Evaluation of Anti-platelet Factor 4/Heparin Antibodies in Hemodialysis Patients: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Evaluation of Anti-platelet Factor 4/Heparin Antibodies in Hemodialysis Patients (NCT02165761), a randomized na study. The primary outcome is Number of Participants With a Prevalence of a Positive Poly-specific Enzyme Immunoassay (EIA) at Day 7 and/or Day 14 Time Points.

2. Clinical Question

The registry’s stated objective was to characterize the prevalence and persistence of anti-PF4/heparin antibodies in the two graft groups. The posted primary outcome is a count of participants with a positive result at either specified time point. It does not report a separate persistence measure or the sequence of results across both time points. The clinical question is therefore narrower than a full description of antibody persistence: it concerns whether participants had a positive screening result at Day 7 and/or Day 14.

3. Trial Design

The registry record describes a randomized, open-label, parallel-group device trial. Participants were assigned to receive either the GORE® Hybrid Vascular Graft or a non-heparin bonded synthetic graft. Masking is listed as none. The trial enrolled 42 participants and is listed as terminated. Its phase is recorded as not applicable.

The condition listed is end-stage renal disease. The stated purpose was to characterize prevalence and persistence of anti-PF4/heparin antibodies in hemodialysis patients receiving the two graft types. The primary outcome timeframe is 14 days after the index procedure, with antibody screening assessed at Day 7 and/or Day 14. The registry describes the assay as a commercial poly-specific EIA detecting antibodies of the IgG, IgA, and/or IgM classes against PF4/polyvinyl sulfonate complexes.

The primary outcome population is not the same as the total enrollment: the registry reports serology samples for 19 of 23 participants in the GORE® group and 16 of 19 in the comparison group. The posted outcome counts are based on those available samples. The registry record does not report why some participants lacked a sample, nor does it give further detail on how assignment was implemented, the intended duration of follow-up beyond the primary timeframe, or the original sample-size justification. The recorded start is 2014-07, and primary completion is recorded as 2017-01-20. No reason for termination is 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

Analysis population for the primary outcome, as defined in the registry: In the GORE® Hybrid Vascular Graft Group 19 out of 23 participants had obtained a serology sample at Day 7 and/or Day 14 for analysis. In the Non-heparin bonded synthetic graft Group 16 out of 19 participants had obtained a serology sample at Day 7 and/or Day 14 for analysis.

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 Number of Participants With a Prevalence of a Positive Poly-specific Enzyme Immunoassay (EIA) at Day 7 and/or Day 14 Time Points, measured over 14 days after index procedure.

The primary endpoint counts participants with a positive result on a poly-specific enzyme immunoassay at Day 7 and/or Day 14 after the index procedure. The assay is described as detecting IgG, IgA, and/or IgM antibodies against PF4/polyvinyl sulfonate complexes. A participant is counted if a positive result occurred at either time point; the posted endpoint does not distinguish a positive result at Day 7 from one at Day 14, or report whether a participant remained positive across both measurements.

This endpoint was used to characterize the prevalence of anti-PF4/heparin antibodies after graft implantation, consistent with the registry’s stated objective. A binary participant count is straightforward to interpret as the number meeting the positive-result definition among participants with serology available. It does not by itself describe antibody concentration, clinical consequences, or persistence in the sense of repeated positive results over time. Those details are not reported in the registry record.

The endpoint’s denominators are 19 participants in the GORE® Hybrid Vascular Graft group and 16 in the non-heparin bonded synthetic graft group, reflecting the participants reported to have a sample at Day 7 and/or Day 14. The counts were 3 and 2, respectively. Because some participants did not contribute a reported serology sample, the endpoint describes the sampled participants rather than an outcome observed for every enrolled participant.

7. Results Posted in the Registry

• Non-heparin Bonded Synthetic Graft: 12.5% (2/16) versus 15.8% (3/19) on control; risk difference -3.3 percentage points (95% CI -26.3 to 19.8), risk ratio 0.79 (0.15–4.17); unadjusted two-proportion z-test p = 0.782.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary endpoint is binary at the participant level: a participant either had a positive poly-specific EIA at Day 7 and/or Day 14, or did not. For a binary outcome, the arm-specific count and denominator describe how often the event was observed in each group. The posted counts are 3 of 19 for the GORE® Hybrid Vascular Graft and 2 of 16 for the non-heparin bonded synthetic graft. Because the outcome is based on participants rather than repeated assay readings, the reported count does not reveal the number positive at each individual time point.

