Arista Hemostatic Powder for Total Knee Post Operative Outcomes Study: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Arista Hemostatic Powder for Total Knee Post Operative Outcomes Study (NCT05522153), a randomized phase 1 study. The primary outcome is Blood Loss.

2. Clinical Question

3. Trial Design

This was a randomized, single-blinded, parallel-group trial, registered as a phase 1 study. The registry lists the trial as completed and records enrollment of 61 participants. The recorded start date is 2021-05-01, and primary completion is listed as 2023-06-08. Those dates describe the registry timeline; they do not establish how long each participant was followed individually beyond the stated outcome timeframe.

Participants were assigned to an Arista group or a control group. The Arista group received 5 grams of Arista hemostatic powder in the wound during surgery and 1 gram of intravenous tranexamic acid before incision. The control group received 1 gram of intravenous tranexamic acid before incision without the powder. The shared tranexamic acid treatment means the contrast addresses the added use of Arista in this setting.

Single blinding is listed, but the identity of the blinded party and the procedures used to maintain blinding are not reported in the registry record. The method used to generate the random sequence, allocation concealment, site count, eligibility criteria, and details of the clinical setting are also not reported. The record does not describe whether participants could receive other interventions or how protocol departures were handled.

The primary endpoint is mean blood loss, measured from incision until 90 days after surgery. The two posted secondary outcomes are thigh circumference and range of motion, both assessed at 3 months after surgery. The registry lists 61 participants enrolled, while the numbers contributing to secondary outcome summaries are smaller than the primary outcome group counts. Reasons for these differences are not reported. The registry contains no reported statistical analyses, so the posted comparisons should be read as descriptive and unadjusted summaries rather than as a complete account of a prespecified analysis plan.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Overall Study

5. Baseline Characteristics

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

6. Primary Endpoint

The registry lists the primary outcome as Blood Loss, measured over Time of incision until 90 days post-op.

The primary endpoint is blood loss, recorded in cubic centimeters and summarized as a mean with a standard deviation for each randomized group. Its stated timeframe runs from the time of incision until 90 days after surgery. The registry says the measurement was calculated according to standard hospital protocol, but does not describe the protocol’s details, the components included in the calculation, or whether the same procedure was applied at every measurement point.

Blood loss is relevant to the trial’s stated question because the study set out to examine whether adding a hemostatic powder to the shared tranexamic acid treatment was associated with a difference in post-operative blood loss after TKA. A continuous measure summarized by its mean can describe the average observed amount in each group. The standard deviation describes how spread out the individual measurements are around that group’s mean; it is not the uncertainty around the mean itself.

The primary outcome group summaries are based on 31 participants in the Arista group and 30 in the control group. The reported mean is 122.6 cubic centimeters for Arista and 133.3 cubic centimeters for control, with standard deviations of 25.3 and 42.2, respectively. These summaries give a descriptive account of the observed measurements. They do not, on their own, establish that any difference is attributable to the assigned treatment. The registry does not report the detailed endpoint measurement protocol or a trial-reported analysis of this endpoint.

7. Results Posted in the Registry

• Arista Group: mean 122.60 versus 133.30 on control; difference -10.70 (95% CI -28.23 to 6.83), standardized effect d = -0.31; z-test p = 0.232.

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.

Thigh Circumference

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Arista Group: mean 50.60 versus 54.00 on control; difference -3.40 (95% CI -6.98 to 0.18), standardized effect d = -0.50; z-test p = 0.062.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Arista Group and the control. The interval gives the range of effects that remain compatible with the data.

Range of Motion

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Arista Group: mean 117.80 versus 114.30 on control; difference 3.50 (95% CI -2.31 to 9.31), standardized effect d = 0.33; z-test p = 0.237.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Arista Group and the control. The interval gives the range of effects that remain compatible with the data.

The two posted secondary endpoints are thigh circumference and range of motion, each assessed at 3 months after surgery. Their group summaries move in different numerical directions: the Arista group has a lower mean thigh circumference and a higher mean range of motion than control. Both unadjusted confidence intervals include zero, and neither comparison is reported as a trial analysis. The overall pattern therefore does not supply a consistent, precise signal across these outcomes.

