Study of Phosphate Levels in Patients With Chronic Kidney Disease: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Study of Phosphate Levels in Patients With Chronic Kidney Disease (NCT00824460), a randomized phase 2 study. The primary outcome is Change From Baseline in Serum-phosphate Levels at the End of Treatment..

2. Clinical Question

The clinical question is about a short-term laboratory outcome in a specific treatment setting: chronic kidney disease with maintenance hemodialysis. It is not a question about clinical events or longer-term outcomes. The registry record describes a phase II dose-finding study intended to examine PA21's ability to lower serum phosphate and its tolerability. The dose groups make dose patterns relevant, while the active-control group gives a randomized comparison with sevelamer hydrochloride.

The posted primary results report mean changes and standard deviations for each group. Negative changes indicate that the measured mean was lower at follow-up than at baseline. Comparisons with the active control quantify the difference between the group means, but the registry record does not report a separate analysis of a dose-response trend. The available results therefore support reading each dose contrast individually, with attention to uncertainty, rather than assuming that the sequence of doses establishes a smoothly increasing or decreasing response.

3. Trial Design

This completed study enrolled 154 participants and was registered as an open-label, randomized, active-controlled, multicenter phase II dose-finding study. It used a parallel-group design: participants were assigned to a PA21 dose group or to sevelamer hydrochloride, rather than crossing over between treatments. Masking was absent. The registry record lists five PA21 doses and one active-control group.

The study began in 2008-12, and primary completion was recorded in 2009-10. The clinical population was people with chronic kidney disease receiving maintenance hemodialysis. The stated study purpose was to investigate whether different PA21 doses could lower serum phosphate and to evaluate tolerability in this population.

For the primary outcome, the registry record identifies the Full Analysis Set as the analysis population. It includes all randomized participants who received at least 1 dose and had at least 1 post-baseline efficacy evaluation while on treatment. Group sizes in the posted primary outcome range from 24 to 26 participants. These outcome-specific counts should not be assumed to represent every person enrolled or every analysis population used for other outcomes.

Random allocation supports comparisons between groups by reducing systematic differences at assignment, although the registry record does not describe the randomization sequence or allocation concealment. With no masking, participants and study staff knew the assigned group; the record does not explain whether outcome assessment or laboratory procedures were masked. Details such as eligibility criteria, treatment adherence, dose adjustment, and the complete follow-up schedule are not reported in the registry record. The original protocol's design assumptions and the rationale for selecting the planned enrollment are also not reported in the registry record.

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

Analysis population for the primary outcome, as defined in the registry: For the Primary Outcome, data from the Full Analysis Set (FAS) was used. The FAS consists of all randomised subjects who received at least 1 dose of study treatment and had at least 1 post-baseline efficacy evaluation (while on treatment).

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.

Population: For baseline characteristics data, from All Randomised patients was used.

Only the first 6 of 7 groups are shown.

6. Primary Endpoint

The registry lists the primary outcome as Change From Baseline in Serum-phosphate Levels at the End of Treatment., measured over 6 weeks after baseline.

The primary endpoint is change from baseline in serum-phosphate levels at the end of treatment, with the timeframe specified as 6 weeks after baseline. It is a continuous measure reported as a mean change in mmol/L, with a standard deviation describing the spread of individual changes within each group. A negative mean change represents a lower average serum-phosphate level at follow-up than at baseline.

Using change from baseline makes each participant's follow-up value interpretable relative to that participant's starting value. The comparison between groups then asks whether average changes differ across randomized assignments. This is a laboratory endpoint aligned with the study's stated dose-finding purpose: the investigators were assessing serum-phosphate changes over the treatment period, not a clinical event endpoint.

Continuous measurements can preserve information about the amount of change rather than reducing results to a category such as improved or not improved. However, a group mean does not show how every participant changed, and the standard deviation is not a confidence interval for the mean or the treatment contrast. The primary endpoint therefore needs to be read together with the group sizes and the uncertainty around the between-group estimates.

