Effect of Vitamin D on the Honeymoon Period in Children and Adolescents With Type 1 Diabetes: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Effect of Vitamin D on the Honeymoon Period in Children and Adolescents With Type 1 Diabetes (NCT01724190), a randomized na study. The primary outcome is IDAA1c.

2. Clinical Question

The registry’s stated purpose was to determine whether vitamin D supplementation increases the number of children and adolescents who enter the honeymoon period after a new diagnosis of type 1 diabetes. The primary outcome operationalizes that question as a participant count at a specified disease duration. The posted results report 5 participants meeting the outcome in the vitamin D arm and 2 in the placebo arm, with arm sizes of 15 and 14, respectively.

This is a comparison of outcome counts and proportions at a single stated time point, not a time-to-event analysis of when remission began or how long it lasted. The registry does not report an outcome definition based on remission duration, nor does it post secondary outcome results. The observed counts can describe what happened among the participants represented in the posted arm results, but they do not by themselves establish what would happen in other patients or under different treatment schedules.

3. Trial Design

The registry describes a randomized, triple-masked, parallel-group trial comparing vitamin D with placebo. It lists Nationwide Children's Hospital as the sponsor and the study status as completed. The phase is recorded as not applicable. Enrollment is listed as 38. The start date is 2012-11, and primary completion is listed as 2014-06.

Participants were assigned to one of two arms. The vitamin D arm is described as receiving oral vitamin D supplementation at 3000 IU daily for 9 months. The placebo arm is described as receiving a placebo solution daily for 9 months. The registry records the masking as triple, but the particular parties masked and the procedures used to maintain masking are not reported in the registry record. Allocation is recorded as randomized; details of sequence generation, concealment, and the allocation ratio are not reported in the registry record.

The primary outcome is a binary participant count: whether each participant met the registry’s partial clinical remission criterion. The outcome timeframe is 9 months of disease duration. The posted results list 15 participants in the vitamin D arm, including 5 meeting the outcome, and 14 in the placebo arm, including 2 meeting it. These outcome arm counts are the counts attached to the posted result and should not be treated as a complete accounting of every enrolled participant without further information. The reasons for the difference between total enrollment and the posted arm counts are not reported in the registry record.

The registry record does not report the trial’s original sample-size justification, its planned statistical analysis, or an analysis population definition. It lists no secondary outcome results and no analyses. The completed status and the posted primary outcome counts describe the record’s available trial information, but do not supply missing protocol or conduct details.

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 IDAA1c, measured over 9 months disease duration.

The primary endpoint is the count of participants who met the partial clinical remission definition at 9 months of disease duration. The registry says remission was assessed using insulin dose adjusted hemoglobin A1c, abbreviated IDAA1c, calculated from HbA1c percentage and daily insulin dose per kilogram. The stated criterion is IDAA1c <9. The endpoint is therefore binary for each participant: the participant either meets that criterion or does not.

This measure combines glycemic status, represented by HbA1c, with insulin requirement. In general, an outcome that uses both a clinical laboratory measure and treatment intensity can describe a defined clinical state more specifically than either component alone. That general rationale does not establish how well the measure performs in this trial or whether the criterion captures every aspect of remission; such validation information is not reported in the registry record.

Reporting a participant count makes the endpoint interpretable as the number meeting the same threshold in each arm. It does not show the distribution of IDAA1c values, how close individual participants were to the threshold, or how the outcome changed during the 9-month period. Those details are not reported in the registry record. The posted results identify 5 participants in the vitamin D arm and 2 in the placebo arm as meeting the criterion. No separate continuous IDAA1c result is posted.

7. Results Posted in the Registry

• Vitamin D: 33.3% (5/15) versus 14.3% (2/14) on control; risk difference 19.0 percentage points (95% CI -11.0 to 49.1), risk ratio 2.33 (0.54–10.14); unadjusted two-proportion z-test p = 0.231.

8. Statistical Interpretation

9. Statistical Methods Explained

The posted outcome is binary: each participant is classified according to whether IDAA1c is below the remission threshold at 9 months of disease duration. For a binary endpoint, the basic arm-level summaries are the number meeting the criterion and the number represented in the arm. The registry reports 5 of 15 in the vitamin D arm and 2 of 14 in the placebo arm. The comparison also reports an unadjusted risk difference and its confidence interval, as well as an unadjusted p-value.

What does a risk difference describe?

In general, a risk difference subtracts the outcome proportion in one group from the outcome proportion in another. Its scale is the difference in proportions, not a ratio. Here, the comparison is framed as vitamin D relative to placebo, and the reported estimate is positive, matching the higher observed remission proportion in the vitamin D arm. A risk difference of zero would represent equal outcome proportions; values above or below zero represent contrasts in opposite directions. This explanation is general, while the trial-specific count and direction come from the posted results.

