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 Dose-response Study of Paricalcitol Injection in Chronic Kidney Disease Patients Receiving Hemodialysis (NCT00667576), a randomized phase 2 study. The primary outcome is Percentage of Subjects With ≥ 50% Decrease From Baseline in Intact Parathyroid Hormone (iPTH) Serum Level.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT00667576 |
| Phase | Phase 2 |
| Condition | Chronic Kidney Disease on Hemodialysis, Secondary Hyperparathyroidism |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | None (open label) |
| Enrollment | 153 |
| Arms in the primary outcome | 5 |
| Lead sponsor | Abbott |
| Results posted | Yes |
2. Clinical Question
Population
Adults with chronic kidney disease receiving hemodialysis and secondary hyperparathyroidism were the population of interest. The record reports 153 enrolled participants. The primary efficacy analysis used a full analysis set of treated participants, with one stated exception: a participant in the paricalcitol 4 µg ± 2 µg group who stopped after the first injection and had no later iPTH measurement was excluded. The record does not give further eligibility details in the information summarized for this comparison.
Intervention
Four paricalcitol schedules were studied. Initial doses were 2 µg or 4 µg, with dose adjustments of either 1 µg or 2 µg. The question was not simply whether paricalcitol was used, but how the initial dose and adjustment increment related to the measured iPTH response over the study period.
Comparator
The fifth schedule used maxacalcitol, with an initial dose of 5 or 10 µg and an incremental adjustment of 2.5 µg. The primary comparison used paricalcitol 2 µg ± 1 µg as its reference group. The randomized parallel design also permits descriptive comparison among the four paricalcitol schedules, although the registry record does not report a formal multi-group analysis.
Primary question
From baseline to Week 13 (Final Visit), what percentage of participants in each group had at least a 50% decrease from baseline in serum intact parathyroid hormone? The outcome is a threshold-based measure of biochemical change, rather than a measure of average change or of time to response. The registry record reports group percentages and provides recalculated unadjusted comparisons against the reference schedule.
3. Trial Design
This was a randomized, parallel-group phase 2 study of paricalcitol injection dose schedules in people with chronic kidney disease receiving hemodialysis and secondary hyperparathyroidism. The registry reports an enrollment of 153 and a completed study. The recorded study dates are 2008-04 for the start and 2009-03 for primary completion. The record identifies Abbott as sponsor.
Five groups were described: four paricalcitol schedules and one maxacalcitol schedule. The paricalcitol groups combined initial doses of 2 µg or 4 µg with adjustment increments of 1 µg or 2 µg. The maxacalcitol group used an initial dose of 5 or 10 µg and an adjustment increment of 2.5 µg. Group sizes for the primary outcome ranged from 30 to 31 participants. The record describes allocation as randomized, masking as none, and the model as parallel. Further details about sequence generation, allocation concealment, or the operational conduct of randomization are not reported in the registry record.
The primary endpoint was evaluated from baseline to Week 13 (Final Visit). Efficacy was analyzed in the full analysis set, defined in the record as treated participants except for one participant in the paricalcitol 4 µg ± 2 µg group who discontinued without an iPTH measurement after the first injection. Missing data were not imputed. The registry record does not report the original sample-size justification, a formal statistical analysis plan, or interim analyses. The posted comparisons are unadjusted recalculations, not a substitute for a sponsor-reported model; the record does not identify a discrepancy between these recalculations and sponsor results.
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 | Paricalcitol 2 µg ± 1 µg | Paricalcitol 2 µg ± 2 µg | Paricalcitol 4 µg ± 1 µg | Paricalcitol 4 µg ± 2 µg | Maxacalcitol 5 or 10 µg ± 2.5 µg |
|---|---|---|---|---|---|
| STARTED | 30 | 31 | 31 | 31 | 30 |
| COMPLETED | 28 | 30 | 29 | 27 | 29 |
| NOT COMPLETED | 2 | 1 | 2 | 4 | 1 |
Reasons for not completing this period:
| Reason | Paricalcitol 2 µg ± 1 µg | Paricalcitol 2 µg ± 2 µg | Paricalcitol 4 µg ± 1 µg | Paricalcitol 4 µg ± 2 µg | Maxacalcitol 5 or 10 µg ± 2.5 µg |
|---|---|---|---|---|---|
| Withdrawal by Subject | 1 | 0 | 1 | 1 | 1 |
| Adverse Event | 1 | 1 | 0 | 0 | 0 |
| Lost to Follow-up | 0 | 0 | 1 | 0 | 0 |
| Protocol Violation | 0 | 0 | 0 | 1 | 0 |
| Physician Decision | 0 | 0 | 0 | 1 | 0 |
| Missed Visit | 0 | 0 | 0 | 1 | 0 |
Analysis population for the primary outcome, as defined in the registry: The efficacy analysis was performed on the full analysis set (FAS). The FAS included all treated patients, except for 1 subject from the paricalcitol 4 ± 2 µg group who discontinued the study without measurement of iPTH after the first drug injection. Missing data were not imputed.
