Trial of Dialysate Sodium in Chronic Hospitalized Hemodialysis Patients: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Trial of Dialysate Sodium in Chronic Hospitalized Hemodialysis Patients (NCT02145260), a randomized na study. The primary outcome is Change in Intra-dialytic Decline in Systolic Blood Pressure.

2. Clinical Question

3. Trial Design

This was a randomized, parallel-group trial of dialysate sodium in chronic hospitalized hemodialysis patients. Participants were assigned to a lower concentration of 138 mmol/L or a higher concentration of 142 mmol/L. The registry lists quadruple masking, but does not report the specific roles or procedures covered by that masking. The trial is listed as completed, with enrollment of 144. The primary outcome data report 69 participants in the lower-sodium group and 70 in the higher-sodium group; the registry record does not explain the difference between the enrollment count and these outcome-group counts.

The intervention was used during the hospital stay for up to a maximum of six inpatient hemodialysis sessions. The primary endpoint timeframe describes average decline measured across up to six sessions occurring over a two-week period. The posted endpoint is participant-level: each session’s decline was calculated as predialysis systolic blood pressure minus the lowest systolic blood pressure during that session, and the session values were averaged for each participant.

The listed sponsor is Brigham and Women’s Hospital. The registry record gives a start date of 2014-07-01 and a primary completion date of 2020-12-31. No trial phase is listed beyond NA. The registry record does not report the original sample-size justification, the detailed randomization procedure, or the allocation concealment procedure. It also does not report the statistical analysis plan in sufficient detail to determine whether additional prespecified analyses were planned. These omissions limit what can be said about the design beyond the listed randomization, masking, parallel structure, intervention groups, and posted outcome data.

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: 3 patients in the lower dialysate sodium arm and 2 patients in the higher dialysate sodium arm were discharged prior to the first study session.

Overall Study

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

6. Primary Endpoint

The registry lists the primary outcome as Change in Intra-dialytic Decline in Systolic Blood Pressure, measured over Average decline in systolic blood pressure will be measured up to a maximum of six inpatient HD sessions, occurring over a two-week time period.

The primary endpoint is the change in intradialytic systolic blood pressure, measured in mm Hg. For each hemodialysis session, the decline is defined as predialysis systolic blood pressure minus the lowest systolic blood pressure reached during the session. The values from a participant’s measured sessions were then averaged, with measurement intended for up to six inpatient sessions over a two-week period.

This is a continuous measure: larger positive values represent a larger decline from the predialysis reading to the session low. Comparing group means provides a summary of the average measured decline in each randomized group. It does not directly count the number of intradialytic hypotension events, nor does it establish how many participants experienced symptoms or required an intervention. The registry describes intradialytic hypotension as an abrupt blood-pressure decline causing symptoms and/or requiring intervention, but the posted primary endpoint is based on the systolic-pressure difference.

General statistical context: A continuous endpoint can preserve information about the degree of change rather than reducing measurements to categories. Its interpretation still depends on how consistently measurements are collected and how participant-level values are summarized. The registry record does not report details such as the number of sessions actually contributing to each participant’s average or how incomplete session measurements were handled.

7. Results Posted in the Registry

• Higher Dialysate Sodium: mean 23.00 versus 26.00 on control; difference -3.00 (95% CI -8.32 to 2.32), standardized effect d = -0.19; z-test p = 0.269.

8. Statistical Interpretation

9. Statistical Methods Explained

The posted primary measure is a continuous endpoint summarized by a mean and standard deviation. The registry describes the outcome as a participant-level average of session-specific declines. First, predialysis systolic blood pressure was compared with the lowest systolic blood pressure during each session. The resulting decline values from a participant’s sessions were then averaged. The comparison is between those participant-level averages in the two randomized groups.

What does the mean difference represent?

The group means are 26.0 mm Hg for lower dialysate sodium and 23.0 mm Hg for higher dialysate sodium. The estimated mean difference is -3.0 mm Hg, with the comparison expressed as higher sodium minus lower sodium. The negative sign means the observed average decline was smaller in the higher-sodium group. It is an estimate based on the observed group data, not a guarantee that each participant had a smaller decline. Differences among participants and uncertainty in the estimate are important to its interpretation.

What does the standard deviation describe?

The standard deviation is 16.0 mm Hg in each group. General statistical context: A standard deviation describes the spread of individual measurements around their group mean. It is not the same as the uncertainty in the estimated mean, and it is not a confidence interval. In this comparison, the endpoint is already an average across the measured sessions for each participant; the standard deviations describe variation across participants’ averages, not variation across all individual dialysis sessions considered separately.

The registry record does not report how many sessions contributed to each participant’s average, whether the maximum number of sessions was reached, or how session-level measurements that were unavailable were handled. It also does not describe whether the analysis accounted for the differing number of sessions per participant. These details could matter when interpreting how each participant-level average was formed.

