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 Trial Of Paricalcitol and Cholecalciferol(Vitamin D3) in the Treatment Of Secondary Hyperparathyroidism in Patients After ROUX-EN-Y Gastric Bypass Surgery (NCT01138475), a randomized phase 3 study. The primary outcome is The Primary Outcome Measure With iPTH.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT01138475 |
| Phase | Phase 3 |
| Condition | Gastric Bypass, Parathyroid Hormone |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Quadruple |
| Enrollment | 49 |
| Arms in the primary outcome | 3 |
| Lead sponsor | Kerstyn C. Zalesin, M.D. |
| Results posted | Yes |
2. Clinical Question
Population
Patients with secondary hyperparathyroidism after Roux-en-Y gastric bypass surgery. The registry describes this group as patients after RYGB and identifies parathyroid hormone as a condition of interest. The recorded primary outcome notes missing data in the paricalcitol and placebo groups, but does not report how many participants were missing from the primary analysis or why.
Intervention
Paricalcitol capsules were compared with cholecalciferol capsules and matching placebo. The study description identifies a double-dummy design, meaning participants in the treatment groups were assigned matching study preparations as part of the masking approach. Details of dosing and adherence are not reported in the registry record.
Comparator
Placebo was the reference group for the posted pairwise comparisons. The record also describes the cholecalciferol and paricalcitol groups as part of a three-arm, parallel-group study. The posted primary comparisons give mean differences for each active group relative to placebo.
Primary question
At 6 weeks, how did the change in iPTH compare among the paricalcitol, cholecalciferol, and placebo groups? The primary measure is reported in pg/mL, with a mean and standard deviation for each arm. The registry describes comparing change from baseline to the final measure, but the detailed baseline values and the sponsor's formal analysis are not reported in the registry record.
The clinical question combines a biochemical endpoint with a broader evaluation of tolerability. The study description also names self-assessed well-being and adverse effects, including hypercalcemia, kidney stones, gastrointestinal effects, and other organ-system effects. The posted results summarized in the registry include several laboratory measures and serious and other adverse-event counts. Those records offer a limited view of the planned questions: the primary measure is reported at 6 weeks, and some secondary measures are posted, but the registry record does not contain a formal analysis for the outcomes.
3. Trial Design
This was a randomized, parallel-group pilot trial described as phase 3. The study record identifies quadruple masking and describes the trial as double-blind, double-dummy, and placebo-controlled. The treatment groups were paricalcitol, cholecalciferol, and placebo. Enrollment was 49. The registry status is completed, with a start date of 2010-07 and primary completion at 2015-08.
The parallel structure means participants were assigned to one study group rather than moving through each treatment in sequence. Random allocation can help balance participant characteristics across groups, while masking is intended to limit the influence of treatment knowledge on participants and study personnel. Those are general design principles; the registry does not report the randomization sequence, allocation concealment procedures, or precisely which roles were masked.
The primary outcome was assessed at 6 weeks. The outcome description says change in iPTH was compared in each arm from baseline to the final measure, with differences compared across the three arms. The arm-level results report means and standard deviations. Primary results are listed for 15 participants in the paricalcitol group, 17 in the cholecalciferol group, and 15 in the placebo group. These group counts should be read as the reported outcome sample sizes, not as a complete account of participant flow.
The registry record does not report the original sample-size calculation, the planned enrollment target, the randomization ratio, intervention doses, treatment adherence, or the full schedule of outcome assessments. The trial is called a pilot, but the specific aims or operational definition of that label are not reported. It is therefore not possible to infer the intended precision, the recruitment plan, or whether the final enrollment matched the original target. The listed study dates establish the broad conduct period, but do not fill in those design details.
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
| Stage | Placebo-controlled | Paricalcitrol | Cholecalciferol |
|---|---|---|---|
| STARTED | 16 | 16 | 17 |
| COMPLETED | 16 | 16 | 17 |
| NOT COMPLETED | 0 | 0 | 0 |
Analysis population for the primary outcome, as defined in the registry: missing data in paricalcitol and placebo group
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.
