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 Oral Paricalcitol in Kidney Transplant Recipients (NCT00587158), a randomized na study. The primary outcome is Number of Subjects With Hyperparathyroidism at One Year.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT00587158 |
| Phase | NA |
| Condition | Transplant; Failure, Kidney, Renal Disease, End Stage, Hyperparathyroidism, Secondary |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | None (open label) |
| Enrollment | 100 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Mayo Clinic |
| Results posted | Yes |
2. Clinical Question
Population
People receiving a kidney transplant under a corticosteroid-avoidance immunosuppressive regimen. The registry record reports 100 participants enrolled. Further eligibility details are not reported in the registry record.
Intervention
Paricalcitol added to the immunosuppressive regimen. The registry describes the regimen as including induction therapy with alemtuzumab and methylprednisolone, followed by maintenance with mycophenolate mofetil and tacrolimus while avoiding corticosteroids. The paricalcitol dose and detailed administration schedule are not reported in the registry record.
Comparator
The same corticosteroid-avoidance immunosuppressive regimen without paricalcitol. Thus the randomized contrast concerns adding paricalcitol, rather than comparing different descriptions of the underlying maintenance regimen.
Primary question
At one year after kidney transplantation, how many participants in each group met the registry definition of hyperparathyroidism? The definition uses a raised parathyroid hormone result in the absence of hypocalcemia, or parathyroidectomy during the first year after transplant.
The registry frames the study around possible effects on overactive parathyroid glands and bone density after transplantation. The primary endpoint addresses the parathyroid question directly. Bone outcomes, including osteopenia or osteoporosis and bone mineral density, are listed as secondary outcomes. The randomized design allows the observed groups to be compared, but the result remains an estimate from the participants and outcomes recorded in this trial. It does not by itself establish what would happen in other populations, under other immunosuppressive regimens, or over periods beyond the reported outcome timeframes.
3. Trial Design
The registry identifies this as a randomized, parallel-group trial with no masking. It lists the phase as NA and reports enrollment of 100 participants. Mayo Clinic is named as the sponsor. The study is marked completed; the recorded start is 2007-01 and primary completion is 2011-11. These registry entries describe the trial structure and record status, but do not provide a full protocol or a complete account of trial conduct.
Participants were assigned to immunosuppression without paricalcitol or immunosuppression with paricalcitol. Both arm descriptions include induction therapy with alemtuzumab and methylprednisolone, followed by a corticosteroid-avoidance maintenance regimen using mycophenolate mofetil and tacrolimus. Paricalcitol is the stated additional intervention in the experimental arm. The registry record does not report its dose, the detailed timing of treatment, adherence, or the exact allocation procedure beyond identifying the study as randomized.
The primary endpoint is the number of participants with hyperparathyroidism at one year after kidney transplantation. The registry lists bone outcomes and other clinical outcomes as secondary measures, including PTH and bone alkaline phosphatase over time, bone mineral density, graft loss or death, and acute cellular rejection. It reports 13 outcome measures and 18 analyses. The available record does not establish whether every listed outcome was measured in every participant or explain the full analysis hierarchy.
The primary analysis population is described as intention-to-treat, with eligibility for that analysis defined as enrollment, at least one dose of study medication, and screening plus any post-screening efficacy data. Missing primary-endpoint values were handled with last observation carried forward. The record does not report the original sample-size justification, detailed eligibility criteria, or a complete statistical 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.
Before assignment: 112 patients were approached for enrollment. Of those, 4 patient's treating physicians did not think corticosteroid free immunosuppression was appropriate, 3 had their transplants cancelled, 3 were found to be vitamin D deficient, 1 withdrew consent prior to randomization \& 1 had a positive final crossmatch and hence were excluded from the study.