How should the confidence interval be read?

The 95% confidence interval for the mean difference is -8.32 to 2.32 mm Hg. General statistical context: A confidence interval expresses the precision of an estimate under the statistical model used. In repeated samples under the same assumptions, intervals constructed by the same method would cover the underlying parameter at the stated rate. For a reader considering this particular interval, the main practical point is that it spans values below and above zero. It does not establish that the groups differ, nor does it establish that they are equivalent.

The registry record does not state the confidence-interval construction method or whether the reported comparison was adjusted for any covariates. The comparison’s listed standard deviations and group counts are consistent with an unadjusted summary comparison, but the registry does not provide a detailed analysis description. The displayed p-value is explicitly unadjusted. No claim about adjustment, a model beyond the posted comparison, or a prespecified testing hierarchy can be made from the record.

What does the p-value add?

The unadjusted p-value is 0.269. General statistical context: A p-value summarizes the compatibility of the observed data with a null hypothesis of no group difference, conditional on the test’s assumptions. It does not measure the probability that the observed effect is due to chance, and it does not tell how important a difference would be in practice. The p-value and confidence interval offer related but distinct descriptions: the interval displays a range of estimates compatible with the data and model, while the p-value summarizes evidence against a point null under the test.

The registry lists two outcome measures and one posted secondary outcome, but no analyses are listed for this endpoint beyond the reported comparison. Whether additional analyses were conducted, planned, or adjusted for multiplicity is not reported in the registry record. The primary outcome’s result should consequently be understood as the posted comparison, not as evidence that all possible analyses or outcomes have been considered.

Why can over-dispersion matter?

General statistical context: Over-dispersion occurs when observed variability is greater than a model assumes. It is especially relevant to outcomes such as counts, where a simple model may assume a particular relationship between the mean and variance. If extra variability is not accounted for, standard errors and uncertainty estimates can be too small. The primary outcome in this trial is a continuous participant-level average, not a count outcome. The registry record does not report an over-dispersion assessment or a model that would make such an assessment applicable. For this endpoint, the more directly relevant concerns are the spread of participant-level averages, the construction of those averages, and the handling of incomplete measurements.

Random allocation is intended, in general, to support a fair comparison by making the assigned groups comparable on average, though randomization does not guarantee identical groups in a particular trial. The registry identifies the allocation as randomized and the design as parallel, but does not report the randomization sequence method or concealment details. Masking is listed as quadruple; the specific people masked and the procedures used are not reported. These design labels are useful context, but they do not replace a full description of trial conduct and analysis.

10. Confidence Intervals and Precision

The estimated mean difference in average systolic blood-pressure decline is -3.0 mm Hg, comparing higher with lower dialysate sodium. Its 95% confidence interval extends from -8.32 to 2.32 mm Hg. The interval includes zero and spans possible differences in either direction. The estimate therefore has limited precision for determining the direction and size of the group difference.

General statistical context: A confidence interval conveys uncertainty about an estimated parameter under the assumptions used to calculate it. A narrower interval would indicate greater precision, while a wider one would indicate less. The interval is not a range containing 95% of individual participant measurements, and it does not mean that there is a 95% probability that the true difference lies within this particular interval.

The group standard deviations are 16.0 mm Hg in both arms, and the endpoint sample sizes are 69 and 70. These figures provide context for the variability and amount of outcome data behind the comparison. The registry record does not report the number of missing outcome measurements, the number of participants excluded from analysis, or the method used to address missingness. Because total enrollment is 144 while the endpoint group counts are 69 and 70, the record does not explain how the outcome analysis population relates to all enrolled participants.

The interval should be considered alongside the unadjusted p-value of 0.269 and the absence of a reported equivalence margin. The results do not show that the groups are identical, and the confidence interval alone does not determine whether any particular difference would be important in practice. The registry record does not report a threshold for a clinically meaningful difference in this measure.

11. 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 planning figures describe participants per arm, not total events. They are illustrations based on the observed effect, not the trial’s original sample-size justification; the original design assumptions are not reported in the registry record. The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. The effect to detect is set to a stated fraction of the observed effect.

At 100% of the observed effect, the illustration gives 447 participants per arm for 80% power and 598 participants per arm for 90% power. At 75% of the observed effect, the corresponding figures are 794 and 1,063 participants per arm. At 50% of the observed effect, they are 1,787 and 2,392 participants per arm. These are planning illustrations, not evidence about the power of the completed trial.