The registry record specifies the analysis population and endpoint timing, but does not report the laboratory measurement schedule, handling of measurements after treatment discontinuation, or the detailed statistical model used in the sponsor's original analysis. Those details limit how fully the endpoint calculation can be reconstructed from the registry record alone.

7. Results Posted in the Registry

• 1.25 g PA21 (250 mg Iron): mean -0.04 versus -0.34 on control; difference 0.30 (95% CI -0.01 to 0.60), standardized effect d = 0.54; z-test p = 0.054.
• 5.0 g PA21 (1,000 mg Iron): mean -0.35 versus -0.34 on control; difference -0.01 (95% CI -0.32 to 0.31), standardized effect d = -0.01; z-test p = 0.965.
• 7.5 g PA21 (1,500 mg Iron): mean -0.40 versus -0.34 on control; difference -0.06 (95% CI -0.30 to 0.17), standardized effect d = -0.15; z-test p = 0.595.
• 10.0 g PA21 (2,000 mg Iron): mean -0.64 versus -0.34 on control; difference -0.30 (95% CI -0.58 to -0.03), standardized effect d = -0.61; z-test p = 0.032.

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.

Change From Baseline in Serum-phosphate Levels at Week 2

• 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:
  • 1.25 g PA21 (250 mg Iron): mean -0.03 versus -0.41 on control; difference 0.38 (95% CI 0.10 to 0.66), standardized effect d = 0.76; z-test p = 0.007.
  • 5.0 g PA21 (1,000 mg Iron): mean -0.36 versus -0.41 on control; difference 0.05 (95% CI -0.17 to 0.27), standardized effect d = 0.13; z-test p = 0.658.
• Interpretation:
  • The 95% confidence interval excludes no difference, so the mean is statistically higher for 1.25 g PA21 (250 mg Iron) than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between 5.0 g PA21 (1,000 mg Iron) and the control. The interval gives the range of effects that remain compatible with the data.

Change From Baseline in Serum-phosphate Levels at Week 4

• 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:
  • 1.25 g PA21 (250 mg Iron): mean -0.03 versus -0.53 on control; difference 0.50 (95% CI 0.29 to 0.71), standardized effect d = 1.35; z-test p = <0.001.
  • 5.0g PA21 (1,000 mg Iron): mean -0.39 versus -0.53 on control; difference 0.14 (95% CI -0.09 to 0.37), standardized effect d = 0.35; z-test p = 0.243.
• Interpretation:
  • The 95% confidence interval excludes no difference, so the mean is statistically higher for 1.25 g PA21 (250 mg Iron) than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between 5.0g PA21 (1,000 mg Iron) and the control. The interval gives the range of effects that remain compatible with the data.

Change From Baseline in Serum-phosphate Levels at Week 5

• 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:
  • 1.25 g PA21 (250 mg Iron): mean -0.05 versus -0.52 on control; difference 0.47 (95% CI 0.17 to 0.77), standardized effect d = 0.90; z-test p = 0.002.
  • 5.0 g PA21 (1,000 mg Iron): mean -0.51 versus -0.52 on control; difference 0.01 (95% CI -0.30 to 0.32), standardized effect d = 0.02; z-test p = 0.950.
• Interpretation:
  • The 95% confidence interval excludes no difference, so the mean is statistically higher for 1.25 g PA21 (250 mg Iron) than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between 5.0 g PA21 (1,000 mg Iron) and the control. The interval gives the range of effects that remain compatible with the data.

The registry record lists secondary changes in serum-phosphate levels at week 2, week 4, and week 5. Across those time points, group means are generally negative, indicating lower average measurements than at baseline. The overall pattern is broadly consistent with changes also observed at the primary endpoint, while the amount of change differs across doses and time points. The active-control group also has negative mean changes. The pattern is therefore not a simple contrast between all PA21 groups and a group with no change.

Only two PA21-versus-control comparisons are posted for each secondary endpoint, even though means are listed for the full set of treatment groups. The available comparisons do not establish how every dose differs from control at each time point. They also do not constitute a formal analysis of change over time or a test of dose-response. The secondary measures can add context about the observed trajectory, but should not be used to replace the primary endpoint or to make claims that require analyses not reported in the registry record.

