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Hyperparathyroidism NA Binary Endpoint NCT01640184

Efficacy and Safety of Ultrasonic Ablation to Treat Secondary Hyperparathyroidism in Chronic Kidney Disease Patients: Complete Statistical Analysis

This analysis examines a randomized, open-label study of ultrasonic ablation, active vitamin D, and parathyroidectomy for secondary hyperparathyroidism in chronic kidney disease. It focuses on the 12-month target iPTH outcome, the posted secondary outcomes, and the limits of interpreting the registry results.

Trial start: 2012-08  ·  Enrollment: 79  ·  Sponsor: Dongliang Zhang, MD
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 Efficacy and Safety of Ultrasonic Ablation to Treat Secondary Hyperparathyroidism in Chronic Kidney Disease Patients (NCT01640184), a randomized na study. The primary outcome is Rate of Achieving the Target on Blood Intact Parathyroid Hormone Level According to Kidney Development Improvement Global Outcome (KDIGO) Guidelines..

79
Enrollment
NA
3
Arms
In the primary outcome
+26.4 pts
Risk difference
Ultrasonic Ablation
-1.2 to 54.0 pts
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT01640184
PhaseNA
ConditionHyperparathyroidism, Disorders of Parathyroid Gland
AllocationRandomized
Design modelParallel
MaskingNone (open label)
Enrollment79
Arms in the primary outcome3
Lead sponsorDongliang Zhang, MD
Results postedYes

2. Clinical Question

Population

The registry describes chronic kidney disease patients with secondary hyperparathyroidism who had not succeeded with medical therapy and could not undergo parathyroidectomy. The investigators’ stated rationale also refers to enlarged parathyroid gland(s) visible at ultrasonography. Further eligibility details are not reported in the registry record.

Intervention

Ultrasonic ablation was delivered as ultrasound-guided percutaneous parathyroid gland radio frequency ablation.

Comparator

The registry lists active vitamin D with general treatments according to KDIGO guidelines and parathyroid surgery as the other treatment groups. The posted primary comparisons use active vitamin D as the reference.

Primary question

At 12 months, what percentage of analyzed participants achieved the target blood intact parathyroid hormone level according to KDIGO guidelines, and how did the percentage in the ultrasonic ablation group compare with active vitamin D and parathyroidectomy?

The clinical question concerns an outcome target rather than the size of the change in iPTH itself. The registry defines the primary endpoint as the rate of achieving the target blood iPTH level. It describes measurement every 3 months for stable patients and more frequent blood testing after ultrasonic ablation, surgery, or impulse therapy with large doses of active vitamin D. Whether the target was assessed using a specific threshold or a detailed rule is not reported in the registry record.

The registry states that the number analyzed was the number of patients who completed the study. The posted primary results include active vitamin D, ultrasonic ablation, and parathyroidectomy groups. They address the target-achievement question, but do not establish which treatment is preferable for an individual patient or identify the effect in groups not described by the registry’s eligibility rationale.

3. Trial Design

The registry record describes a randomized, parallel-group study with no masking. It is marked completed and reports enrollment of 79. The listed phase is NA. The record gives a study start of 2012-08 and primary completion of 2014-11. Further details of random sequence generation, allocation concealment, or the procedures used to maintain allocation are not reported in the registry record.

Three treatment groups are described. The active vitamin D group received oral medicine and other general treatments according to the suggestions in KDIGO guidelines. The ultrasonic ablation group received ultrasound-guided percutaneous parathyroid gland radio frequency ablation. The parathyroidectomy group received parathyroid surgery. The posted primary comparisons use active vitamin D as the reference group.

For the primary outcome, the registry says that the analysis population consisted of patients who completed the study. The posted group results list 26 participants for active vitamin D, 21 for ultrasonic ablation, and 20 for parathyroidectomy. These are the outcome-specific analysis counts, not an explanation of the disposition of every enrolled participant. Reasons for non-completion, treatment changes, and the handling of missing endpoint measurements are not reported in the registry record.