General statistical context: Power is the probability that a study will reject a specified null hypothesis under an assumed true effect and model. The 80% and 90% columns represent different planning targets: under the stated assumptions, the higher target requires a larger planned sample than the lower target. Smaller effects are harder to distinguish from random variation, so planning to detect a smaller effect requires more participants. The figures depend on the assumptions listed and should not be interpreted as universal requirements for future studies.

The sample-size figures are not observed power. They do not change the interpretation of the trial’s estimate, confidence interval, or p-value, and they cannot establish whether the original trial was adequately designed because its own planning assumptions are not reported.

12. 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 = -3.000; pooled standard deviation σ = 16.000.
2. n = 2 × (1.96 + 0.842)² × 16.000² / -3.000² = 446.5, rounded up to 447 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 <- -3                      # observed difference in means
sigma <- 16                     # 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(2145260)
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 = 447 (80% power), 598 (90% power)
 75% of observed effect: n per arm = 794 (80% power), 1,063 (90% power)
 50% of observed effect: n per arm = 1,787 (80% power), 2,392 (90% power)
power.t.test: 447.5 
Simulated power at n = 447 per arm: 0.793 (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.

13. Multiplicity, Missing Data and Analysis Populations

The registry record lists two outcome measures and identifies one secondary outcome: change in predialysis high-sensitivity Troponin I. The posted primary result concerns average decline in systolic blood pressure. No numerical result for the listed secondary outcome is present in the record summarized for this analysis. The registry record also lists no analyses for the outcomes.

Multiplicity arises when several outcomes, time points, subgroups, or statistical tests are considered. General statistical context: As the number of tests increases, the chance of obtaining at least one apparently unusual result under a set of null hypotheses can increase. Trial protocols may define a primary outcome, testing order, or adjustment approach to address this. The registry record does not report whether multiplicity adjustments were planned or applied, whether there was a testing hierarchy, or whether other outcomes or analyses were prespecified. The unadjusted p-value of 0.269 should therefore be read as the reported unadjusted comparison; the record does not support claims about a broader multiplicity strategy.

Missing-data methods and analysis populations are also not described in enough detail to assess. Overall enrollment is 144, while the primary outcome reports group counts of 69 and 70. The record does not explain the difference, identify how many participants had missing endpoint data, state whether all randomized participants were analyzed in their assigned groups, or describe any imputation or other missing-data procedure. It is not possible to determine whether the displayed counts represent all randomized participants, participants with observed outcomes, or another analysis set.

The endpoint averages data across up to six sessions, but the registry record does not report how participants with fewer measured sessions were handled or whether incomplete session data were included. It also does not report whether the analysis accounted for variation in session counts. These unknowns are relevant to understanding the endpoint construction and the population represented by the posted estimate. They should not be filled in by assumption.

14. Safety Results

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

Deaths

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: nstemi non-st segment elevation myocardial infarction (1.4%), post-operative bleed (1.4%).

The registry reports serious adverse events for 1 participant in the lower-sodium group and 1 participant in the higher-sodium group. The corresponding at-risk counts are 69 and 70. It reports other, non-serious adverse events for 28 participants in the lower-sodium group and 24 in the higher-sodium group, with the same group at-risk counts. Deaths are listed as 0 in each group.

The registry also lists “NSTEMI non-ST segment elevation myocardial infarction” and “post-operative bleed” among the top serious-event terms, each reported as 1.4%. The record does not provide enough information in these figures to establish a causal relationship between an event and an assigned dialysate sodium group. These counts describe events recorded during the trial, not comparative proof of safety or harm.

General statistical context: Adverse-event counts should be interpreted in light of the number of participants observed, the period of observation, event definitions, and how events were collected. The registry record does not give detailed event narratives, severity gradations beyond the serious-event classification, exposure-adjusted rates, or a statistical comparison of the groups. The counts are descriptive and do not establish that the groups have identical safety profiles.

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

The posted primary outcome is the average decline in systolic blood pressure during hemodialysis, calculated for each participant from session-specific predialysis and lowest intradialytic measurements. The observed group means were 26.0 mm Hg with lower dialysate sodium and 23.0 mm Hg with higher dialysate sodium. The estimated difference, higher minus lower, was -3.0 mm Hg, with a 95% confidence interval from -8.32 to 2.32 mm Hg and an unadjusted p-value of 0.269.

These data describe an average blood-pressure measure in the groups represented by the posted outcome counts. The confidence interval includes zero and values on either side of it, so the estimate is not precise enough to settle the direction or size of the difference. The result does not establish equivalence, because the registry record does not report an equivalence margin or a noninferiority design. Nor does a non-significant test establish that the interventions have the same effect.

The primary endpoint is not a direct tally of symptomatic intradialytic hypotension events, interventions required, cardiac ischemia, or patient-centered outcomes. The registry lists change in predialysis high-sensitivity Troponin I as a secondary outcome, but its numerical result is not reported in the registry record. The primary result cannot be used to infer that secondary result or other clinical effects.

