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Actinic Keratosis Phase 3 Event-Rate Endpoint NCT03115476

A Trial to Compare the Incidence of Squamous Cell Carcinoma (SCC) and Other Skin Neoplasia on Skin Areas Treated With Ingenol Disoxate Gel or Vehicle Gel for Actinic Keratosis on Face and Chest or Scalp: Complete Statistical Analysis

This analysis examines a randomized, open-label extension trial of ingenol disoxate gel versus vehicle gel and the reported incidence of squamous cell carcinoma and other skin neoplasia in treatment areas. It contrasts the registry’s time-to-event analyses with simple rate-based re-calculations and considers the precision and limits of those results.

Trial start: 2017-06-16  ·  Enrollment: 563  ·  Sponsor: LEO Pharma
Scope of this record

This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.

1. Trial at a Glance

This page covers the registry results for A Trial to Compare the Incidence of Squamous Cell Carcinoma (SCC) and Other Skin Neoplasia on Skin Areas Treated With Ingenol Disoxate Gel or Vehicle Gel for Actinic Keratosis on Face and Chest or Scalp (NCT03115476), a randomized phase 3 study. The primary outcome is Time to First Squamous Cell Carcinoma (SCC) in the Treatment Area.

563
Enrollment
Phase 3
3
Arms
In the primary outcome
2.20
Rate ratio
Ingenol Disoxate Gel 0.018%
0.77–6.24
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT03115476
PhasePhase 3
ConditionActinic Keratosis, Squamous Cell Carcinoma
AllocationRandomized
Design modelParallel
MaskingNone (open label)
Enrollment563
Arms in the primary outcome3
Lead sponsorLEO Pharma
Results postedYes

2. Clinical Question

Population

People with actinic keratosis who had been randomized and applied investigational product in one of four main trials. The primary outcome description calls this the Full Analysis Set and gives its size as 1234 subjects. The registry lists enrollment of 563 for this extension trial; the difference between these population figures is not reconciled in the registry record.

Intervention

Ingenol disoxate gel 0.018% or ingenol disoxate gel 0.037%, evaluated during an extension period after the main trials.

Comparator

Vehicle gel. The registry describes a randomized, parallel-group comparison and reports no masking.

Primary question

During follow-up of up to 24 months, how did the time to first squamous cell carcinoma in the treatment area compare among the ingenol disoxate groups and vehicle? The outcome description expresses the relative difference as a hazard ratio and also reports incidence rates per 100 patient years.

The clinical rationale in the registry is that treating actinic keratoses may be intended to reduce progression to squamous cell carcinoma. The study therefore followed participants for squamous cell carcinoma and other skin neoplasia in the treatment area, rather than assessing only an immediate response to treatment. The primary endpoint focused on the first squamous cell carcinoma; a secondary endpoint included first squamous cell carcinoma or other skin neoplasia. The registry describes the extension as lasting 2 years, with total follow-up for each participant planned to be 3 years and 2 months across the main trials and extension. The outcome timeframe itself begins at Visit 2, specified as 6 months after Month 14 of the main trial, and continues to the event or up to 24 months.

3. Trial Design

This was a Phase 3, randomized, parallel-group trial with no masking, sponsored by LEO Pharma. The registry lists three groups: ingenol disoxate gel 0.018%, ingenol disoxate gel 0.037%, and vehicle gel. The trial began on 2017-06-16, had a primary completion date of 2018-03-12, and is listed as terminated. The registry enrollment figure is 563.

The outcome description identifies a Full Analysis Set of 1234 subjects who were randomized and applied investigational product in one of four main trials. The relationship between this analysis population and the extension trial’s listed enrollment of 563 is not reported in the registry record. The extension is described as drawing on trials LP0084-1193, -1194, -1195 and -1196. The record describes a planned 2-year extension, intended to bring total follow-up to 3 years and 2 months for each participant. The primary endpoint timeframe is up to 24 months, beginning at Visit 2, which is specified as 6 months after Month 14 of the main trial.

The reported outcomes are event rates per 100 patient years, with 95% confidence intervals, and a time-to-event analysis. The registry reports an overall likelihood ratio test for a hazard ratio across the three groups. The arm descriptions contain no further detail. The randomization procedure, allocation ratio, reasons for termination, and the trial’s original sample-size justification are not reported in the registry record. Although the registry states that masking was absent, other operational details about conduct and follow-up are not reported in the registry record. These gaps limit how fully the design and analysis process can be reconstructed from the record alone.