The registry describes iPTH testing every 3 months for stable patients, with more frequent testing after the procedures or during impulse therapy with large doses of active vitamin D. This means the stated measurement schedule was not identical in frequency across all clinical circumstances. The record does not explain whether this difference affected endpoint ascertainment or how repeated measurements were used to classify target achievement.

The original sample-size justification, trial-specific statistical analysis plan, and details of any interim analyses are not reported in the registry record. The planning illustrations associated with the results are based on observed effects and should not be mistaken for the assumptions used to design the original trial.

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

StageActive Vitamin DUltrasonic AblationParathyroidectomy
STARTED342322
COMPLETED262120
NOT COMPLETED822

Reasons for not completing this period:

ReasonActive Vitamin DUltrasonic AblationParathyroidectomy
Death100
Lost to Follow-up410
Physician Decision300
Withdrawal by Subject011
Protocol Violation001

Analysis population for the primary outcome, as defined in the registry: Number of participants analyzed is the number of patients completed 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.

CharacteristicUnitActive Vitamin DUltrasonic AblationParathyroidectomyTotal
Participants analysed34232279
Age, Continuousyears56.3 (20 to 74)52.0 (24 to 73)55.2 (26 to 69)55.3 (20 to 74)
Sex: Female, Male: FemaleParticipants20121345
Sex: Female, Male: MaleParticipants1411934
Race (NIH/OMB): American Indian or Alaska NativeParticipants0000
Race (NIH/OMB): AsianParticipants34232279
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants0000
Race (NIH/OMB): Black or African AmericanParticipants0000
Race (NIH/OMB): WhiteParticipants0000
Race (NIH/OMB): More than one raceParticipants0000
Race (NIH/OMB): Unknown or Not ReportedParticipants0000
Region of Enrollment: Chinaparticipants34232279
Ca-baselinemmol/L2.31 (SD 0.27)2.43 (SD 0.30)2.53 (SD 0.23)2.41 (SD 0.30)
P-baselinemmol/L1.95 (SD 0.49)2.14 (SD 0.66)2.12 (SD 0.45)2.10 (SD 0.51)
iPTH-baselineng/ml239.84 (SD 299.01)1550.6 (SD 521.7)1779.9 (SD 514.1)1201.8 (SD 498.7)
BALP-baselinemicrogram/L17.31 (SD 6.38)18.84 (SD 17.94)19.27 (SD 14.87)17.98 (SD 13.32)

6. Primary Endpoint

The registry lists the primary outcome as Rate of Achieving the Target on Blood Intact Parathyroid Hormone Level According to Kidney Development Improvement Global Outcome (KDIGO) Guidelines., measured over 12 months.

ElementRegistry entry
Result typeNumber
Measure of spreadnot applicable
Unitpercentage of participants
Endpoint classificationBinary Endpoint

The primary endpoint is the percentage of participants achieving the target blood intact parathyroid hormone (iPTH) level according to KDIGO guidelines at 12 months. It is a binary outcome for each participant: the endpoint records whether the target was achieved, then summarizes the proportion of analyzed participants who achieved it in each group. The registry describes the analysis population as patients who completed the study.

A target-based endpoint can be clinically interpretable because it connects a laboratory measure to a stated treatment goal, rather than reporting only the average iPTH value. Comparing the percentages across groups describes how often participants reached that goal under the study’s treatment approaches. It does not, by itself, show the amount of iPTH change among individuals, how long target achievement was maintained, or whether other clinical outcomes changed.

The registry says iPTH was measured every 3 months for stable patients and more frequently after ultrasonic ablation, surgery, or impulse therapy with large doses of active vitamin D. It does not report the exact target definition, the rule for handling measurements that differ over time, or whether a participant had to meet the target at a particular visit or across multiple visits. Those details matter when interpreting what “achieving the target” means operationally.