The registry describes a randomized comparison, which is relevant to interpreting group differences, but it does not provide a detailed account of randomization procedures, endpoint missingness, analysis populations, or the statistical analysis plan. The overall enrollment count and outcome counts differ, and the reason is not reported in the registry record. These limitations leave uncertainty about how the posted analysis population relates to all enrolled participants.

Accordingly, the result is best understood as an imprecise estimate of the difference in average systolic-pressure decline, not as a definitive conclusion about clinical benefit, harm, or equivalence. It does not provide medical advice or determine which dialysate sodium concentration should be used for an individual.

16. Why This Trial Matters Statistically

This trial addresses a statistical challenge common in clinical research: a physiologically motivated intervention may be evaluated using a continuous measurement that varies considerably among participants. Here, the endpoint is a participant-level average of systolic-pressure declines across measured dialysis sessions. The group means and their variability need to be considered together rather than treating the difference between means as a complete account of the evidence.

The estimated difference is -3.0 mm Hg, while the standard deviation is 16.0 mm Hg in each group. The 95% confidence interval, -8.32 to 2.32 mm Hg, shows that the estimate has substantial uncertainty and includes values in both directions. This illustrates why a point estimate alone can be misleading: the same observed estimate should be read with its precision and the underlying variability.

The trial also highlights the importance of clearly defining how repeated measurements contribute to a participant-level endpoint. Each session’s decline was calculated from predialysis pressure and the session low, then averaged for each participant. The registry record does not report how many sessions contributed for each person or how incomplete session measurements were handled. Such information matters when interpreting what the group means represent.

Finally, the registry identifies a randomized design and a completed trial, but does not report several details needed for a full statistical appraisal, including the original sample-size justification, missing-data methods, and analysis populations. Distinguishing the posted results from unreported design and analysis details is essential: the available estimate can be described accurately, while unresolved questions remain unresolved rather than being filled by assumptions.

17. 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 does not report the trial’s original sample-size justification, so the planning illustrations based on the observed effect cannot be used to reconstruct the design rationale. It also does not report a detailed statistical analysis plan, including whether covariate adjustment, interim analyses, subgroup analyses, or multiplicity procedures were planned or used. These details should not be inferred from the posted unadjusted result.

Although the endpoint description specifies averaging session-level declines for each participant, the record does not state how many sessions each participant contributed, how sessions with unavailable measurements were handled, or whether differing numbers of sessions were accounted for analytically. This limits assessment of the consistency and completeness of the participant-level averages.

The reported primary outcome counts are 69 in the lower-sodium group and 70 in the higher-sodium group, compared with overall enrollment of 144. The reason for this difference is not reported in the registry record. The record does not identify the analysis population, explain any exclusions, report the extent or pattern of missing outcome data, or describe a method for handling missing data. Consequently, the relationship between enrollment and the analyzed endpoint population is unclear.

The endpoint measures average decline in systolic blood pressure, not a direct count of symptomatic or intervention-requiring hypotension events. The listed secondary outcome, change in predialysis high-sensitivity Troponin I, has no numerical result reported in the registry record. The posted primary endpoint therefore does not address all outcomes motivating the study.

Finally, the registry lists quadruple masking but does not describe who was masked or how masking was maintained. Random sequence generation and allocation concealment details are also not reported in the registry record. These limitations constrain a full assessment of trial conduct and the scope of conclusions that can be drawn from the posted comparison.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Trial of Dialysate Sodium in Chronic Hospitalized Hemodialysis Patients — NCT02145260.
• Registry record last updated 2022-10-31; status last verified 2022-10.
• Results first posted 2022-10-31.
• 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.

21. Record Summary

The registry record describes a completed, randomized, parallel-group trial comparing dialysate sodium concentrations of 138 mmol/L and 142 mmol/L in hospitalized adults receiving chronic hemodialysis. Quadruple masking is listed. Enrollment was 144, the sponsor was Brigham and Women’s Hospital, and the registry gives a start date of 2014-07-01 and a primary completion date of 2020-12-31.

The primary endpoint was the participant-level average decline in systolic blood pressure across measured inpatient dialysis sessions, for up to six sessions over a two-week period. The group means were 26.0 mm Hg in the lower-sodium group and 23.0 mm Hg in the higher-sodium group. The mean difference was -3.0 mm Hg, with a 95% confidence interval from -8.32 to 2.32 mm Hg and an unadjusted p-value of 0.269.

The record lists change in predialysis high-sensitivity Troponin I as a secondary outcome but does not report its numerical result. The reason that outcome counts of 69 and 70 differ from overall enrollment is not reported in the registry record. The original sample-size rationale and detailed analysis and missing-data methods are also not reported.