Pharmacokinetics of Vitamin D in Multiple Sclerosis and in Health: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Pharmacokinetics of Vitamin D in Multiple Sclerosis and in Health (NCT01667796), a na na study. The primary outcome is Change in Mean Serum Level of 25-hydroxyvitamin D.

2. Clinical Question

3. Trial Design

NCT01667796 is a completed pilot study titled “Pharmacokinetics of Vitamin D in Multiple Sclerosis and in Health.” Its official title describes pharmacodynamic and immunologic effects of vitamin D supplementation in patients with multiple sclerosis and healthy controls. The registry lists the condition as relapsing-remitting multiple sclerosis and records an enrollment of 57. The study start is listed as 2010-11 and primary completion as 2014-03.

The registry describes a single-group model, with no allocation method listed and no masking. Although it includes people with multiple sclerosis and healthy controls, both groups were to receive vitamin D3 at 5000 IU/day by mouth for 90 days. Thus, the comparison concerns differences between populations under the same supplementation plan. It is not a randomized comparison of supplementation against placebo, no supplementation, or another treatment. The registry record specifically cautions that the arms are not a like-for-like control comparison.

The study’s stated purpose was to assess whether the two populations attain a similar increase in serum 25-hydroxyvitamin D. It also aimed to assess whether immunologic responses or relevant gene-expression responses differ between them. The registry lists secondary outcomes involving T cell subsets, gene expression microarray, cytokine levels, and the percentage of B cells. The phase is listed as NA. Further details on eligibility criteria, recruitment procedures, participant characteristics, adherence monitoring, or the rationale for the enrollment target are not reported in the registry record.

The primary completion date indicates when primary outcome collection was recorded as complete, but it does not by itself establish how many participants completed follow-up or contributed to each analysis. Those analysis-population details are 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

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 Mean Serum Level of 25-hydroxyvitamin D, measured over Baseline to 90 days.

The primary endpoint is change in mean serum 25-hydroxyvitamin D, measured in nmol/L, from baseline to 90 days. This biomarker is the measure used to address the study’s central question: whether people with multiple sclerosis and healthy controls have similar serum responses during the vitamin D3 supplementation period. The registry describes serial measurements and a comparison of the two groups, rather than a single unstructured comparison of values.

A mean provides a group-level summary of a continuous measurement. The registry lists standard deviation as the dispersion measure, which describes variation in observed values around the mean. These summaries would help readers understand both the average measured level and how much participants’ measurements vary. However, the numerical means, changes, standard deviations, group contrast, confidence interval, and inferential result are not reported in the registry record. The endpoint’s description therefore establishes what was intended to be measured, but not the direction, size, or precision of the observed difference.

As a general statistical point, serum concentration is a biological measurement, not by itself a direct measure of clinical benefit. The registry’s endpoint can address the stated biomarker comparison, but interpreting clinical consequences would require evidence beyond the numerical outcome information. The endpoint should be read as a comparison of biomarker patterns between these populations during supplementation, without attributing any observed change solely to supplementation in the absence of an untreated comparison group.

7. Why No Re-analysis Is Shown

8. Statistical Interpretation

9. Statistical Methods Explained

The registry names generalized estimating equations, or GEE, as the method for comparing serial serum 25(OH)D measurements between participants with multiple sclerosis and healthy controls. It also states that an autoregressive with lag one correlation matrix was used to account for repeated measurements and within-subject correlations. The registry does not report the fitted coefficients, uncertainty estimates, covariates, or other implementation details.

Why use a repeated-measures method? General statistical explanation: when a study measures the same participant more than once, the resulting observations are related. A participant’s measurements may tend to resemble one another more than measurements from different participants. Treating every observation as independent can give an inaccurate account of uncertainty. A repeated-measures method represents the dependence within participants while estimating the population-level relationship of interest. In this study, that relationship concerns serial serum measurements and differences between the two participant groups.

GEE is generally used to estimate average associations across a population while accommodating correlated observations within clusters, such as repeated records from the same person. In the registry’s description, the participant is the source of the within-subject correlation, and the repeated serum measurements are the observations. The method does not make the groups randomized or remove confounding that may arise from differences between them. Its role is to address the correlation structure of repeated measurements, not to turn an observational group comparison into a randomized treatment comparison.

What does the autoregressive structure represent? General statistical explanation: an autoregressive correlation structure represents a pattern in which measurements closer together in an ordered series are expected to be more correlated than measurements farther apart. The registry specifies an autoregressive structure with lag one. This is a modeling choice for the dependence among serial observations; it is not a description of the size or direction of the serum response. The record does not give the actual correlation estimates or enough measurement-schedule detail to assess how well this structure matched the observed data.

How should the mean and standard deviation be read? The primary outcome is a continuous measure, and the record specifies a mean with standard deviation. A mean summarizes the central level or change across participants. A standard deviation describes the spread of measurements around that mean. They answer different questions: the mean describes the group-level average, while the standard deviation describes participant-level variability. A standard deviation is not the same as a standard error or confidence interval, and it does not by itself express how precisely a group difference has been estimated. The registry does not report the numerical values for these summaries.

