Etanercept and Vascular Function in Psoriasis: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Etanercept and Vascular Function in Psoriasis (NCT01989689), a randomized phase 2 study. The primary outcome is Vascular Function as Measured by Brachial Artery Flow-mediated Dilation (FMD).

2. Clinical Question

The clinical question concerns vascular function in people receiving treatment for plaque psoriasis. The registry summary says investigators planned to measure the health of the vascular system of subjects taking etanercept. FMD is the named primary measure. Its reported values describe a change in artery diameter in response to increased blood flow, with the outcome expressed as a percentage of the baseline diameter.

Because this was a crossover trial, each assigned sequence involved both etanercept and placebo at different periods. This design can allow within-person comparisons, but interpreting a crossover analysis depends on how outcomes were measured and analyzed across periods. The registry record does not report a treatment-period estimate, a sequence or period analysis, or a description of how the baseline endpoint relates to the crossover periods. The posted mean comparison should therefore be read as a comparison between the reported sequence groups at baseline, not as a direct estimate of the effect of etanercept versus placebo.

3. Trial Design

The registry describes a randomized, triple-masked, phase 2 crossover trial sponsored by Emory University. The trial enrolled 24 participants and is listed as completed. Its start is recorded as 2010-08 and its primary completion as 2013-09. The condition listed is psoriasis.

Participants were assigned to one of two treatment sequences. The Etanercept/Placebo sequence received subcutaneous etanercept at 50mg twice weekly for 3 months and then placebo for an additional 3 months. The Placebo/Etanercept sequence received placebo injections for 3 months and then etanercept for an additional 3 months. Randomization assigns the sequence; crossover means that the sequence changes treatment over time. In principle, this structure can support comparisons within participants as well as between sequences, but the statistical analysis must account for the repeated observations and the treatment periods.

The primary outcome is identified as vascular function measured by brachial artery FMD. Its timeframe is listed as baseline. This matters because a baseline measurement is not, by itself, an outcome contrast between treatment periods. The registry record does not report when the primary outcome was measured relative to each treatment period, or how the analysis used measurements from the crossover schedule.

The record lists three outcome measures but no posted analyses. It also does not report the trial's original sample-size justification, its prespecified statistical model, handling of period or sequence effects, or rules for analysis populations. Those details cannot be inferred from the crossover label. The available group summaries and comparison can be described, but they do not establish how the investigators analyzed the trial's repeated measurements.

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.

Baseline

Treatment Period 1 ( 3 Months)

Reasons for not completing this period:

Treatment Period ( 3 Months)

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 Vascular Function as Measured by Brachial Artery Flow-mediated Dilation (FMD), measured over Baseline.

The primary endpoint is vascular function measured by brachial artery flow-mediated dilation. FMD is reported as a percentage of brachial artery diameter and summarized as a mean with a standard deviation. The registry describes bedside ultrasonography using a high-resolution 10-megahertz (MHz) transducer. The artery is measured before and after suprasystolic inflation of a blood-pressure cuff for 5 minutes in the ipsilateral upper arm. FMD is calculated as the difference between hyperemic and baseline diameter, divided by baseline diameter, multiplied by 100.

As a general statistical and physiological concept, FMD is used as a functional measure of how an artery dilates following a flow stimulus. A continuous measure retains information about the degree of response rather than reducing observations to categories such as improved or not improved. Reporting its mean and standard deviation describes the group's average and the spread of participant measurements.

The registry gives the primary endpoint timeframe as baseline. That label is important when interpreting the reported values: they are baseline group summaries, not a reported change from baseline or a contrast between the etanercept and placebo periods. The registry record does not report a treatment-period endpoint definition or a change-score analysis. Consequently, the endpoint's stated biological role does not turn the posted baseline comparison into evidence about a treatment effect.

7. Results Posted in the Registry

• Placebo/ Etanercept: mean 11.15 versus 9.71 on control; difference 1.44 (95% CI -4.72 to 7.60), standardized effect d = 0.19; z-test p = 0.647.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is continuous and is summarized by a mean and standard deviation. A mean describes the central average of the measured FMD values in a group. A standard deviation describes how spread out individual measurements are around that mean. These summaries are useful for understanding the data's scale and variability, but they do not by themselves show how measurements changed during treatment or how participants responded individually.

What does the mean difference represent?

