Monocentric Randomized Study, Assessing the Interests of the Determination of Vitamin D in Prison Population. (Vitamine D): Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Monocentric Randomized Study, Assessing the Interests of the Determination of Vitamin D in Prison Population. (Vitamine D) (NCT02044133), a randomized na study. The primary outcome is Dosage of Vitamin D.

2. Clinical Question

The study description frames the question as whether measuring vitamin D belongs in the biological assessment at prison entry. The randomized comparison therefore concerns two schedules for measuring vitamin D. The recorded primary endpoint is the vitamin D level at six months; it is not described as a change from entry, and the registry does not report a primary comparison of entry levels.

The reported arm means at six months were 28.2 ng/mL in the arm measured at entry and six months, and 14.6 ng/mL in the arm measured only at six months. The unadjusted mean difference is reported as -13.6 for the latter arm relative to the former. These results describe the posted endpoint comparison; they do not by themselves explain why the arm means differed or establish the value of entry testing for other settings.

3. Trial Design

The registry describes a randomized, parallel-group study with no masking. Its title calls it monocentric. The listed sponsor is Centre Hospitalier Departemental Vendee. The study was marked completed, with enrollment listed as 54. The registry records the start as 2014-01 and primary completion as 2016-01.

Participants were assigned to one of two measurement schedules. In one arm, vitamin D was measured at entry to prison and six months after entry. In the other arm, measurement took place six months after entry only. Both arms therefore had a planned six-month measurement according to the arm descriptions, while the entry measurement distinguished the schedules. The intervention is classified as “other” and named “Dosage Vitamine D”; the record describes measurement rather than a vitamin D treatment.

The primary outcome was the mean vitamin D level at six months, measured in ng/mL. The listed analysis population is ITT analyse. The registry reports arm-level means and standard deviations, with 26.0 participants listed for the entry-and-six-month arm and 28.0 for the six-month-only arm. It also lists one primary outcome measure and one reported analysis.

The registry does not report the method used to generate the random sequence, allocation concealment, specific eligibility criteria, or the trial's original sample-size assumptions. It also does not report whether participants or staff knew the assigned measurement schedule beyond the stated absence of masking. These omissions limit what can be said about implementation and safeguards against bias from the record alone.

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:

Analysis population for the primary outcome, as defined in the registry: ITT analyse

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 Dosage of Vitamin D, measured over 6 month.

The primary endpoint is vitamin D level at six months, expressed in ng/mL. It is a continuous measurement, and the registry describes the summary measure as a mean with standard deviation. The endpoint is intended to describe the vitamin D level observed at the common six-month time point under the two measurement schedules.

For a continuous endpoint, a mean conveys the central level across the observations included in an arm, while a standard deviation describes how dispersed those observations are around the mean. These summaries allow the arm averages and their uncertainty to be compared. The posted means are 28.2 in the arm with measurements at entry and six months, and 14.6 in the arm with measurement at six months only. The corresponding standard deviations are 8.6 and 9.8.

The registry's study description asks about the interest of including vitamin D measurement in the biological assessment at prison entry. However, the primary endpoint specified in the record is the six-month level, rather than a change in level from entry or a direct measure of the consequences of testing. The record does not describe a threshold-based endpoint, a clinical outcome, or a decision outcome. Thus, this endpoint answers a comparison about six-month measured levels; it does not alone quantify the broader usefulness of entry testing.

The record does not explain why this particular endpoint and time point were selected, or report a clinically meaningful difference. Those rationales are not reported in the registry record.

7. Results Posted in the Registry

• Dosage of Vitamine D 6 Month: mean 14.60 versus 28.20 on control; difference -13.60 (95% CI -18.51 to -8.69), standardized effect d = -1.47; z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary measure is continuous: vitamin D level in ng/mL. The registry identifies the summary parameter as a mean and the measure of spread as a standard deviation. The means describe the center of the observed levels in each arm; the standard deviations describe variation among those levels. In general, a standard deviation is not the same as a standard error: the former describes participant-level spread, while the latter describes uncertainty in an estimated mean.

What does the mean difference represent?

The posted comparison uses the arm with measurement at entry and six months as the reference, and reports the six-month-only arm relative to it. The mean difference is -13.6, with a 95% confidence interval from -18.51 to -8.69. This is an unadjusted comparison derived from the posted summary statistics. “Unadjusted” means the estimate is not reported as controlling for other variables. The record does not report an adjusted analysis of the continuous endpoint.

The sign depends on the order of subtraction. With the six-month-only arm compared against the entry-and-six-month arm, a negative estimate means the former arm's mean was lower. The arm means are 14.6 and 28.2, respectively. The reported estimate and its interval should be interpreted in that stated direction, rather than as a difference in the opposite order.