Overall Study
| Stage | Immunosuppression Without Paricalcitol (Control) | Immunosuppression With Paricalcitol |
|---|---|---|
| STARTED | 49 | 51 |
| Continued in Study | 45 | 46 |
| COMPLETED | 44 | 43 |
| NOT COMPLETED | 5 | 8 |
Reasons for not completing this period:
| Reason | Immunosuppression Without Paricalcitol (Control) | Immunosuppression With Paricalcitol |
|---|---|---|
| Did not want to do 24 hr urine collect. | 4 | 3 |
| Physician Decision | 0 | 1 |
| Lost to Follow-up | 1 | 2 |
| Death | 0 | 1 |
| Subject did not want to take study med | 0 | 1 |
Analysis population for the primary outcome, as defined in the registry: Analysis was performed by the intention-to-treat principle, comprised of all subjects enrolled, who will have taken at least one dose of study medication and have both screening and any post-screening efficacy data recorded. The last observation was carried forward for missing values.
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 | Immunosuppression Without Paricalcitol (Control) | Immunosuppression With Paricalcitol | Total |
|---|---|---|---|---|
| Participants analysed | 49 | 51 | 100 | |
| Age Continuous | years | 47.7 (SD 10.0) | 48.5 (SD 10.3) | 48.1 (SD 10.1) |
| Sex: Female, Male: Female | Participants | 16 | 18 | 34 |
| Sex: Female, Male: Male | Participants | 33 | 33 | 66 |
| Race/Ethnicity, Customized: American Indian or Alaska Native | Participants | 2 | 0 | 2 |
| Race/Ethnicity, Customized: Asian | Participants | 1 | 0 | 1 |
| Race/Ethnicity, Customized: Native Hawaiian or Other Pacific Islander | Participants | 0 | 1 | 1 |
| Race/Ethnicity, Customized: Black or African American | Participants | 3 | 0 | 3 |
| Race/Ethnicity, Customized: White | Participants | 42 | 49 | 91 |
| Race/Ethnicity, Customized: More than one race | Participants | 0 | 0 | 0 |
| Race/Ethnicity, Customized: Unknown or Not Reported | Participants | 0 | 0 | 0 |
| Race/Ethnicity, Customized: Hispanic | Participants | 1 | 1 | 2 |
| Region of Enrollment: United States | participants | 49 | 51 | 100 |
| Diabetes | participants | 12 | 10 | 22 |
| First transplant | participants | 47 | 50 | 97 |
| Cause of End-Stage Renal Disease: Adult Polycystic Kidney Disease | participants | 14 | 16 | 30 |
| Cause of End-Stage Renal Disease: Diabetic | participants | 10 | 8 | 18 |
| Cause of End-Stage Renal Disease: Glomerulonephritis | participants | 17 | 16 | 33 |
| Cause of End-Stage Renal Disease: Hypertension | participants | 1 | 3 | 4 |
| Cause of End-Stage Renal Disease: Other | participants | 7 | 8 | 15 |
| Living kidney donor | participants | 48 | 48 | 96 |
| Degree of interstitial fibrosis: Mild fibrosis at baseline | Participants | 2 | 3 | 5 |
| Degree of interstitial fibrosis: Moderate to severe fibrosis at baseline | Participants | 0 | 0 | 0 |
6. Primary Endpoint
The registry lists the primary outcome as Number of Subjects With Hyperparathyroidism at One Year, measured over 1 year post kidney transplant.
| Element | Registry entry |
|---|---|
| Result type | Number |
| Measure of spread | not applicable |
| Unit | Participants |
| Endpoint classification | Binary Endpoint |
The primary endpoint counts participants classified as having hyperparathyroidism one year after kidney transplantation. The registry defines hyperparathyroidism as a parathyroid hormone blood value greater than 65 picograms/milliliter when hypocalcemia is absent, or as having undergone parathyroidectomy during the first year after transplant. The endpoint is therefore a binary classification: each participant either meets the definition or does not.
Parathyroid hormone is described in the registry as a blood-test measure of how well the parathyroid gland is working. Counting participants who meet a specified definition makes it possible to compare the frequency of this outcome between the randomized groups. The endpoint combines a laboratory threshold with a surgical event; these are alternative ways to qualify under the registry definition, not separate primary outcomes.
A one-year endpoint focuses the comparison on the period identified in the study summary as the first year after transplantation. It does not describe the course of parathyroid hormone beyond that timeframe. Nor does the count alone describe the severity, duration, or subsequent course of hyperparathyroidism. Those questions would require additional outcome information. The registry record reports the definition and timeframe, but does not report details such as the timing or frequency of blood draws used to determine each participant’s classification.