The posted comparison is a mean difference of 1.44, calculated for the Placebo/Etanercept sequence group relative to the Etanercept/Placebo sequence group. The two group means are 11.15 and 9.71, respectively. This comparison describes a difference between the posted baseline sequence-group averages. It is not a within-person difference between the etanercept and placebo treatment periods. Since the registry labels the design as crossover, distinguishing these estimands is essential: the sequence-group baseline comparison and a treatment-period crossover contrast answer different questions.

The comparison is labeled unadjusted. In general, an unadjusted comparison uses the observed group summaries without accounting for additional covariates or design features in a model. The registry record does not report an adjusted model or a treatment-period model. It therefore does not establish whether the investigators used methods that account for the repeated measurements, period effects, sequence effects, or possible carryover effects that can matter in crossover studies.

How should the p-value be read?

The unadjusted p-value is 0.647. In general, a p-value measures how compatible the observed data are with a specified null hypothesis under a statistical model and its assumptions. It is not the probability that the null hypothesis is true, and it is not a measure of the size or clinical importance of a difference. A p-value also does not resolve whether the comparison is the right one for the trial design. Here, it accompanies a baseline sequence-group comparison, while a crossover treatment effect is not reported.

Why does the confidence interval matter?

The 95% confidence interval for the mean difference extends from -4.716 to 7.596. As a general explanation, a confidence interval describes the uncertainty around an estimate under the method used to calculate it. The observed data are consistent with a range of possible group differences rather than one precisely determined value. The interval crosses zero, so it includes no difference as well as values in either direction. This does not prove equivalence or establish that any potentially important difference is absent.

The interval's width reflects limited precision. The two groups include 11 and 13 participants, and their standard deviations are 7.49 and 7.87. In general, higher variability and smaller groups make it harder to estimate a mean difference precisely. Precision concerns how tightly the data locate the estimate; it is distinct from whether an estimate is statistically significant.

What does over-dispersion mean in general?

For continuous outcomes, variability is reflected in the spread of measurements. More generally, over-dispersion refers to data varying more than a statistical model expects. When that happens, standard errors based on an overly restrictive variability assumption can be too small, and confidence intervals can be too narrow. The posted summaries give standard deviations, but the registry record does not report an over-dispersion assessment or a model for the repeated crossover observations. The concept is therefore relevant as a general methodological consideration, not a reported finding from this trial.

What is not reported about the analysis?

The registry record lists no posted analyses. It does not report the original statistical analysis plan, the model used for the primary endpoint, the treatment contrast used by the investigators, or whether estimates were adjusted for baseline values or other factors. It does not report how missing measurements were handled, the analysis population, or whether tests or estimates accounted for the crossover structure. These omissions limit what can be inferred from the posted summary comparison. No investigator analysis is available in the registry record to take precedence over the unadjusted recalculation.

In general, a suitable crossover analysis uses the design and measurement schedule to define the treatment contrast, and accounts for repeated observations on the same participant. Depending on the protocol and data, period and sequence can be relevant. That general description is not a claim about the method used in this trial; the registry record does not report those details. The numerical comparison should therefore remain labeled as an unadjusted baseline group comparison, rather than being presented as a full crossover analysis.

10. Confidence Intervals and Precision

The posted mean difference is 1.44, with a 95% confidence interval from -4.716 to 7.596. This interval is the main guide to the precision of the baseline comparison. It is wide and includes zero, as well as both negative and positive differences. Thus, the estimate does not identify a narrow range of plausible differences between the two sequence groups at baseline.

As a general explanation, a confidence interval is a range produced by a statistical method to express uncertainty around an estimate. Under the method's assumptions, intervals constructed in this way have a stated long-run coverage property. For an individual interval, it is more useful to focus on which values remain compatible with the observed data and the calculation than to interpret it as a probability distribution for the true value.

The observed group means were 9.71 and 11.15. The corresponding standard deviations were 7.49 and 7.87, based on 11 and 13 participants. Variation among measurements and the limited group sizes both contribute to uncertainty. The interval should not be read as demonstrating equivalence: no equivalence margin is reported in the registry record, and an interval spanning zero is not, by itself, an equivalence test.

Precision of this baseline comparison is also distinct from precision of a treatment effect. The endpoint timeframe is listed as baseline, and the registry does not report a treatment-period contrast. Even a more precise baseline difference would not answer the separate question of how FMD changed under etanercept relative to placebo in the crossover periods.

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 participants per arm, not total events. They are illustrative calculations based on the observed effect, not the trial's original design assumptions. The calculation assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set to the stated fraction of the observed effect. The trial's original sample-size justification and design assumptions are not reported in the registry record.