These secondary measures add descriptive context to the primary blood-loss comparison, but they do not replace it. The trial’s stated purpose mentions blood loss, hematoma formation, and range of motion, while the registry lists thigh circumference and range of motion as secondary outcomes. Hematoma formation is not included among the posted outcome measures. The registry does not explain how thigh circumference relates to hematoma assessment or whether either secondary measure was intended as a proxy for another clinical feature.

Unadjusted secondary results carry less weight when multiple outcomes are examined because the chance of at least one apparently notable finding can increase as more comparisons are made. In general, a prespecified hierarchy or a multiplicity adjustment can address some of this issue, but the registry does not report such a plan. Nor does it report whether these outcomes were prespecified, whether the analyses followed a common model, or whether secondary analyses were exploratory.

The outcome-specific participant counts are also smaller than the primary endpoint counts. Without information about why participants did not contribute to each secondary measure or how missing observations were handled, the group summaries may not represent the same set of participants. These limitations make the secondary findings descriptive rather than confirmatory. Their role is to indicate what was recorded at the stated follow-up, while the available registry information does not support strong conclusions about the consistency or reliability of secondary effects.

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

• Thigh Circumference
• Range of Motion

9. Statistical Interpretation

10. Statistical Methods Explained

The posted outcome is continuous, meaning it is recorded on a numeric scale rather than as a count of participants in categories. The registry summarizes each group with a mean and standard deviation. The mean describes the group’s average observed measurement. The standard deviation describes the dispersion of individual measurements around that average. A larger standard deviation indicates greater spread among observed values, but does not by itself show whether the mean estimate is more or less precise; precision also depends on the number of observations and the analysis.

What does the mean difference represent?

The comparison is expressed as the Arista group mean minus the control group mean. For blood loss, the posted estimate is -10.7 cubic centimeters. A negative value means the reported Arista group mean is numerically lower than the reported control group mean. This direction is a description of the observed summaries, not a causal conclusion by itself. The registry’s comparison uses the group means and reports an interval and an unadjusted p-value. The method used for the trial’s own primary analysis is not reported in the registry record.

What does a confidence interval convey?

A confidence interval describes uncertainty around an estimated difference under the assumptions of the method used to construct it. It gives a range of values that are reasonably compatible with the observed data and that method. The primary interval extends from -28.23 to 6.831 cubic centimeters. Since zero lies within the interval, the posted estimate does not rule out no difference in means. The interval also spans values below and above zero, indicating uncertainty about direction as well as size. A confidence interval is not a guarantee that the true value lies within its limits, and it does not express the probability that a specific treatment effect is true.

How should the p-value be read?

The unadjusted p-value for the primary comparison is 0.232. In general, a p-value describes how unusual data at least as discrepant as those observed would be under a specified null model and its assumptions. It is not the probability that the null hypothesis is true, the probability that the result arose by chance, or a measure of clinical importance. The record does not describe the test or model used for the trial’s own analysis; the reported comparison is identified as unadjusted. The p-value should therefore be read alongside the estimated difference and confidence interval, not as a standalone verdict.

Why can over-dispersion matter?

In general, over-dispersion means that observed variation is greater than a statistical model expects. If a model understates variability, standard errors may be too small and intervals may be too narrow, making evidence appear more precise than it is. This concept is especially relevant to outcomes modeled as counts or categories. The posted primary endpoint is summarized as a continuous measure with a mean and standard deviation. The registry does not report a model diagnostic or a finding of over-dispersion, so no claim about it can be made for this trial.

More generally, the reliability of a continuous-outcome comparison depends on how the outcome was measured, whether observations are independent, how the distribution and variability are handled, and whether the analysis respects the randomized design. The registry says the blood-loss measure followed standard hospital protocol but does not describe the protocol or the analysis model. It is therefore not possible to assess those details from this record.

What does randomization contribute?

In general, random allocation is intended to make treatment groups comparable on average at the time of assignment, including with respect to factors that were not measured. That supports interpreting a between-group contrast as an effect of assignment when the randomization is properly implemented and the analysis preserves the comparison. The registry records randomization and a parallel-group model, but the sequence-generation and allocation-concealment procedures are not reported. The analysis population is also not defined in the record.