7. Results Posted in the Registry
- Immunosuppression With Paricalcitol: 29.4% (15/51) versus 63.3% (31/49) on control; risk difference -33.9 percentage points (95% CI -52.3 to -15.5), risk ratio 0.46 (0.29–0.75); unadjusted two-proportion z-test p = <0.001.
Risk difference: Immunosuppression With Paricalcitol
95% CI: -52.3 to -15.5 percentage points
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 |
|---|---|---|---|---|
| Number of Subjects With Osteopenia/Osteoporosis of the Hip at One Year | Binary Endpoint | Risk difference | +7.8 pts (-10.8 to 26.5) | 483 per arm |
| Number of Subjects With Osteopenia/Osteoporosis of the Lumbar Spine at One Year | Binary Endpoint | Risk difference | +12.4 pts (-6.3 to 31.1) | 201 per arm |
| Change in Lumbar Spine Bone Mineral Density (BMD) | Continuous Endpoint | Mean difference | 0.00 (-0.22 to 0.22) | n/a |
Number of Subjects With Osteopenia/Osteoporosis of the Hip at One Year
- Endpoint type: Binary: the number of participants with the event, compared as proportions.
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Immunosuppression With Paricalcitol: 29.3% (12/41) versus 21.4% (9/42) on control; risk difference 7.8 percentage points (95% CI -10.8 to 26.5), risk ratio 1.37 (0.65–2.89); unadjusted two-proportion z-test p = 0.411.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Immunosuppression With Paricalcitol and the control. The interval gives the range of effects that remain compatible with the data.
Number of Subjects With Osteopenia/Osteoporosis of the Lumbar Spine at One Year
- Endpoint type: Binary: the number of participants with the event, compared as proportions.
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Immunosuppression With Paricalcitol: 33.3% (14/42) versus 20.9% (9/43) on control; risk difference 12.4 percentage points (95% CI -6.3 to 31.1), risk ratio 1.59 (0.77–3.28); unadjusted two-proportion z-test p = 0.198.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Immunosuppression With Paricalcitol and the control. The interval gives the range of effects that remain compatible with the data.
Change in Lumbar Spine Bone Mineral Density (BMD)
- 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:
- Immunosuppression With Paricalcitol: mean 0.35 versus 0.35 on control; difference 0.00 (95% CI -0.22 to 0.22), standardized effect d = 0.00; z-test p = 1.000.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Immunosuppression With Paricalcitol and the control. The interval gives the range of effects that remain compatible with the data.
The registered secondary outcomes broaden the scope beyond the primary parathyroid endpoint. They include hip and lumbar-spine osteopenia or osteoporosis, PTH and bone alkaline phosphatase over time, bone mineral density changes, death or renal graft loss, and acute cellular rejection. The record lists 12 posted secondary outcomes, while the available numeric findings cover only some of the outcomes and analyses in the registry.
Across the reported bone findings, the pattern does not show a consistent, clearly separated difference between groups: the binary bone outcomes have intervals that include no difference, and the posted lumbar-spine bone mineral density change has the same reported group mean in each arm. These results do not reproduce the clear separation seen in the primary hyperparathyroidism comparison. They also do not establish equivalence or rule out differences, because the secondary estimates have uncertainty and the record does not report a formal equivalence framework.
These outcomes are related to the study’s broader question about parathyroid and bone changes after transplantation, but they measure different aspects of that question. A result on the primary endpoint should not be assumed to predict a bone-density result, graft outcome, or rejection outcome. Conversely, the secondary outcomes do not redefine the primary finding.