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 2 µg ± 1 µg | Paricalcitol 2 µg ± 2 µg | Paricalcitol 4 µg ± 1 µg | Paricalcitol 4 µg ± 2 µg | Maxacalcitol 5 or 10 µg ± 2.5 µg | Total |
|---|---|---|---|---|---|---|---|
| Participants analysed | 30 | 31 | 31 | 31 | 30 | 153 | |
| Age, Categorical: <=18 years | Participants | 0 | 0 | 0 | 0 | 0 | 0 |
| Age, Categorical: Between 18 and 65 years | Participants | 19 | 18 | 19 | 19 | 12 | 87 |
| Age, Categorical: >=65 years | Participants | 11 | 13 | 12 | 12 | 18 | 66 |
| Age Continuous | years | 62.1 (SD 11.94) | 60.7 (SD 11.80) | 58.1 (SD 12.35) | 61.5 (SD 11.17) | 64.1 (SD 11.98) | 61.3 (SD 11.86) |
| Sex: Female, Male: Female | Participants | 18 | 14 | 11 | 14 | 7 | 64 |
| Sex: Female, Male: Male | Participants | 12 | 17 | 20 | 17 | 23 | 89 |
| Region of Enrollment: Japan | participants | 30 | 31 | 31 | 31 | 30 | 153 |
6. Primary Endpoint
The registry lists the primary outcome as Percentage of Subjects With ≥ 50% Decrease From Baseline in Intact Parathyroid Hormone (iPTH) Serum Level, measured over Baseline to Week 13 (Final Visit).
| Element | Registry entry |
|---|---|
| Result type | Number |
| Measure of spread | not applicable |
| Unit | Percentage of participants |
| Endpoint classification | Binary Endpoint |
The primary endpoint is the percentage of participants whose serum intact parathyroid hormone (iPTH) level decreased by at least 50% from baseline by Week 13 (Final Visit). Each participant is classified according to whether the stated threshold was reached; the group result is the share meeting that criterion. This makes the outcome a binary response measure, even though the underlying laboratory value is continuous.
A threshold endpoint can make a result easier to interpret as the proportion reaching a specified degree of change. It also discards information: participants just short of the threshold and participants with little change are both counted as not meeting it, while participants with very different decreases beyond the threshold are grouped together. It therefore answers a different question from the mean change in iPTH, which is listed as a secondary outcome.
The registry record reports the endpoint over the baseline-to-Week-13 interval and specifies the full analysis set used for efficacy. One participant without an iPTH measurement after the first injection was excluded from that set, and missing data were not imputed. These details matter because the reported percentages describe the analysis population and handling of missing measurements, not necessarily every enrolled participant. The endpoint is a biochemical measure and, on its own, does not describe clinical outcomes or establish the broader consequences of a change in iPTH.
7. Results Posted in the Registry
- Paricalcitol 2 µg ± 2 µg: 41.9% (13/31) versus 53.3% (16/30) on control; risk difference -11.4 percentage points (95% CI -36.3 to 13.5), risk ratio 0.79 (0.46–1.34); unadjusted two-proportion z-test p = 0.373.
- Paricalcitol 4 µg ± 1 µg: 38.7% (12/31) versus 53.3% (16/30) on control; risk difference -14.6 percentage points (95% CI -39.4 to 10.1), risk ratio 0.73 (0.42–1.26); unadjusted two-proportion z-test p = 0.252.
- Paricalcitol 4 µg ± 2 µg: 56.7% (17/30) versus 53.3% (16/30) on control; risk difference 3.3 percentage points (95% CI -21.8 to 28.5), risk ratio 1.06 (0.67–1.68); unadjusted two-proportion z-test p = 0.795.
- Maxacalcitol 5 or 10 µg ± 2.5 µg: 43.3% (13/30) versus 53.3% (16/30) on control; risk difference -10.0 percentage points (95% CI -35.2 to 15.2), risk ratio 0.81 (0.48–1.38); unadjusted two-proportion z-test p = 0.438.