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: 1234 participants were randomised and applied investigational medicinal product (IMP) in the trials LP0084-1193, -1194, -1195, -1196 (main trials, Period 1). A total of 563 participants from the main trials continued and were enrolled into this extension follow-up trial (LP0084-1369, Period 2).

Main Trials (LP0084-119x)

StageIngenol Disoxate Gel 0.018%Ingenol Disoxate Gel 0.037%Vehicle Gel
STARTED407418409
COMPLETED407418409
NOT COMPLETED000

LP0084-1369

StageIngenol Disoxate Gel 0.018%Ingenol Disoxate Gel 0.037%Vehicle Gel
STARTED191210162
COMPLETED000
NOT COMPLETED191210162

Reasons for not completing this period:

ReasonIngenol Disoxate Gel 0.018%Ingenol Disoxate Gel 0.037%Vehicle Gel
Death102
Trial terminated by Sponsor190210160

Analysis population for the primary outcome, as defined in the registry: Full Analysis Set: 1234 subjects who were randomised and applied IMP in one of 4 Main Trials

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

Population: Of the 1234 participants who were randomised and applied IMP in the Main Trials (Period1) a total of 563 participants continued into this extension follow-up trial. The endpoints in this trial are time to event endpoints, starting at randomisation in the Main Trials, and therefore the full analysis set consists of 1234 participants

CharacteristicUnitIngenol Disoxate Gel 0.018%Ingenol Disoxate Gel 0.037%Vehicle GelTotal
Participants analysed191210162563
Age, Categorical: <=18 yearsParticipants0000
Age, Categorical: Between 18 and 65 yearsParticipants575543155
Age, Categorical: >=65 yearsParticipants134155119408
Age, Continuousyears69 (48 to 88)71 (36 to 94)69 (48 to 92)70 (36 to 94)
Sex: Female, Male: FemaleParticipants6703097
Sex: Female, Male: MaleParticipants124210132466
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants93012
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants182206162550
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants0101
Race (NIH/OMB): American Indian or Alaska NativeParticipants0000
Race (NIH/OMB): AsianParticipants0000
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants0000
Race (NIH/OMB): Black or African AmericanParticipants0000
Race (NIH/OMB): WhiteParticipants190209162561
Race (NIH/OMB): More than one raceParticipants1001
Race (NIH/OMB): Unknown or Not ReportedParticipants0101
Region of Enrollment: Canadaparticipants436253158
Region of Enrollment: United Statesparticipants9810470272
Region of Enrollment: United Kingdomparticipants12131237
Region of Enrollment: Franceparticipants26412
Region of Enrollment: Germanyparticipants19251761
Region of Enrollment: Spainparticipants170623
Fitzpatrick skin type: Type IParticipants34262888
Fitzpatrick skin type: Type IIParticipants10911694319
Fitzpatrick skin type: Type IIIParticipants425435131
Fitzpatrick skin type: Type IVParticipants413421
Fitzpatrick skin type: Type VParticipants2114

6. Primary Endpoint

The registry lists the primary outcome as Time to First Squamous Cell Carcinoma (SCC) in the Treatment Area, measured over From Visit 2 (6 months after Month 14 of main trial) to first SCC in the treatment area, up to 24 months.

ElementRegistry entry
Result typeNumber
Measure of spread95% Confidence Interval
UnitSCC events per 100 patient years
Endpoint classificationEvent-Rate Endpoint

The primary endpoint is time to first squamous cell carcinoma in the treatment area. It is measured from the stated follow-up start—Visit 2, 6 months after Month 14 of the main trial—until the first such event or the end of follow-up, up to 24 months. The registry also presents observed incidence rates per 100 patient years for each group. A patient-year rate expresses events in relation to accumulated time at risk, so participants with different amounts of follow-up can contribute to the rate according to their observed exposure time.

Time-to-event methods are used because the timing of an event and the duration of observation both matter. A participant who has not experienced the event by the end of observation is not necessarily known never to experience it; their observed time contributes up to the point their follow-up ends. The hazard ratio describes the relative instantaneous event rate over follow-up under the model used for the analysis. It is not the same quantity as a ratio of crude incidence rates, and it depends on the time-to-event analysis.

