage, not a median time to progression or an estimate of overall survival. Overall survival and progression-free survival are separately listed among the outcomes, and the registry identifies the 6-month progression-free survival measure as primary.

The recorded values are 20.0 for the ketogenic diet and transient fasting arm and 16.0 for the standard nutrition arm. The event counts are 4 in each arm. The registry record does not report the endpoint’s missing-data rules, whether participants with incomplete follow-up were included in the denominator, or how deaths and other events were handled in the RANO assessment. Those details matter when interpreting a fixed-time proportion, so the result should be understood in the context of the endpoint description available in the record.

7. Results Posted in the Registry

• Ketogenic Diet and Transient Fasting: 20.0% (4/20) versus 18.2% (4/22) on control; risk difference 1.8 percentage points (95% CI -22.0 to 25.6), risk ratio 1.10 (0.32–3.83); unadjusted two-proportion z-test p = 0.881.

8. Statistical Interpretation

9. Statistical Methods Explained

The posted primary outcome is binary: each participant contributes to a group percentage according to whether the progression-free survival criterion is met at 6 months. The registry gives the arm percentages and event counts. The recalculated comparisons use those summary counts without adjustment for other variables. The comparison is therefore an unadjusted contrast between the groups as represented in the posted summaries.

What does a risk difference describe?

A risk difference expresses the difference between two group proportions on the absolute scale. A value of zero corresponds to equal proportions. A positive or negative value indicates the direction of the difference according to the order in which the groups are compared. The recalculated risk difference is 0.018, with interval limits of -0.22 and 0.256. Because the interval includes zero, the posted data do not pin down the direction of the underlying difference. General explanation: an absolute-scale measure is often useful because it expresses the comparison in terms of the outcome proportion itself rather than a multiple of one group’s value.

How do relative measures differ?

A risk ratio compares proportions by division, while an odds ratio compares odds. A value of 1 represents no relative difference for either measure. The recalculated risk ratio is 1.1, with interval limits of 0.316 and 3.826. The recalculated odds ratio is 1.125, with interval limits of 0.241 and 5.252. Their broad intervals span values below and above 1, indicating uncertainty about the direction and magnitude of the relative association. General explanation: ratios can appear larger or smaller depending on the scale, so they should be interpreted alongside the absolute comparison and the event frequencies.

What does the p-value contribute?

The unadjusted p-value is 0.881. General explanation: a p-value describes how unusual the observed data, or data more extreme, would be under a statistical model that assumes no group difference. It is not the probability that the null hypothesis is true, nor does it measure the probability that the result will replicate. A large p-value does not prove equality or establish that any possible difference is unimportant. Its meaning depends on the model, endpoint, and analysis choices. The p-value belongs to the unadjusted recalculation and should not be mistaken for an adjusted or sponsor-reported analysis.

Why does the interval matter?

An interval places the point estimate in context by showing a range of values compatible with the data under the calculation’s assumptions. General explanation: a narrow interval indicates greater precision, while a wide interval indicates that a range of effect sizes remains plausible. The interval around the recalculated risk difference crosses zero and is broad relative to the point estimate. That pattern limits confidence about both the presence and size of a group difference. The registry record does not identify the interval’s confidence level or give a detailed method for its construction, so no further assumptions about that method should be inferred.

What does unadjusted mean?

An unadjusted comparison uses the group outcome summaries without accounting for additional participant characteristics or other model terms. It can be a transparent description of the observed group contrast, but it does not address possible chance imbalances or other sources of variation that an adjusted analysis might consider. Randomization is a design feature intended to support fair comparisons, but the record does not provide enough detail to determine what additional analyses were planned or performed. The registry lists 0 analyses and does not report a model specification, covariates, or an analysis population.

General explanation: binary outcome analyses can also be affected by sparse event counts. With few events, estimates can be unstable, and uncertainty intervals can be wide. The primary outcome has 4 events in each arm. The recalculated intervals reflect substantial uncertainty in the group comparison; they should not be interpreted as precise estimates merely because a single point estimate is reported. No further calculations are needed to make that qualitative observation.

Over-dispersion is a general concern when outcome variation is greater than a model assumes. It can make standard errors too small if the model does not account for that extra variation. The registry record does not report a model for over-dispersion or a method that would allow it to be assessed for this endpoint. More generally, any statistical method depends on assumptions about how observations arise and how outcomes are recorded. The available aggregate counts do not allow those assumptions to be examined in detail.