| Characteristic | Unit | Paricalcitol | Cholecalciferol | Placebo | Total |
|---|---|---|---|---|---|
| Participants analysed | 16 | 17 | 16 | 49 | |
| Age, Categorical: <=18 years | Participants | 0 | 0 | 0 | 0 |
| Age, Categorical: Between 18 and 65 years | Participants | 16 | 17 | 16 | 49 |
| Age, Categorical: >=65 years | Participants | 0 | 0 | 0 | 0 |
| Age, Continuous | years | 55 (SD 9) | 55 (SD 10) | 51 (SD 11) | 53.8 (SD 9.9) |
| Sex: Female, Male: Female | Participants | 15 | 11 | 15 | 41 |
| Sex: Female, Male: Male | Participants | 1 | 6 | 1 | 8 |
| Region of Enrollment: United States | participants | 16 | 17 | 17 | 49 |
| PTH | ng/mL | 96 (SD 27) | 90 (SD 15) | 101 (SD 25) | 96 (SD 24) |
| alkaline phosphatase | u/L | 87 (SD 19) | 97 (SD 29) | 101 (SD 32) | 95 (SD 27) |
| serum calcium | mg/dL | 9.4 (SD 0.3) | 9.3 (SD 0.3) | 9.4 (SD 0.4) | 9.3 (SD 0.3) |
| 25 OH vitamin D | ng/dL | 30 (SD 16) | 32 (SD 13) | 30 (SD 7) | 30 (SD 12) |
| serum phosphorous | mg/dL | 3.9 (SD 0.6) | 3.7 (SD 0.5) | 3.7 (SD 0.5) | 3.7 (SD 0.5) |
| 24 hour urine calcium | mmol | 89 (SD 81) | 106 (SD 139) | 131 (SD 91) | 109 (SD 105) |
| osteocalcin | ng/mL | 39 (SD 19) | 36 (SD 17) | 40 (SD 20) | 39 (SD 19) |
| Urine N-telopeptide cross linked | nmol | 64 (SD 26) | 73 (SD 30) | 82 (SD 55) | 73 (SD 40) |
| bone specific alkaline phosphatase | U/L | 15 (SD 5) | 19 (SD 8.1) | 19 (SD 10) | 18 (SD 8.2) |
6. Primary Endpoint
The registry lists the primary outcome as The Primary Outcome Measure With iPTH, measured over 6 weeks.
| Element | Registry entry |
|---|---|
| Result type | Mean |
| Measure of spread | Standard Deviation |
| Unit | pg/mL |
| Endpoint classification | Continuous Endpoint |
The primary endpoint is change in intact parathyroid hormone, abbreviated iPTH, from baseline to the final measurement at 6 weeks. It is expressed in pg/mL. The registry describes comparing each arm's change and then comparing the three arms. The posted arm summaries are means with standard deviations: 72.0 for paricalcitol, 87.0 for cholecalciferol, and 82.0 for placebo. Because the outcome is described as change, these summaries concern change rather than a standalone final iPTH concentration.
iPTH is used in this trial because the stated objective is to evaluate reduction in parathyroid hormone among patients with secondary hyperparathyroidism after RYGB. A continuous laboratory measure can retain information about the magnitude of change across participants, rather than reducing the outcome to a yes-or-no category. That is a general reason to use continuous endpoints, not evidence that a particular change is clinically important.
The endpoint's usefulness depends on how it was measured and analyzed. The registry lists the unit, summary statistic, and timeframe, but does not report the laboratory method, prespecified clinically meaningful difference, handling of baseline values in the model, or a complete analysis population. It notes missing data in the paricalcitol and placebo groups without giving the number missing or the reasons. The results therefore describe the posted group summaries and their recalculated contrasts, while the sponsor's full analysis and the practical significance of any change are not reported in the registry record.
7. Results Posted in the Registry
- Paricalcitol: mean 72.00 versus 82.00 on control; difference -10.00 (95% CI -31.83 to 11.83), standardized effect d = -0.33; z-test p = 0.369.
- Cholecalciferol: mean 87.00 versus 82.00 on control; difference 5.00 (95% CI -20.46 to 30.46), standardized effect d = 0.13; z-test p = 0.700.
Mean difference: Paricalcitol
95% CI: -31.83 to 11.83
Recalculated from the posted summary statistics
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 outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Alkaline Phosphatase | Continuous Endpoint | Mean difference | -14.00 (-33.63 to 5.63) | 64 per arm |
| Serum Calcium | Continuous Endpoint | Mean difference | 0.00 (-1.31 to 1.31) | n/a |
| Serum 25 OH Vitamin D | Continuous Endpoint | Mean difference | 2.00 (-3.28 to 7.28) | 222 per arm |
Alkaline Phosphatase
- 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:
- Paricalcitol: mean 87.00 versus 101.00 on control; difference -14.00 (95% CI -33.63 to 5.63), standardized effect d = -0.50; z-test p = 0.162.