The 80% power column gives the illustrative number of participants per arm for a design with an 80% chance of detecting the specified effect under the stated assumptions, if that effect and model assumptions were correct. The 90% power column describes the corresponding planning target for a 90% chance. These are design-planning concepts, not probabilities that the observed result is correct or that the treatment has an effect.

For planning at 100% of the observed effect, the figures are 449 participants per arm for 80% power and 601 participants per arm for 90% power. Planning for 75% of the observed effect gives 798 participants per arm for 80% power and 1,069 participants per arm for 90% power. Planning for 50% of the observed effect gives 1,796 participants per arm for 80% power and 2,404 participants per arm for 90% power. Smaller target effects require more participants because they are harder to distinguish from random variation.

These figures are not observed power. They should be read as planning illustrations conditional on the listed assumptions and effect sizes, not as a retrospective assessment of the trial's success or as evidence about its original intended sample size.

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 = 1.440; pooled standard deviation σ = 7.700.
2. n = 2 × (1.96 + 0.842)² × 7.700² / 1.440² = 448.8, rounded up to 449 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 <- 1.44                      # observed difference in means
sigma <- 7.69959798242149                     # 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(1989689)
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 = 449 (80% power), 601 (90% power)
 75% of observed effect: n per arm = 798 (80% power), 1,069 (90% power)
 50% of observed effect: n per arm = 1,796 (80% power), 2,404 (90% power)
power.t.test: 449.8 
Simulated power at n = 449 per arm: 0.803 (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. Multiplicity, Missing Data and Analysis Populations

The registry record lists three outcome measures and no posted analyses. It does not identify the full set of statistical hypotheses, distinguish confirmatory from exploratory analyses, or report a multiplicity adjustment. Multiplicity arises when several outcomes, time points, subgroups, or comparisons are tested. As a general concept, conducting many tests can increase the chance that at least one result appears unusual by chance. Whether an adjustment is appropriate depends on the intended questions and analysis plan, which are not reported in the registry record.

The record identifies one primary endpoint: vascular function measured by brachial artery FMD, with a baseline timeframe. It also lists no secondary outcomes posted. There is not enough information to determine how the three outcome measures relate to one another, whether additional measurements were planned, or which analyses were designated as primary in the original protocol. The unadjusted p-value should therefore be understood as a single reported comparison, not as a complete account of all analyses that may have been planned or conducted.

Missing-data handling is not reported in the registry record. The posted group summaries include 11 and 13 participants, while enrollment is listed as 24, but the record does not describe whether all enrolled participants contributed to the endpoint, whether measurements were missing, or how any missing observations were addressed. The record also does not report an analysis population definition, exclusions, or whether all randomized participants were included in the comparison.

These issues are especially relevant to a crossover trial, where measurements may be collected in multiple periods for each participant. The registry does not say how incomplete treatment sequences, missing period measurements, or possible effects of treatment order were handled. These are methodological questions, not established problems in the data. Without the analysis plan and population details, readers cannot assess whether missingness or multiplicity affected the reported inference.

14. Safety Results

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

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 5% reporting threshold.

The registry lists serious adverse events for 11 participants at risk in the Etanercept/Placebo sequence and 13 at risk in the Placebo/Etanercept sequence. The serious adverse event count is 0 in each sequence group. The registry also lists 0 other adverse events in each group, with the same at-risk counts. No serious-event terms are listed.

These are counts as posted for the sequence groups. A zero count means that no events in the corresponding category are recorded in the registry results for the listed at-risk participants; it does not establish that no event of any kind occurred outside the reported categories or reporting period. The record does not provide event-level descriptions or additional detail about the period covered by these counts.

Deaths are not reported in the registry record. The posted adverse-event summaries should be interpreted descriptively, particularly given the trial's enrollment of 24. They do not provide a comparative statistical safety analysis, and they should not be taken as a general conclusion about safety.

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

The posted result establishes what was recorded for baseline FMD in the two randomized sequence groups: the Etanercept/Placebo group mean was 9.71, and the Placebo/Etanercept group mean was 11.15. The unadjusted difference was 1.44, with a 95% confidence interval from -4.716 to 7.596 and an unadjusted p-value of 0.647. The summaries also show standard deviations of 7.49 and 7.87 in groups of 11 and 13 participants.

Those results do not establish that the treatment sequences differ at baseline, nor do they establish that they are equivalent. The confidence interval spans zero and a range of values in both directions. The p-value does not demonstrate that there is no difference, and it cannot be interpreted as the probability that there is no effect.