The result is therefore best read as a group-level proportion tied to the registry’s target definition and completion-based analysis population. The exact endpoint rule is not reported in the registry record, which limits how fully the classification can be reproduced or compared with other studies.

7. Results Posted in the Registry

Risk difference: Ultrasonic Ablation

+26.4

95% CI: -1.2 to 54.0 percentage points

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals8.427.847.266.585.9105Active Vitamin D (n=26)Ultrasonic Ablation (n=21)Parathyroidectomy (n=20)% of participants (95% CI)
Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Ultrasonic AblationParathyroidectomy-7.851130506988risk difference (percentage points) 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
Incidence of Injury on the Recurrent Laryngeal Nerve (RLN).Binary EndpointRisk difference+10.0 pts (-3.1 to 23.1)n/a
Changes of the Blood Levels on Calcium During 12 Months.Continuous EndpointMean difference-0.50 (-0.62 to -0.38)3 per arm
Changes of Blood Levels on Phosphorus During 12 Months.Continuous EndpointMean difference-0.40 (-0.60 to -0.20)13 per arm

Incidence of Injury on the Recurrent Laryngeal Nerve (RLN).

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Parathyroidectomy-5.250.856.95131925risk difference (percentage points) vs control (95% CI)

Changes of the Blood Levels on Calcium During 12 Months.

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Ultrasonic AblationParathyroidectomy-0.67-0.53-0.38-0.24-0.090.05mean difference vs control (95% CI)

Changes of Blood Levels on Phosphorus During 12 Months.

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Ultrasonic AblationParathyroidectomy-0.90-0.71-0.51-0.32-0.130.07mean difference vs control (95% CI)

The secondary outcomes broaden the picture beyond target iPTH achievement. They include recurrent laryngeal nerve injury and blood measures of calcium, phosphorus, iPTH, and bone specific alkaline phosphatase. The registry posts numerical results for recurrent laryngeal nerve injury, calcium, and phosphorus. Numerical results for iPTH changes and bone specific alkaline phosphatase are not reported in the registry record, despite being listed as secondary outcomes.

The posted secondary summaries suggest that the blood-measure comparisons do not all point in the same direction or represent the same clinical question as the primary endpoint. The primary result concerns whether participants met an iPTH target; secondary measures describe blood levels or an adverse event. A change or difference in a continuous laboratory measure cannot be treated as interchangeable with target attainment, and neither automatically establishes a broader clinical benefit.

The secondary analyses are unadjusted recalculations, and the registry does not report formal analyses for these outcomes. They should therefore be considered exploratory descriptions rather than confirmatory evidence. Multiple secondary outcomes create multiple opportunities to see an apparently notable difference by chance. The record does not report whether any multiplicity adjustment or hierarchy among outcomes was prespecified.

Outcome-specific sample sizes also vary, and missing-data details are not available. The record does not say whether the same participants contributed to each secondary result or how incomplete measurements were addressed. These gaps make it difficult to judge whether differences across endpoints reflect treatment effects, differences in analyzed populations, or chance.

The best overall reading is that secondary findings add context but do not independently settle the primary question. Their directions and precision can help identify topics for further study, but the unadjusted nature of the summaries and missing analysis details make them less weighty than a fully specified, prespecified analysis. Results for unposted outcomes should not be inferred from the primary result or from the available secondary measures.

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

9. Statistical Interpretation

Clinical Biostats interpretation

In the posted primary results, target achievement was 30.8% with active vitamin D, 57.1% with ultrasonic ablation, and 90.0% with parathyroidectomy. These are the observed percentages in the outcome groups, not estimates adjusted for baseline characteristics. The registry does not report an adjusted primary analysis.

Against active vitamin D, the recalculated unadjusted risk difference for ultrasonic ablation is 0.264, with a confidence interval that includes zero; its unadjusted p-value is 0.069. The posted results are compatible with a higher target-achievement rate in the ultrasonic ablation group, but the interval also allows little or no difference. The unadjusted comparison does not meet the conventional 0.05 threshold. This should not be interpreted as proof that the groups are equivalent: the estimate is imprecise, and a failure to meet a threshold does not establish absence of an effect.