The endpoint is clinically relevant to the registry’s stated rationale concerning actinic keratosis and progression to squamous cell carcinoma. However, the results describe observed outcomes during the specified follow-up, not a complete account of lifetime risk. The registry’s description gives the endpoint and timeframe, but further details of censoring rules, event adjudication, and the handling of incomplete follow-up are not reported in the registry record.

7. Results Posted in the Registry

Rate ratio: Ingenol Disoxate Gel 0.018%

2.20

95% CI: 0.77 to 6.24

Recalculated from the posted summary statistics

Treatment effect versus the control arm
Forest plot of rate ratio vs control (95% CI)Ingenol Disoxate Gel 0.018%Ingenol Disoxate Gel 0.037%0.140.310.711.613.658.27rate ratio vs control (95% CI)

8. Secondary Efficacy Endpoints

The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.

Secondary outcomeTypeEffect measureEstimate (95% CI)Planning size, 80% power
Time to First Squamous Cell Carcinoma (SCC) or Other Skin Neoplasia in the Treatment AreaEvent-Rate EndpointRate ratio3.21 (1.75 to 5.89)475 per arm

Time to First Squamous Cell Carcinoma (SCC) or Other Skin Neoplasia in the Treatment Area

Treatment effect versus the control arm
Forest plot of rate ratio vs control (95% CI)Ingenol Disoxate Gel 0.018%Ingenol Disoxate Gel 0.037%0.340.631.162.143.947.28rate ratio vs control (95% CI)

The secondary endpoint combines first squamous cell carcinoma with other skin neoplasia in the treatment area, making it broader than the primary endpoint. The overall sponsor analysis for this endpoint gives a hazard ratio of 1.99, with a 95% confidence interval from 1.17 to 3.62 and p < 0.01. The rate-based comparisons show a different pattern across the two active groups: the 0.018% comparison has a rate ratio above 1, while the 0.037% comparison is near 1. This contrast does not form a consistent dose pattern across the secondary results and should be interpreted cautiously.

The broader endpoint’s overall time-to-event result is not the same question as the primary analysis of first squamous cell carcinoma alone. Adding other skin neoplasia changes the event definition, and the registry’s summary does not establish which event types account for the overall result. The secondary findings may provide context about the combined endpoint, but they cannot be used to replace or retrospectively redefine the primary outcome.

Unadjusted secondary results carry less weight because multiple outcomes and comparisons can increase the chance of apparently notable findings. The registry record does not report a multiplicity correction, a testing hierarchy, or a strategy that would preserve a stated overall error rate across the primary and secondary analyses. The secondary result should therefore be treated as evidence requiring cautious interpretation, rather than as a standalone confirmatory conclusion. It also does not resolve the uncertainty in the primary endpoint, which measured squamous cell carcinoma alone and had a broad interval around the overall hazard ratio.

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

9. Statistical Interpretation

Clinical Biostats interpretation

For the primary outcome, observed rates were 2.77 events per 100 patient years in the 0.018% group, 0.88 in the 0.037% group, and 1.26 in the vehicle group. Their 95% confidence intervals were 1.55 to 4.57, 0.28 to 2.04, and 0.46 to 2.74, respectively. These intervals overlap. The rates are descriptive summaries; they do not alone account for the full time-to-event analysis.

The registry’s reported overall time-to-event analysis across all three groups gave a hazard ratio of 1.43, with a 95% confidence interval from 0.61 to 3.9 and p = 0.43. This interval includes the value corresponding to no relative difference in hazard, and the p-value does not provide strong evidence against the null hypothesis under that analysis. The registry does not report separate sponsor time-to-event estimates for each active dose versus vehicle.

Simple, unadjusted rate-based re-calculations compare each active group with vehicle. For 0.018%, the estimated rate ratio is 2.198, with a 95% confidence interval from 0.774 to 6.24 and p = 0.139. For 0.037%, it is 0.698, with a 95% confidence interval from 0.184 to 2.654 and p = 0.598. Both intervals include a rate ratio of 1, the value representing equal rates. These re-calculations are not the sponsor’s time-to-event analysis; they use the posted group rates and a simple rate-comparison approach.

Neither the group rates nor the pairwise re-calculations establish a precise difference in primary outcome rates. The confidence intervals permit a range of relative effects, including no difference, and are wide. The estimates point in different directions for the two doses, but the event-rate data are too imprecise to treat those directions as stable evidence of a dose pattern. The overall sponsor analysis, which is the registry’s reported inferential analysis for the primary endpoint, also has an interval spanning the no-difference value.