These recalculated measures are simple summaries, not a replacement for a prespecified analysis of participant-level data. They do not address missing outcomes, adjustment, timing of events, or multiplicity. The registry record does not report those methods. The result should accordingly be read as a descriptive, unadjusted comparison accompanied by substantial statistical uncertainty.

10. Confidence Intervals and Precision

The recalculated risk difference is 0.018, and its interval ranges from -0.22 to 0.256. This interval includes zero and spans values on both sides of it. The point estimate is therefore not precise enough to establish the direction of the underlying difference from the posted summaries alone. The risk ratio and odds ratio intervals are also broad: 0.316 to 3.826 for the risk ratio and 0.241 to 5.252 for the odds ratio.

General explanation: an interval is a way to express uncertainty around an estimate. Under the method’s assumptions, its limits indicate the range of estimates compatible with the observed data at the interval’s stated confidence level. The registry record does not report that confidence level or the full interval method, so the limits should be read as the uncertainty interval attached to the recalculation, without assuming additional methodological detail.

The posted event counts are 4 in each group, with arm sizes of 20 and 22. A limited number of observed events can leave a wide range of possible underlying effects consistent with the data. The interval does not show that all values within it are equally likely, and it does not indicate that effects outside it are impossible. It gives a more complete picture of uncertainty than the point estimate alone.

Precision is distinct from whether an estimate is statistically significant. A wide interval can include the no-difference value and still leave open the possibility of meaningful differences in either direction. The unadjusted p-value of 0.881 does not resolve that uncertainty. The registry record does not report a precision target or the original sample-size justification, so the observed interval cannot be assessed against a documented design goal.

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 estimates are illustrations based on the observed effect, not the trial’s original design assumptions. They use a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. The assumed effect to detect is set at a stated fraction of the observed effect. The registry record does not report the trial’s original sample-size justification or design assumptions.

These figures are participants per arm for 80% power and participants per arm for 90% power. Power describes the chance, under the assumed effect and statistical model, of detecting a difference at the specified significance level. The 80% column gives the per-arm planning estimate under an 80% target; the 90% column gives the estimate under a 90% target. Higher target power generally requires more participants when the other assumptions are held constant.

At 100% of the observed effect, the illustration gives 7,334 participants per arm for 80% power and 9,818 participants per arm for 90% power. At 75% of the observed effect, it gives 12,920 participants per arm for 80% power and 17,295 participants per arm for 90% power. At 50% of the observed effect, it gives 28,801 participants per arm for 80% power and 38,555 participants per arm for 90% power. Smaller effects need more participants to detect under these assumptions, which is why the estimates increase as the assumed fraction of the observed effect decreases.

These are planning illustrations, not observed power. They do not indicate the probability that the completed trial’s result is correct, and they do not replace the trial’s actual outcome analysis. Because the observed effect is uncertain, planning around it also inherits that uncertainty. The estimates should be used to understand how the stated assumptions affect a hypothetical design, not as evidence that the trial was planned to recruit those numbers.

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, p₀ and p₁ are the control and treatment proportions, and p̄ is their average.

Worked calculation for this trial

1. Control proportion p₀ = 0.182; treatment proportion p₁ = 0.200; average p̄ = 0.191.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.5558 = 1.0894.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.5557 = 0.4677.
4. n = (1.0894 + 0.4677)² / (0.0182)² = 7,333.6, rounded up to 7,334 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 <- 0.181818181818182                          # control proportion
p1 <- 0.2                          # 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(1754350)
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 = 7,334 (80% power), 9,818 (90% power)
 75% of observed effect: n per arm = 12,920 (80% power), 17,295 (90% power)
 50% of observed effect: n per arm = 28,801 (80% power), 38,555 (90% power)
power.prop.test: 7333.6 
Simulated power at n = 7,334 per arm: 0.796 (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.

13. Multiplicity, Missing Data and Analysis Populations

The registry lists 10 secondary outcomes in addition to the primary outcome. They include feasibility, safety and tolerability, progression-free survival, overall survival, frequency of seizures, ketosis, quality of life measured by the EORTC Quality of Life Questionnaire, and depression. The record lists 11 outcome measures overall and 0 analyses. The presence of multiple outcomes raises a general interpretive issue: when many statistical comparisons are made, the chance of at least one apparently notable result can increase unless the analysis plan addresses multiplicity.