How should the confidence interval be understood?

In general, a confidence interval expresses statistical uncertainty around an estimate. A 95% confidence interval is produced by a procedure designed to cover the underlying parameter in 95% of repeated samples when its assumptions hold. It is not a range containing 95% of individual participants' measurements, and it does not assign a 95% probability to the fixed parameter being within this particular interval.

For this result, the interval extends from -18.51 to -8.69. The whole interval is on the negative side of zero, so the interval is consistent with a lower mean in the six-month-only arm under the specified direction of comparison. Its width communicates uncertainty around the estimated difference, while the standard deviations communicate spread in the individual measurements. These are different kinds of information.

What does the p-value say?

The posted summary-statistics comparison gives p <0.001. In general, a p-value describes how incompatible the observed data, or data more extreme, would be with a specified null hypothesis under the analysis assumptions. It is not the probability that the null hypothesis is true, and it does not measure the size or clinical importance of a difference. The registry does not describe the null hypothesis or provide the full details of the recalculation procedure beyond the comparison and summary statistics.

The sponsor's reported analysis is separately listed as Chi-squared, with p <0.001, and classified as a superiority analysis. The registry does not report a test statistic, degrees of freedom, confidence interval, or a detailed explanation of how that analysis was applied to the continuous vitamin D endpoint. A Chi-squared test and a mean-difference analysis are not interchangeable descriptions. The similar reported p-value threshold does not supply the missing methodological detail.

Why do distributional assumptions matter?

In general, methods for comparing means use assumptions about the sampling distribution of the estimated difference. Normal-based methods can be useful for continuous outcomes, but their performance depends on factors such as the outcome distribution and the adequacy of the approximation. The registry record does not report diagnostic checks, a distributional assessment, or a detailed statistical analysis plan. No conclusion about whether those checks were performed can be drawn from their absence in the record.

Over-dispersion is a general concern when observed variability is greater than a model allows. A model that understates variability can produce confidence intervals that are too narrow and p-values that are too small. The posted standard deviations, 8.6 and 9.8, describe observed spread, but do not by themselves establish whether a particular model was adequate. The registry does not report an over-dispersion assessment, so this remains a general methodological consideration rather than a documented issue in this study.

How does randomization relate to the comparison?

In general, random assignment aims to make treatment or strategy groups comparable in expectation, reducing systematic differences in baseline characteristics. It does not guarantee that every characteristic is balanced in a particular trial, and it does not eliminate missing data, measurement problems, or departures from the assigned strategy. Here, the registry identifies the study as randomized but does not report the sequence-generation procedure, concealment method, or baseline characteristics. The extent to which allocation was implemented as intended is therefore not assessable from this record.

The primary outcome population is named as ITT analyse. In general, an intention-to-treat approach analyzes participants according to randomized assignment, regardless of adherence, but the label alone does not establish exactly how this study handled participants without endpoint measurements. The record does not explain missing-data methods, exclusions, or the analysis population's operational definition.

The posted recalculation is a simple unadjusted comparison of the arm summary statistics. It helps express the observed contrast in the original units and quantify uncertainty, but it does not replace a fully documented prespecified analysis. The record does not report whether the sponsor's analysis was prespecified, whether interim analyses occurred, or what statistical plan was used. Those matters are not reported in the registry record.

10. Confidence Intervals and Precision

The estimated mean difference is -13.6 ng/mL for the six-month-only arm relative to the arm measured at entry and six months. Its 95% confidence interval ranges from -18.51 to -8.69 ng/mL. The interval quantifies uncertainty in the estimated difference, subject to the assumptions of the analysis. It does not describe the range of vitamin D levels among participants.

Because the interval does not include zero, the posted summary-statistics comparison is consistent with a difference in means in the direction observed. The interval's endpoints are both negative, so the compatible differences under this calculation favor a lower mean in the six-month-only arm. That statistical pattern should be separated from the question of whether the magnitude is meaningful for clinical decisions. The registry does not report a clinically important threshold or link the result to a clinical outcome.

The standard deviations, 8.6 and 9.8 ng/mL, describe variability within the two arms. They are not confidence intervals and should not be read as uncertainty about the difference. The registry gives standard errors of 1.687 and 1.852 for the arm means, but does not provide confidence intervals for each separate mean.

Precision depends on the observed variability, the amount of information available, and the analysis assumptions. The record does not report missing-data handling or diagnostics that would allow a fuller assessment of uncertainty. The stated interval is therefore useful for interpreting the posted unadjusted comparison, while not resolving limitations in the reporting or establishing how well the result would generalize beyond this study.

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. They are illustrations based on the observed effect, not the trial's original design assumptions; those original assumptions are not reported in the registry record. The stated planning method uses a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. It considers effects expressed as a stated fraction of the observed effect.