The registry reports no trial analyses. The posted comparison statistics are unadjusted, and the registry does not state whether they represent the sponsor’s prespecified primary analysis. There is no reported model-adjusted estimate, stratified analysis, or sensitivity analysis. Accordingly, explanations of interval interpretation and p-values are general statistical principles, while the numerical comparisons are the unadjusted estimates posted for this study.

11. Confidence Intervals and Precision

The primary comparison estimates a mean difference of -10.7 cubic centimeters. Its 95% confidence interval runs from -28.23 to 6.831 cubic centimeters. This interval is wide enough to include values on both sides of zero. In practical statistical terms, the estimate does not sharply distinguish a lower average in the Arista group from no mean difference or a higher average in that group. The interval communicates uncertainty in the estimated contrast rather than the spread of individual blood-loss values; the standard deviations describe that separate feature of the data.

Confidence intervals are useful because they show both the direction and the range of values compatible with the data and method. The interval should not be interpreted as a range containing every individual participant’s outcome, nor as the probability that the true mean difference lies within the range. Its interpretation also depends on the statistical method and assumptions. The method used for a trial-reported analysis is not reported in the registry record.

The posted primary group counts are 31 and 30. The standard deviations are 25.3 cubic centimeters for Arista and 42.2 cubic centimeters for control. These values describe the observed variation in each group, while the confidence interval describes uncertainty in the estimated between-group difference. Taken together, the data offer a point estimate and a range, but the interval leaves substantial uncertainty about the difference’s size and direction.

A p-value of 0.232 accompanies the unadjusted primary comparison. It does not measure precision and does not establish that the groups are equivalent. Precision is more directly conveyed by the confidence interval, interpreted with the study’s design and analysis limitations in mind. The registry does not report an equivalence margin or a non-inferiority margin, so the result should not be described as demonstrating equivalence or non-inferiority.

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.

The sample-size figures are planning illustrations expressed as participants per arm, not total events. Their 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 a stated fraction of the observed effect. These are planning assumptions for the illustration; the trial’s original sample-size assumptions and justification are not reported in the registry record.

For the primary blood-loss comparison, planning for 100% of the observed effect gives 165 participants per arm for 80% power and 221 participants per arm for 90% power. Planning for 75% of the observed effect gives 293 participants per arm for 80% power and 392 participants per arm for 90% power. Planning for 50% of the observed effect gives 659 participants per arm for 80% power and 882 participants per arm for 90% power.

In plain terms, the 80% power column gives the illustrated number of participants per arm for a design with an 80% chance of detecting the specified effect under the stated assumptions, if that effect is truly present. The 90% column expresses the corresponding planning target for a higher chance of detection under those assumptions. Smaller effects are harder to distinguish from random variation, so detecting them requires more participants in this illustration. The sample-size figures are not observed power; they are not a retrospective measure of what the completed trial could detect.

The illustrations use the observed effect as their reference. An observed effect from a small trial can itself be uncertain, so planning around it does not establish the effect expected in a future study. The figures also do not account for design features or analysis choices that are not included in the stated assumptions. The sample-size planning illustration is therefore useful for understanding how target effect size and desired power relate to planned enrollment, but it is not evidence about treatment effects and does not reveal the original design rationale.

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 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 = -10.700; pooled standard deviation σ = 34.653.
2. n = 2 × (1.96 + 0.842)² × 34.653² / -10.700² = 164.6, rounded up to 165 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 <- -10.7                      # observed difference in means
sigma <- 34.6525269947033                     # 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(5522153)
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 = 165 (80% power), 221 (90% power)
 75% of observed effect: n per arm = 293 (80% power), 392 (90% power)
 50% of observed effect: n per arm = 659 (80% power), 882 (90% power)
power.t.test: 165.6 
Simulated power at n = 165 per arm: 0.793 (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.

14. Multiplicity, Missing Data and Analysis Populations

Multiplicity arises when investigators evaluate more than one outcome or make more than one statistical comparison. In general, each additional test creates another opportunity for a result to appear unusual by chance under a null model. A prespecified primary endpoint, a hierarchy of outcomes, or an adjustment for multiple comparisons can help control how results are interpreted. The registry identifies blood loss as the primary outcome and lists thigh circumference and range of motion as secondary outcomes, but it does not report a multiplicity strategy. No claim can therefore be made about whether the trial’s intended analysis controlled for multiple testing.