For parathyroidectomy versus active vitamin D, the recalculated unadjusted risk difference is 0.592, with a confidence interval that does not include zero; the unadjusted p-value is <0.001. The posted data therefore show a substantially higher observed target-achievement percentage in the parathyroidectomy group than in the active vitamin D group. This comparison is still based on the available group results and does not account for unreported design or analysis details.

These are separate comparisons with active vitamin D. The record does not provide a direct statistical comparison between ultrasonic ablation and parathyroidectomy. The fact that the observed percentages differ between those two groups is not itself a test of their difference. The recalculated contrasts should be read as unadjusted descriptions of the posted summary data, not as sponsor-reported adjusted estimates.

Interpretation is also constrained by the number of analyzed participants and the registry’s completion-based analysis population. The number of enrolled participants is 79, whereas the primary outcome counts are 26, 21, and 20 across the three groups. The registry does not explain the difference between enrollment and these analysis counts, or report whether missing outcomes could be related to treatment or outcome status. If completion differed in a way related to target achievement, the observed percentages could be affected.

The primary outcome is one part of the study’s evidence. Secondary outcomes include recurrent laryngeal nerve injury and blood measures, but not all listed secondary outcomes have numerical results posted. Secondary findings have less evidential weight when analyses are unadjusted and when the record does not report how multiple outcomes were handled. Overall, the primary results support a descriptive contrast between groups; they do not by themselves settle causal, comparative, or patient-level questions.

10. Statistical Methods Explained

The registry identifies a randomized, parallel-group study with no masking. Randomization is intended to create groups that are comparable on average at the start of a study, including with respect to measured and unmeasured factors. In practice, the credibility of that protection depends on how sequence generation and allocation were conducted. Those details are not reported in the registry record. With no masking, participants and study personnel were not masked according to the registry entry; the record does not say whether outcome assessors or analysts were masked separately.

What does the primary percentage represent?

The endpoint is a proportion: the number of analyzed participants who achieved the target divided by the number analyzed in that group. It describes the frequency of target achievement in the observed group. A difference between two such proportions is a risk difference, expressed in the registry’s comparison data as a proportion-scale contrast. Positive estimates in the posted comparisons indicate a higher target-achievement proportion in the intervention group than in active vitamin D. The estimates are recalculated, unadjusted comparisons of posted summary statistics.

A risk difference keeps the comparison on an absolute scale: it describes the separation between group proportions. Other relative measures, such as a risk ratio or odds ratio, express the contrast differently and can sound larger or smaller depending on the scale. Neither scale removes uncertainty or addresses possible bias from missing outcomes or differences in care. For the primary outcome, the registry record does not report a sponsor analysis or an adjusted model.

How should a p-value be read?

A p-value describes how incompatible the observed data are with a specified null model, under the assumptions of the calculation. It is not the probability that the null hypothesis is true, nor does it measure the probability that a result will be reproduced. A small p-value does not show that an effect is clinically important; a larger p-value does not prove there is no effect. The primary comparison of ultrasonic ablation with active vitamin D has an unadjusted p-value of 0.069, while the parathyroidectomy comparison has an unadjusted p-value of <0.001. The registry does not report the trial’s prespecified test, analysis plan, or any multiplicity procedure, so these recalculated p-values should be treated as unadjusted summaries.

What does a confidence interval add?

A confidence interval communicates the uncertainty around an estimate under the statistical method used to calculate it. A wider interval indicates less precision than a narrower interval on the same scale. For the ultrasonic ablation comparison, the risk-difference interval includes zero, so the posted summary data are compatible with no difference as well as with a higher target-achievement proportion. For the parathyroidectomy comparison, the interval excludes zero and lies in the direction of a higher proportion. These statements concern the recalculated unadjusted intervals, not an adjusted sponsor analysis.