For planning at 100% of the observed effect, the illustration lists 8 participants per arm for 80% power and 10 participants per arm for 90% power. At 75% of the observed effect, it lists 13 participants per arm for 80% power and 18 participants per arm for 90% power. At 50% of the observed effect, it lists 30 participants per arm for 80% power and 39 participants per arm for 90% power.

In plain language, a power target describes the probability that a planned study would detect an effect of the specified size under the planning assumptions if that effect were truly present. The 80% column gives the per-arm sample size associated with an 80% target, and the 90% column gives the per-arm size associated with a 90% target. A higher target generally calls for more participants under otherwise comparable assumptions. Smaller effects also require more participants to detect, which is why the entries increase as the assumed fraction of the observed effect decreases.

These figures are planning illustrations, not observed power for this completed study. They depend on using the observed result as the basis for the effect sizes and should not be treated as the study's original sample-size justification.

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 = -13.600; pooled standard deviation σ = 9.243.
2. n = 2 × (1.96 + 0.842)² × 9.243² / -13.600² = 7.3, rounded up to 8 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 <- -13.6                      # observed difference in means
sigma <- 9.2425437723938                     # 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(2044133)
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 = 8 (80% power), 10 (90% power)
 75% of observed effect: n per arm = 13 (80% power), 18 (90% power)
 50% of observed effect: n per arm = 30 (80% power), 39 (90% power)
power.t.test: 8.3 
Simulated power at n = 8 per arm: 0.778 (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. Analyses Reported by the Sponsor

The sponsor-reported analysis lists a Chi-squared method, a superiority analysis, and p <0.001. The registry does not report its test statistic, confidence interval, or enough detail to establish exactly how the Chi-squared method was applied to the continuous endpoint of vitamin D level.

The separate unadjusted recalculation uses the posted group means and standard deviations to report a mean difference of -13.6, with a 95% confidence interval from -18.51 to -8.69 and p <0.001. This expresses the contrast directly in ng/mL and gives an interval for its precision. It is not the same method description as the sponsor's reported Chi-squared analysis.

The registry does not flag a discrepancy between the sponsor result and the recalculation. The sponsor's own analysis remains the primary reported analysis; the recalculation is a supplementary interpretation of the posted summaries, not a replacement for the sponsor analysis. Both results report p-values below 0.001, but the record does not provide enough detail to compare their assumptions or infer that they are statistically equivalent. No claim about prespecification can be made because the statistical plan is not reported in the registry record.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists one primary outcome measure and one reported analysis, and no secondary outcomes are posted. It does not report a multiplicity adjustment or explain whether multiple comparisons were planned. With no posted secondary results, the record does not support an assessment of a broader family of outcome tests or of how such tests may have been handled.

The primary population is described as ITT analyse. That label indicates the stated analysis population, but the registry does not define its implementation. It does not report how participants with missing six-month vitamin D measurements were handled, whether all randomized participants were included in the endpoint analysis, or whether any participants were excluded from the analysis. The outcome summaries list 26.0 and 28.0 participants in the two arms, but the record does not provide a participant-flow account or explain the relationship between those figures and the enrollment listing.

Missing outcome data can affect both the estimated group means and the uncertainty around a comparison. In general, the implications depend on how much data are missing, why they are missing, and what assumptions are used in analysis. Those details are not reported in the registry record, so the direction or magnitude of any possible missing-data effect cannot be assessed.

The record also does not report an imputation method, sensitivity analysis, per-protocol analysis, or other analysis populations. It does not report whether interim analyses were conducted, whether stopping rules existed, or the statistical plan's approach to multiplicity. These omissions do not show that such procedures were absent; they mean they cannot be characterized from the registry record.

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 0% reporting threshold.

The adverse-event record lists zero serious adverse events in the arm measured at entry and six months, among 26 participants at risk, and zero in the six-month-only arm, among 28 participants at risk. Thus, the registry reports no serious adverse events in either listed arm during the recorded period.

These figures describe the entries in the registry, not proof that no adverse events occurred outside the recorded definition or observation period. The registry does not provide the observation window, event-collection procedures, or details about how serious events were defined. Death counts are not reported. The record also lists zero other adverse events in each arm, but the absence of event details limits interpretation of that entry.

Zero recorded serious events cannot establish equivalent safety between schedules, particularly without a reported analysis, confidence interval, or further follow-up information. The study compares measurement schedules rather than a vitamin D treatment, and the safety figures should not be interpreted as evidence about supplementation. They are a report of the recorded serious-event counts for the two study arms.