Unadjusted secondary results carry less weight because several outcomes and comparisons create multiple opportunities to observe small p-values by chance. The record does not report a multiplicity adjustment, a hierarchy of outcome testing, or whether these secondary comparisons were prespecified. Nor does it report a longitudinal model that would account for repeated measurements from the same participants. The week-specific summaries should therefore be treated as descriptive and exploratory evidence, interpreted alongside the primary endpoint rather than as independent confirmation.

Group sizes at later time points are not identical across arms and are smaller in some groups than at the primary time point. The record does not explain the reasons for the changing counts or give missing-data methods. Consequently, apparent changes in the pattern between time points could reflect actual variation in measurements, differences in who contributed data, or both. The posted summaries do not separate those possibilities.

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

• Change From Baseline in Serum-phosphate Levels at Week 2
• Change From Baseline in Serum-phosphate Levels at Week 4
• Change From Baseline in Serum-phosphate Levels at Week 5

9. Statistical Interpretation

10. Statistical Methods Explained

The posted primary outcome is a continuous endpoint: each group is summarized by its mean change from baseline and standard deviation. A mean describes the central value of the observed changes, while a standard deviation describes how dispersed those changes were within that group. The standard deviation is about variation among participants, not uncertainty in the estimated mean difference.

What does the between-group estimate represent?

The mean difference compares the reported mean change in a PA21 group with the reported mean change in the sevelamer hydrochloride group. The contrast is expressed in mmol/L. A negative estimate means the PA21 group had a more negative mean change than the active-control group; a positive estimate means its mean change was less negative. This direction is a description of the contrast, not a judgment about clinical importance.

The registry record reports group summaries and no reported analyses. The contrast estimates accompanying those summaries are unadjusted comparisons. They are not a substitute for a fully specified model-based analysis, which might account for prespecified covariates or other design features. The record does not report whether the sponsor used an adjusted model, how missing observations were handled, or whether an alternative analysis population was examined.

How should standard deviations be distinguished from standard errors?

A standard deviation describes the spread of participant-level values. A standard error describes uncertainty in an estimated quantity, such as a group mean. Standard errors tend to be smaller when the estimate is based on more observations, all else being equal. Neither one is an interval by itself. A confidence interval combines an estimate and its uncertainty to display a range of values compatible with the data under the calculation's assumptions.

The group standard deviations and sample sizes help explain why estimates can be imprecise. For example, when group sizes are limited and participant outcomes vary, a modest difference between means can be difficult to estimate precisely. This is a general statistical point, not a claim about a particular participant or measurement in this study.

What does an unadjusted p-value say?

A p-value evaluates how unusual data at least as incompatible with a specified null hypothesis would be, under the assumptions of the statistical test. It does not give the probability that the null hypothesis is true, the probability that a result will replicate, or the size of an effect. The p-values posted for the primary contrasts are unadjusted. Because several dose groups are compared with the same active control, chance findings become a relevant concern when interpreting the collection of tests. The registry record does not report a multiplicity procedure.

Confidence intervals add information that a p-value alone does not: they show the range of estimates compatible with the data under the interval method. Intervals that include zero indicate that the data are compatible with both directions of a mean difference at the corresponding confidence level. That does not prove no difference; the interval may also include differences of meaningful size. The confidence interval method and confidence level are not specified in the registry record, so interpretation should not assume details beyond the posted estimates and intervals.

Why does the analysis population matter?

The primary endpoint uses the Full Analysis Set, defined as randomized participants who received at least 1 dose and had at least 1 post-baseline efficacy evaluation while on treatment. This is narrower than all randomized participants because it requires treatment exposure and an available efficacy evaluation. Participants without such a measurement are not included in that definition. The registry record does not report the number excluded from each group or the reasons for missing primary measurements.

Using a population defined by post-randomization events can affect how closely the analysis preserves the advantages of random assignment. In general, missing-data and analysis-population choices can influence estimates if inclusion is related to outcome or treatment experience. The record does not provide enough detail to assess that possibility. No claim about the direction or size of any resulting bias can be made from the posted summaries.

How should the sample-size illustrations be understood?