What does the risk difference describe?

A risk difference subtracts the event proportion in one group from that in the other. In this comparison, the reported estimate is for the non-heparin bonded synthetic graft group relative to the GORE® group, and is -0.033. A value of zero corresponds to equal observed proportions under this measure. The confidence interval from -0.263 to 0.198 describes a range of values compatible with the data and the interval method’s assumptions. It includes zero, as well as values on either side, so the estimate is not precise enough to settle the direction or size of a difference.

How do relative measures differ?

The risk ratio compares the event proportions by division; the odds ratio compares the odds of an event. The posted risk ratio is 0.792, with an interval from 0.150 to 4.168. The posted odds ratio is 0.762, with an interval from 0.111 to 5.237. A ratio of one represents equal values under the corresponding measure. The wide intervals indicate substantial uncertainty in these relative comparisons. With few events, a small change in observed counts can have a noticeable influence on ratio estimates, so these measures should not be interpreted as highly stable quantities.

What does the p-value tell us?

The unadjusted p-value is 0.782. In general, a p-value describes how unusual data at least as discrepant as those observed would be under a specified null model and test procedure. It does not measure the probability that the null hypothesis is true, and it does not quantify the size or clinical importance of an effect. Here, it should be interpreted alongside the count data and the broad confidence intervals. The registry record lists no posted analysis set beyond the posted comparison, and no sponsor analysis is listed.

Why does sparse data matter?

When event counts are low, statistical estimates can be sensitive to individual observations. Confidence intervals may consequently be broad, especially for relative measures. This is a general feature of binary outcomes with sparse events, not evidence that a particular estimate is wrong. The posted counts permit direct description of the observed samples, but provide limited precision for distinguishing possible differences between groups.

What is the role of the planning illustration?

The sample-size figures are planning illustrations based on fractions of the observed effect, not results from the trial’s original design process. Their assumptions are a two-sided significance level of 0.05, equal allocation between groups, and a normal approximation. The registry record does not report the trial’s original sample-size justification or its own design assumptions. The planning figures should therefore be treated as hypothetical guidance about the scale of a future study under those stated assumptions, not as evidence about the performance of this trial.

In general, statistical methods rely on assumptions about how observations were obtained and how outcomes are distributed. A binary outcome does not require modeling a continuous distribution for the event itself, but the comparison still depends on the validity of group definitions, outcome ascertainment, and handling of missing observations. The registry record does not report enough methodological detail to assess all such choices or to reconstruct an analysis protocol.

10. Confidence Intervals and Precision

Precision concerns how narrowly an estimate is determined by the observed data. The reported risk difference is -0.033, and its confidence interval extends from -0.263 to 0.198. This interval includes zero and covers negative and positive values. It is therefore compatible with no difference as well as with differences in either direction, under the statistical method used to construct it. The estimate should not be read as a precise measure of the underlying contrast.

The relative-effect intervals are also broad: the risk ratio is 0.792, with a confidence interval from 0.150 to 4.168, and the odds ratio is 0.762, with a confidence interval from 0.111 to 5.237. In general, a confidence interval represents uncertainty about an estimated quantity under specified statistical assumptions; it is not a range that guarantees the true value lies within it, nor does it assign equal probability to every value in the interval.

The limited number of positive outcomes contributes to the uncertainty. The outcome counts are 3 and 2, with analysis denominators of 19 and 16. Even though the trial enrolled 42 participants, the primary outcome uses the smaller reported serology groups. The registry record does not provide a missing-data analysis that would show how conclusions might change under other assumptions about participants without serology samples.

The broad intervals matter more than a simple reading of the point estimate alone. The point estimate favors one direction according to the chosen contrast, but the uncertainty includes plausible values on both sides of no difference. Thus, these posted results do not identify a narrow or dependable estimate of the comparison.

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 participants and not total events. They are illustrative calculations based on the observed effect, with the effect to detect set in turn to 100%, 75%, and 50% of that observed effect. For 100% of the observed effect, the figures are 1,761 participants per arm for 80% power and 2,357 participants per arm for 90% power. For 75% of the observed effect, they are 3,207 participants per arm for 80% power and 4,293 participants per arm for 90% power. For 50% of the observed effect, they are 7,385 participants per arm for 80% power and 9,885 participants per arm for 90% power.