The record lists no reported analyses. It does not give a statistical analysis plan, identify the exact test or model used for the trial’s own analysis, or say whether the secondary comparisons were prespecified. The unadjusted comparison statistics should not be treated as a complete report of all planned or conducted analyses. Whether additional analyses were performed is not reported in the registry record.

The number of participants with posted measurements differs across endpoints. The primary outcome summaries use 31 participants in the Arista group and 30 in control. At 3 months, thigh circumference summaries use 30 and 26 participants, and range of motion summaries use 30 and 24. The registry does not report the reasons for these differences, whether they reflect missing measurements, exclusions, or another process, or how any missing values were handled.

The analysis population is not defined. The record does not say whether all randomized participants were analyzed according to assigned group, whether any participants were excluded after randomization, or how adherence to assigned treatment was considered. Without that information, it is not possible to determine whether the posted summaries correspond to an intention-to-treat population, a per-protocol population, or another analysis set.

These omissions matter because missingness and analysis-population choices can affect the interpretation of a randomized comparison. If the availability of an outcome is related to participant characteristics or outcome values, analyses restricted to those with measurements may differ from the results that would have been obtained with complete follow-up. That is a general concern, not a finding established for this trial. The registry does not provide enough information to assess the direction or extent of any such effect.

15. Safety Results

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

Deaths

Other (non-serious) adverse events

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

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: readmission due to pain (9.7%).

The registry reports serious adverse events for 3 of 31 participants at risk in the Arista group and 2 of 28 at risk in the control group. Other adverse events are reported for 2 of 31 at risk in the Arista group and 0 of 28 at risk in the control group. Deaths are reported as 0 in each group. These are the recorded counts and denominators; they should not be converted into comparative conclusions without additional information about event definitions, collection, and analysis.

The serious-adverse-event denominator in the control group is 28, while the primary-outcome control group count is 30. The registry does not explain the difference. It also does not report the period over which adverse events were collected, severity criteria beyond the serious classification, attribution to treatment, or whether participants could have experienced more than one event. The counts should therefore be read as registry summaries rather than as a complete safety analysis.

The registry lists “Readmission due to pain” as a top serious adverse event term, at 9.7%. The record does not clarify the denominator or event-counting basis for that percentage. The figures do not establish that an event was caused by either assigned treatment, and they are not sufficient to compare safety reliably. No medical advice or treatment recommendation follows from these reported counts.

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

The trial addresses a specific comparison in TKA: Arista powder added to intravenous tranexamic acid versus intravenous tranexamic acid alone. The posted primary summaries show mean blood loss of 122.6 cubic centimeters in the Arista group and 133.3 cubic centimeters in the control group. The unadjusted estimated mean difference is -10.7 cubic centimeters, and its 95% confidence interval ranges from -28.23 to 6.831. This is an estimate with meaningful uncertainty, not a definitive answer about the true difference.

The result does not establish that the groups are the same. A confidence interval that includes zero means the posted comparison remains compatible with no difference, but also with differences in either direction within the interval. Likewise, the unadjusted p-value of 0.232 is not proof that the null hypothesis is true or that the assigned treatments have identical effects. The registry does not report an equivalence or non-inferiority objective.

The result also does not establish that the observed numerical difference was caused by Arista. Randomization is recorded, but details of implementation and the trial’s analysis plan are not reported. The record says blood loss was calculated according to standard hospital protocol without describing that protocol. These gaps limit independent appraisal of the measurement and analysis.

The secondary outcome summaries do not remove this uncertainty. Their intervals include zero, the participant counts are smaller than for the primary outcome, and the registry does not report a plan for interpreting multiple outcomes. The trial’s stated purpose mentions hematoma formation, but hematoma formation is not among the posted outcome measures.

Finally, results from this trial should not be generalized beyond the population, setting, and protocol without supporting information. Eligibility criteria and detailed participant characteristics are not reported in the registry record. The statistical findings describe the posted group data and their uncertainty; they do not, by themselves, constitute medical guidance or establish a treatment recommendation.

