Vitamin D in Vulnerable Adults (VIVA-VA): Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Vitamin D in Vulnerable Adults (VIVA-VA) (NCT01170273), a randomized phase 3 study. The primary outcome is Change in Short Physical Performance Battery Test Score.

2. Clinical Question

3. Trial Design

This was a phase 3 randomized trial with a parallel-group design. The registry describes masking as quadruple, meaning it records the trial as having four categories of people masked, but it does not identify those categories or explain the masking procedures. Details about allocation concealment and the randomization process are not reported in the registry record.

The two listed arms were placebo and cholecalciferol 4000 IU daily. The registry reports enrollment of 130. For the primary outcome, the posted group summaries list 56 participants in the placebo arm and 57 in the cholecalciferol arm. The reasons that the primary-outcome group counts differ from the enrollment figure are not reported in the registry record. These counts should not be treated as an explanation of participant flow, since information about exclusions, withdrawals, and outcome availability is not reported.

The trial concerns male veterans age 65 to 95, according to the brief summary. The registry lists frail elderly people and vitamin D deficiency as conditions. It describes the primary outcome timeframe as baseline and 9 months. The start is recorded as 2010-08, primary completion as 2014-06, and study status as completed. The sponsor is the VA Office of Research and Development.

The registry does not report the trial’s original sample-size assumptions, the planned analysis population, the detailed statistical analysis plan, or whether interim analyses were planned or conducted. It lists one primary outcome measure and no posted secondary outcomes. These omissions limit what can be inferred about the protocol and the context for the reported analysis.

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

Reasons for not completing this period:

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 Short Physical Performance Battery Test Score, measured over baseline and 9 months.

The primary endpoint is change in the Short Physical Performance Battery score from baseline to 9 months. The battery assesses lower-extremity function through static balance, gait speed, and getting in and out of a chair. The total score is the sum of the three component scores and ranges from 0 to 12; lower scores reflect more severe limitations, while higher scores reflect fewer limitations. Each component ranges from 0 to 4, with 0 indicating the worse outcome and 4 the best outcome.

A composite measure can provide a single summary of performance across related tasks. The SPPB includes both balance and mobility-related activities, so its total score summarizes performance across the three listed areas rather than reporting each area separately. This is a general explanation of why a composite endpoint may be used; the registry record does not state why this endpoint was selected for this trial.

The posted result is a mean, appropriate to a continuous score, with standard deviation as the reported measure of spread within each group. The registry does not give separate results for balance, gait speed, or chair-rise performance. It also does not report the baseline and 9-month component scores separately, so the endpoint result cannot identify which task contributed most to the group summaries.

7. Results Posted in the Registry

• Cholecalciferol 4000 IU: mean 7.00 versus 7.30 on control; difference -0.30 (95% CI -0.91 to 0.31), standardized effect d = -0.18; z-test p = 0.336.

8. Statistical Interpretation

9. Statistical Methods Explained

The registry reports a continuous primary outcome summarized as a mean, with standard deviation as the measure of spread. The comparison is between the mean change in the placebo arm and the mean change in the cholecalciferol 4000 IU arm. The posted means are 7.3 and 7.0, respectively, and the reported mean difference is -0.3. The registry’s comparison gives a confidence interval from -0.911 to 0.311 and an unadjusted p-value of 0.336.

What does a mean difference describe?

In general, a mean difference expresses how far apart the group averages are, with the direction depending on which group is subtracted from which. For this comparison, the registry identifies cholecalciferol as the comparison arm and placebo as the control. The negative estimate is consistent with the posted group means: the reported mean change is lower in the cholecalciferol group. A mean difference is expressed in the original outcome units, so this estimate is in SPPB score units.

A mean summarizes the central value of a continuous measure, while a standard deviation describes how spread out observations are around that mean. The reported standard deviations are 1.69 for placebo and 1.62 for cholecalciferol. They describe within-group variability, not the precision of the difference estimate. Precision for the difference is reflected by its confidence interval.

What does the confidence interval add?

In general, a confidence interval gives a range of values compatible with the data under the interval’s statistical procedure and assumptions. It communicates uncertainty around an estimate rather than replacing the estimate. The registry’s interval runs from -0.911 to 0.311. Because the range crosses zero, it includes no difference as well as differences in either direction. The confidence level and the procedure used to construct the interval are not reported in the registry record, so they should not be inferred from the displayed limits.