Interpretation should account for the trial’s terminated status, the distinction between the extension enrollment and described analysis population, the absence of masking, and the limited methodological detail in the record. The registry does not report why the trial was terminated or whether that affected follow-up or analysis. The findings concern the specified treatment-area outcome and follow-up period; they do not answer broader questions about all skin lesions, longer-term outcomes, or other populations.

10. Statistical Methods Explained

The registry reports two related kinds of summary for the primary endpoint: incidence rates and a time-to-event analysis. They answer connected but distinct questions. A rate describes the number of events relative to accumulated person-time. A time-to-event analysis uses the observed time until an event, while also accounting for participants whose event has not occurred by the end of their observed follow-up. The registry names the sponsor’s method as a likelihood ratio test and its parameter as a hazard ratio.

What does a rate ratio describe?

A rate ratio compares the event rate in one group with the rate in another. A value of 1 represents equal rates; values above or below 1 indicate higher or lower rates in the numerator group, respectively. The re-calculated comparisons use the vehicle rate as the reference and compare each ingenol disoxate rate with it. These are simple, unadjusted comparisons based on the posted summary rates. They are not adjusted for participant characteristics and do not replace the sponsor’s time-to-event analysis.

For the primary outcome, the re-calculations use a Poisson rate framework and confidence intervals based on the posted rates. The Poisson model is a common approach for count events observed over exposure time. In general, it assumes that event counts vary in a way captured by the modeled rate and exposure. If real-world variation is greater than the model allows—called over-dispersion—the resulting uncertainty can be understated. The registry does not report an over-dispersion assessment, so the impact of that issue on these re-calculations is unknown. These model considerations are general statistical cautions, not claims that over-dispersion occurred in this trial.

How do rate ratios differ from hazard ratios?

The reported hazard ratio comes from a time-to-event analysis, whereas the re-calculated rate ratio compares overall rates. A hazard ratio concerns relative event hazards over the follow-up period under the time-to-event model. A rate ratio compares event occurrence per unit of exposure. Their estimates need not match, especially when they summarize data differently or use different assumptions. The sponsor’s overall hazard ratio covers all three groups in the reported analysis; the simple re-calculations make two separate active-versus-vehicle comparisons. They should therefore not be treated as competing estimates of precisely the same contrast.

A likelihood ratio test evaluates how well a model including the tested effect fits relative to a model without that effect. The registry reports an overall test, with a hazard ratio and confidence interval, across the three groups. The record does not give enough detail to reconstruct the model specification, its covariates, or its handling of follow-up and censoring. A hazard ratio is a model-based summary, not a direct count of events and not a measure of absolute risk.

What does a confidence interval add?

A confidence interval communicates statistical uncertainty around an estimate. In repeated use of the same method under its assumptions, intervals constructed at a stated confidence level have a specified long-run coverage property. For an individual analysis, the interval identifies values reasonably compatible with the observed data and model; it does not guarantee that the true value lies within those particular endpoints. An interval spanning the null value indicates that the data are compatible with no relative difference as well as with effects in either direction, depending on its endpoints.

Wide intervals indicate limited precision. Sparse events, limited exposure time, and variability can all contribute to uncertainty in event-rate analyses. The primary rate intervals and the sponsor’s hazard-ratio interval are broad enough that the exact relative difference remains uncertain. A p-value addresses the compatibility of the data with a specified null model; it does not measure the size or clinical importance of an effect. Nor does a non-small p-value prove that groups are equivalent.

How should the secondary analysis be viewed?

The secondary endpoint expands the event definition to first squamous cell carcinoma or other skin neoplasia in the treatment area. The registry reports an overall hazard ratio and pairwise rate comparisons for this outcome. Because it is secondary, its results are not interchangeable with the primary endpoint. The broader endpoint includes additional event types, and the registry does not report whether the analysis was intended to confirm a separate hypothesis or how secondary inference was prioritized.

Multiplicity arises when several outcomes, groups, or comparisons are tested. If many tests are considered, the chance of at least one apparently unusual result can increase. The registry record does not report a multiplicity adjustment or a prespecified hierarchy for interpreting the secondary endpoint. Accordingly, its unadjusted findings should be regarded as less conclusive than a result from a prespecified, multiplicity-controlled primary analysis.