17. Why This Trial Matters Statistically

This trial is statistically informative because it makes a randomized comparison between two treatment strategies that share intravenous tranexamic acid, with Arista powder as the added component in one group. That design frames the question as an incremental comparison rather than a comparison of the powder against no intervention. Stating the contrast clearly is essential to interpreting what the estimate addresses.

The record also illustrates why an estimate should be read together with its uncertainty. The primary comparison has a numerical point estimate, but its confidence interval includes values in both directions relative to zero. A p-value alone would not convey that range or the uncertainty about the size and direction of the difference. Mean and standard deviation summaries likewise have different roles: one describes the group average and the other the spread of observed measurements.

Enrollment was 61, and the outcome-specific counts are smaller for the secondary measures. This highlights the importance of reporting the analysis population and the reasons outcomes are unavailable. Without those details, readers cannot assess whether the available-case summaries preserve the randomized comparison or how robust they are to missing observations.

The record lists a primary endpoint and two secondary outcomes, but does not report a multiplicity plan or trial analyses. That makes the distinction between primary and secondary evidence especially important. A disciplined interpretation does not elevate a secondary pattern into a confirmatory claim when the analysis strategy and missing-data handling are not described.

The sample-size planning illustration also shows how target effect size and desired power influence enrollment planning, but it is not the trial’s original design justification or an estimate of observed power. Separating planning calculations from the completed trial’s results helps avoid overstating what a small study can establish. Together, these statistical considerations make transparent reporting of methods, endpoint definitions, uncertainty, and analysis populations central to interpreting clinical trial evidence.

18. Limitations

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

Several limitations specific to the registry record constrain interpretation. The primary blood-loss measure is described as calculated according to standard hospital protocol, but the components, measurement procedures, and aggregation across the stated timeframe are not specified. The record therefore does not allow readers to reproduce or fully evaluate the endpoint definition.

The registry does not describe eligibility criteria, participant characteristics, recruitment setting, random-sequence generation, or allocation concealment. Single blinding is listed, but the blinded party and safeguards are not identified. These omissions make it difficult to judge applicability and the implementation of the design from the record alone.

Although 61 participants were enrolled, the registry does not define the analysis population or explain differences in endpoint-specific counts. Secondary outcome summaries include fewer participants than the primary outcome summaries, and the reasons and handling of unavailable measurements are not reported. This leaves uncertainty about whether the analyzed groups retain the original randomized comparison.

The record lists no reported analyses and does not provide a statistical analysis plan, an original sample-size justification, or a multiplicity approach. It is not possible to verify from the registry whether the posted comparisons reflect the prespecified analysis or whether other analyses were conducted. The listed sample-size illustrations are based on the observed effect and stated planning assumptions; they are not evidence of the trial’s original design rationale.

The registry’s brief study purpose mentions hematoma formation, but the listed outcome measures include blood loss, thigh circumference, and range of motion. It does not report a hematoma outcome measure. Safety reporting also lacks details on collection period, event definitions, attribution, and the reason for the differing control-group denominator. These are limitations of the available record, not proof that the underlying study failed to collect or analyze those details.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Arista Hemostatic Powder for Total Knee Post Operative Outcomes Study — NCT05522153.
• Registry record last updated 2024-09-19; status last verified 2024-04.
• Results first posted 2024-09-19.
• 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.

22. Record Summary

The registry describes a completed, randomized, single-blinded, parallel-group phase 1 trial of Arista hemostatic powder in total knee arthroplasty, with 61 participants enrolled. The Arista group received powder in the wound plus intravenous tranexamic acid; the control group received intravenous tranexamic acid alone.

The primary endpoint was mean blood loss, measured from incision until 90 days after surgery. The posted means were 122.6 cubic centimeters for Arista and 133.3 cubic centimeters for control. The unadjusted mean difference was -10.7 cubic centimeters, with a 95% confidence interval from -28.23 to 6.831 and an unadjusted p-value of 0.232.

Thigh circumference and range of motion were listed as secondary outcomes at 3 months. The registry contains no reported analyses and does not report the trial’s analysis plan, missing-data procedures, or multiplicity strategy. The posted comparisons are best interpreted as descriptive estimates with uncertainty and reporting limitations.