The usual repeated-sampling interpretation is that a confidence-interval procedure will cover the true quantity at its stated confidence level in the long run if its assumptions hold. It does not mean there is a specified probability that the fixed true effect lies within the particular calculated interval. The confidence level for the recalculated intervals is not stated in the registry record, so it should not be inferred from the registry’s sample-size planning assumptions.

Why does the analysis population matter?

The registry defines the primary analyzed population by study completion. A completion-based analysis can differ from an analysis that retains participants in their randomized groups regardless of completion. If the reasons for not completing are related to treatment or the outcome, restricting the analysis to completers can affect the comparison. The record does not report participant flow, reasons for missingness, imputation, or sensitivity analyses. It is therefore not possible to assess how missing endpoint data were handled or whether the completion-based results are robust to alternative assumptions.

What can the secondary comparisons tell us?

For continuous outcomes, a mean difference describes the separation between group averages on the measurement scale. The registry posts group means and standard deviations for calcium and phosphorus at the stated baseline and 12-month timeframe, and recalculated mean differences against active vitamin D. Standard deviations describe variability among observations; they are not confidence intervals for the mean. A mean difference does not convey the full distribution of individual measurements or whether changes were consistent across participants.

For a binary outcome such as recurrent laryngeal nerve injury, a group count describes how many participants were recorded with the event. A risk difference compares the event proportions. When event counts are small, estimates can be unstable and intervals can be broad. The secondary results have no reported analyses in the registry record; the comparisons presented are unadjusted recalculations. Multiple outcomes and comparisons also increase the chance that some patterns will appear notable by chance if no multiplicity strategy is used. Whether a strategy was prespecified is not reported in the registry record.

The sample-size illustrations use a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. They use fractions of the observed effect as planning targets. These assumptions describe the illustrations, not the original trial’s design; the original design assumptions are not reported in the registry record.

11. Confidence Intervals and Precision

The posted primary percentages are 30.8% for active vitamin D, 57.1% for ultrasonic ablation, and 90.0% for parathyroidectomy. The recalculated unadjusted risk difference is 0.264 for ultrasonic ablation versus active vitamin D, with an interval that includes zero. For parathyroidectomy versus active vitamin D, the recalculated risk difference is 0.592, with an interval that excludes zero. These intervals reflect uncertainty around the contrasts; they do not account for unreported analysis choices or possible bias from missing outcomes.

The interval for ultrasonic ablation spans a range of plausible contrasts that includes little or no difference, as well as a positive difference. Its unadjusted p-value is 0.069. Thus, the observed percentage is higher than the active vitamin D percentage, but the estimate is not precise enough to rule out no difference under the recalculated analysis. This is not evidence that the treatments are equivalent.

The parathyroidectomy interval is more clearly separated from zero in the direction of a higher target-achievement rate, and the unadjusted p-value is <0.001. This supports a clear statistical contrast in the posted summary data versus active vitamin D. It does not demonstrate that the difference is free of bias, clinically important, or directly applicable beyond the trial population.

Precision depends on both the size of the estimate and the amount of information in the data. The primary analyzed groups are modest in size, and the record reports no adjustment for other variables. The registry does not report the confidence level or method used for sponsor-reported intervals, and the posted intervals are recalculated from summary statistics. The available intervals should therefore be read as uncertainty measures for those recalculations, not as a substitute for a complete analysis plan.

For the secondary outcomes, the posted confidence intervals also convey substantial uncertainty, particularly for event outcomes with few recorded events. A confidence interval that includes no difference does not establish that the groups are the same. Conversely, an interval excluding no difference does not resolve the issues of multiple outcomes or missing analysis details. Statistical precision is only one component of the strength of evidence.

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 effect5573
75% of the observed effect96128
50% of the observed effect211281
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect5010020050040%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, pooled-variance normal approximation for two proportions. Counts were reconstructed from the posted percentages and arm sizes, so small rounding differences are possible. Calculated for the comparison: Ultrasonic Ablation.