- Cholecalciferol: mean 94.00 versus 101.00 on control; difference -7.00 (95% CI -26.79 to 12.79), standardized effect d = -0.24; z-test p = 0.488.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Paricalcitol and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Cholecalciferol and the control. The interval gives the range of effects that remain compatible with the data.
Serum Calcium
- 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 errors.
- Result:
- Paricalcitrol: mean 9.30 versus 9.30 on control; difference 0.00 (95% CI -1.31 to 1.31), standardized effect d = 0.00; z-test p = 1.000.
- Cholecalciferol: mean 9.40 versus 9.30 on control; difference 0.10 (95% CI -1.21 to 1.41), standardized effect d = 0.05; z-test p = 0.881.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Paricalcitrol and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Cholecalciferol and the control. The interval gives the range of effects that remain compatible with the data.
Serum 25 OH Vitamin D
- 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:
- Paricalcitrol: mean 27.00 versus 25.00 on control; difference 2.00 (95% CI -3.28 to 7.28), standardized effect d = 0.27; z-test p = 0.458.
- Cholecalciferol: mean 38.00 versus 25.00 on control; difference 13.00 (95% CI 4.91 to 21.09), standardized effect d = 1.08; z-test p = 0.002.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Paricalcitrol and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval excludes no difference, so the mean is statistically higher for Cholecalciferol than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The secondary measures cover several types of laboratory information, including alkaline phosphatase, serum calcium, Serum 25 OH Vitamin D, serum phosphorus, osteocalcin, N-Telopeptide Cross Linked Urine, bone-specific alkaline phosphatase, and 24 Hour Urine Calcium. This range gives context around the primary iPTH question, but different biomarkers represent different biological measurements and should not be treated as interchangeable indicators of the same outcome.
Among the secondary results with posted summaries, the direction of the estimates is not uniform across measures. Both active-group alkaline phosphatase means are lower than placebo, serum calcium means are close across groups, and the vitamin D measure is higher for cholecalciferol than placebo. The posted paricalcitol comparison for the vitamin D measure is less distinct. This broad pattern is descriptive; it does not establish that the treatments caused changes in the secondary measures.
These results do not alter the primary iPTH interpretation. The primary comparisons remain imprecise, with intervals that include zero. Secondary outcomes may help characterize what else was measured, but they cannot answer the primary question in place of the primary endpoint. Nor do multiple biomarker patterns necessarily point in the same clinical direction.
Unadjusted secondary findings carry less weight because multiple outcomes and comparisons increase the chance of seeing an apparently notable result by chance. The registry record does not report a multiplicity strategy, a prespecified hierarchy among secondary outcomes, or formal analyses for them. Several listed secondary outcomes do not have detailed numerical summaries in the record. As a result, the available secondary pattern is incomplete and should be considered exploratory rather than confirmatory.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Alkaline Phosphatase
- Serum Calcium
- Serum 25 OH Vitamin D
- Serum Phosphorus
- Osteocalcin
- N-Telopeptide Cross Linked Urine
- Bone Specific Alkaline Phosphatase
- 24 Hour Urine Calcium
9. Statistical Interpretation
The primary outcome summaries are 72.0 pg/mL for paricalcitol, 87.0 pg/mL for cholecalciferol, and 82.0 pg/mL for placebo. In the unadjusted recalculated comparisons with placebo, the mean difference is -10.0 pg/mL for paricalcitol, with a reported interval from -31.83 to 11.83, and 5.0 pg/mL for cholecalciferol, with an interval from -20.46 to 30.46. The corresponding unadjusted p-values are 0.369 and 0.7. These estimates are directions and magnitudes of group contrasts; they do not establish that either treatment caused a difference.
Both primary intervals include zero, so the posted estimates are compatible with no mean difference as well as with differences in either direction. Their breadth indicates substantial uncertainty about the size and direction of the contrasts. The p-values are not small under conventional null-testing interpretation, but they should not be treated as proof that the groups are equivalent. Equivalence would require a prespecified margin and an analysis designed to assess whether plausible differences fall within that margin; neither is reported in the registry record.