Risk difference: Paricalcitol 2 µg ± 2 µg
95% CI: -36.3 to 13.5 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 |
|---|---|---|---|---|
| Percentage of Subjects With Intact Parathyroid Hormone (iPTH) ≤ 180 Picograms/Milliliter (pg/mL) | Binary Endpoint | Risk difference | -4.4 pts (-28.2 to 19.4) | 1,824 per arm |
| Percentage of Subjects With 2 or More Decreases of ≥ 50% From Baseline in Intact Parathyroid Hormone (iPTH) Level | Binary Endpoint | Risk difference | +10.0 pts (-0.7 to 20.7) | n/a |
| Duration of 2 Consecutive Decreases of ≥ 50% From Baseline in Intact Parathyroid Hormone (iPTH) Values | Continuous Endpoint | Mean difference | 3.90 (-3.62 to 11.42) | 217 per arm |
Percentage of Subjects With Intact Parathyroid Hormone (iPTH) ≤ 180 Picograms/Milliliter (pg/mL)
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Paricalcitol 2 µg ± 2 µg: 32.3% (10/31) versus 36.7% (11/30) on control; risk difference -4.4 percentage points (95% CI -28.2 to 19.4), risk ratio 0.88 (0.44–1.76); unadjusted two-proportion z-test p = 0.717.
- Paricalcitol 4 µg ± 1 µg: 32.3% (10/31) versus 36.7% (11/30) on control; risk difference -4.4 percentage points (95% CI -28.2 to 19.4), risk ratio 0.88 (0.44–1.76); unadjusted two-proportion z-test p = 0.717.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Paricalcitol 2 µg ± 2 µg 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 Paricalcitol 4 µg ± 1 µg and the control. The interval gives the range of effects that remain compatible with the data.
Percentage of Subjects With 2 or More Decreases of ≥ 50% From Baseline in Intact Parathyroid Hormone (iPTH) Level
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Paricalcitol 2 µg ± 2 µg: 100.0% (31/31) versus 90.0% (27/30) on control; risk difference 10.0 percentage points (95% CI -0.7 to 20.7), risk ratio 1.11 (0.99–1.25); unadjusted two-proportion z-test p = 0.071.
- Paricalcitol 4 µg ± 1 µg: 90.3% (28/31) versus 90.0% (27/30) on control; risk difference 0.3 percentage points (95% CI -14.6 to 15.3), risk ratio 1.00 (0.85–1.18); unadjusted two-proportion z-test p = 0.966.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Paricalcitol 2 µg ± 2 µg 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 Paricalcitol 4 µg ± 1 µg and the control. The interval gives the range of effects that remain compatible with the data.
Duration of 2 Consecutive Decreases of ≥ 50% From Baseline in Intact Parathyroid Hormone (iPTH) Values
- 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 2 µg ± 2 µg: mean 27.70 versus 23.80 on control; difference 3.90 (95% CI -3.62 to 11.42), standardized effect d = 0.27; z-test p = 0.309.
- Paricalcitol 4 µg ± 1 µg: mean 29.00 versus 23.80 on control; difference 5.20 (95% CI -2.62 to 13.02), standardized effect d = 0.35; z-test p = 0.193.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Paricalcitol 2 µg ± 2 µg 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 Paricalcitol 4 µg ± 1 µg and the control. The interval gives the range of effects that remain compatible with the data.
The secondary outcomes broaden the picture beyond whether a participant crossed the primary 50% decrease threshold at Week 13. They include mean change in iPTH, reaching an iPTH value of 180 pg/mL or less, repeated decreases of at least 50%, and durations associated with consecutive measurements. These outcomes address magnitude, threshold attainment, repetition, and duration, so they are related to the primary endpoint but do not ask precisely the same question.
The numerical results that are posted show a broadly similar pattern of group percentages across some threshold-based measures, while other measures describe durations or changes on a continuous scale. This is not a direct replication of the primary endpoint: a repeated response criterion or an absolute iPTH threshold can classify participants differently from a single relative decrease. The secondary measures can add context, but they should not be collapsed into one overall claim about the schedules.
Numerical results are not reported in the registry record for every listed secondary measure. In addition, the registry record contains no reported formal analyses for the displayed secondary outcomes. The posted recalculated comparisons are unadjusted, and the record does not state a multiplicity strategy or a hierarchy that would identify a single secondary outcome as confirmatory.