Unadjusted secondary tests carry less weight when multiple outcomes and analyses are examined. Even if each test is conducted appropriately on its own, considering many results increases the chance of at least one apparently notable result arising by chance. The registry record does not report a multiplicity adjustment or a prespecified hierarchy for interpreting these secondary tests. The secondary findings are therefore best treated as additional, less definitive evidence rather than as independent confirmation of the primary result.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Number of Subjects With Osteopenia/Osteoporosis of the Hip at One Year
- Number of Subjects With Osteopenia/Osteoporosis of the Lumbar Spine at One Year
- Serum Parathyroid Hormone (PTH) Level Over Time
- Serum Bone Alkaline Phosphatase (BAP) Level Over Time
- Change in Lumbar Spine Bone Mineral Density (BMD)
- Change in Hip Bone Mineral Density (BMD)
- Number of Subjects Who Died or Lost Their Renal Graft During First Year
- Episodes of Acute Cellular Rejection (ACR) of the Renal Transplant
9. Statistical Interpretation
At one year, 31 of 49 participants in the group without paricalcitol met the primary endpoint, compared with 15 of 51 participants in the group with paricalcitol. The unadjusted recalculation estimates a lower event risk in the paricalcitol group, with a risk difference of -0.339. The posted interval for that estimate lies entirely below no difference. The recalculated unadjusted p-value is <0.001, and the registry’s own Fisher exact analysis reports p< 0.001.
These are group-level findings for the recorded endpoint, not a direct measurement of an individual participant’s response. The magnitude of the observed difference is substantial within this sample, but its precision still matters: an interval describes a range of estimates compatible with the data and the method used. It does not identify a guaranteed effect in a future group. The trial is relatively small in absolute enrollment, and the number contributing to this endpoint differs by arm from total enrollment.
The result is specific to the stated population, regimen, definition, and one-year timeframe. The two arms share the described corticosteroid-avoidance immunosuppression, so the comparison concerns adding paricalcitol to that setting. The registry record does not report the dose details or enough eligibility information to determine how closely other transplant populations would match the participants in this trial.
The primary endpoint result should be read alongside the secondary outcomes and the safety counts, not as a complete account of all potential benefits and harms. The registry lists multiple secondary outcomes, and results are available for several bone measures. Such secondary comparisons are less conclusive when many outcomes are examined without a reported multiplicity strategy. Missing-data handling also matters: the primary analysis used last observation carried forward, but the record does not report how many values were missing or how sensitive the result was to that choice.
The statistical evidence in the registry supports a difference between the recorded groups for the primary endpoint under the reported analyses. It does not, by itself, establish a causal mechanism, settle the results of other outcomes, or demonstrate that the same estimate would recur in another trial. Interpretation should retain both parts of the result: the observed contrast is clear in these data, while its scope and generalizability remain constrained by the trial record.
10. Statistical Methods Explained
The primary endpoint is binary because the registry classifies each participant according to whether the hyperparathyroidism definition was met. The arm counts therefore consist of participants meeting the definition and the total number included in that endpoint analysis. A comparison of the groups can be expressed as an absolute risk difference, a risk ratio, or an odds ratio. These are distinct effect measures: a risk difference compares event probabilities by subtraction, a risk ratio compares them by division, and an odds ratio compares event odds. Their numerical scales differ, so they should not be treated as interchangeable.
The unadjusted recalculation uses the posted counts and denominators and does not adjust for other characteristics. The estimated risk difference is -0.339, with a posted interval from -0.522 to -0.154. In this setting, a negative risk difference means the observed event proportion was lower in the paricalcitol group than in the control group. The interval does not include zero, the value corresponding to no absolute risk difference. This is a summary of uncertainty under the calculation’s assumptions, not a guarantee about the effect in another sample.
The registry reports a Fisher Exact analysis for the primary comparison. Fisher’s exact test is a general statistical method for comparing categorical outcomes between groups, using the observed allocation of event and non-event counts. It is especially useful when the available counts do not support reliance on a large-sample approximation. The registry reports p< 0.001. A p-value describes how surprising data at least as incompatible with the null hypothesis would be under the test’s assumptions if the null hypothesis were true. It is not the probability that the null hypothesis is true, nor a measure of clinical importance.
The recalculated p-value is unadjusted and reported as <0.001. Its purpose is to accompany the simple comparison reconstructed from the posted summary counts. The sponsor’s analysis is also a Fisher exact test, and the registry-reported result takes precedence when describing the sponsor’s own analysis. The two analyses point to the same broad statistical conclusion for the primary endpoint, while their p-values are not identical.
For binary outcomes, confidence intervals describe uncertainty around an estimated contrast. An interval for a risk difference is interpreted on the absolute probability scale. If it includes zero, values consistent with no risk difference remain within the interval; if it excludes zero, the interval does not include that null value under the interval method. These statements do not establish whether an effect is important in practice, and an interval does not assign a probability to the true effect. The registry does not identify the interval method for the recalculated risk difference.