The planning figures are participants per arm for 80% power and participants per arm for 90% power. They are not total sample sizes, and they are not total event counts. The assumptions listed for these illustrations are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The target effect is a stated fraction of the observed effect. The trial’s original design assumptions are not reported in the registry record.

Power is the chance, under a specified planning model and effect, of detecting a difference at the chosen significance level. The 80% column gives the estimated participants per arm for an 80% chance of detecting the selected effect under those assumptions; the 90% column gives the corresponding estimate for a 90% chance. These are forward-looking planning illustrations, not a measure of how much power the completed trial had. This is not observed power.

The rows use 100%, 75%, and 50% of the observed effect. As the effect used for planning becomes smaller, more participants are needed to distinguish it from random variation with the same target power. This principle applies across the displayed comparisons and outcomes, though the numerical requirements differ according to the observed effect and the variability or event rate used in each calculation.

The figures are sensitive to the assumptions. Equal allocation, the normal approximation, and the observed effect may not match a future study’s design or true effect. Planning from the observed effect can be optimistic because an estimate from a small study can be exaggerated by random variation. A future design would also need to consider its outcome definitions, missing-data approach, number of comparisons, and any adjustment strategy; those matters are not encoded in these simple illustrations.

For example, the primary ultrasonic ablation comparison lists 55 participants per arm for 80% power and 73 participants per arm for 90% power when planning for 100% of the observed effect. For 50% of that observed effect, the corresponding figures are 211 and 281 participants per arm. The contrast between these planning scenarios illustrates why smaller target effects require more participants, not what the original trial planned or achieved.

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 √(2p̄(1−p̄)) + z1−β √(p0(1−p0) + p1(1−p1)) ]2 / (p1 − p0)2

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 = 0.308; treatment proportion p1 = 0.571; average p̄ = 0.440.
  2. First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.7019 = 1.3757.
  3. Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.6767 = 0.5695.
  4. n = (1.3757 + 0.5695)2 / (0.2637)2 = 54.4, rounded up to 55 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 <- 0.307692307692308                          # control proportion
p1 <- 0.571428571428571                          # 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(1640184)
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 = 55 (80% power), 73 (90% power)
 75% of observed effect: n per arm = 96 (80% power), 128 (90% power)
 50% of observed effect: n per arm = 211 (80% power), 281 (90% power)
power.prop.test: 54.4 
Simulated power at n = 55 per arm: 0.793 (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.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists a primary endpoint and several secondary outcomes, with multiple treatment groups and possible pairwise comparisons. Testing several outcomes and contrasts increases the chance that at least one result will appear statistically notable by chance. A prespecified hierarchy, adjustment procedure, or decision rule can help control that risk. Whether the trial used such a strategy is not reported in the registry record.

The posted primary comparisons are recalculated and unadjusted. The secondary comparisons are also unadjusted recalculations, and the registry reports no analyses for the secondary outcomes. The p-values should therefore not be read as multiplicity-adjusted evidence. The record does not report the complete statistical analysis plan, whether the primary contrast was selected in advance, or whether any planned comparisons were omitted from the posted results.

Missing-data handling is another important uncertainty. For the primary outcome, the registry says the analyzed participants were those who completed the study. It does not report reasons for non-completion, how many participants were missing an endpoint in each randomized group, whether participants were analyzed in their assigned groups, or whether imputation or sensitivity analyses were used. The registry’s overall enrollment is 79, while the posted primary outcome group counts are 26, 21, and 20; the record does not account for the difference between enrollment and the outcome-specific analysis counts.

These details matter because the completers may differ from those without endpoint data. If completion or measurement availability is related to treatment response, a completer-only proportion may not represent all randomized participants. The available summaries cannot show whether the direction or size of the primary comparison would persist under different missing-data assumptions.