For the secondary measures with posted comparisons, the observed pattern is mixed across laboratory domains. The alkaline phosphatase estimates are below placebo for both active groups, while the serum calcium estimates are close to placebo. Serum 25 OH Vitamin D is higher in the cholecalciferol group than placebo in the posted comparison; the paricalcitol comparison is less distinct. These secondary comparisons do not replace the primary question about iPTH. They also deserve more caution because multiple outcomes and contrasts create more opportunities for chance findings, and no multiplicity strategy is reported.
The cholecalciferol comparison for Serum 25 OH Vitamin D has a reported mean difference of 13.0 ng/dL, interval 4.91 to 21.09, and unadjusted p-value 0.002. This is a secondary result, not the primary iPTH result. Its apparent precision and p-value should be considered alongside the number of outcomes examined and the absence of a reported multiplicity adjustment. The registry does not report a formal analysis for the secondary endpoints.
For the posted safety counts, no serious adverse events or other adverse events are listed as affecting participants in any group. The numbers at risk differ slightly across the safety groups and are 16 for paricalcitol, 17 for cholecalciferol, and 16 for placebo. These are observed registry counts in a small pilot study, not evidence that adverse effects cannot occur. Death counts are not reported in the registry record. Overall, the posted findings are descriptive and imprecise for the primary question, with incomplete reporting of analysis procedures and missing data.
10. Statistical Methods Explained
Several statistical ideas help distinguish the posted summaries from stronger claims about treatment effects. The outcome is continuous, so each arm is described by a mean and a measure of spread. For the primary endpoint, the spread is a standard deviation. A mean describes the group's average reported change; a standard deviation describes variation among participant-level values. Neither quantity by itself tells how certain the mean or the between-group contrast is.
What does a mean difference represent?
A mean difference compares the average outcome in one group with the average in another. The primary contrasts use placebo as the reference. The paricalcitol estimate is -10.0 pg/mL, meaning the reported average change in that group is lower than the placebo average by that amount under the contrast's stated direction. The cholecalciferol estimate is 5.0 pg/mL, meaning its reported average is higher than the placebo average by that amount. These are unadjusted recalculations from the posted summary statistics, rather than a reported sponsor model. They do not account for covariates or other adjustments.
Change scores compare a participant's measurement at follow-up with a baseline measurement. A group mean change summarizes those participant-level changes. The record describes this approach but does not give the baseline summaries, the exact calculation convention, or whether the comparison was based on change scores or an adjusted model in the sponsor's analysis. These details matter because different analytic approaches can yield different estimates, particularly when baseline values vary between groups.
How should uncertainty be read?
A confidence interval is a range of values compatible with the observed data under the assumptions of the method used to calculate it. In general, a wider interval represents less precision than a narrower interval. For the primary iPTH comparisons, the reported intervals extend across zero and include both negative and positive differences. This means the data do not pin down the direction or size of the mean contrast with much precision. A confidence interval is not a range containing most individual participant outcomes; it concerns the estimated contrast.
The registry does not identify the confidence level or the method used for the posted interval calculation. It also does not report a formal sponsor analysis. The intervals and p-values accompanying the comparisons are recalculated, unadjusted summaries. They should therefore be read as descriptive statistical comparisons from the posted means and spreads, not as a substitute for a prespecified analysis plan or participant-level analysis.
What do the p-values say?
A p-value describes how unusual the observed data, or data more extreme, would be under a particular null hypothesis and the assumptions of the test. It does not give the probability that the null hypothesis is true, and it does not measure the clinical importance of a difference. The primary p-values are 0.369 and 0.7. In isolation, these values do not provide strong evidence against a null of no mean difference. They also do not demonstrate that the treatments have identical effects or that an important effect has been ruled out.
The p-values are unadjusted. When several outcomes and comparisons are examined, the chance of at least one apparently unusual result can increase. Adjustment methods or a prespecified hierarchy can address that issue, but no such approach is reported in the registry record. This is especially relevant to secondary outcomes, where the registry lists multiple laboratory measures and comparisons.
Why do spread measures matter?
The standard deviation reflects how dispersed participant values are around the mean. Greater variability makes it harder to estimate a group mean difference precisely unless there is more information. Standard error, by contrast, describes uncertainty in an estimated mean. The primary endpoint and most displayed laboratory summaries use standard deviations, while Serum Calcium is reported with standard errors. Those quantities are not interchangeable. The registry does not explain the reason for the different reporting choice, so the summaries should be read according to the dispersion measure stated for each outcome.