How should the p-value be read?

In general, a p-value evaluates how compatible the observed data are with a specified null model, conditional on the model and analysis assumptions. It is not the probability that the null hypothesis is true, nor does it measure the size or practical importance of an effect. The registry reports an unadjusted p-value of 0.336. The test used to produce it, the model specification, and any covariate adjustment are not reported in the registry record. The p-value should therefore be read as the posted unadjusted result rather than as evidence about an undocumented analysis plan.

What does the standardized effect size mean?

The registry reports a standardized effect size of -0.181 and a pooled standard deviation of 1.655. In general, a standardized effect expresses a group difference in standard-deviation units, which can help describe its scale independently of the outcome’s original units. Its sign indicates the direction of the comparison, while its magnitude is interpreted in relation to the variability in the outcome. The standardized estimate is a rescaling of the observed comparison; it does not remove uncertainty or resolve limitations in the underlying outcome data.

The registry identifies randomization, a parallel model, and quadruple masking. These design features describe the trial structure, but the record does not provide enough detail to determine the specific randomization procedure, masking roles, allocation concealment, or statistical test. It also does not report whether the primary analysis adjusted for baseline SPPB score, how missing outcomes were handled, or which analysis population was used. The estimate can be described as posted, but those unreported details constrain independent assessment of its analytical basis.

In general, random assignment is intended to make treatment groups comparable at the time of assignment, while masking is intended to reduce the influence of knowledge of assignment on trial conduct or assessment. The extent to which those aims were achieved cannot be evaluated from the listed design labels alone. The registry does not report adherence, treatment discontinuation, or other implementation details relevant to understanding the observed outcome contrast.

10. Confidence Intervals and Precision

The reported mean difference is -0.3 SPPB units for cholecalciferol compared with placebo. Its confidence interval ranges from -0.911 to 0.311. The interval includes zero, so the posted data do not rule out no difference in the group means under the interval procedure. The negative values in the interval are compatible with a lower mean change in the cholecalciferol arm; the positive values are compatible with a higher mean change in that arm.

In general, a confidence interval conveys both the direction and precision of an estimate. A narrower interval would indicate less uncertainty about the range of values compatible with the data under the method used. This interval spans values on both sides of zero, and the point estimate should not be read as a precise determination of the direction or size of a group difference. The confidence level and interval method are not reported in the registry record, so the interval should be described using its posted limits without assigning an unreported confidence level.

The unadjusted p-value is 0.336. It is another summary of the comparison under a statistical model, not a measure of the estimate’s precision or of the probability that one treatment is better. The registry does not report the test used or any adjustment for covariates. The posted standard deviations, 1.69 for placebo and 1.62 for cholecalciferol, describe outcome variability within groups; they should not be mistaken for the uncertainty range around the mean difference.

The interval and p-value concern the recorded primary outcome comparison. They do not address uncertainty due to unreported missing-data procedures, analysis-population choices, or the suitability of the statistical assumptions. The record does not include component-level estimates or secondary outcomes that could add context to the precision of the overall SPPB result.

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 are participants per arm, not total events. The registry’s 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 as a stated fraction of the observed effect. These are planning illustrations computed from the observed effect; the trial’s own original design assumptions are not reported in the registry record.

For planning based on 100% of the observed effect, the figures are 478 participants per arm for 80% power and 640 participants per arm for 90% power. For planning based on 75% of the observed effect, they are 850 participants per arm for 80% power and 1,138 participants per arm for 90% power. For planning based on 50% of the observed effect, they are 1,912 participants per arm for 80% power and 2,559 participants per arm for 90% power.

In general, power is the probability that a study would detect an effect of the specified size under the assumed design and analysis conditions if that effect were present. The 80% and 90% columns represent different target probabilities for detecting the planning effect. A smaller target effect requires more participants under the listed assumptions, which is why the figures rise as the assumed fraction of the observed effect decreases. These calculations are not observed power; they are illustrations of planning requirements under stated assumptions, not a retrospective measure of the trial’s success.