The reported analysis population is called intention-to-treat, but the registry’s description also specifies that participants had taken at least one dose and had screening and post-screening efficacy data. That definition should be read as written rather than assumed to match every common use of the intention-to-treat label. The record says the last observation was carried forward for missing primary-endpoint values. This method substitutes an earlier recorded value for a missing later value. It can affect results when outcomes change over time, and its suitability depends on assumptions about the missing data and the outcome process. The number of missing primary values and sensitivity analyses are not reported in the registry record.
The trial was randomized and parallel-group, but masking is listed as none. In general, random assignment is intended to make treatment groups comparable at baseline on average, while lack of masking can leave participants or study personnel aware of assignment. Awareness can potentially affect care, measurement, or reporting; the registry record does not quantify whether such effects occurred. The record does not report the random sequence method, concealment procedures, or adjusted primary analyses.
Statistical significance and estimation answer different questions. A test result indicates how the data relate to a specified null model under a particular procedure. An effect estimate describes the direction and magnitude of the group contrast, while its interval describes precision. Both are needed for interpretation. The result should also be understood in the context of the endpoint definition, analysis population, missing-data handling, and the fact that other outcomes were assessed.
General statistical context: over-dispersion is variability greater than a model expects, and it can make standard errors too small if the model fails to account for that extra variability. The primary endpoint is a binary count comparison analyzed with Fisher’s exact test, not a reported over-dispersed count model. The registry does not report an analysis issue involving over-dispersion.
11. Confidence Intervals and Precision
The primary risk-difference interval runs from -0.522 to -0.154. Because the interval lies on the negative side of zero, the range of estimates retained by this calculation corresponds to a lower observed event risk in the paricalcitol group. The interval is not especially narrow: the data are compatible with a range of effect magnitudes, even though the interval does not include no difference. Its endpoints describe statistical uncertainty, not a prediction interval for individual outcomes.
A confidence interval is a procedure for expressing the precision of an estimate. In general, repeated use of a correctly specified procedure would produce intervals that cover the target parameter at the procedure’s stated rate. The interpretation is not that there is a particular probability that the fixed true effect lies inside this single observed interval. The registry-reported Fisher exact analysis gives a p-value, while the risk-difference interval is part of the unadjusted recalculation; the registry record does not specify the interval method for that recalculation.
The endpoint totals are 49 and 51 participants, and the event counts are 31 and 15. The amount of information available for an estimate depends on both group sizes and outcome frequencies. A confidence interval captures sampling uncertainty under its method, but does not account automatically for every limitation, such as missing outcome data, measurement choices, or lack of masking. The missing-data approach for the primary endpoint was last observation carried forward, and the record does not report the number of imputed values or a sensitivity analysis.
Precision should therefore be considered together with design and scope. The interval supports a difference in this recorded comparison, while leaving uncertainty about the exact magnitude and about how well the estimate applies beyond this trial’s participants, regimen, and timeframe.
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 | 33 | 44 |
| 75% of the observed effect | 60 | 80 |
| 50% of the observed effect | 135 | 180 |
The planning figures are illustrations based on the observed effect, not the trial’s original design calculation. The registry record does not report the trial’s own sample-size justification or original planning assumptions. The illustration assumes a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. It considers effects equal to the observed effect and fractions of that effect. The listed figures are participants per arm, not totals across both arms.
For planning at 100% of the observed primary effect, the illustration gives 33 participants per arm for 80% power and 44 participants per arm for 90% power. For planning at 75% of the observed effect, the corresponding figures are 60 and 80 participants per arm. For planning at 50% of the observed effect, they are 135 and 180 participants per arm.
In plain terms, the 80% power column gives the approximate per-arm size that the stated assumptions associate with an 80% chance of detecting the specified effect using the stated test threshold, if that effect and assumptions were correct. The 90% power column describes the analogous target at 90% power. A smaller effect is harder to distinguish from random variation, so the planning calculation requires more participants per arm as the assumed effect becomes smaller.