General statistical explanation: when multiple outcomes and group comparisons are examined, some apparent differences can arise by chance. Unadjusted secondary results therefore carry less weight than a prespecified, appropriately analyzed primary result, especially when the analysis plan and multiplicity handling are not reported. The secondary results are best treated as descriptive and hypothesis-generating context. They neither replace the primary endpoint nor resolve the uncertainty in its group comparisons.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Mean Change From Baseline in Intact Parathyroid Hormone (iPTH) Level
- Percentage of Subjects With Intact Parathyroid Hormone (iPTH) ≤ 180 Picograms/Milliliter (pg/mL)
- Percentage of Subjects With 2 or More Decreases of ≥ 50% From Baseline in Intact Parathyroid Hormone (iPTH) Level
- Duration of 2 Consecutive Decreases of ≥ 50% From Baseline in Intact Parathyroid Hormone (iPTH) Values
- Duration of 2 Consecutive Intact Parathyroid Hormone (iPTH) Values ≤ 180 pg/mL
9. Statistical Interpretation
For the primary endpoint, the posted percentages were 53.3% for paricalcitol 2 µg ± 1 µg, 41.9% for paricalcitol 2 µg ± 2 µg, 38.7% for paricalcitol 4 µg ± 1 µg, 56.7% for paricalcitol 4 µg ± 2 µg, and 43.3% for maxacalcitol 5 or 10 µg ± 2.5 µg. These are the observed group proportions meeting the threshold in the efficacy analysis; they should not be read as proof that one schedule is superior to another.
The unadjusted recalculated comparisons use paricalcitol 2 µg ± 1 µg as the reference. The reported p-values for the other four groups are 0.373, 0.252, 0.795, and 0.438, respectively. The corresponding recalculated confidence intervals for the risk differences all include no difference. Taken together, these summaries do not show a clear statistical separation between the reference group and any one of the other schedules. They also do not demonstrate that the groups are equivalent: the intervals are broad enough to include differences in either direction.
Group sizes were small, with 30 or 31 participants in each primary-outcome group. With relatively few participants, a percentage can be sensitive to the outcome of an individual participant, and estimates can remain imprecise even when the observed percentages differ. The recalculated p-values are unadjusted, so they do not account for the several comparisons or the several outcomes in the registry. Their interpretation should therefore be cautious, especially if considered as a collection rather than as individual comparisons.
The outcome is a threshold response at a specified visit. It does not show the full distribution of iPTH changes, the timing or persistence of changes, or whether a participant had a clinically important outcome. Other listed outcomes address some additional aspects, including repeated decreases and a threshold iPTH value, but not all are accompanied by numerical results in the registry record. No formal adjusted analysis is reported. The most defensible reading is descriptive: the observed response percentages varied across the five schedules, while the unadjusted comparisons against the reference group were uncertain and did not establish a clear difference.
10. Statistical Methods Explained
The primary result is a binary percentage: participants are counted according to whether their iPTH decreased by at least 50% from baseline by Week 13. The posted percentage is the number meeting that criterion divided by the analysis group size. This kind of endpoint focuses on reaching a threshold, rather than on how far each participant’s measurement changed.
What does a risk difference express?
General statistical explanation: a risk difference is the difference between the proportions experiencing an outcome in two groups. A value of zero represents equal observed proportions; a positive or negative value indicates which group has the larger proportion, according to the subtraction order used. The recalculated comparisons use paricalcitol 2 µg ± 1 µg as the reference and report unadjusted risk differences. Their confidence intervals all include zero, so the summaries are compatible with no difference as well as with differences in either direction.
What does a p-value contribute?
General statistical explanation: a p-value describes how unusual data at least as discrepant as those observed would be under a specified null model. It is not the probability that the null hypothesis is true, and it does not measure the size or clinical importance of an effect. The posted p-values are unadjusted recalculations. They are best read alongside the group percentages and confidence intervals, rather than as stand-alone evidence.
Why are confidence intervals useful?
General statistical explanation: a confidence interval gives a range of values compatible with the data under the method’s assumptions and conveys uncertainty around an estimate. A narrow interval indicates greater precision than a wide interval, while an interval containing zero for a risk difference does not establish that the groups are identical. The registry record does not report sponsor confidence intervals for the primary endpoint; the intervals discussed in this statistical comparison are recalculated from the posted summary data.
What does randomization contribute?