The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. In plain language, the 80% power column gives the illustrative participants per arm for a design with an 80% chance of detecting the specified effect under those assumptions if that effect were present. The 90% power column gives the corresponding planning amount for a 90% chance. These are not observed power calculations for this trial.

The planning figures increase as the target effect becomes smaller: detecting a smaller effect generally requires more participants because a smaller contrast is harder to distinguish from random variation. The accompanying curve expresses the same general relationship between target effect and planning sample size; it is a planning aid rather than an observed trial result. The registry record does not report the original trial’s sample-size justification or design assumptions, so these illustrative estimates should not be treated as the intended enrollment target for the trial.

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 = 0.158; treatment proportion p₁ = 0.125; average p̄ = 0.141.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.4928 = 0.9659.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.4923 = 0.4143.
4. n = (0.9659 + 0.4143)² / (-0.0329)² = 1,760.6, rounded up to 1,761 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 <- 0.157894736842105                          # control proportion
p1 <- 0.125                          # 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(2165761)
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 = 1,761 (80% power), 2,357 (90% power)
 75% of observed effect: n per arm = 3,207 (80% power), 4,293 (90% power)
 50% of observed effect: n per arm = 7,385 (80% power), 9,885 (90% power)
power.prop.test: 1760.6 
Simulated power at n = 1,761 per arm: 0.806 (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 record lists one primary outcome measure, no posted secondary outcome results, and no posted analyses. It does not report a multiplicity plan, such as how statistical testing would be managed across multiple endpoints, time points, or interim looks. The absence of a posted plan does not establish whether one existed outside the registry record. The endpoint combines positive results at Day 7 and/or Day 14, but separate time-specific comparisons are not posted.

For the primary endpoint, serology samples were available at Day 7 and/or Day 14 for 19 of 23 participants in the GORE® Hybrid Vascular Graft group and 16 of 19 participants in the non-heparin bonded synthetic graft group. The posted event counts use the sampled participants as denominators. The registry record does not report why samples were unavailable, whether missingness differed for any reason, or how missing outcomes were handled in a prespecified analysis. It also does not report a sensitivity analysis for missing data.

The registry identifies a randomized parallel-group design, but the posted outcome results do not describe a separate intention-to-treat analysis population, a per-protocol population, or other analysis populations. The outcome description identifies the participants with samples, which is the population represented by the displayed counts. It would not be appropriate to assume that participants without a sample had negative results or to infer their outcomes.

Multiplicity and missing-data details matter because repeated testing can affect how evidence is interpreted, while incomplete outcomes can affect the representativeness of an estimate. Without a reported analysis plan, the registry record does not permit assessment of any adjustments or alternative analysis choices that may have been used. These limits do not change the descriptive counts among participants with samples, but they constrain broader interpretation.

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 5.0% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: cellulitis of legs (5.3%), septic shock (5.3%), sigmoid diverticulitis (5.3%), urinary tract infection (5.3%), muscle weakness upper limb (5.3%).

The registry lists serious adverse events for 6 of 23 participants in the Hybrid Vascular Graft test group and 5 of 19 participants in the Non-Heparin Synthetic Graft control group. Other adverse events are listed for 4 of 23 and 8 of 19 participants, respectively. Deaths are listed for 1 participant in each group. These counts describe the registry’s reported safety categories and denominators; they do not establish that an event was caused by a graft or by the trial.

The serious-event terms listed include cellulitis of legs, septic shock, sigmoid diverticulitis, urinary tract infection, muscle weakness upper limb, and seizure, each reported as 5.3%. The registry record does not provide enough detail to attribute these events to a treatment, assess their timing relative to graft placement, or compare their severity beyond the serious-event classification. These data should be read as descriptive safety reporting, not as a causal comparison or a complete account of risk.

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

The posted primary outcome documents positive antibody screening results in a small number of sampled participants: 3 of 19 in the GORE® Hybrid Vascular Graft group and 2 of 16 in the non-heparin bonded synthetic graft group. The risk difference is -0.033 for the non-heparin bonded synthetic graft group relative to the GORE® group, but its confidence interval includes zero and extends in both directions. The p-value is 0.782. Together, these statistics indicate that the observed data do not precisely determine the direction or size of a difference.

They do not prove that the groups are equivalent, and they do not establish that a difference exists. The uncertainty is substantial, as reflected in the intervals for the risk difference, risk ratio, and odds ratio. The counts describe only participants with serology samples reported at Day 7 and/or Day 14. The registry record does not report a missing-data analysis that would establish whether those participants represent all assigned participants for this endpoint.