What does the unadjusted label mean?

In general, an unadjusted comparison uses the observed arm data without accounting for additional covariates in a regression or other adjusted model. That can make the estimate straightforward to interpret, but it does not control for chance imbalances in participant characteristics. The registry comparison is labeled unadjusted. Whether any adjusted analyses were conducted outside the posted registry results is not reported in the registry record. The record also does not specify the exact test used to produce the p-value or the interval construction method, so those details should not be inferred.

How should the p-value be read?

In general, a p-value is calculated under a statistical model that assumes a null hypothesis, commonly no difference between the groups. It measures how incompatible the observed data are with that model, given the test’s assumptions. It is not the probability that the null is true, the chance that the result occurred by chance, or a measure of clinical importance. The posted unadjusted p-value is 0.231. The registry does not report whether the analysis was prespecified or whether other analyses were performed.

Why are counts and proportions both useful?

Counts make clear how many participants met the endpoint, while proportions account for the number represented in each arm. The two arm counts are not identical in size, so counts alone do not describe the contrast on a common scale. A risk difference puts the arm proportions on an absolute scale. General statistical interpretation still depends on the quality and completeness of the outcome data. The record does not report an account of missing outcomes, exclusions, or participant flow by arm.

What can randomization contribute?

In general, random assignment aims to make groups comparable with respect to both measured and unmeasured participant characteristics, on average. In a small trial, chance imbalances can remain, and the posted outcome comparison can be imprecise. The registry lists the allocation as randomized but does not describe the sequence-generation or concealment methods. Randomization is a design feature; it does not remove uncertainty in the estimate or resolve missing information about who contributed to the posted results.

The registry’s statistical analysis plan, model specifications, prespecified contrasts, and handling of missing data are not reported in the registry record. The posted comparison can be described as unadjusted, but a fuller assessment of analysis choices and their alignment with the original plan is not possible from this record alone.

10. Confidence Intervals and Precision

The confidence interval for the reported risk difference extends from -0.110 to 0.491. It spans zero, so the data are compatible with no difference as well as with contrasts in either direction. The range is broad relative to the observed comparison, indicating limited precision. The estimate should not be read as an exact effect: the interval emphasizes that the data do not identify one narrow value with confidence.

In general, a confidence interval is a range generated by a statistical procedure that, under its assumptions and across repeated studies, would contain the target quantity at the stated confidence level at the corresponding long-run frequency. The confidence level itself is not reported in the registry record, so it should not be inferred from the interval alone. A confidence interval is not a range containing a specified proportion of individual participants, and it is not a statement that the true effect has a particular probability of lying within this one calculated interval.

The limited number of posted outcomes is important to precision. The registry reports 5 participants meeting the endpoint in the vitamin D arm and 2 in the placebo arm. With relatively few outcome events, small changes in the observed counts can substantially affect an estimated contrast. The posted interval reflects uncertainty in the comparison, while the registry does not report additional model-based adjustments that might change the estimate or its precision.

The interval should be considered alongside the point estimate and the unadjusted p-value of 0.231. The p-value does not replace the interval: it does not show the range of effect sizes compatible with the data. Nor does an interval that crosses zero prove that there is no difference. Taken together, the reported statistics show an observed contrast but leave substantial uncertainty about its magnitude and direction. The interval construction method and confidence level are not reported in the registry record.

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 illustrations based on the observed effect, not the trial’s original design calculation. They are expressed as participants per arm for 80% power and participants per arm for 90% power. The assumptions listed for the illustration are a two-sided significance level of 0.05, equal allocation between the two arms, a normal approximation, and an effect to detect set to the stated fraction of the observed effect. These are planning assumptions for the illustration; the trial’s own original design assumptions are not reported in the registry record.

For planning an effect equal to 100% of the observed effect, the figures are 78 participants per arm for 80% power and 103 participants per arm for 90% power. For planning an effect equal to 75% of the observed effect, the figures are 129 participants per arm for 80% power and 172 participants per arm for 90% power. For planning an effect equal to 50% of the observed effect, the figures are 266 participants per arm for 80% power and 356 participants per arm for 90% power.

In general, power is the probability that a specified statistical procedure will reject its null hypothesis when a particular effect is true, under the planning assumptions. The 80% and 90% columns describe two different target probabilities for a future study, not outcomes observed in this trial. The figures indicate the planned participants needed in each arm under the stated assumptions. Smaller effects require more participants to detect with the same target power, as reflected by the increasing planning figures for smaller fractions of the observed effect. These values are not observed power.