For a comparison, an estimated difference between groups would describe the magnitude and direction of the contrast, while a confidence interval would express the range of values compatible with the data under the analysis assumptions. A p-value, if reported, would address a different question about compatibility with a specified null hypothesis. These are general statistical interpretations; none of those numerical results is reported for the primary endpoint in the registry record. Therefore, the endpoint definition and method description cannot be used to reconstruct the result.

What can the model not establish? A GEE analysis accounts for the specified within-participant correlation, but it does not address every source of bias. In particular, it does not create an untreated comparison group, balance population characteristics through random allocation, guarantee complete follow-up, or establish that participants adhered to the supplementation plan. These issues require design information and data that are not reported in the registry record. The interpretation of any model estimate would also depend on how the outcome, group, time, and any covariates were represented in the fitted model; those details are not reported.

The study lists secondary outcomes related to T cell subsets, gene expression, cytokines, and B cells. The primary method description is specific to serial serum 25(OH)D measurements. It does not establish which statistical methods were used for every secondary outcome, how each endpoint was defined analytically, or whether adjustments were made for multiple testing. Those items are not reported in the registry record.

The sample-size assumptions describe a planning illustration based on an observed effect, not the design justification used by the investigators. The illustration assumes a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation; the effect to detect is expressed as a stated fraction of the observed effect. For non-time-to-event outcomes, the illustration is expressed as participants per arm. These assumptions do not show that the study was planned or conducted with those settings, and they do not provide observed power. The registry does not report its own sample-size justification or the numerical illustration results.

Finally, model-based inference depends on the data included and the assumptions used for estimation. The registry does not describe missing-data procedures, the analysis population, handling of protocol deviations, or sensitivity analyses. It is therefore not possible to assess from the registry record whether the fitted analysis represented all enrolled participants, only those with complete measurements, or another defined set.

10. Confidence Intervals for Each Arm

No two-arm comparison is shown for this trial, but each arm's mean can be given with a t-based 95% confidence interval computed from the posted mean, spread and number of participants.

R code and output

arm <- c("MS Subjects", "Healthy Controls")
n   <- c(24, 29)
m   <- c(65.9, 82.4)
sp  <- c(5.9, 5.2)
sd  <- sp      # posted standard deviations
for (i in seq_along(n)) {
  se <- sd[i] / sqrt(n[i]); h <- qt(0.975, n[i] - 1) * se
  cat(sprintf("CARM|%s|%d|%.3f|%.3f|%.3f|%.3f\n", arm[i], n[i], m[i], sd[i], m[i] - h, m[i] + h))
}

CARM  MS Subjects  24  65.900  5.900  63.409  68.391
CARM  Healthy Controls  29  82.400  5.200  80.422  84.378

11. Multiplicity, Missing Data and Analysis Populations

The registry lists five outcome measures and two analyses. The primary outcome is change in mean serum 25-hydroxyvitamin D, while secondary outcomes concern T cell subsets, gene expression, cytokine levels, and B cell percentages. The registry record does not report a multiplicity strategy, such as a hierarchy of outcomes, an adjustment to significance thresholds, or a distinction between confirmatory and exploratory analyses. The number of outcomes alone does not establish how many statistical tests were performed or how the investigators interpreted them.

The missingness of repeated measurements is relevant because the primary analysis uses serial observations. The registry does not report the amount or pattern of missing data, reasons for missingness, or the method used to handle incomplete follow-up. It also does not state whether any imputation, likelihood-based procedure, or sensitivity analysis was used. Without these details, readers cannot assess how missing observations may have affected the comparison.

The analysis population is not reported in the registry record. Although the total enrollment is 57 and the safety entries list 27 MS subjects and 30 healthy controls at risk, those safety counts do not establish who contributed primary endpoint data or whether every enrolled participant was included in the outcome analysis. The record does not identify an intention-to-treat, per-protocol, or other analysis population.

Further details about exclusions, protocol deviations, interim analyses, and the prespecified statistical analysis plan are not reported in the registry record. No assumptions about those procedures can be made from the outcome description alone.

12. 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 0% reporting threshold.

Most frequent non-serious adverse event terms

The registry reports serious adverse-event counts separately for MS subjects and healthy controls. It lists zero affected among 27 MS subjects at risk and zero affected among 30 healthy controls at risk. These are the reported counts for the registry’s serious adverse-event fields; the record does not list serious adverse-event terms.

For other adverse events, the record lists zero affected among 27 MS subjects at risk and one affected among 30 healthy controls at risk. The event term, severity, timing, relationship to vitamin D3, and outcome are not reported in the registry record. The count alone does not establish whether an event was caused by the supplement.

Deaths are listed as null for both groups. Null is not the same as a reported count of zero, so deaths should be described as not reported in the registry record. The safety entries do not provide detail on how events were collected, their duration of observation, or whether all participants contributed equally to safety follow-up. These limitations matter when interpreting event counts, particularly in a pilot study.

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

The registry record defines a comparison of serum 25-hydroxyvitamin D measurements between people with multiple sclerosis and healthy controls during a 90-day vitamin D3 supplementation plan. It also describes an analysis intended to account for serial measurements within participants. This design and endpoint clarify what the investigators sought to examine: whether the two populations had similar biomarker changes during supplementation.