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 = -0.300; pooled standard deviation σ = 1.655.
2. n = 2 × (1.96 + 0.842)² × 1.655² / -0.300² = 477.8, rounded up to 478 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 <- -0.3                      # observed difference in means
sigma <- 1.65505477441271                     # 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(1170273)
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 = 478 (80% power), 640 (90% power)
 75% of observed effect: n per arm = 850 (80% power), 1,138 (90% power)
 50% of observed effect: n per arm = 1,912 (80% power), 2,559 (90% power)
power.t.test: 478.7 
Simulated power at n = 478 per arm: 0.804 (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 lists one primary outcome measure, the change in SPPB score, and reports no secondary outcomes. It lists no analysis records. The record therefore does not provide a set of additional posted efficacy results with which to examine whether findings were consistent across multiple outcomes. Whether other outcomes were collected but not posted is not reported in the registry record.

Multiplicity refers, in general, to the increased chance of a false-positive result when multiple hypotheses are tested. Statistical approaches can address that issue, but whether a multiplicity adjustment was planned or used for this trial is not reported in the registry record. The reported p-value is identified as unadjusted. The trial’s full analysis plan and any strategy for selecting or prioritizing outcomes are not reported.

The registry does not report how missing primary-outcome values were handled, whether imputation was used, or how participants with incomplete follow-up were treated. It does not provide an analysis population description, such as whether the primary analysis included all randomized participants or a subset. The posted primary-outcome group summaries list 56 participants for placebo and 57 for cholecalciferol, while registry enrollment is 130. The participant flow and reasons for the difference between these counts are not reported in the registry record.

In general, missing-data procedures and analysis-population definitions can affect the interpretation of a group comparison, particularly when outcome availability differs from enrollment. Without those details, it is not possible to determine from the registry record whether the posted estimates reflect a particular intention-to-treat, per-protocol, or other analysis population. Such labels should not be assigned to the reported result without documentation.

Interim analyses, stopping rules, baseline adjustment, and other model choices are also not reported in the registry record. Their absence from the record does not establish whether they were or were not part of the trial’s conduct. It means that these aspects cannot be evaluated from the posted information.

14. 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 serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: cancer (1.6%), pneumonia (1.6%), pulmonary edema (1.6%), prostate cancer (1.6%), lung cancer (1.6%).

The registry reports serious adverse events for groups described as at risk: 5 serious events among 64 at risk in the placebo group and 2 among 66 at risk in the cholecalciferol group. For other adverse events, it reports 12 among 64 at risk in the placebo group and 11 among 66 at risk in the cholecalciferol group. These are counts and denominators as recorded; the registry does not explain the event definitions, collection procedures, or whether the counts represent participants with events or event occurrences.

The listed serious-event terms include cancer, pneumonia, pulmonary edema, prostate cancer, and lung cancer, each reported as 1.6%, and renal mass, reported as 1.5%. The registry does not give enough detail in this record to attribute these terms to a particular arm or to clarify possible overlap among terms. Death counts are not reported in the registry record.

Adverse-event figures describe events recorded during the trial and should not be interpreted on their own as proof that an intervention caused or prevented an event. The record does not report details about event severity beyond the serious-event classification, timing, relatedness assessment, or statistical comparison of adverse events. These limitations matter when interpreting safety counts.

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

The result describes the mean change in SPPB score reported for the two trial groups at the stated baseline-to-9-month timeframe. The placebo mean change is 7.3, and the cholecalciferol 4000 IU mean change is 7.0. The reported mean difference is -0.3, with a confidence interval from -0.911 to 0.311 and an unadjusted p-value of 0.336.

Because the interval includes zero and values on both sides of zero, the posted estimate does not precisely determine the direction or size of a difference between group means. It does not demonstrate equivalence, and it does not establish that there was no difference. A non-significant result, considered by itself, is not evidence that two groups are identical. The interval gives a more informative sense of uncertainty than the point estimate alone, while still depending on the unreported interval method and its assumptions.

The endpoint is a composite measure of balance, gait speed, and chair-rise performance. The overall score cannot show whether any one component changed differently between groups. The record does not report component-specific results, additional primary-outcome timepoints, or secondary outcomes. It also does not report how missing values or the analysis population were handled, which limits assessment of the result’s analytical context.