The registry record does not report whether any multiplicity adjustment was planned or used, whether the secondary outcomes were organized into a testing hierarchy, or which comparisons were considered confirmatory. It also does not provide results for the listed secondary outcomes in the posted summaries. No conclusion about those outcomes, or about adjustment for multiple testing, can therefore be drawn from the record.

Missing-data handling is also not reported in the registry record. The available primary outcome summaries include event counts and arm sizes, but the record does not say whether any participants had missing 6-month assessments, how incomplete follow-up was treated, or whether any imputation or sensitivity analysis was used. For a fixed-time percentage, the denominator and the treatment of participants without an observed assessment can affect interpretation. The posted summary does not provide enough detail to determine those choices.

The analysis population is not reported in the registry record. In particular, the record does not state whether the primary result was analyzed by original randomized assignment, according to treatment received, or under another definition. The randomization and parallel-group design are recorded, but those design labels do not establish the analysis population or resolve missing-data choices. These omissions limit assessment of how closely the reported comparison follows a prespecified analysis strategy.

General explanation: multiplicity, missing outcomes, and analysis-population definitions are related but distinct issues. Multiplicity concerns interpretation across multiple tests; missing-data methods concern unobserved outcomes; and analysis-population rules specify which participants contribute to an estimate. A clear report describes each separately. Since those details are not reported in the registry record, the unadjusted primary comparison should be interpreted as a limited summary rather than a complete account of the analysis plan.

14. 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 non-serious adverse event terms

The registry reports serious adverse events in 0 participants in the ketogenic diet and transient fasting arm and 0 participants in the standard nutrition arm. The numbers at risk for this safety summary are 20 and 22, respectively. The record also reports 0 deaths in each arm. No serious adverse event terms are listed.

For other adverse events, the record reports 4 affected participants in the ketogenic diet and transient fasting arm and 5 in the standard nutrition arm. The corresponding numbers at risk are 20 and 22. These are counts, not estimates of event severity or a comparison adjusted for follow-up or participant characteristics. They should not be combined with the serious adverse event counts as though they described the same category.

The registry record does not report the definitions used for serious or other adverse events, the specific terms for the other events, their timing, duration, or relationship to the study interventions. It also does not describe how safety events were collected or whether reporting completeness differed between arms. Zero recorded serious adverse events should therefore be read as the reported count, not as proof that serious events were impossible or that the approaches had no safety concerns.

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

The primary result describes the proportion meeting the progression-free survival criterion at 6 months after reirradiation in each randomized group. The reported percentages are 20.0 for ketogenic diet and transient fasting and 16.0 for standard nutrition. The unadjusted recalculation gives a risk difference of 0.018, with an interval from -0.22 to 0.256, and a p-value of 0.881. The interval spans no difference and effects in either direction, so the estimate is imprecise.

These data do not establish that one nutrition approach caused better or worse progression-free survival. The point estimate alone does not show a reliable treatment effect, while the broad interval means the result also cannot establish that the groups are equivalent. The posted summary is compatible with a range of possible underlying differences. The result should be described as uncertain rather than as proof of benefit, no effect, or harm.

The endpoint is a fixed-time percentage, not a measure of how long each participant remained progression-free. It does not answer the separate question of overall survival, and it cannot summarize the full course of disease. The registry lists other outcomes, including overall survival, safety and tolerability, seizures, ketosis, quality of life, and depression, but the record does not report their results in the summaries.

Interpretation is limited by the information available about the analysis. The registry does not report the missing-data rules, analysis population, adjustment strategy, or multiplicity plan. It also does not provide a detailed statistical analysis plan or the original sample-size justification. The unadjusted recalculation is therefore best treated as a transparent comparison of the posted summaries, not as a complete evaluation of all prespecified analyses.

The safety counts provide a separate descriptive picture: no serious adverse events or deaths are reported in either arm, while other adverse events are reported in both. Event definitions, terms, and collection details are not reported in the registry record. Those counts do not by themselves establish comparative safety. Overall, the result is a limited and uncertain estimate from a randomized comparison, and it should not be extended beyond the outcome and follow-up point that were reported.

16. Why This Trial Matters Statistically

This study is statistically informative because it pairs a randomized design with a fixed-time binary endpoint and a small number of observed primary events. Randomization is intended to support comparison between groups, while the event counts and percentages provide a direct description of what was recorded. The central challenge is that the estimates remain uncertain: the recalculated interval for the risk difference crosses zero and covers a broad range.