The same concern applies to secondary outcomes. The registry does not report the number analyzed for every secondary measure in a way that clarifies missing observations, nor does it explain how repeated measurements were reduced to the posted summaries. Numerical results for some listed secondary outcomes are absent. Together, unreported multiplicity and missing-data procedures limit the strength of conclusions that can be drawn from nominal unadjusted comparisons.

15. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Active Vitamin D1342.9%
Ultrasonic Ablation0230.0%
Parathyroidectomy0220.0%
Participants with at least one serious adverse event
Serious adverse events by armActive Vitamin D2.9%Ultrasonic Ablation0.0%Parathyroidectomy0.0%% of participants with at least one serious adverse event

Other (non-serious) adverse events

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

ArmParticipants affected of at risk
Active Vitamin D0 of 34
Ultrasonic Ablation5 of 23
Parathyroidectomy15 of 22

Most frequent serious adverse event terms

Event termOrgan systemActive Vitamin DUltrasonic AblationParathyroidectomy
DeathCardiac disorders1 of 340 of 230 of 22

Most frequent non-serious adverse event terms

Event termOrgan systemActive Vitamin DUltrasonic AblationParathyroidectomy
HypocalcemiaInjury, poisoning and procedural complications0 of 342 of 2315 of 22
HoarseInjury, poisoning and procedural complications0 of 345 of 238 of 22

Serious events with the highest arm-level rate: death (2.9%).

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 records serious adverse events among 34 participants at risk in the active vitamin D group, 23 in the ultrasonic ablation group, and 22 in the parathyroidectomy group. The serious-event counts are 1, 0, and 0, respectively. These counts describe the registry’s recorded serious adverse events; they should not be interpreted as a complete comparison of safety without details about event definitions, surveillance, timing, or missing reporting.

The registry also lists Death at 2.9% among the top serious terms. Group-specific death counts are not reported in the registry record. The record lists other adverse events affecting 0 participants in active vitamin D, 5 in ultrasonic ablation, and 15 in parathyroidectomy, with the respective at-risk groups stated above. The record does not provide enough detail in these summaries to assess event type, severity, duration, or causal attribution.

Small event counts can be highly uncertain and do not establish that an event cannot occur in a group. Differences in recorded counts are descriptive; the registry does not report a formal safety comparison or analysis plan. Safety findings should be read alongside the limitations in event reporting and the absence of group-specific death counts.

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

The primary result describes the percentage of analyzed participants who achieved the registry-defined iPTH target at 12 months. In the posted data, the observed target-achievement percentage is higher for ultrasonic ablation than for active vitamin D, while the recalculated unadjusted interval includes no difference. The parathyroidectomy group also has a higher observed percentage than active vitamin D, with an unadjusted interval excluding no difference and p <0.001. These are group-level statistical comparisons, not guarantees about outcomes for individual participants.

The findings do not establish that ultrasonic ablation is equivalent to active vitamin D, or that it is equivalent to parathyroidectomy. No direct statistical comparison between ultrasonic ablation and parathyroidectomy is reported. Nor do the results establish the comparative effect in populations beyond the study’s stated clinical context. Details about eligibility, treatment adherence, participant flow, missing-data handling, and adjusted analyses are not reported in the registry record.

The endpoint is target attainment, not a complete account of health outcomes. The registry lists secondary laboratory outcomes and recurrent laryngeal nerve injury, but numerical results are missing for some listed outcomes and formal secondary analyses are not reported. The safety summaries are counts, not a full evaluation of adverse-event timing, seriousness, or attribution. Consequently, the primary result alone cannot represent the overall balance of benefits and harms.

Statistical significance is not the same as clinical importance. The size of a group difference, its uncertainty, the endpoint definition, and the reliability of data collection all matter. The posted results provide a signal for further interpretation, but the registry record leaves important questions unanswered about analysis choices and completeness. They should be understood as evidence from one completed trial record, not as a treatment recommendation or a definitive answer to every comparative question.