Over-dispersion is a general concern when observed variation is greater than a statistical model assumes. If a model underestimates variability, standard errors may be too small and intervals may be too narrow. The registry record does not report a model assessment for over-dispersion, and the posted primary summaries are not enough to evaluate the distribution of individual outcomes. For a continuous endpoint, distribution shape, outliers, and missing observations can all affect the reliability of mean-based inference.
What can be concluded from recalculation?
The displayed contrasts are simple unadjusted recalculations based on group-level summaries. Such calculations are useful for a transparent comparison, but they do not reproduce analyses that might use baseline adjustment, repeated measurements, covariates, or a particular missing-data method. The registry contains no reported analysis entries for the primary outcome, and the listed secondary outcomes also have no reported formal analyses. The study's statistical analysis plan, model specification, assumptions, and handling of protocol deviations are not reported in the registry record.
General statistical interpretation also depends on design and conduct. Randomization supports a causal comparison when allocation is implemented as intended and outcome data are handled appropriately. Masking may reduce some forms of bias, but the exact masking procedures and success are not reported. The small outcome-group counts and noted missing data limit precision and make the unreported analysis choices important. The numerical summaries can describe what was posted, but they cannot resolve those gaps.
11. Confidence Intervals and Precision
The primary comparisons have broad reported intervals: -31.83 to 11.83 pg/mL for paricalcitol versus placebo, and -20.46 to 30.46 pg/mL for cholecalciferol versus placebo. Each interval includes zero and permits effects in either direction. The estimates therefore have limited precision: the posted summaries do not narrowly locate the underlying mean difference.
Precision is distinct from whether a result meets a threshold for statistical significance. A p-value does not tell how narrowly an effect has been estimated, and a non-small p-value does not show that any meaningful difference has been excluded. In general, intervals communicate a range of uncertainty around an estimate, while a point estimate alone gives only one value. The primary intervals make clear that a range of plausible differences remains compatible with the observed summaries.
The outcome group sizes are 15, 17, and 15, with missing data noted in the paricalcitol and placebo groups. Small groups and missing observations can leave estimates less stable, although the registry record does not quantify how the missingness affected precision. The record does not report the confidence level or calculation method for the intervals. This limits the detail with which their repeated-sampling interpretation can be assessed.
Some secondary results have narrower-looking or more separated estimates, but their interpretation also depends on their analysis status and multiplicity. The Serum 25 OH Vitamin D comparison for cholecalciferol has a reported interval from 4.91 to 21.09 ng/dL, while other secondary intervals include zero. These secondary findings do not improve the precision of the primary iPTH contrast. No formal sponsor analyses or multiplicity-adjusted intervals are reported in the registry record.
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 detect | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 147 | 196 |
| 75% of the observed effect | 260 | 348 |
| 50% of the observed effect | 585 | 783 |
The planning figures are participants per arm for the continuous outcomes. They are not total event counts. They use a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each row considers an effect set to the stated fraction of the observed effect. The figures are planning illustrations based on observed effects, not the trial's original design assumptions; those original assumptions are not reported in the registry record.
The 80% power column gives the illustrative participants per arm for a design that would have an 80% chance of detecting the specified effect under the stated assumptions, if that effect were the true effect and the assumptions held. The 90% power column gives the corresponding per-arm planning count for a higher chance of detecting that effect. These are design calculations, not an estimate of how likely the completed trial was to find a result.
Rows that plan for 75% or 50% of the observed effect use smaller target effects than the row based on 100% of the observed effect. Smaller effects are harder to distinguish from random variation, so they require more participants. For example, the primary paricalcitol comparison lists 147 participants per arm for 80% power when planning for 100% of the observed effect, and 585 participants per arm when planning for 50% of the observed effect. For the primary cholecalciferol comparison, the corresponding figures are 883 and 3,532 participants per arm. The figures illustrate how strongly planning needs can depend on the assumed target effect.
These calculations are not observed power. Observed power is not a useful substitute for interpreting the estimate and its uncertainty after a trial; the confidence interval and the design assumptions are more informative. The registry record does not report whether these planning assumptions were used when the trial was designed, or whether any original sample-size calculation was performed.
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 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
- Observed difference Δ = -10.000; pooled standard deviation σ = 30.504.