The sample-size illustrations use the observed effect as a starting point and show planning scenarios for detecting the full observed effect or a smaller fraction. They are not the original trial's design justification. Their assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. Planning for a smaller effect requires more participants, because a smaller separation between group means is harder to distinguish from random variation under otherwise similar assumptions. These calculations do not establish the power of the completed study.

The registry record identifies a mean endpoint and reports standard deviations, so the general concepts of variation, precision, and between-group comparison are relevant. It does not report a detailed statistical analysis plan, planned covariate adjustment, interim analyses, or the method used for the sponsor's original statistical testing. Those omissions matter when trying to reconcile posted descriptive results with any full clinical study report.

11. Confidence Intervals and Precision

Confidence intervals express the uncertainty around an estimated between-group mean difference. They show a range of values compatible with the observed data under the calculation method; they do not guarantee that the true effect lies inside the interval. A narrow interval indicates greater precision than a wide interval, all else being equal. An interval that crosses zero is compatible with differences in either direction, as well as no difference, at the interval's confidence level.

For the primary comparison of 10.0 g PA21 with sevelamer hydrochloride, the mean difference was -0.303 mmol/L and the posted confidence interval ran from -0.581 to -0.025. The interval excludes zero, consistent with the unadjusted p-value of 0.032. The comparison for 1.25 g had an estimate of 0.299 mmol/L and an interval that included zero; the comparison for 5.0 g was close to zero and its interval also included zero. The 7.5 g and 12.5 g intervals included zero as well. These intervals convey uncertainty about each contrast, not the probability that a specific effect is true.

Precision is limited in part by the group sizes, which were between 24 and 26 for the primary endpoint, and by the observed variation in changes. The intervals for the comparisons differ in width, so they do not support equal confidence in all estimates. The registry record does not identify the confidence level or interval method. It also does not report whether the sponsor's original analysis used adjustment or a different statistical model. Accordingly, the posted intervals are best read as uncertainty descriptions for the stated contrasts, not as a complete measure of every source of uncertainty.

12. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

The sample-size illustrations are planning calculations for two-group comparisons, not records of the enrollment in the six-arm trial. For continuous outcomes such as this one, the figures are participants per arm, not a total number of events. They assume a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each scenario uses either the observed effect or a stated fraction of that effect as the target to detect.

The 80% power column gives the number of participants per arm estimated to provide an 80% chance of detecting the target effect under the listed assumptions, if that effect is present and the assumptions hold. The 90% power column uses a higher target probability of detecting that same effect, so its planning requirement is larger. Planning for 75% of the observed effect or 50% of the observed effect means targeting a smaller difference than the observed estimate; smaller effects need more participants to distinguish them from random variation.

These are illustrations derived from observed estimates and should not be read as the sample-size justification used when the trial was designed. The original design assumptions are not reported in the registry record. The calculations also do not account for the multiple dose groups as a family of comparisons or for any missing outcome measurements unless those factors are reflected in the stated assumptions. This is not observed power: it does not describe the probability that the completed study's result is correct or that it would be statistically significant in a repeat study.

Very small observed contrasts can generate extremely large planning figures. That reflects the difficulty of reliably distinguishing a small estimated mean difference from random variation under the calculation's assumptions, not a guarantee that the observed estimate is the true effect. The figures are useful for understanding how planning depends on the assumed effect size, but require clinical and design judgment before being used for a future study.

13. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = 0.299; pooled standard deviation σ = 0.558.
2. n = 2 × (1.96 + 0.842)² × 0.558² / 0.299² = 54.6, rounded up to 55 participants per arm for 80% power.

The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
delta <- 0.299                      # observed difference in means
sigma <- 0.557799022946437                     # 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(824460)
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 = 55 (80% power), 74 (90% power)
 75% of observed effect: n per arm = 98 (80% power), 131 (90% power)
 50% of observed effect: n per arm = 219 (80% power), 293 (90% power)
power.t.test: 55.6 
Simulated power at n = 55 per arm: 0.795 (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 primary outcome compares five PA21 dose groups with one active control, and the registry record also lists three secondary time points. Looking across several comparisons increases the chance that at least one unadjusted result appears notable even when the underlying differences are limited. This is the general multiplicity problem. The registry record does not report a correction procedure, a testing hierarchy, or a prespecified strategy for controlling the family-wise error rate or another error measure.