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, p₀ and p₁ are the control and treatment proportions, and p̄ is their average.

Worked calculation for this trial

1. Control proportion p₀ = 0.143; treatment proportion p₁ = 0.333; average p̄ = 0.238.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6023 = 1.1806.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.5871 = 0.4941.
4. n = (1.1806 + 0.4941)² / (0.1905)² = 77.3, rounded up to 78 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
p0 <- 0.142857142857143                          # control proportion
p1 <- 0.333333333333333                          # treatment proportion
n_per_arm <- function(power, frac = 1) {
  q1 <- p0 + (p1 - p0) * frac               # smaller effect = fraction of the observed difference
  pbar <- (p0 + q1) / 2
  z_b <- qnorm(power)
  ceiling(round((z_a * sqrt(2 * pbar * (1 - pbar)) + z_b * sqrt(p0 * (1 - p0) + q1 * (1 - q1)))^2 / (q1 - p0)^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 (unrounded n per arm)
cat("power.prop.test:", round(power.prop.test(p1 = p0, p2 = p1, power = 0.80)$n, 1), "\n")

# Simulation: how often does the z-test reject at the 80%-power sample size?
set.seed(1724190)
n    <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z  <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))

Output from running the code

100% of observed effect: n per arm = 78 (80% power), 103 (90% power)
 75% of observed effect: n per arm = 129 (80% power), 172 (90% power)
 50% of observed effect: n per arm = 266 (80% power), 356 (90% power)
power.prop.test: 77.3 
Simulated power at n = 78 per arm: 0.814 (20000 replicates)

The simulation draws many pairs of event counts at the planned sample size and counts how often the two-proportion z-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 and no secondary outcome results. It reports one posted primary comparison, described as unadjusted. The number of analyses is recorded as zero, despite the presence of outcome counts and a comparison in the results record. The registry does not explain this entry, so it is not possible to determine whether other analyses were conducted or how the posted comparison relates to a prespecified analysis plan.

Multiplicity concerns arise in general when investigators test multiple outcomes, time points, subgroups, or alternative models. If many comparisons are considered, the chance of at least one apparently unusual result can increase unless the analysis plan addresses that possibility. The registry record does not report a multiplicity adjustment, a hierarchy of outcomes, or a plan for managing multiple tests. With only one primary outcome listed, the record does not establish whether other planned comparisons existed.

The posted arm counts are 15 in the vitamin D group and 14 in the placebo group, while total enrollment is listed as 38. The registry record does not explain how participants not represented in the posted arm counts were handled. It does not report the number with missing endpoint data, reasons for missingness, or an imputation or sensitivity-analysis procedure. The analysis population is also not reported in the registry record. It is therefore not possible to determine whether the result reflects all randomized participants, participants who completed treatment, or another set of participants.

In general, missing data can affect both the estimate and its uncertainty, especially if the chance of having an observed outcome is related to treatment assignment or participant status. The direction and size of any such effect depend on the missingness pattern and the analysis approach. Neither is documented in the registry record. The posted comparison can be interpreted as a result for the participants represented by the arm-specific outcome counts, but broader claims about the full enrolled population require information not present in the record.

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.

The registry reports serious adverse events affecting 0 of 15 participants at risk in the vitamin D arm and 0 of 14 participants at risk in the placebo arm. It also reports other adverse events affecting 0 of 15 at risk in the vitamin D arm and 0 of 14 at risk in the placebo arm. No serious adverse event terms are listed. Deaths are not reported in the registry record.

These figures describe the events recorded in the registry for the stated at-risk counts. They do not establish that no adverse events occurred outside the categories or reporting period represented in the record. The adverse-event timeframe and detailed collection procedures are not reported in the registry record. The zero counts also do not rule out uncommon events, particularly when the number of participants at risk is limited.

In general, safety counts should be interpreted with the size of the exposed group, follow-up duration, event definitions, and completeness of reporting in mind. The record gives arm-level at-risk counts and affected-participant counts but does not provide event narratives or additional safety analyses. These posted figures are descriptive and do not support a broader conclusion about safety.

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

The results describe the primary outcome recorded for this trial: participants meeting the partial clinical remission criterion at 9 months of disease duration. The posted counts are 5 in the vitamin D arm and 2 in the placebo arm. The unadjusted risk difference is positive, and its confidence interval includes zero. The unadjusted p-value is 0.231. Together, these results show a difference in the observed counts, but also substantial uncertainty in the estimated contrast.