The result also does not answer every aspect of the registry’s stated interest in antibody persistence. The primary endpoint combines positive findings across the specified time points, without reporting separate results at each time or the pattern of repeated results. It does not describe antibody concentration or other clinical outcomes. No secondary outcome results are posted.

The safety counts are descriptive and do not show that events were caused by a device. The trial is listed as terminated, but the reason is not reported in the registry record. No conclusion about the reason for termination or its relationship to outcomes can be drawn from the status alone. Overall, the posted information supports a cautious description of the observed samples, not a broad conclusion about graft performance or clinical benefit.

16. Why This Trial Matters Statistically

This trial illustrates how a randomized design and a sparse binary endpoint can still yield substantial uncertainty. Random allocation is intended to support a fair comparison between groups, but the precision of the result also depends on how many outcome events are observed and how complete outcome ascertainment is. Here the primary outcome counts were 3 and 2, and the endpoint denominators were 19 and 16. The resulting confidence intervals are broad.

It also highlights the importance of defining the analysis population. The trial enrolled 42 participants, while the primary outcome description identifies smaller groups with serology samples. Those denominators determine the posted outcome proportions and the comparison. Without further information on unavailable samples or missing-data methods, readers cannot determine how sensitive the result might be to the outcome status of participants without samples.

Another statistical distinction is between a point estimate and its precision. The risk difference has a specific direction, but its interval includes zero and substantial values in either direction. A single point estimate can seem more decisive than the evidence warrants if uncertainty is ignored. The broad ratio intervals reinforce that caution.

Finally, the planning illustration is not the original design rationale. It translates the observed effect into hypothetical sample-size requirements under stated assumptions, while the registry record does not report the trial’s own sample-size justification. This distinction helps prevent retrospective planning calculations from being mistaken for the design target or for evidence that the trial was adequately or inadequately powered.

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 principal limitation is the small number of positive primary outcomes: 3 in the GORE® Hybrid Vascular Graft group and 2 in the non-heparin bonded synthetic graft group. The confidence intervals are wide, so the comparative effect is not estimated precisely. The trial’s enrolled total was 42, but serology was reported for 19 of 23 participants in the GORE® group and 16 of 19 in the comparison group. The reasons for unavailable samples and their possible effect on the result are not reported in the registry record.

The endpoint records a positive result at Day 7 and/or Day 14, rather than reporting each time point separately. The registry does not provide data on repeated positive results or a detailed assessment of persistence. No secondary outcomes or analyses are posted, and the record does not describe a multiplicity strategy, analysis populations, or a missing-data sensitivity analysis.

The registry lists the trial as terminated but does not report why. Its original sample-size justification and design assumptions are also not reported in the registry record. Although the listed design is randomized and parallel-group, further details about allocation procedures and outcome-analysis methods are not available in the record. These limitations make it difficult to assess the full analysis process or generalize the observed sampled-participant counts beyond the reported outcome population.

Safety reporting is also descriptive: the event counts do not establish causality, and the record does not provide details sufficient to attribute events to either graft. The posted findings should therefore be interpreted in the context of limited outcome information, incomplete serology sampling, sparse events, and broad statistical uncertainty.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Evaluation of Anti-platelet Factor 4/Heparin Antibodies in Hemodialysis Patients — NCT02165761.
• Registry record last updated 2018-02-19; status last verified 2018-02.
• Results first posted 2018-02-19.
• 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

NCT02165761 is a randomized, open-label, parallel-group device trial comparing the GORE® Hybrid Vascular Graft with a non-heparin bonded synthetic vascular graft in hemodialysis patients with end-stage renal disease. The registry lists 42 participants enrolled, a start of 2014-07, primary completion on 2017-01-20, and status as terminated. The reason for termination is not reported in the registry record.

The primary outcome counts participants with a positive poly-specific EIA at Day 7 and/or Day 14 after the index procedure. Results were reported for 19 of 23 participants in the GORE® group and 16 of 19 in the comparison group; positive counts were 3 and 2. The reported risk difference is -0.033, with a confidence interval from -0.263 to 0.198 and an unadjusted p-value of 0.782. No secondary outcome results or posted analyses are listed. The record also reports serious adverse events, other adverse events, and deaths descriptively, without establishing causation.