The record identifies the primary analysis population as participants randomized and applying investigational product in one of four main trials. It does not report detailed inclusion rules, missing-data methods, censoring procedures, or sensitivity analyses. These details matter because time-to-event analyses depend on how follow-up ends and how participants with incomplete observation are handled. The absence of those details in the registry record limits independent assessment of robustness.

11. Confidence Intervals and Precision

Precision is limited for the primary outcome. The observed rates are accompanied by 95% confidence intervals that span a substantial range. In the 0.018% group, the rate is 2.77 per 100 patient years, with an interval from 1.55 to 4.57. In the 0.037% group, the rate is 0.88, with an interval from 0.28 to 2.04. Vehicle has a rate of 1.26, with an interval from 0.46 to 2.74. The overlap across these intervals reflects uncertainty in the estimated group rates; interval overlap alone is not a formal test of the difference between groups.

The sponsor’s overall primary hazard ratio is 1.43, with a 95% confidence interval from 0.61 to 3.9. This interval includes the no-difference value and covers estimates in either direction. The pairwise rate-ratio re-calculations are also imprecise: the 0.018% comparison has an interval from 0.774 to 6.24, and the 0.037% comparison has an interval from 0.184 to 2.654. Each includes 1. These ranges do not support a precise estimate of the relative rate for either dose versus vehicle.

Confidence intervals do not show that all values inside them are equally likely, and they do not account for limitations that are not represented in the model. They should be read alongside the analysis method, follow-up, and event information. The registry reports rates per 100 patient years and confidence intervals, but does not give the group-specific event counts or total accumulated person-time. The precision of the estimates, as reflected in the intervals, is therefore more informative than treating a point estimate as definitive.

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 detectParticipants per arm, 80% powerParticipants per arm, 90% power
100% of the observed effect2,9213,911
75% of the observed effect5,5477,425
50% of the observed effect13,44818,003
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect2,0005,00010,00020,00050,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Treat these figures cautiously. The observed difference is imprecise: its confidence interval includes no difference at all. A sample size built on a noisy estimate can be far too small or too large, so the smaller-effect rows are the more cautious guide.
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, Poisson model with equal follow-up (from the outcome time frame: 0.50 years per participant). Real event counts are usually over-dispersed, so a negative binomial model would need more participants than shown; treat these figures as a lower bound. Calculated for the comparison: Ingenol Disoxate Gel 0.018%.

The planning figures are illustrations based on the observed effects, not the original trial’s design calculation. The original sample-size assumptions are not reported in the registry record. The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each planning row considers an effect equal to a stated fraction of the observed effect. For time-to-event outcomes, the figures represent total events using the Schoenfeld approach; for other outcomes, they represent participants per arm. The comparisons in this analysis are time-to-event comparisons, so the event-count interpretation applies.

The 80% power column indicates the planned number of total events under the stated assumptions for a design with an 80% chance of detecting the chosen effect if that effect were the true one. The 90% power column uses a higher chance of detection, which generally requires more information. These values do not describe how much power the completed trial had. This is not observed power.

Rows planning for 75% or 50% of the observed effect represent smaller target effects than planning for 100% of the observed effect. Smaller effects are harder to distinguish from random variation, so more events are needed under the same assumptions. For example, the primary 0.018% comparison lists 2,921 total events for 80% power when planning for 100% of the observed effect, and 5,547 when planning for 75%. The corresponding 0.037% comparison lists 23,515 and 39,692. Those figures are planning illustrations, not claims about the trial’s achieved enrollment or event count. Their scale also emphasizes that estimates from a study with relatively limited information may be too imprecise to distinguish modest effects.

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 = (z1−α/2 + z1−β)2 (1/λ0 + 1/λ1) / ( T · [ln(λ1/λ0)]2 )

n is the number of participants in each arm, λ0 and λ1 are event rates per patient-year, and T is follow-up per participant in years. This assumes Poisson counts and equal follow-up.