General statistical explanation: random assignment is intended to make group membership independent of participants’ measured and unmeasured characteristics on average. It supports comparisons between groups, but it does not guarantee balance in a modest-sized study, and the registry record does not provide detailed information about the randomization procedure. The design is described as randomized and parallel, with no masking. The record does not report further operational details about allocation or masking.
How should the analysis population be understood?
The efficacy population was the full analysis set of treated participants, excluding one participant in the paricalcitol 4 µg ± 2 µg group who discontinued without an iPTH measurement after the first injection. The record states that missing data were not imputed. Thus, the displayed primary percentages are based on observed efficacy data under that stated population rule. They are not a complete-case summary of every enrolled participant unless that happens to coincide with the defined set; the registry does not provide further details about other missing measurements or sensitivity analyses.
What are the limits of the reported comparisons?
The registry record lists no reported formal analyses for the displayed outcomes. The comparisons discussed are unadjusted recalculations from the posted group summaries, rather than a reported adjusted model. The record does not describe covariate adjustment, an analysis hierarchy, or a correction for multiple comparisons. General statistical explanation: testing several comparisons increases the chance that at least one result may appear notable by chance if each is judged separately. This is one reason not to treat an unadjusted p-value as definitive evidence, particularly when there are multiple dose schedules and outcome measures.
The registry also does not report the original statistical plan, original sample-size justification, or interim analyses. Those absences do not establish that such procedures were not used; they mean their details are not reported in the registry record. As a result, the recalculated analyses can describe the posted summary data, but they cannot reconstruct every planned analysis or replace a full protocol-level account.
11. Confidence Intervals and Precision
Precision concerns how tightly the data locate the underlying group difference, not simply whether the point estimates are numerically different. For the primary endpoint, the comparison intervals are wide and each includes zero risk difference. They therefore allow both a lower and a higher response proportion relative to paricalcitol 2 µg ± 1 µg. This pattern is consistent with uncertainty, rather than a precise estimate of no effect.
The primary groups include 30 or 31 participants each. With group sizes of this scale, the estimated percentages can shift noticeably with a small number of different participant outcomes. The reported percentages are useful descriptions of the observed groups, but precision is limited. The recalculated p-values similarly do not resolve whether modest differences exist. A p-value above conventional thresholds is not evidence that the schedules are equivalent, and the registry record does not report an equivalence or non-inferiority analysis.
Confidence intervals are particularly important because they show the range of effect sizes still compatible with the data under the recalculation method. The intervals described for the primary comparisons are recalculated and unadjusted; they are not sponsor-reported intervals in the registry record. No adjustment for the several comparisons is reported. Accordingly, the interval interpretation applies to each comparison as calculated, not to a jointly adjusted set of conclusions across all groups.
Precision is also distinct from the amount of information in the endpoint. A threshold response compresses the underlying laboratory measurements into two categories, which can make the result accessible but leaves out the magnitude of changes within each category. The registry record does not give primary-endpoint confidence intervals as sponsor results, nor does it report further information that would narrow the uncertainty. The observed percentages should therefore be interpreted as estimates with substantial uncertainty, not as exact underlying response rates.
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 | 301 | 402 |
| 75% of the observed effect | 536 | 717 |
| 50% of the observed effect | 1,208 | 1,616 |
The planning figures are illustrations based on the observed effect in a comparison, not the original design calculation for the trial. The original sample-size assumptions are not reported in the registry record. For these binary-outcome comparisons, the figures are participants per arm; the total-number-of-events convention applies to time-to-event calculations, not to these comparisons.
The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set to the stated fraction of the observed effect. Planning for 100% of the observed effect means using the full observed difference as the target; planning for 75% or 50% means targeting a smaller difference. Because smaller effects are harder to distinguish from random variation, the figures increase as the target effect becomes smaller.
The 80% power column describes the planned number of participants per arm under those assumptions for an 80% chance of detecting the selected effect if that effect were the true one. The 90% power column uses a higher chance of detection and consequently requires more participants under the same assumptions. These are planning calculations, not a statement about what the completed study achieved. They are not observed power.
These illustrations also depend on the observed effect, which is uncertain in a study with small groups. The figures should not be interpreted as a recommendation or as evidence that the trial was designed around these particular assumptions. They show how the required group size changes when the target difference changes while the stated calculation assumptions are held in place. They do not include a reported allowance for missing data or any other original design adjustment; such original assumptions are not reported in the registry record.
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 = 0.533; treatment proportion p1 = 0.419; average p̄ = 0.476.
- First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.7063 = 1.3844.
- Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.7017 = 0.5906.
- n = (1.3844 + 0.5906)2 / (-0.1140)2 = 300.2, rounded up to 301 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 <- 0.533333333333333 # control proportion
p1 <- 0.419354838709677 # 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(667576)
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 = 301 (80% power), 402 (90% power)
75% of observed effect: n per arm = 536 (80% power), 717 (90% power)
50% of observed effect: n per arm = 1,208 (80% power), 1,616 (90% power)
power.prop.test: 300.2
Simulated power at n = 301 per arm: 0.798 (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 record does not report whether the original statistical plan specified a multiplicity adjustment, a testing hierarchy, or a particular approach to multiple dose-group comparisons. It also does not report interim analyses. These procedures may or may not have been part of the original conduct; their details are not reported in the registry record.
Multiplicity matters because the study includes several schedules and several outcomes. General statistical explanation: when many hypotheses are tested, the chance of at least one apparently unusual result can rise if each test is interpreted independently. An adjustment or a prespecified hierarchy can control how evidence is assessed across those tests. Without a reported approach, the unadjusted p-values should not be treated as controlling the overall false-positive risk across all comparisons.
The primary efficacy population is described as the full analysis set of treated participants, except for one participant in the paricalcitol 4 µg ± 2 µg group who discontinued without an iPTH measurement after the first injection. Missing data were not imputed. The record does not give a sensitivity analysis for this exclusion or additional information about missing measurements. The reported percentages therefore need to be interpreted with the stated analysis-set definition in mind.
The registry record reports no formal analyses for the posted outcomes. It does not give the original sample-size justification, a complete statistical analysis plan, or details of any model-based adjustment. The recalculated comparisons are unadjusted summaries. Their estimates and intervals can help describe the posted group data, but they cannot establish how the original investigators planned to address multiplicity, missingness, or other analysis decisions. Those details should be treated as not reported in the registry record, rather than inferred from the posted summaries.
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 |
|---|---|---|---|
| Paricalcitol 2 µg ± 1 µg | 1 | 30 | 3.3% |
| Paricalcitol 2 µg ± 2 µg | 2 | 31 | 6.5% |
| Paricalcitol 4 µg ± 1 µg | 3 | 31 | 9.7% |
| Paricalcitol 4 µg ± 2 µg | 2 | 31 | 6.5% |
| Maxacalcitol 5 or 10 µg ± 2.5 µg | 2 | 30 | 6.7% |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 5% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Paricalcitol 2 µg ± 1 µg | 30 of 30 |
| Paricalcitol 2 µg ± 2 µg | 29 of 31 |
| Paricalcitol 4 µg ± 1 µg | 30 of 31 |
| Paricalcitol 4 µg ± 2 µg | 28 of 31 |
| Maxacalcitol 5 or 10 µg ± 2.5 µg | 29 of 30 |
Most frequent serious adverse event terms
| Event term | Organ system | Paricalcitol 2 µg ± 1 µg | Paricalcitol 2 µg ± 2 µg | Paricalcitol 4 µg ± 1 µg | Paricalcitol 4 µg ± 2 µg | Maxacalcitol 5 or 10 µg ± 2.5 µg |
|---|---|---|---|---|---|---|
| shunt stenosis | Injury, poisoning and procedural complications | 1 of 30 | 0 of 31 | 0 of 31 | 0 of 31 | 0 of 30 |
| shunt aneurysm | Injury, poisoning and procedural complications | 0 of 30 | 1 of 31 | 0 of 31 | 0 of 31 | 0 of 30 |
| spinal osteoarthritis | Musculoskeletal and connective tissue disorders | 0 of 30 | 1 of 31 | 0 of 31 | 0 of 31 | 0 of 30 |
| ventricular extrasystoles | Cardiac disorders | 0 of 30 | 0 of 31 | 1 of 31 | 0 of 31 | 0 of 30 |
| muscular weakness | Musculoskeletal and connective tissue disorders | 0 of 30 | 0 of 31 | 1 of 31 | 0 of 31 | 0 of 30 |
| cerebellar infarction | Nervous system disorders | 0 of 30 | 0 of 31 | 1 of 31 | 0 of 31 | 0 of 30 |