These values are not observed power. They do not tell how likely the completed trial was to find its observed result, and they are not evidence that the original trial was designed using these assumptions. They are hypothetical planning estimates tied to the effect observed in the posted data.
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, p0 and p1 are the control and treatment proportions, and p̄ is their average.
Worked calculation for this trial
- Control proportion p0 = 0.633; treatment proportion p1 = 0.294; average p̄ = 0.463.
- First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.7052 = 1.3822.
- Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.6633 = 0.5583.
- n = (1.3822 + 0.5583)2 / (-0.3385)2 = 32.9, rounded up to 33 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 <- 0.63265306122449 # control proportion
p1 <- 0.294117647058824 # 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(587158)
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 = 33 (80% power), 44 (90% power)
75% of observed effect: n per arm = 60 (80% power), 80 (90% power)
50% of observed effect: n per arm = 135 (80% power), 180 (90% power)
power.prop.test: 32.9
Simulated power at n = 33 per arm: 0.834 (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. Analyses Reported by the Sponsor
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| Fisher Exact | not reported | < 0.001 |
The registry reports the sponsor’s primary comparison as a Fisher Exact analysis with p< 0.001. The unadjusted recalculation from the posted event counts gives p < 0.001. Both indicate that the observed group counts are inconsistent with a no-difference null under their respective calculations. The recalculated estimate is an absolute risk difference, which adds a magnitude and direction to the test result.
The sponsor’s p-value and the recalculated p-value are not identical. The registry record does not report enough detail to attribute the difference to a particular implementation choice, and no discrepancy is flagged in the record. The sponsor’s own analysis is the primary reference for what the study reported; the recalculation is a transparent, simple unadjusted comparison based on posted summary statistics. It should not be presented as a replacement for the sponsor’s analysis or as evidence of an error.
A p-value alone does not describe the effect’s size or precision. The estimate and its interval should be read alongside the sponsor’s test result. Neither the registry p-value nor the recalculated result establishes the outcome of any secondary endpoint or resolves questions about missing data, multiplicity, or generalizability.
15. Multiplicity, Missing Data and Analysis Populations
The registry lists 13 outcome measures and 18 analyses. Evaluating multiple endpoints or analyses raises a multiplicity question: when many statistical tests are considered, the chance of obtaining at least one apparently unusual result by chance can increase. Common approaches include defining a primary endpoint in advance, specifying an order for testing, or adjusting the threshold for multiple comparisons. The registry record identifies a primary outcome but does not report a multiplicity adjustment, a testing hierarchy, or details of how secondary analyses were selected for emphasis.
This absence does not establish that no plan existed outside the registry record. It means the approach is not reported in the registry record, so the secondary p-values cannot be assumed to have been adjusted or interpreted under a stated family-wise plan. The primary result is distinguished in the record as the primary endpoint; multiplicity concerns remain especially relevant when drawing conclusions from the several secondary outcomes.
The primary analysis population is described as intention-to-treat and includes enrolled participants who took at least one dose and had screening and post-screening efficacy data. The phrase should be interpreted with that registry definition in view. The record also says last observation was carried forward for missing primary-endpoint values. This identifies a method but not the extent of missingness or the assumptions underlying it. Counts of missing values by arm, reasons for missingness, and sensitivity analyses are not reported in the registry record.
For the secondary outcomes, the missing-data approach and analysis populations are not reported in the registry record. Nor are interim analyses, stopping rules, or the original statistical analysis plan reported. These omissions limit the ability to assess whether all outcomes were analyzed as planned, how incomplete follow-up was handled across endpoints, or whether the reported tests reflect a prespecified strategy. They do not invalidate the posted counts; rather, they constrain how confidently the wider collection of results can be interpreted.