Worked calculation for this trial

  1. Control rate λ0 = 0.0126; treatment rate λ1 = 0.0277 events per patient-year; follow-up T = 0.50 years.
  2. n = (1.96 + 0.842)2 × (1/0.0126 + 1/0.0277) / (0.50 × [ln(2.198)]2) = 2,921.0, rounded up to 2,921 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
lambda0 <- 0.0126                      # control rate, events per patient-year
lambda1 <- 0.0277                      # treatment rate
tt      <- 0.5                       # follow-up per participant, years
n_per_arm <- function(power, frac = 1) {
  l1 <- lambda0 * (lambda1 / lambda0)^frac   # smaller effect = fraction of the observed log rate ratio
  ceiling(round((z_a + qnorm(power))^2 * (1 / lambda0 + 1 / l1) / (tt * log(l1 / lambda0)^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 = ",")))

# Simulation 1: Poisson counts. Simulation 2: over-dispersed counts (variance = 1.5 x mean), analysed with the matching variance.
set.seed(3115476)
n    <- n_per_arm(0.80)
reps <- 20000
m0 <- lambda0 * n * tt; m1 <- lambda1 * n * tt
x0 <- rpois(reps, m0); x1 <- rpois(reps, m1)
z  <- log(x1 / x0) / sqrt(1 / x0 + 1 / x1)
cat(sprintf("Simulated power, Poisson counts, n = %s per arm: %.3f\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE)))
phi <- 1.5
y0 <- rnbinom(reps, mu = m0, size = m0 / (phi - 1)); y1 <- rnbinom(reps, mu = m1, size = m1 / (phi - 1))
z2 <- log(y1 / y0) / sqrt(phi * (1 / y0 + 1 / y1))
cat(sprintf("Simulated power, over-dispersed counts (phi = 1.5), same n: %.3f\n", mean(abs(z2) > z_a, na.rm = TRUE)))

Output from running the code

100% of observed effect: n per arm = 2,921 (80% power), 3,911 (90% power)
 75% of observed effect: n per arm = 5,547 (80% power), 7,425 (90% power)
 50% of observed effect: n per arm = 13,448 (80% power), 18,003 (90% power)
Simulated power, Poisson counts, n = 2,921 per arm: 0.824
Simulated power, over-dispersed counts (phi = 1.5), same n: 0.650

The first simulation draws Poisson counts and should land close to the target power. The second allows extra variability (variance 1.5 times the mean, a purely illustrative value), which lowers the power at the same sample size, so rate trials usually need more participants than the Poisson formula suggests.

14. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
likelihood ratio testHazard Ratio (HR) 1.430.61 to 3.90.430

The registry’s reported primary analysis is an overall likelihood ratio test across the three groups. It gives a hazard ratio of 1.43, a 95% confidence interval from 0.61 to 3.9, and p = 0.43. That is the sponsor’s own reported analysis and should be treated as the primary inferential result in the registry record.

The additional rate-ratio estimates are simple, unadjusted re-calculations from the posted group rates. They compare each ingenol disoxate group separately with vehicle and use a rate-based approach rather than the sponsor’s reported overall time-to-event analysis. The estimates and p-values therefore need not reproduce the sponsor’s result: the estimands, contrasts, and statistical methods differ. The registry does not report a discrepancy between its posted results and these re-calculations, but that does not make the analyses identical.

The re-calculations can help readers understand the direction and approximate scale of the pairwise rate comparisons, while the sponsor’s overall hazard-ratio analysis remains the reported primary analysis. Neither should be described as proving equivalence or as establishing a definitive difference. The sponsor’s confidence interval is broad and includes the no-difference value; the pairwise rate-ratio intervals also include 1.

15. Multiplicity, Missing Data and Analysis Populations

The registry reports one primary endpoint and one secondary endpoint, with an overall time-to-event analysis for each and pairwise rate-based comparisons available for the groups. Testing more than one outcome or contrast creates a multiplicity concern: the more questions examined, the greater the chance that some result may appear unusual by chance alone. This matters especially when a secondary result is interpreted alongside several group comparisons.

The registry record does not report a multiplicity adjustment, a prespecified order for testing outcomes, or a plan distinguishing confirmatory from exploratory analyses. It is therefore not possible to determine from the record whether the reported p-values account for the set of tests conducted. The secondary endpoint’s reported p-value should be read as unadjusted unless the registry record states otherwise; no such adjustment is described.

Important information about missing data is also not reported in the registry record. The record does not specify how participants with incomplete follow-up were handled, what censoring rules were applied, whether missing endpoint assessments were imputed, or whether sensitivity analyses evaluated alternative assumptions. These details can affect time-to-event estimates because participants may contribute different amounts of observed time, and their status after follow-up ends is unknown.