| iliac artery stenosis | Vascular disorders | 0 of 30 | 0 of 31 | 1 of 31 | 0 of 31 | 0 of 30 |
| arteriosclerosis obliterans | Vascular disorders | 0 of 30 | 0 of 31 | 0 of 31 | 1 of 31 | 0 of 30 |
| femoral neck fracture | Injury, poisoning and procedural complications | 0 of 30 | 0 of 31 | 0 of 31 | 1 of 31 | 0 of 30 |
| pulmonary oedema | Respiratory, thoracic and mediastinal disorders | 0 of 30 | 0 of 31 | 0 of 31 | 0 of 31 | 1 of 30 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Paricalcitol 2 µg ± 1 µg | Paricalcitol 2 µg ± 2 µg | Paricalcitol 4 µg ± 1 µg | Paricalcitol 4 µg ± 2 µg | Maxacalcitol 5 or 10 µg ± 2.5 µg |
|---|---|---|---|---|---|---|
| hypercalcaemia | Metabolism and nutrition disorders | 12 of 30 | 19 of 31 | 20 of 31 | 23 of 31 | 13 of 30 |
| nasopharyngitis | Infections and infestations | 9 of 30 | 9 of 31 | 10 of 31 | 9 of 31 | 9 of 30 |
| hyperphosphataemia | Metabolism and nutrition disorders | 6 of 30 | 10 of 31 | 6 of 31 | 12 of 31 | 8 of 30 |
| hypertension | Vascular disorders | 1 of 30 | 6 of 31 | 1 of 31 | 3 of 31 | 4 of 30 |
| constipation | Gastrointestinal disorders | 2 of 30 | 4 of 31 | 1 of 31 | 1 of 31 | 2 of 30 |
| pruritus | Skin and subcutaneous tissue disorders | 1 of 30 | 3 of 31 | 0 of 31 | 2 of 31 | 4 of 30 |
| diarrhea | Gastrointestinal disorders | 3 of 30 | 3 of 31 | 2 of 31 | 1 of 31 | 0 of 30 |
| back pain | Musculoskeletal and connective tissue disorders | 2 of 30 | 1 of 31 | 1 of 31 | 1 of 31 | 3 of 30 |
| headache | Nervous system disorders | 0 of 30 | 3 of 31 | 2 of 31 | 3 of 31 | 0 of 30 |
| contusion | Injury, poisoning and procedural complications | 0 of 30 | 1 of 31 | 0 of 31 | 2 of 31 | 4 of 30 |
Serious events with the highest arm-level rate: shunt stenosis (3.3%), pulmonary oedema (3.3%), chest pain (3.3%), shunt aneurysm (3.2%), spinal osteoarthritis (3.2%).
The registry reports serious adverse events in each of the five groups. The recorded counts were 1 of 30 for paricalcitol 2 µg ± 1 µg, 2 of 31 for paricalcitol 2 µg ± 2 µg, 3 of 31 for paricalcitol 4 µg ± 1 µg, 2 of 31 for paricalcitol 4 µg ± 2 µg, and 2 of 30 for maxacalcitol 5 or 10 µg ± 2.5 µg. These figures describe participants with serious adverse events in the registry record; they do not establish that a particular treatment caused an event.
The record also lists serious-event terms with percentages: shunt stenosis, pulmonary oedema, and chest pain at 3.3% each; shunt aneurysm, spinal osteoarthritis, and ventricular extrasystoles at 3.2% each. These terms are descriptive reports, not comparative estimates between groups. The registry record does not report deaths for the groups. The event counts are small, and the study’s size does not support precise conclusions about differences in uncommon serious events.
16. What the Result Does, and Does Not, Mean
The results describe what was observed in a randomized study comparing five dose schedules over a defined period. For the primary endpoint, the groups had different observed percentages meeting the at-least-50% iPTH decrease criterion by Week 13. The recalculated unadjusted comparisons against paricalcitol 2 µg ± 1 µg had confidence intervals that included no difference and p-values that did not establish a clear separation. This is an uncertain result, not proof that the schedules are the same.
Randomization supports comparisons among assigned groups, but the registry does not report detailed randomization procedures or a formal adjusted analysis. The study was phase 2 and the primary groups were small. No masking was used, and the primary outcome was a laboratory measure. These features should be kept in view when interpreting the observed group differences and the uncertainty around them.
The endpoint does not by itself establish a clinical benefit, harm, or the consequences of a change in iPTH. It records whether a relative threshold was met at a specified visit, not an overall measure of health or patient experience. The secondary outcomes add other descriptions of iPTH, but they do not turn an uncertain primary comparison into a definitive one. Likewise, the serious adverse-event counts are descriptive and do not establish comparative safety.