- n = 2 × (1.96 + 0.842)2 × 30.5042 / -10.0002 = 146.1, rounded up to 147 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 # observed difference in means
sigma <- 30.5040980853393 # 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(1138475)
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 = 147 (80% power), 196 (90% power)
75% of observed effect: n per arm = 260 (80% power), 348 (90% power)
50% of observed effect: n per arm = 585 (80% power), 783 (90% power)
power.t.test: 147
Simulated power at n = 147 per arm: 0.799 (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
The registry record does not report a statistical analysis plan, a multiplicity adjustment, or a hierarchy that distinguishes confirmatory outcomes from exploratory ones. The primary endpoint is identified, but the planned method for testing it is not reported. The record also lists multiple secondary outcomes, which raises the general issue of multiplicity: when many outcomes or contrasts are examined, some may appear notable by chance even if there is no underlying effect. Without a stated plan, it is not possible to determine how the sponsor intended to manage that issue.
The posted comparisons are unadjusted recalculations from group summaries. They do not account for multiple testing, baseline covariates, or any model-based adjustments unless those are reflected in the posted summaries, which is not described. No formal analyses are listed for the primary or secondary outcomes. Interim analyses, stopping rules, and any planned subgroup analyses are not reported in the registry record.
Missing data are explicitly noted for the primary outcome in the paricalcitol and placebo groups. The number of missing values, reasons for missingness, timing of missingness, and approach to handling it are not reported. The outcome summaries give group counts, but the registry does not provide a participant flow accounting for randomized, treated, measured, and analyzed participants. It also does not describe whether the analysis followed an intention-to-treat, per-protocol, or other population definition.
These omissions matter because results can depend on which participants contribute to the analysis and how missing outcomes are handled. General methods include complete-case analysis, imputation, or model-based approaches, but none can be attributed to this study from the registry record. The missing-data note does not establish the direction or size of any resulting bias. It signals that the posted primary summaries should be interpreted with caution, especially because the group counts are small and no sensitivity analyses are reported.
15. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Paricalcitriol | 0 | 16 | 0.0% |
| Cholecalciferol | 0 | 17 | 0.0% |
| Placebo | 0 | 16 | 0.0% |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 0% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Paricalcitriol | 0 of 16 |
| Cholecalciferol | 0 of 17 |
| Placebo | 0 of 16 |
The registry lists zero participants affected by serious adverse events and zero affected by other adverse events in each safety group. The numbers at risk are 16 for paricalcitol, 17 for cholecalciferol, and 16 for placebo. These are observed counts in the registry record. They should not be read as proof that no adverse effects can occur or that the groups have equivalent safety profiles.
With small numbers at risk, an absence of recorded events provides limited information about uncommon outcomes. The registry does not report event-specific descriptions in the serious-event list, and the top serious-event terms are empty. Death counts are not reported in the registry record. The brief study description names hypercalcemia, kidney stones, gastrointestinal effects, and other organ-system effects as safety questions, but the posted aggregate counts do not provide detailed rates for each event type.
Interpretation is also limited by the absence of information about surveillance, duration of safety follow-up, severity grading, and the rules used to classify events. The group counts describe what the registry posted, not a complete assessment of comparative safety.
16. What the Result Does, and Does Not, Mean
The posted results describe average changes in iPTH over the 6-week timeframe and show modestly sized, uncertain unadjusted contrasts against placebo. The paricalcitol estimate is below the placebo mean, while the cholecalciferol estimate is above it. Both reported primary intervals include zero and span differences in either direction. The results therefore do not precisely determine the size or direction of a primary between-group difference.
That uncertainty should not be translated into a claim that the treatments are equivalent, or into a claim that an effect is absent. A study can fail to distinguish a difference from zero when the estimate is imprecise. Establishing equivalence or excluding a meaningful difference requires a prespecified margin and an appropriate design and analysis. Such information is not reported in the registry record.
The secondary results provide additional laboratory context, but they do not resolve the primary uncertainty. The vitamin D comparison for cholecalciferol is the clearest separated secondary estimate among the outcomes with detailed comparisons, while other posted secondary comparisons are less distinct. Because the registry does not report a multiplicity plan or formal analysis, this secondary finding should not be treated as confirmatory evidence about the primary outcome.