The record does not report the numerical primary results. It therefore does not show the observed size or direction of the change, the difference between groups, or the precision of that difference. It is not possible from this record to conclude whether the groups had similar responses or whether any difference was small, large, or uncertain. No clinical interpretation of the biomarker comparison should be inferred in the absence of those results.

The comparison also does not estimate the effect of vitamin D3 relative to no supplementation. Both groups were to receive the supplement, and allocation is listed as NA. The group contrast may describe differences between these populations while they follow the same supplementation plan, but it cannot separate supplementation-related change from other changes over time without an untreated or randomized comparison. The registry itself notes that the arms are not a like-for-like control comparison.

General statistical explanation: estimates and confidence intervals are needed to assess both magnitude and precision. A statistically significant result, if one were reported, would not by itself establish clinical importance; conversely, a result that is not statistically significant would not demonstrate equivalence. The registry record does not report a confidence interval, a test result, or an equivalence margin. It consequently does not establish equivalence or non-equivalence between the groups.

The safety entries report no serious adverse events in either group, one other adverse event among healthy controls, and no other adverse events among MS subjects. Death counts are not reported. These limited counts are descriptive and do not establish causality or provide a complete characterization of safety.

14. Why This Trial Matters Statistically

This study raises a useful statistical distinction between a response within groups and a comparison between groups. The investigators’ stated interest was whether people with multiple sclerosis and healthy controls attain a similar increase in serum 25-hydroxyvitamin D during supplementation. Because both populations were assigned vitamin D3, the central comparison is between populations receiving the same plan, not between supplementation and an untreated control. Keeping that distinction clear prevents an observational group contrast from being interpreted as a randomized treatment effect.

The repeated measurement structure also matters. Serum values collected serially from the same participant are not necessarily independent. The registry’s use of GEE and an autoregressive with lag one correlation matrix indicates that within-person dependence was considered in the planned analysis. This is an important feature of the analysis description, although the record does not report enough model detail or numerical output to evaluate the estimates.

The record is also a reminder that a well-described endpoint is not the same as a reported result. The primary measurement, unit, timeframe, and method are specified, but the numerical comparison and its uncertainty are not reported. Without those results, readers cannot assess the magnitude or precision of the biomarker difference. A statistical method cannot compensate for absent outcome estimates in the registry record.

Finally, the pilot purpose and the broader set of immunologic and gene-expression outcomes make clarity about multiplicity and analysis populations especially relevant. The record lists these outcome areas but does not describe how multiple analyses were prioritized, how missing measurements were handled, or which participants entered each analysis. Those gaps limit interpretation and illustrate why outcome reporting should include estimates, uncertainty, and transparent analytic decisions.

15. 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 most direct limitation for interpretation is that numerical primary endpoint results are not reported in the registry record. The mean changes, group contrast, dispersion values, confidence interval, and p-value are absent. Without them, the magnitude, direction, and precision of the comparison cannot be evaluated. The registry also does not provide numerical results for the listed secondary outcomes.

The design limits causal interpretation. Both groups were to receive vitamin D3, allocation is listed as NA, and the registry identifies the study as not being a randomized comparison. Healthy controls therefore are not an untreated or randomized control group. Any difference between the groups could reflect population differences as well as differences in response during supplementation. The design cannot isolate the effect of supplementation relative to no supplementation.

The registry does not report participant characteristics, eligibility details, adherence, actual supplement exposure, or completion of the planned 90-day period. It also does not state how many participants contributed data to the primary analysis. These omissions make it difficult to judge the analyzed population and the applicability of any result.

Important analytic details are not reported, including the model specification beyond the stated GEE correlation structure, covariate adjustment, missing-data handling, multiplicity procedures, and sensitivity analyses. The registry also does not report the trial’s own sample-size justification or details of interim analyses. These limitations are specific to the information available in the registry record and should not be filled in by assumption.

16. Related Tutorials

17. Related Statistical Calculators

18. Sources

• ClinicalTrials.gov: Pharmacokinetics of Vitamin D in Multiple Sclerosis and in Health — NCT01667796.
• Registry record last updated 2019-03-05; status last verified 2019-03.
• Results first posted 2016-02-01.
• 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.

19. Record Summary

NCT01667796 is a completed pilot study of oral vitamin D3 in people with relapsing-remitting multiple sclerosis and healthy controls. The registry records enrollment of 57 and a plan for both groups to receive 5000 IU/day for 90 days. The primary endpoint is change in mean serum 25-hydroxyvitamin D from baseline to 90 days.

The planned comparison uses generalized estimating equations with an autoregressive with lag one correlation matrix for serial measurements. The groups were not randomized as a like-for-like control comparison, and no untreated group is described. Numerical primary and secondary outcome results, analysis-population details, missing-data methods, and multiplicity procedures are not reported in the registry record.

Safety entries list no serious adverse events in either group, one other adverse event among healthy controls, and no other adverse events among MS subjects. Death counts are not reported. These data support a description of the study’s design and reporting, but do not establish the size or precision of the primary biomarker comparison.