The registry record does not report the original sample-size justification, a complete statistical analysis plan, multiplicity handling, or interim analyses. Those absences limit what can be inferred about the study’s intended statistical decision process. The posted summaries can support a careful description of the data and their precision, but they cannot answer every question about dose selection, long-term outcomes, or comparative clinical effects. No treatment recommendation follows from these results alone.
17. Why This Trial Matters Statistically
This study is statistically informative because it compares several initial-dose and adjustment-increment combinations rather than only a single experimental schedule against a control. The layout allows readers to see how the observed response percentages varied across the four paricalcitol schedules and the maxacalcitol schedule. At the same time, five groups divide the enrolled participants into relatively small sets, so the percentage estimates and comparisons remain uncertain.
The primary endpoint also illustrates an important distinction between threshold outcomes and continuous measurements. A percentage meeting a 50% decrease criterion is straightforward to interpret as a group response rate, but it omits information about the size of each participant’s change. The listed secondary outcomes address some complementary questions, such as repeated decreases, a specified iPTH threshold, and duration. They do not eliminate the need to consider the primary endpoint’s limitations or the absence of reported formal analyses.
Finally, the record makes clear why statistical interpretation depends on more than a point estimate or p-value. The unadjusted recalculations have intervals that include no difference, and the registry does not describe multiplicity control or the original analysis plan. The planning illustrations show how sample-size requirements depend on the effect targeted, but they are not the study’s original design assumptions. Together, these features make the trial a useful example of reading group summaries cautiously: distinguish observed patterns from precise comparative evidence, and distinguish posted analyses from unreported design details.
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.
- Participant counts were reconstructed from posted percentages and arm sizes, so small rounding differences are possible.
The primary groups included 30 or 31 participants, limiting the precision of response percentages and the ability to distinguish modest differences. The recalculated primary comparisons are unadjusted, and their intervals include no difference. The registry record does not report a multiplicity plan, so the several comparisons and outcomes cannot be interpreted as a single controlled family of tests.
The study was unmasked. The primary endpoint is an objective laboratory threshold, but the registry record does not describe additional safeguards or how outcome assessment was conducted. The endpoint also reduces a continuous iPTH change to whether a participant crossed a fixed relative threshold by Week 13; it does not show the full distribution or longer-term pattern of change.
Missing data were not imputed. The efficacy population excluded one participant in the paricalcitol 4 µg ± 2 µg group who discontinued without an iPTH measurement after the first injection. The record does not report sensitivity analyses or further missing-data details. The registry also does not report the original sample-size justification, a complete statistical analysis plan, interim analyses, or sponsor-reported formal analyses for the outcomes summarized. These gaps restrict assessment of how the original analysis was planned and how robust the conclusions are to alternative assumptions.
Finally, the study’s listed outcomes focus on iPTH and reported adverse events. The registry record does not provide a basis for conclusions about outcomes not measured or not reported, or about longer-term comparative effects. The serious-event counts are small and descriptive. These limitations mean the posted results are best understood as a short-term, phase 2 comparison with uncertain estimates rather than as definitive comparative evidence.
19. Related Tutorials
20. Related Statistical Calculators
21. Sources
- ClinicalTrials.gov: Dose-response Study of Paricalcitol Injection in Chronic Kidney Disease Patients Receiving Hemodialysis — NCT00667576.
- Registry record last updated 2012-01-20; status last verified 2012-01.
- Results first posted 2010-04-02.
- 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.
Continue through the Clinical Biostats statistical pathway
Use this trial's endpoint as a starting point for deeper study of effect measures, confidence intervals, and sample-size planning.
22. Record Summary
The registry describes a completed randomized, unmasked, parallel phase 2 study of paricalcitol injection schedules in people with chronic kidney disease receiving hemodialysis and secondary hyperparathyroidism. It reports 153 enrolled participants and five groups: four paricalcitol dose schedules and one maxacalcitol schedule.
The primary outcome was the percentage with at least a 50% decrease in serum iPTH from baseline to Week 13. The observed group percentages ranged from 38.7% to 56.7%. Unadjusted recalculated comparisons against paricalcitol 2 µg ± 1 µg did not establish a clear difference, and their confidence intervals included no difference.
The efficacy set excluded one participant without a post-injection iPTH measurement, and missing data were not imputed. The registry record does not report the original sample-size justification, complete statistical plan, or multiplicity handling. Secondary outcomes and serious adverse events add descriptive context but do not resolve the uncertainty in the primary comparisons.