Acceptability of the NuvaRing Among Students: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Acceptability of the NuvaRing Among Students (NCT00635570), a randomized phase 4 study. The primary outcome is Adherence Rate (Rate of Perfect Method Use).

2. Clinical Question

3. Trial Design

The registry record describes the ACCEPT study as a completed Phase IV randomized trial with a parallel-group design. Participants were assigned to use either the contraceptive vaginal ring NuvaRing or the oral contraceptive pill Ortho Tri-cyclen Lo. The record lists 136 participants in the ring arm and 137 in the pill arm. It reports an enrollment of 273.

The trial was unmasked: participants and study personnel were not blinded to the assigned method. The registry record does not describe how the random sequence was generated, how assignment was concealed, or whether any other safeguards were used to reduce bias during enrollment or follow-up. Those details are not reported in the registry record.

The study focused on acceptability among female undergraduate or graduate students. The brief summary says that compliance, side effects, overall acceptability, and intent to continue use were assessed. The listed secondary outcomes are satisfaction rate and continuation rate. The record identifies four outcome measures and four analyses, but the additional outcome details and their analysis populations are not fully described in the material reported for the primary result.

The record lists the University of Chicago as sponsor and gives a study start of 2008-07, primary completion of 2009-01, and status of completed. The original sample-size rationale, planned analysis details, and procedures for handling missing outcome data are not reported in the registry record. The current sample-size planning illustrations are based on the observed effect and should not be read as a description of the trial’s original design.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Before assignment: We screened 276 participants, of whom 273 were eligible because 3 of them did not meet inclusion criteria.

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 Adherence Rate (Rate of Perfect Method Use), measured over For the first 3 months.

The primary endpoint is the adherence rate, described as the rate of perfect method use. It is reported as the percentage of participants meeting the study’s definition during the first 3 months. Perfect use meant reporting never missing a pill or never removing the vaginal ring for more than 2 hours during days 1-21 of all three monthly cycles. The definition therefore differs in its specific behavior for the pill and ring, while applying a common idea of consistent use across the assigned method.

An adherence endpoint can help characterize whether participants followed the assigned method as specified during the study period. It addresses use behavior rather than whether pregnancy occurred, and it is not itself a measure of overall satisfaction or intent to continue. Those topics are reflected in the listed secondary outcomes, but the posted primary result concerns perfect use.

The posted arm values are 57.0% for the vaginal ring and 45.0% for the oral contraceptive pill. The registry record also reports counts used in the unadjusted recalculation: 78 in the ring group and 62 in the pill group. It does not describe how missing or incomplete adherence reports were classified, whether all randomized participants contributed to this endpoint, or whether the outcome was assessed in a particular analysis population.

7. Results Posted in the Registry

• Oral Contraceptive Pill: 45.3% (62/137) versus 57.4% (78/136) on control; risk difference -12.1 percentage points (95% CI -23.9 to -0.3), risk ratio 0.79 (0.62–1.00); unadjusted two-proportion z-test p = 0.046.

8. Statistical Interpretation

9. Statistical Methods Explained

What does the risk difference describe?

A risk difference compares the proportions experiencing an outcome in two groups by subtracting one group’s proportion from the other. For this unadjusted recalculation, the oral contraceptive pill is compared with the contraceptive vaginal ring. The negative estimate of -0.121 therefore points toward a lower observed perfect-adherence proportion in the pill arm under that ordering. A risk difference is expressed on a proportion scale; it is not a relative measure such as a ratio.

This is a general explanation of the statistic. The recalculated estimate uses the posted outcome counts and group sizes and does not adjust for other participant characteristics. It describes the observed group comparison, not a causal effect isolated from every possible source of bias. Randomization supports a comparative design, but details about sequence generation, allocation concealment, missing data, and analysis populations are not reported in the registry record.

What does the chi-squared test assess?

A chi-squared test is a general method for assessing whether observed categorical outcome proportions differ between groups. The registry record identifies the sponsor’s method as a corrected chi-squared test and reports p=0.05. A p-value describes how compatible the observed data are with a statistical null model under the test’s assumptions; it is not the probability that the null hypothesis is true, and it does not measure the size or practical importance of the difference.