17. Why This Trial Matters Statistically

This trial is statistically interesting because it places a procedure, a medical treatment, and surgery in a randomized parallel-group comparison, while reporting a target-based biochemical endpoint. The endpoint asks whether participants reached a specified goal rather than only how group averages differ. That distinction illustrates how clinical interpretation depends on the way an outcome is defined and summarized.

The three observed primary percentages also show why estimates and uncertainty must be read together. The comparison of ultrasonic ablation with active vitamin D has an observed separation but a confidence interval that includes no difference. The parathyroidectomy comparison is more clearly separated from the reference group in the recalculated analysis. Treating both contrasts simply as “positive” or “negative” would discard important information about precision and the different strength of evidence.

The registry’s completion-based analysis population and absent missing-data explanation highlight a recurring issue in trial interpretation: randomization supports comparability at assignment, but analysis restricted to completers may weaken that protection if completion is related to outcomes. The study also has several secondary outcomes, yet the registry does not report a multiplicity strategy or formal secondary analyses. These issues demonstrate why a registry result needs more than a p-value to support a strong conclusion.

Finally, the planning illustrations show the dependence of sample-size requirements on the effect targeted for detection. They are based on observed effects and simple listed assumptions, not on the trial’s unreported original design. Separating planning power from observed results is essential: a post hoc calculation cannot make an uncertain estimate more precise. The record therefore offers useful material for learning how design, endpoint choice, precision, missingness, and multiplicity jointly shape interpretation.

18. Limitations

Several limitations are specific to the available record. The eligibility description is brief and does not provide detailed inclusion or exclusion criteria, disease severity, or baseline clinical characteristics. The investigators’ rationale describes patients who had not succeeded with medical therapy and could not undergo parathyroidectomy, as well as enlarged glands visible by ultrasonography, but the record does not show how consistently those features defined enrollment.

The primary endpoint depends on a KDIGO target, but the exact operational definition is not reported in the registry record. The timing and frequency of iPTH measurement could differ by clinical circumstance, and the record does not explain how multiple values were used to determine achievement at 12 months. This makes it difficult to reproduce the endpoint classification from the description alone.

The registry reports outcome analysis counts that are lower than the enrollment figure, but it does not explain participant flow or reasons for non-completion. The stated analysis population includes patients who completed the study, and the record does not describe imputation, sensitivity analysis, or an intention-to-treat approach. The possible influence of missing outcomes therefore cannot be assessed.

The study is open-label, and the registry does not report whether outcome assessors were masked. It also does not provide a full protocol or statistical analysis plan, details of allocation concealment, adjusted analyses, or multiplicity handling. These omissions are especially relevant because there are multiple groups and secondary outcomes.

For safety, serious adverse events are summarized by group, but group-specific death counts are not reported and event definitions and attribution are not described. Some listed secondary outcomes have no numerical results in the registry record. These limitations restrict both the completeness of the clinical picture and the strength of any comparative conclusions.

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22. Record Summary

The registry record describes a completed randomized, open-label, parallel-group study with enrollment of 79. It compares active vitamin D, ultrasound-guided percutaneous ultrasonic ablation, and parathyroidectomy in chronic kidney disease patients with secondary hyperparathyroidism. The primary endpoint is target iPTH achievement at 12 months, analyzed among participants who completed the study.

Posted primary results show target achievement of 30.8% with active vitamin D, 57.1% with ultrasonic ablation, and 90.0% with parathyroidectomy. Recalculated unadjusted comparisons show an uncertain difference for ultrasonic ablation versus active vitamin D and a clearer difference for parathyroidectomy versus active vitamin D. The registry record does not report adjusted primary analyses, the original statistical plan, or how missing outcomes were handled.

Secondary results and adverse-event counts provide additional context, but some listed secondary outcomes lack numerical results and the record does not describe multiplicity procedures. The results are informative as posted group summaries, with important limits on precision, completeness, and interpretation.

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