The example also illustrates why the point estimate, interval, and p-value should be read together. A point estimate gives one summary of the observed contrast. The interval communicates uncertainty about its magnitude and direction. The p-value of 0.881 does not prove equal outcomes, just as the numerical difference in the posted percentages does not by itself prove a group effect. Looking at these measures together discourages conclusions based on a single number.

Another statistical issue is that the primary endpoint captures status at a specified time rather than the timing of progression-free survival events. That choice has a clear interpretation, but it does not provide the same information as a time-to-event analysis. The registry lists progression-free survival as the primary outcome and also lists overall survival among the secondary outcomes. The record does not provide enough analysis detail to infer additional time-to-event results.

The trial also has several registered secondary outcomes. Without a reported multiplicity plan, analysis population, or missing-data method, readers cannot fully evaluate how those outcomes were intended to inform inference. The large planning estimates based on fractions of the observed effect further illustrate that study size depends strongly on the effect assumed for planning. Those illustrations are not evidence of the original design rationale or the probability that the completed study detected an effect.

For biostatistical interpretation, the case is a reminder to distinguish design features, observed summaries, recalculated comparisons, and unreported analytical decisions. The randomized and parallel-group labels are useful context, but they do not supply missing methodological detail. The posted primary comparison offers a bounded description of the recorded result, while important questions about precision, analysis choices, and other outcomes remain unresolved.

17. 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.
• Participant counts were reconstructed from posted percentages and arm sizes, so small rounding differences are possible.

Several limitations are specific to the information recorded for this trial. The primary outcome is reported as a percentage at 6 months after reirradiation, with the assessment based on RANO criteria, but the registry record does not provide a detailed endpoint definition, assessment schedule, or rules for incomplete assessments. The record also does not identify the interval confidence level or fully describe the method used for the recalculated uncertainty estimates.

The posted primary outcome has 4 events in each arm. With these sparse counts, the recalculated risk-difference interval is broad, as are the relative-measure intervals. The result therefore has limited precision. The arm sizes for the primary comparison are 20 and 22, while the registry’s overall enrollment entry is 50; the record does not explain the relationship between overall enrollment and the primary-outcome denominators or provide participant flow information.

The registry does not report the original sample-size justification, analysis population, missing-data handling, covariate adjustment, or multiplicity procedures. It lists 0 analyses, and it does not provide detailed results for the secondary outcomes in the posted summaries. The record therefore does not support a full assessment of analysis decisions, robustness, or consistency across outcomes.

The study is recorded as randomized, parallel, and unmasked. The registry record does not give further detail about sequence generation, allocation concealment, adherence to the assigned nutrition approach, or assessment masking. These details are relevant to understanding potential sources of bias, but their absence from the record does not establish that any particular method was or was not used. The safety entries likewise lack event terms and collection details. Together, these limits counsel against conclusions broader than the recorded 6-month primary comparison and the descriptive safety counts.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Calorie-restricted, Ketogenic Diet and Transient Fasting During Reirradiation for Patients With Recurrent Glioblastoma — NCT01754350.
• Registry record last updated 2021-06-02; status last verified 2021-05.
• Results first posted 2021-06-02.
• 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.

21. Record Summary

The registry record describes a completed randomized, unmasked, parallel-group study of a calorie-restricted ketogenic diet and transient fasting versus standard nutrition during reirradiation for recurrent glioblastoma. Enrollment is listed as 50. The study start is recorded as 2013-05 and primary completion as 2017-12. The phase is listed as NA.

The primary outcome is progression-free survival at 6 months after reirradiation, expressed as a percentage and assessed using RANO criteria. The reported values are 20.0 in the intervention arm and 16.0 in the standard nutrition arm. An unadjusted recalculation gives a risk difference of 0.018, with an interval from -0.22 to 0.256, and a p-value of 0.881. The uncertainty interval includes zero and is broad.

The registry lists 10 secondary outcomes and 11 outcome measures overall, while listing 0 analyses. It does not report the analysis population, missing-data rules, multiplicity procedures, or original sample-size justification. Serious adverse events and deaths are recorded as 0 in both arms; other adverse events are recorded in both. These results are descriptive and do not resolve the uncertainty around the primary comparison.