The findings do not establish that vitamin D caused the observed difference. The interval is compatible with no difference and with effects in either direction, and the small posted outcome counts limit precision. The record does not report the original statistical plan, analysis population, missing-data handling, or details of participant flow that would help assess the robustness of the comparison. The registry’s randomized design is relevant, but the available result alone cannot resolve these uncertainties.

The findings also do not show when remission began, how long remission lasted, or how individual IDAA1c values changed. The outcome is a threshold-based participant count at one stated disease duration. No secondary outcome results are posted. Therefore, the result should not be extended to outcomes or time points that the registry does not report.

More generally, a trial result is an estimate from a particular study population and design, not a guarantee of the same outcome in every setting. The registry lists enrollment of 38, but the primary outcome results list arm counts of 15 and 14; the reason for that difference is not reported. This limits the ability to determine exactly which participants are represented in the comparison. The record also does not report the confidence level or method used for the interval.

The appropriate statistical reading is limited: the posted data show a numerically higher remission count in the vitamin D arm, while the uncertainty remains broad. They neither demonstrate a clear difference nor establish that the groups are equivalent. No medical recommendation follows from these registry results alone.

16. Why This Trial Matters Statistically

This trial is statistically informative as an example of how a clinically meaningful question can be expressed as a threshold-based binary endpoint. The registry defines partial clinical remission using IDAA1c <9 at 9 months of disease duration, then reports the number of participants meeting that criterion in each arm. This makes the outcome and comparison straightforward to describe, while also narrowing the interpretation to one threshold and one stated assessment time.

The comparison also illustrates why an observed difference and a clear statistical conclusion are not the same thing. The vitamin D arm has a larger reported remission count than the placebo arm, but the confidence interval for the risk difference crosses zero and the unadjusted p-value is 0.231. The estimate is therefore uncertain, and its direction alone should not be treated as decisive evidence.

The listed enrollment and outcome arm counts raise a further statistical issue: readers need to know which participants contributed to an analysis. The registry does not explain why the total enrollment of 38 differs from the arm sizes attached to the primary result, or how missing outcomes were handled. Transparent participant flow and a prespecified analysis plan are important for evaluating how an estimate relates to the randomized groups.

Finally, the planning illustrations show how sample-size requirements depend on the target effect and desired power under specified assumptions. They are distinct from the trial’s original design justification, which is not reported in the registry record, and they are not observed power. This distinction helps keep a retrospective planning calculation separate from evidence about the actual trial design and results.

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 posted outcome information is limited to a single primary endpoint at 9 months of disease duration. The registry does not post secondary outcomes, continuous IDAA1c values, additional time points, or a description of remission onset or duration. As a result, interpretation is restricted to whether participants crossed the stated IDAA1c threshold at the stated time.

The registry lists enrollment of 38, while the primary outcome result lists 15 participants in the vitamin D arm and 14 in the placebo arm. The reasons for this difference are not reported in the registry record. Participant flow, withdrawals, exclusions, missing outcome counts, and the analysis population are not reported, limiting assessment of how representative the outcome counts are of the randomized groups.

The record gives no original sample-size justification, protocol statistical plan, or description of interim analyses. The confidence interval method and confidence level are also not reported. Although an unadjusted comparison is posted, the test used and any additional analyses are not described. The registry does not state whether the endpoint definition or analysis was changed during the study.

The masking is recorded as triple, but the parties masked and methods used to preserve masking are not specified. The randomization methods beyond the allocation label are not reported. Adverse-event figures are limited to the listed at-risk and affected counts; event-collection duration and further safety details are not reported. These limitations do not invalidate the posted counts, but they constrain how fully the trial’s design, conduct, and analysis can be evaluated from the registry record.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Effect of Vitamin D on the Honeymoon Period in Children and Adolescents With Type 1 Diabetes — NCT01724190.
• Registry record last updated 2024-02-28; status last verified 2024-02.
• Results first posted 2024-02-28.
• 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 describes a completed, randomized, triple-masked, parallel-group study sponsored by Nationwide Children's Hospital. It lists 38 enrolled participants and compares daily oral vitamin D supplementation with a daily placebo solution over 9 months. The primary outcome is the count meeting the partial clinical remission criterion, IDAA1c <9, at 9 months of disease duration.

The posted primary result lists 5 of 15 participants meeting the criterion in the vitamin D arm and 2 of 14 in the placebo arm. The reported unadjusted risk-difference interval crosses zero, and the unadjusted p-value is 0.231. The registry does not report secondary outcome results, an analysis population, missing-data handling, or the original sample-size justification. It records no serious or other adverse events in the listed at-risk groups; deaths are not reported in the registry record.