The safety record lists no affected participants for serious or other adverse events in the groups, but the study's small safety counts cannot establish the absence of risk. The reported sample sizes, missing primary data, and limited analysis details constrain what can be learned from the record. The trial describes a randomized comparison in a specific post-RYGB population; the registry results alone do not establish how findings would apply to other populations or settings.
In general, statistical results quantify evidence under particular assumptions; they do not determine whether a laboratory change is important to patients. The registry does not report a clinically meaningful difference for iPTH, patient-level outcomes tied to the biomarker changes, or a complete account of the sponsor's analysis. The sound interpretation is therefore bounded: the record offers estimates and uncertainty for a small pilot comparison, not a definitive conclusion about treatment benefit or harm.
17. Why This Trial Matters Statistically
This study is statistically instructive because its primary question is framed around a continuous biomarker and a short follow-up comparison among three randomized groups. The contrast estimates are easy to state, but their intervals show why the point estimate alone is insufficient. A negative estimate in one comparison and a positive estimate in another do not by themselves establish different treatment effects; uncertainty and the comparator structure matter.
The pilot designation and the observed outcome-group sizes make precision central to interpretation. The planning illustrations show that required participants per arm vary substantially when the target effect changes. This is a general feature of power planning: an assumed effect that is smaller than the observed estimate calls for larger groups under otherwise fixed assumptions. The registry does not report whether those illustrations resemble the original design plan.
The record also illustrates why missing-data and multiplicity reporting are part of the statistical result, not administrative details. Missing primary data are noted, but counts and handling are absent. Multiple secondary measures are listed, but the analysis plan and multiplicity approach are not. Those omissions limit the strength of conclusions even when group means, contrasts, and p-values are available.
Finally, the safety counts show the distinction between no observed events in a small set of participants and evidence that risk is absent. Statistical interpretation requires attention to what was measured, how much information was collected, and what procedures governed the analysis. This record is useful for understanding those limits in a randomized pilot study.
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.
The registry results leave important design and analysis details unresolved. The outcome description notes missing data in the paricalcitol and placebo groups, but does not state the number missing, the reasons, or how those observations were handled. Participant flow and the exact analysis population are not reported. These omissions make it difficult to assess whether the arm summaries represent all randomized participants or a subset with observed measurements.
The record does not report baseline iPTH values, laboratory assay details, intervention doses, adherence, or the statistical model used by the sponsor. It also does not report the confidence-interval method or level. The unadjusted recalculated comparisons are based on posted group summaries and cannot account for participant-level features or reproduce an unreported sponsor analysis.
The study is identified as a pilot, and the primary outcome groups are small. The record does not report the original sample-size justification or whether recruitment reached its intended target. The planning illustrations are based on observed effects and should not be mistaken for the trial's design rationale. The number of detailed secondary results is also limited relative to the range of listed secondary outcomes.
Multiplicity procedures, interim analyses, stopping rules, subgroup plans, protocol deviations, and sensitivity analyses are not reported in the registry record. The safety summary provides aggregate affected-participant counts but not detailed event descriptions, severity, follow-up duration, or death counts. These gaps limit both statistical and safety interpretation. They do not establish that any particular bias occurred; they define uncertainty about how the posted results were generated and what they represent.
19. Related Tutorials
20. Related Statistical Calculators
21. Sources
- ClinicalTrials.gov: Trial Of Paricalcitol and Cholecalciferol(Vitamin D3) in the Treatment Of Secondary Hyperparathyroidism in Patients After ROUX-EN-Y Gastric Bypass Surgery — NCT01138475.
- Registry record last updated 2017-03-22; status last verified 2016-08.
- Results first posted 2017-03-22.
- 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.
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22. Record Summary
The registry record describes a completed phase 3 randomized, quadruple-masked, parallel-group pilot trial of paricalcitol, cholecalciferol, and placebo in patients with secondary hyperparathyroidism after Roux-en-Y gastric bypass. Enrollment was 49. The primary endpoint was change in iPTH at 6 weeks, reported as a mean with standard deviation.
The unadjusted recalculated primary comparisons against placebo are imprecise, and both reported intervals include zero. Several secondary laboratory outcomes are listed, with detailed results available for some measures. The record notes missing primary data in the paricalcitol and placebo groups, but does not report the missing-data method, formal analysis plan, or multiplicity strategy. Safety summaries list no affected participants for serious or other adverse events in the three groups; death counts are not reported in the registry record.