The analysis population is described as 1234 subjects randomized and applying investigational product in one of four main trials. The registry’s extension enrollment is 563, but the record does not explain how these figures relate. Detailed population exclusions and the analysis handling of participants who did not complete follow-up are not reported in the registry record. Without this information, the effect of missing follow-up, population selection, or deviations from the intended analysis cannot be assessed. These are limitations of what can be concluded from the registry record, not evidence that a particular problem occurred.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Ingenol Disoxate Gel 0.018%01910.0%
Ingenol Disoxate Gel 0.037%12110.5%
Vehicle Gel01610.0%
Participants with at least one serious adverse event
Serious adverse events by armIngenol Disoxate Gel 0.018%0.0%Ingenol Disoxate Gel 0.037%0.5%Vehicle Gel0.0%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
Ingenol Disoxate Gel 0.018%1 of 191
Ingenol Disoxate Gel 0.037%0 of 211
Vehicle Gel2 of 161

Other (non-serious) adverse events

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

ArmParticipants affected of at risk
Ingenol Disoxate Gel 0.018%16 of 191
Ingenol Disoxate Gel 0.037%6 of 211
Vehicle Gel10 of 161

Most frequent serious adverse event terms

Event termOrgan systemIngenol Disoxate Gel 0.018%Ingenol Disoxate Gel 0.037%Vehicle Gel
Malignant melanomaNeoplasms benign, malignant and unspecified (incl cysts and polyps)0 of 1911 of 2110 of 161

Most frequent non-serious adverse event terms

Event termOrgan systemIngenol Disoxate Gel 0.018%Ingenol Disoxate Gel 0.037%Vehicle Gel
Application site scarGeneral disorders8 of 1915 of 2117 of 161
Squamous cell carcinoma of skinNeoplasms benign, malignant and unspecified (incl cysts and polyps)2 of 1910 of 2113 of 161
Basal cell carcinomaNeoplasms benign, malignant and unspecified (incl cysts and polyps)4 of 1910 of 2110 of 161
Bowen's diseaseNeoplasms benign, malignant and unspecified (incl cysts and polyps)3 of 1910 of 2111 of 161
Application site papulesGeneral disorders1 of 1910 of 2110 of 161
Inflammation of woundInjury, poisoning and procedural complications1 of 1910 of 2110 of 161
Skin abrasionInjury, poisoning and procedural complications0 of 1911 of 2110 of 161
ScarInjury, poisoning and procedural complications1 of 1910 of 2110 of 161
RosaceaSkin and subcutaneous tissue disorders1 of 1910 of 2110 of 161

Serious events with the highest arm-level rate: malignant melanoma (0.5%).

Do not overextend the safety comparison. Serious-adverse-event counts are safety observations, not efficacy outcomes, and should not be combined with the primary result into a single benefit-risk number.

The registry’s serious adverse event figures are presented by group among participants listed as at risk. For serious adverse events, the counts are 0 among 191 at risk in the 0.018% group, 1 among 211 at risk in the 0.037% group, and 0 among 161 at risk in the vehicle group. The record identifies malignant melanoma as a top serious term and gives its frequency as 0.5%. Deaths are listed as 1, 0, and 2 across the three groups, respectively.

These are descriptive counts, not adjusted comparisons. The registry does not provide enough detail in this summary to assess timing, duration, attribution, or whether events overlapped with other reported categories. The broader other-adverse-event counts are 16, 6, and 10 among the groups’ respective at-risk populations, but the record’s summary does not support a causal interpretation of those differences. Group sizes and follow-up may differ, and the extension trial is listed as terminated. These figures should be read as safety information reported in the registry, not as a determination that an event was caused by a treatment or as a complete assessment of risk.

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

The primary results describe squamous cell carcinoma incidence in treatment areas during follow-up of up to 24 months. The observed rates vary across the three groups, but the primary sponsor analysis has a wide confidence interval that includes the no-difference value. The simple pairwise rate-based re-calculations are also imprecise and include a rate ratio of 1 for both comparisons. Taken together, the posted primary results do not estimate a precise relative difference between either ingenol disoxate group and vehicle.

This does not establish that the groups have identical rates. A confidence interval that includes no difference can also include meaningful differences in either direction. Conversely, a point estimate alone should not be treated as proof of an effect. The secondary endpoint combines squamous cell carcinoma and other skin neoplasia, so its results address a broader outcome and do not change what the primary endpoint measured.