The result applies to the posted comparison in this randomized trial of male veterans age 65 to 95 and to the recorded 9-month endpoint. The registry does not provide evidence about longer-term outcomes or populations not described in the trial summary. It does not support a treatment recommendation or a conclusion about outcomes beyond the measures and timeframe recorded.

In general, trial results are interpreted by considering the estimated effect, its uncertainty, the outcome’s meaning, and the design and analysis details. The posted point estimate alone is not a complete account of those considerations. The registry record supports describing the observed group summaries and their uncertainty, while leaving several design and analysis details unresolved.

16. Why This Trial Matters Statistically

This trial is statistically notable because it reports a continuous functional outcome as a group mean change, alongside the variation within each group and an estimated between-group difference. These quantities answer different questions: the means describe the group summaries, the standard deviations describe within-group spread, and the confidence interval describes uncertainty around the estimated contrast.

The SPPB combines balance, gait speed, and chair-rise performance into a single score. A composite can make a complex functional construct easier to summarize, but its overall result does not identify which component is responsible for a difference or for variation in the total score. Since the registry does not report component-specific results, interpretation must remain at the level of the total SPPB score.

The confidence interval spans zero and values in both directions. This illustrates why a point estimate should not be interpreted without considering precision: the estimate is -0.3, but the posted interval includes a range of plausible directions under its statistical procedure. The record does not report the confidence level or interval method, which is a further reason to avoid overinterpreting the displayed limits.

The planning illustrations also show how required sample sizes depend on the effect selected for planning. Under the recorded assumptions, planning around a smaller fraction of the observed effect yields larger participant requirements per arm. These illustrations are distinct from the trial’s original design rationale, which is not reported in the registry record, and do not indicate the trial’s observed power.

Finally, the record’s limited analysis details are relevant to statistical interpretation. Missing-data handling, analysis populations, multiplicity procedures, and the model used for the primary comparison are not reported. Recognizing these gaps helps distinguish what the posted estimate says from what cannot be established from the registry record.

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 describes the population as male veterans age 65 to 95, so the result should not be assumed to represent other populations. The trial summary refers to sedentary people and the registry lists frail elderly people and vitamin D deficiency, but detailed eligibility criteria and baseline vitamin D status are not reported. The extent to which participants had these characteristics is therefore not clear from the record.

The primary outcome is a composite SPPB score. Separate results for balance, gait speed, and chair-rise performance are not reported, nor are baseline and follow-up component scores. The posted result therefore cannot show whether the overall score reflects similar patterns across all three tasks. Results at timepoints beyond baseline and 9 months are not reported.

The registry reports enrollment of 130, while the primary-outcome summaries list 56 participants in the placebo arm and 57 in the cholecalciferol arm. Participant flow and reasons for the differing counts are not reported in the registry record. Follow-up completeness, withdrawals, missing values, and their handling are also not reported. The analysis population and baseline-adjustment approach are not reported.

Further trial details that could aid interpretation are absent from the record, including adherence information, treatment discontinuation, the randomization procedure, the roles covered by quadruple masking, and the full statistical analysis plan. Secondary outcomes are not posted, and no analysis records are listed. The registry also does not report longer-term outcomes or details needed to assess the clinical meaning of changes in the composite score beyond its stated scale.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Vitamin D in Vulnerable Adults (VIVA-VA) — NCT01170273.
• Registry record last updated 2016-12-21; status last verified 2016-10.
• Results first posted 2016-12-21.
• 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

Vitamin D in Vulnerable Adults (VIVA-VA), NCT01170273, is recorded as a completed phase 3 randomized, quadruple-masked, parallel trial sponsored by the VA Office of Research and Development. The registry reports enrollment of 130 and a study start of 2010-08, with primary completion in 2014-06. The study concerned male veterans age 65 to 95 and compared cholecalciferol 4000 IU daily with a placebo capsule.

The primary endpoint was change in Short Physical Performance Battery score from baseline to 9 months. The posted mean changes are 7.3 for placebo and 7.0 for cholecalciferol, with a reported mean difference of -0.3 and a confidence interval from -0.911 to 0.311. The unadjusted p-value is 0.336. The registry lists no posted secondary outcomes and no analysis records. Important details about missing data and the primary analysis are not reported in the registry record.