The primary comparison for 10.0 g PA21 has an unadjusted p-value of 0.032. Without a reported multiplicity plan, that value should be understood as an unadjusted result for one comparison, rather than as evidence that takes account of all dose and time-point tests. The same caution applies to the secondary p-values. No reported analyses are listed in the record, so it is not possible to determine whether the posted comparisons reproduce the sponsor's planned inferential approach.

Missing-data handling is also not reported in the registry record. The primary Full Analysis Set excludes randomized participants who did not receive treatment or did not have a post-baseline efficacy evaluation while on treatment, by definition. The record does not provide counts or reasons for missing primary outcome values, details about imputation, or sensitivity analyses for missingness. It therefore cannot establish whether missing data could have changed the estimates.

The primary analysis population is described, but a separate intention-to-treat analysis of all randomized participants is not reported. The record also does not report per-protocol results or explain how treatment discontinuations were handled. These omissions limit assessment of how results depend on the population definition and data availability.

Interim analyses, stopping rules, and the complete statistical analysis plan are not reported in the registry record. These details should not be inferred from the completed status or from the observed p-values. Without them, the posted results can be described, but the full prespecification and decision process cannot be evaluated.

15. Safety Results

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

Other (non-serious) adverse events

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

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: staphylococcal sepsis (4.2%), fluid overload (4.2%), ischaemic stroke (4.0%), asthma (3.8%), diverticular perforation (3.8%).

The registry record reports serious adverse events for each group as the number of participants affected and the number at risk. The posted figures are 2 of 26 for 1.25 g PA21, 2 of 26 for 5.0 g, 1 of 25 for 7.5 g, 1 of 27 for 10.0 g, 2 of 24 for 12.5 g, and 2 of 26 for sevelamer hydrochloride. These are counts of participants with serious adverse events, not counts of all individual events.

For other, non-serious adverse events, the posted affected-participant counts are 13 of 26, 16 of 26, 13 of 25, 18 of 27, 17 of 24, and 13 of 26, respectively, in the same group order. The record also lists serious-event terms with percentages, including Staphylococcal sepsis and Fluid overload at 4.2% each, Ischaemic stroke at 4.0%, and Asthma, Diverticular perforation, and Myocardial infarction at 3.8% each. The registry record does not report deaths.

These figures are descriptive. Group sizes are small, and the registry record does not provide enough information to make a comparative safety analysis, such as event timing, exposure-adjusted rates, or statistical tests. The counts should not be interpreted as establishing that one group is safer than another.

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

The posted results describe mean serum-phosphate changes during a short treatment period in people with chronic kidney disease receiving maintenance hemodialysis. All groups had negative mean changes from baseline. The largest-magnitude negative primary mean was in the 10.0 g PA21 group, and its unadjusted comparison with sevelamer hydrochloride had an estimate of -0.303 mmol/L with a confidence interval excluding zero. The other primary contrasts were less distinct from zero in their posted intervals.

Those findings do not by themselves establish that PA21 produces a clinically important difference, that any dose is preferable, or that a dose-response relationship has been demonstrated. The registry record does not report a threshold for clinical importance or a formal dose-trend analysis. The contrasts are among several comparisons, and no multiplicity adjustment is reported. The study was open-label, and the registry record does not describe masking of outcome assessment.

The reported outcome is a laboratory measure at 6 weeks after baseline. It does not provide evidence about long-term clinical outcomes, quality of life, or outcomes beyond the stated follow-up. The posted adverse-event summaries describe affected-participant counts, but they do not establish comparative safety. Deaths are not reported in the registry record.

Results also apply to the defined Full Analysis Set: randomized participants who received at least 1 dose and had at least 1 post-baseline efficacy evaluation while on treatment. The record does not detail missing-data methods or the participants excluded from this set. Accordingly, the posted comparisons are informative as trial summaries, but they do not answer every question about treatment effect, clinical relevance, or generalizability.