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

The result shows that the six-month mean vitamin D level differed between the two randomized measurement-schedule arms in the posted analysis. The mean was 28.2 ng/mL in the arm measured at entry and six months, and 14.6 ng/mL in the arm measured at six months only. The reported difference for the latter arm relative to the former is -13.6, with a 95% confidence interval from -18.51 to -8.69 and p <0.001.

This is a comparison of observed levels at six months under the assigned measurement schedules. It is not a comparison of vitamin D supplementation with no supplementation: no supplementation intervention is described in the registry. Nor is the endpoint reported as a within-person change from entry. The record's description focuses on whether entry testing belongs in the biological assessment, while its primary endpoint is the six-month level.

The result does not by itself establish why the observed levels differed. Randomization concerns assignment to a measurement strategy, but the record does not report detailed information about care, implementation, adherence, missing measurements, or potential influences on levels. It also does not report a clinical outcome, decision consequence, or threshold that would indicate the practical importance of the difference.

The confidence interval supports a statistically clear difference under the posted unadjusted calculation, but statistical evidence of a difference is not the same as evidence that the difference is clinically important. The record does not report results for other populations, other settings, or other time points. Conclusions should therefore remain limited to the reported six-month comparison in this study of men entering the prison of La Roche sur Yon.

17. Why This Trial Matters Statistically

This trial illustrates a distinction between a study's motivating question and its measured primary endpoint. The registry describes an interest in vitamin D measurement as part of entry assessment, but the primary outcome is vitamin D level at six months. That endpoint compares levels at a common follow-up time; it does not directly measure whether entry testing changes clinical decisions or improves health outcomes.

The randomized design offers a framework for comparing measurement schedules, while the absence of masking and the limited reporting of allocation procedures leave important design details unclear. The record identifies the study as randomized and parallel, yet does not report sequence generation, allocation concealment, baseline characteristics, or the full analysis plan. Statistical interpretation depends not only on the result, but also on knowing how assignment and analysis were carried out.

The reported mean difference and confidence interval demonstrate why effect size and precision complement a p-value. The p-value is below 0.001, while the interval expresses the range of differences compatible with the unadjusted calculation. Neither statistic tells readers whether a difference is clinically consequential; that requires context the registry does not report.

The contrast between the sponsor's Chi-squared analysis and the recalculated mean difference also highlights the value of transparent statistical reporting. A test name and p-value alone do not explain the estimated effect, its uncertainty, or the assumptions used. Reporting an effect on the endpoint's original scale makes the comparison easier to interpret, while full methodological details are necessary to evaluate robustness.

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.

The registry record leaves several trial-specific limitations unresolved. It describes a population of men entering the prison of La Roche sur Yon, but does not report detailed eligibility criteria, baseline characteristics, or information that would show how representative the enrolled participants were. The setting and population are narrow, so applicability to other groups or settings cannot be assessed from this record.

The entry-and-six-month arm had two scheduled measurements, while the comparator had a measurement at six months only. The primary endpoint is the six-month level, not a change from entry. The record does not describe additional outcomes that would show whether entry measurement affected clinical decisions or subsequent care. It also does not report other factors that might help explain the observed difference between arm means.

Important operational and analysis details are missing. The record does not report the randomization sequence or concealment procedure, the handling of missing measurements, adherence to assigned schedules, or a detailed statistical plan. Although the primary analysis population is named as ITT analyse, the record does not define how that population was formed. The sponsor's analysis is listed as Chi-squared without a test statistic or further explanation.

The enrollment listing and endpoint arm counts do not come with a flow account explaining whether measurements were unavailable or participants were excluded. The registry does not report a clinically meaningful threshold for the endpoint, or a rationale for the sample size used in the original study. These limitations restrict evaluation of bias, precision, clinical meaning, and generalizability; they do not establish that any particular problem occurred.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Monocentric Randomized Study, Assessing the Interests of the Determination of Vitamin D in Prison Population. (Vitamine D) — NCT02044133.
• Registry record last updated 2025-09-12; status last verified 2025-08.
• Results first posted 2025-09-12.
• 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

NCT02044133 is a completed randomized, parallel-group study that the title describes as monocentric. It compared vitamin D measurement at prison entry and six months with measurement at six months only among men entering the prison of La Roche sur Yon. The registry lists enrollment as 54 and identifies the sponsor as Centre Hospitalier Departemental Vendee.

The primary endpoint was mean vitamin D level in ng/mL at six months in the ITT analyse population. The posted means were 28.2 and 14.6, with a reported unadjusted mean difference of -13.6 for the six-month-only arm relative to the entry-and-six-month arm. The 95% confidence interval was -18.51 to -8.69, and the p-value was <0.001.

The sponsor analysis is listed as Chi-squared with p <0.001. The registry reports zero serious adverse events in each arm. Missing-data handling, the original sample-size rationale, and detailed statistical methods are not reported in the registry record.