The findings apply to the described participants, treatment areas, and follow-up period. They do not establish what would happen with longer observation, in a different population, or for skin outcomes outside the treatment area. The registry’s listed enrollment of 563 and the primary outcome’s described analysis population of 1234 are not reconciled in the record, and details of missing-data handling and the reason for termination are not reported. These uncertainties constrain interpretation.

Statistical evidence is not a treatment recommendation. The registry results describe observed event rates and model-based comparisons; they do not by themselves establish causation, a complete safety profile, or the long-term balance of benefits and harms. The most defensible reading is that the primary estimates are uncertain, while the secondary results warrant caution because they concern a broader endpoint and the record does not describe multiplicity control.

18. Why This Trial Matters Statistically

This trial illustrates why endpoint choice matters. Time to first squamous cell carcinoma and time to first squamous cell carcinoma or other skin neoplasia are related outcomes, but they count different events. A finding for the broader endpoint cannot simply be transferred to the narrower primary endpoint. Keeping the event definition clear helps prevent a secondary result from being mistaken for an answer to the primary question.

It also shows why estimates need to be read with their uncertainty. Incidence rates and hazard ratios are different summaries, and each relies on its own analysis approach. The sponsor’s overall hazard ratio and the simple active-versus-vehicle rate ratios are not interchangeable. Confidence intervals convey that the primary estimates allow a wide range of relative effects, rather than a precise conclusion.

The planning illustrations show how event scarcity can constrain studies of relatively uncommon outcomes. Under the stated assumptions, planning for smaller effects requires substantially more events. This does not establish what the trial should have enrolled or whether its original design was adequate; its own planning justification is not reported in the registry record. It does make clear why a modest number of observed events can yield broad intervals even when follow-up is clinically meaningful.

Finally, the record highlights the importance of transparent reporting. The extension’s enrollment figure differs from the population stated for the primary analysis, and the record does not explain the relationship. Information about missing follow-up, censoring, multiplicity, and termination is also absent. Those details are essential for readers assessing how robustly a registry result answers its stated question.

19. Limitations

Several trial-specific limits affect interpretation. The registry lists enrollment of 563, while the primary outcome description identifies a Full Analysis Set of 1234 subjects randomized and applying investigational product in one of four main trials. The record does not explain how those figures relate, so the precise connection between the extension enrollment and the analyzed population is unclear.

The trial is listed as terminated, but the reason and its consequences for recruitment, follow-up, or analysis are not reported in the registry record. The extension was intended to provide up to 24 months of follow-up for its endpoint; actual group-specific follow-up duration and total person-time are not reported in the summary. Event counts for the primary endpoint are also not reported there, limiting assessment of how sparse events contributed to the broad intervals.

The trial was unmasked, according to the registry. The record does not describe event adjudication or whether assessors were masked to group assignment. This is relevant context for an outcome involving identification and classification of skin neoplasia, although the available information does not establish that outcome assessment was biased.

Key analysis details are not reported in the registry record, including the censoring and missing-data rules, model covariates, sensitivity analyses, and multiplicity strategy. The sponsor’s overall analysis and the simple re-calculations also answer different statistical questions. The secondary outcome includes other skin neoplasia and should not be treated as interchangeable with the primary endpoint. These limitations call for cautious interpretation without implying that an unreported issue necessarily affected the results.

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23. Record Summary

NCT03115476 is a randomized, open-label, parallel-group Phase 3 extension trial comparing ingenol disoxate gel 0.018%, ingenol disoxate gel 0.037%, and vehicle gel. It was sponsored by LEO Pharma, began on 2017-06-16, had primary completion on 2018-03-12, and is listed as terminated. Registry enrollment is 563.

The primary outcome is time to first squamous cell carcinoma in the treatment area, with rates reported per 100 patient years and follow-up up to 24 months. The sponsor’s overall analysis reports a hazard ratio of 1.43, with a 95% confidence interval from 0.61 to 3.9 and p = 0.43. Simple pairwise rate-based re-calculations are imprecise and do not establish a clear difference from vehicle. The secondary endpoint combines squamous cell carcinoma with other skin neoplasia and has a different event definition. The record leaves important details about population reconciliation, missing data, multiplicity, and termination unexplained.

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