Reading the estimates alongside their confidence intervals is important. The interval for the 10.0 g comparison is compatible with a range of differences, not a single exact effect. For the remaining comparisons, intervals crossing zero indicate uncertainty about the direction and magnitude of the contrast; they do not prove equivalence. A conclusion of equivalence or non-inferiority would require a prespecified margin and an appropriate analysis, neither of which is reported in the registry record.

17. Why This Trial Matters Statistically

This trial illustrates why dose-finding results should be read as a set of estimates rather than as a search for a single p-value. Five PA21 dose groups were compared with the same active control, and observed mean changes did not form a strictly increasing sequence across doses. Without a reported formal dose-response model, the group summaries alone cannot establish a dose-response relationship.

The primary endpoint is continuous, so the magnitude and precision of differences matter alongside statistical testing. The 10.0 g comparison has an unadjusted p-value below 0.05 and an interval excluding zero, while other contrasts are more uncertain. Yet multiple comparisons, modest group sizes, and unreported multiplicity handling make it important not to treat one result as definitive evidence from the full set of comparisons.

The study also shows the difference between a planning calculation and a trial's original design justification. Planning illustrations based on observed estimates can demonstrate how smaller target effects require larger groups. They cannot reveal the assumptions used to select enrollment before results were known, and the registry record does not report those original assumptions.

Finally, the record distinguishes several kinds of uncertainty that are often conflated: participant-level variability, uncertainty in a mean difference, multiplicity across tests, and possible effects of missing outcomes. The posted summaries address only some of these. Recognizing what the registry does and does not report is central to statistically responsible interpretation.

18. Limitations

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

Several details needed for a fuller evaluation are not reported in the registry record. These include the eligibility criteria, the randomization and allocation-concealment procedures, the original sample-size justification, the prespecified statistical analysis plan, and the exact method used to calculate confidence intervals and p-values. The record also does not state whether any interim analyses or stopping rules were used.

The primary analysis uses a Full Analysis Set that requires treatment exposure and at least 1 post-baseline efficacy evaluation while on treatment. Counts and reasons for participants who did not meet that definition are not reported. Missing-data procedures and sensitivity analyses are also not reported. This makes it difficult to assess how incomplete outcome data might affect the group estimates.

The trial was open-label, and information about blinding of laboratory staff or outcome assessors is not reported. The endpoint is a laboratory measure over a short timeframe; the record does not provide longer-term results or clinical outcome data. The posted adverse-event summaries give affected-participant counts but do not include event timing, exposure-adjusted rates, or a comparative inferential analysis. Deaths are not reported.

Finally, the primary comparison set includes several dose groups against a shared active control, with additional secondary time points. Multiplicity adjustment and a prespecified testing hierarchy are not reported. Thus, the unadjusted comparisons should be regarded with caution, particularly when interpreting individual p-values across the full set of outcomes and doses. These limitations describe missing information in the registry record; they do not establish that a specific bias occurred.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Study of Phosphate Levels in Patients With Chronic Kidney Disease — NCT00824460.
• Registry record last updated 2014-04-01; status last verified 2014-03.
• Results first posted 2014-04-01.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

22. Record Summary

NCT00824460 is a completed, randomized, open-label, parallel-group phase II dose-finding study in people with chronic kidney disease on maintenance hemodialysis. It enrolled 154 participants and compared five PA21 dose groups with sevelamer hydrochloride. The primary endpoint was mean change from baseline in serum-phosphate levels 6 weeks after baseline.

All groups had negative mean changes. The 10.0 g PA21 group had the most negative posted primary mean and a mean difference of -0.303 mmol/L versus active control, with an unadjusted p-value of 0.032. Other primary contrasts had intervals that included zero. The registry record also lists secondary measurements at weeks 2, 4, and 5 and descriptive adverse-event counts.

The registry record does not report multiplicity handling, missing-data methods, original sample-size assumptions, or the full statistical analysis plan. The estimates therefore describe the posted results, while leaving important aspects of the planned and sponsor-reported analysis unclear.