16. 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 |
|---|---|---|---|
| Immunosuppression Without Paricalcitol (Control) | 16 | 49 | 32.7% |
| Immunosuppression With Paricalcitol | 27 | 51 | 52.9% |
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 |
|---|---|
| Immunosuppression Without Paricalcitol (Control) | 14 of 49 |
| Immunosuppression With Paricalcitol | 32 of 51 |
Most frequent serious adverse event terms
| Event term | Organ system | Immunosuppression Without Paricalcitol (Control) | Immunosuppression With Paricalcitol |
|---|---|---|---|
| hydronephrosis | Renal and urinary disorders | 1 of 49 | 4 of 51 |
| bilateral native nephrectomy | Surgical and medical procedures | 1 of 49 | 4 of 51 |
| Urinary Tract Infection | Infections and infestations | 0 of 49 | 5 of 51 |
| hernia repair | Surgical and medical procedures | 0 of 49 | 4 of 51 |
| lymphocele | Injury, poisoning and procedural complications | 2 of 49 | 2 of 51 |
| ureteric revision | Injury, poisoning and procedural complications | 2 of 49 | 2 of 51 |
| wound complication | Injury, poisoning and procedural complications | 2 of 49 | 1 of 51 |
| fever | General disorders | 1 of 49 | 1 of 51 |
| hyperkalemia | Metabolism and nutrition disorders | 1 of 49 | 1 of 51 |
| acute kidney injury | Renal and urinary disorders | 1 of 49 | 1 of 51 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Immunosuppression Without Paricalcitol (Control) | Immunosuppression With Paricalcitol |
|---|---|---|---|
| Urinary Tract Infections | Infections and infestations | 0 of 49 | 10 of 51 |
| Post transplant diabetes mellitus | Endocrine disorders | 2 of 49 | 4 of 51 |
| diarrhea | Gastrointestinal disorders | 1 of 49 | 3 of 51 |
| BK viremia | Infections and infestations | 4 of 49 | 0 of 51 |
| Wound Complication | Injury, poisoning and procedural complications | 3 of 49 | 0 of 51 |
| pneumonia | Infections and infestations | 1 of 49 | 1 of 51 |
| Cytomegalovirus viremia | Infections and infestations | 0 of 49 | 2 of 51 |
| glomerulonephritis | Renal and urinary disorders | 1 of 49 | 1 of 51 |
| allergy to Bactrim | Immune system disorders | 0 of 49 | 1 of 51 |
| gout | Metabolism and nutrition disorders | 0 of 49 | 1 of 51 |
Serious events with the highest arm-level rate: urinary tract infection (9.8%), hydronephrosis (7.8%), bilateral native nephrectomy (7.8%), hernia repair (7.8%), lymphocele (4.1%).
The registry reports serious adverse events affecting 16 of 49 participants in the group without paricalcitol and 27 of 51 participants in the group with paricalcitol. Other adverse events are reported for 14 of 49 and 32 of 51 participants, respectively. These are counts of participants with reported events in the registry categories; they do not by themselves show that the study treatment caused an event or that the groups differ in event severity.
The listed serious-event terms include urinary tract infection, hydronephrosis, bilateral native nephrectomy, hernia repair, lymphocele, and ureteric revision. The registry lists the corresponding values as 9.8%, 7.8%, 7.8%, 7.8%, 4.1%, and 4.1%, respectively. The record does not provide enough information in these summary figures to interpret each term as an attributable treatment effect. Death counts are not reported in the registry record.
Safety counts require context about how events were defined, collected, and attributed, as well as the time at risk and completeness of reporting. The summary does not provide a detailed causal assessment or a statistical comparison of adverse events. These numbers describe what the registry reports; they should not be read as proof that an intervention caused or prevented any particular event.
17. What the Result Does, and Does Not, Mean
The primary result means that, in the recorded one-year comparison, fewer participants in the paricalcitol group met the registry definition of hyperparathyroidism than in the group receiving immunosuppression without paricalcitol. The risk-difference estimate and its interval indicate a group contrast that is negative and distinguishable from no difference under the recalculation. The registry’s Fisher exact result is consistent with a statistically notable difference in the primary endpoint.
That finding does not prove that paricalcitol will produce the same result in every kidney transplant recipient, under every immunosuppressive regimen, or over a different follow-up period. The randomized comparison offers evidence about the groups enrolled in this trial, but the registry does not report enough eligibility and treatment detail to define all limits of generalization. The lack of masking and the stated missing-data approach are also relevant to interpretation.
The result does not establish that bone density improved. The available secondary bone findings do not show the same clear separation as the primary endpoint, and they have their own uncertainty. Nor does the primary result establish an effect on graft loss, death, rejection, or other outcomes. Each outcome is a separate question, and the registry record does not provide complete numeric results for every listed measure.