More importantly, the comparison is not reported as an etanercept-versus-placebo contrast across the crossover periods. The primary timeframe is baseline, and the registry record does not include treatment-period means, within-participant changes, or a crossover model. The posted comparison therefore cannot answer whether FMD changed during etanercept relative to placebo.

The registry also does not report the trial's statistical plan, analysis population, missing-data methods, or sample-size justification. Those omissions prevent readers from assessing whether the posted comparison matches the intended primary analysis or how the crossover design was handled. The planning figures are conditional illustrations, not results from the trial and not observed power.

The most defensible reading is descriptive: the available baseline group averages differ by the stated amount, with substantial uncertainty around that comparison. No treatment efficacy or clinical benefit conclusion follows from these baseline summaries. The registry data also do not support a broad safety conclusion from the zero reported adverse-event counts.

16. Why This Trial Matters Statistically

This trial is statistically interesting because its randomized crossover design and its posted endpoint summaries invite different kinds of comparisons. A crossover can be useful when the same participants receive both interventions at different times, because within-participant comparisons can account for some stable differences between people. But that benefit depends on measuring the outcome across treatment periods and analyzing those repeated observations appropriately.

The primary endpoint is listed at baseline, while the posted numerical comparison is between the sequence groups at baseline. That is a comparison of group averages before the registry's described switching schedule can define a treatment-period contrast. Readers therefore need to distinguish the trial's design label from the estimand represented by the available statistics. A randomized crossover trial does not make every comparison of its groups an estimate of the treatment effect.

The confidence interval is also instructive. It ranges from -4.716 to 7.596 around a mean difference of 1.44, showing that this sample does not tightly estimate the baseline group difference. This illustrates why a point estimate and p-value should be read alongside an interval and the outcome's variability. It also reinforces that failure to establish a difference is not the same as evidence of equivalence.

Finally, the record contains no posted analyses despite listing three outcome measures. This makes the distinction between registry summaries and a full analysis especially important. Understanding the target comparison, measurement timing, analysis population, missing-data handling, and crossover model is necessary to interpret a treatment effect. Those details are not reported in the registry record, so the numerical summaries are informative descriptively but limited for causal interpretation.

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.

The chief limitation is that the primary endpoint timeframe is listed as baseline, while the intervention descriptions specify sequential treatment periods. The registry record does not report post-treatment or period-specific FMD results. It also does not report a within-participant treatment contrast or a model that accounts for the crossover design. The posted mean difference is therefore a baseline comparison between treatment sequences, not a reported estimate of the etanercept-versus-placebo effect.

The groups are small, with 11 and 13 participants contributing to the posted outcome summaries. The standard deviations are 7.49 and 7.87, and the confidence interval from -4.716 to 7.596 is broad. These features limit precision for the baseline comparison. The record does not report a sample-size justification, so the enrollment cannot be assessed against the trial's original design target.

The registry record does not report the statistical analysis plan, an adjusted analysis, period or sequence handling, missing-data methods, or analysis populations. It also does not explain how the three listed outcome measures relate to the primary endpoint or whether multiplicity was considered. These omissions prevent assessment of whether the reported comparison represents the prespecified analysis.

Safety results are limited to the recorded counts of zero serious and zero other adverse events in each sequence group. Death counts are not reported in the registry record. Event definitions, timing details, and a comparative safety analysis are not reported. These limitations apply to interpretation of the registry entries; they do not establish that unreported information was absent from the trial itself.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Etanercept and Vascular Function in Psoriasis — NCT01989689.
• Registry record last updated 2014-12-19; status last verified 2014-12.
• Results first posted 2014-12-19.
• 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, triple-masked, phase 2 crossover trial sponsored by Emory University. It enrolled 24 participants with psoriasis. The record lists a start of 2010-08 and primary completion of 2013-09.

Participants were assigned to etanercept followed by placebo, or placebo followed by etanercept. The primary outcome was brachial artery FMD, reported as a mean and standard deviation, with the timeframe listed as baseline. The posted sequence-group means were 9.71 and 11.15; the unadjusted mean difference was 1.44, with a 95% confidence interval from -4.716 to 7.596 and an unadjusted p-value of 0.647.

The registry lists three outcome measures and no posted analyses. It does not report a treatment-period analysis, the statistical plan, missing-data methods, analysis populations, or the original sample-size justification. The available result is a baseline sequence-group comparison and does not estimate an etanercept-versus-placebo effect across crossover periods.