Statistical evidence is not the same as proof of mechanism or a complete assessment of benefits and harms. The endpoint combines a PTH threshold with parathyroidectomy, and the summary does not report detailed information about measurement schedules or missing observations. Serious and other adverse-event counts are also descriptive and do not, by themselves, establish causation. The overall meaning is therefore focused: a difference was observed for the defined primary outcome in this randomized comparison, while the estimate’s scope and the interpretation of other outcomes remain limited by the information reported.
18. Why This Trial Matters Statistically
This trial is statistically instructive because it pairs a clearly defined binary primary endpoint with a randomized comparison and reports both group counts and a sponsor test. The counts make the absolute contrast understandable, while the risk-difference estimate and interval show more than a significance label alone. Together, these elements illustrate why effect size, uncertainty, and a hypothesis test answer related but different questions.
The endpoint definition also shows how a clinical outcome can combine a laboratory threshold and a clinical procedure. Such definitions need to be read closely: the analysis concerns participants meeting the stated rule, not every possible meaning of parathyroid disease. A one-year count is a focused measure, but cannot describe longer-term patterns or the full course of a condition.
The record also highlights the distinction between a primary result and a collection of secondary analyses. Secondary bone measures address related but separate questions, and multiple unadjusted tests require caution. A notable primary result does not make every secondary result confirmatory, and a nonsignificant secondary result does not establish that groups are equivalent.
Finally, the trial demonstrates how registry records can make some statistical features visible while leaving other important details unreported. The primary missing-data method is named, but the amount of missing information and sensitivity analyses are not. The original sample-size rationale and multiplicity strategy are also not reported. Those limits do not erase the observed result; they shape how narrowly and cautiously it should be interpreted.
19. 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 record leaves several trial-specific interpretive gaps. Eligibility criteria and participant characteristics beyond the transplant context are not reported in the registry record, limiting assessment of which patients the results represent. The detailed paricalcitol dose, administration schedule, adherence, and treatment changes are also not reported. The arm description for paricalcitol is incomplete in the record, so details should not be inferred from it.
Masking is listed as none. The record does not describe procedures to reduce the potential influence of treatment awareness on outcome assessment or reporting. The primary endpoint includes a blood-test criterion and a surgical criterion, but the schedule for PTH measurement and the number meeting each part of the definition are not reported in the registry record.
The primary analysis uses last observation carried forward for missing values, but the number of missing primary observations, reasons for missingness, and sensitivity analyses are not reported. Secondary-outcome handling of missing data is not reported in the registry record. The stated intention-to-treat population has an operational definition involving at least one dose and available efficacy data, which readers should distinguish from broader assumptions sometimes attached to that label.
The record does not report the original sample-size justification, a detailed statistical analysis plan, multiplicity procedures, interim analyses, or stopping rules. While the primary result is accompanied by a sponsor test and a recalculated estimate, these omissions constrain assessment of whether all analyses followed a prespecified plan. The available secondary results are partial relative to the listed outcome measures, and the safety summary does not provide a causal assessment or death counts.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Oral Paricalcitol in Kidney Transplant Recipients — NCT00587158.
- Registry record last updated 2013-05-13; status last verified 2013-05.
- Results first posted 2013-05-08.
- 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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23. Record Summary
The registry describes a completed, randomized, parallel-group trial without masking, sponsored by Mayo Clinic, comparing immunosuppression with and without paricalcitol in kidney transplant recipients. Enrollment was 100. The primary endpoint was hyperparathyroidism at one year after transplantation, defined by a PTH threshold in the absence of hypocalcemia or by parathyroidectomy during the first year.
The endpoint was recorded for 31 of 49 participants in the control group and 15 of 51 in the paricalcitol group. The sponsor reported a Fisher exact p-value of 0.001; the unadjusted recalculation gives p < 0.001 and a negative risk difference. Secondary bone findings are less conclusive, and the registry lists adverse-event counts in both arms.
The record does not report the original sample-size rationale, multiplicity strategy, detailed eligibility criteria, or several missing-data details. The primary finding is specific to the recorded endpoint, regimen, participants, and one-year timeframe.