The corrected chi-squared result is the sponsor’s reported analysis. The separate unadjusted recalculation gives p=0.046. The discrepancy is flagged in the record, so the sponsor’s own analysis takes precedence. The record does not specify the exact correction used or explain why the two reported p-values differ. No additional assumptions about the sponsor’s method should be inferred.

Why consider a confidence interval as well as a p-value?

A confidence interval gives a range of estimates compatible with the data and the method used, rather than reducing the result to a single point estimate. In general, narrower intervals indicate greater precision and wider intervals indicate more uncertainty. A confidence interval does not guarantee that the true effect lies within its limits, and its interpretation depends on the statistical procedure and assumptions used.

The recalculated interval for the risk difference is -0.239 to -0.003 after rounding to three decimal places. The confidence level for that recalculated interval is not reported in the registry record. The interval is from the unadjusted recalculation, not from the sponsor’s corrected chi-squared analysis. The record does not report an interval for the sponsor’s test.

Why can an unadjusted recalculation differ from the reported analysis?

Different statistical procedures can produce somewhat different estimates of uncertainty and p-values, even when they use the same underlying groups. Corrections to a test, choices about the analysis population, handling of missing observations, and rounding can affect reported results. These are general reasons why analyses may differ; the registry record does not identify which, if any, explains the discrepancy in this trial.

The recalculation is explicitly unadjusted and uses the posted summary counts. It should not be treated as a reconstruction of every element of the sponsor’s analysis. In particular, the record does not provide a full statistical analysis plan, the exact test implementation, or information about whether any additional data or analysis choices entered the sponsor’s calculation.

What is over-dispersion, and is it relevant?

In general, over-dispersion occurs when data vary more than a statistical model expects. It matters for models that make assumptions about variability because underestimated variability can make uncertainty appear too small. The primary endpoint is reported as a binary percentage, and the record identifies a corrected chi-squared test for the sponsor’s comparison. The available information does not report an over-dispersion assessment or a model for which such an assessment was made. There is therefore no basis in the registry record for claiming that over-dispersion was present or that a particular adjustment was needed.

More broadly, a binary endpoint reduces each participant’s adherence experience to whether the stated perfect-use definition was met. That can make groups easier to compare, but it does not preserve every detail of adherence behavior, such as how often a lapse occurred or how long it lasted. The registry’s definition sets the rule for this endpoint; additional measures of the pattern or timing of use are not reported in the primary result.

10. Confidence Intervals and Precision

Precision concerns how much uncertainty surrounds an estimate. The posted adherence percentages are 57.0% for the contraceptive vaginal ring and 45.0% for the oral contraceptive pill. The unadjusted recalculation reports a risk difference of -0.121 for pill relative to ring, with a recalculated interval from -0.239 to -0.003 after rounding to three decimal places. The registry record does not report the confidence level for this interval, so it should not be labeled with a confidence percentage that is absent from the record.

The interval is entirely below zero after rounding, but its upper endpoint is close to zero. In general, this means that the recalculated values are compatible with a range of negative differences whose magnitudes vary. It does not mean that every value in the range is equally likely, nor does it account for biases or uncertainties not captured by the calculation. The interval is part of the simple unadjusted recalculation, not the sponsor’s corrected chi-squared analysis.

The sponsor reports p=0.05, while the recalculated unadjusted p-value is 0.046. The record flags a discrepancy, and the sponsor’s own analysis takes precedence. Since a confidence interval for the sponsor’s analysis is not reported, the recalculated interval should not be presented as if it were the sponsor’s uncertainty estimate. The available precision information applies to the posted summary statistics and the recalculation based on them.

Precision is also distinct from generalizability. Even a precise estimate would describe the trial’s population, endpoint definition, and follow-up period; it would not by itself establish that the same comparison applies in other populations or over longer periods. The record does not report additional precision measures for the listed secondary outcomes.

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 sample-size figures are planning illustrations based on the observed effect, not the trial’s original design assumptions. They give participants per arm for a two-group comparison. The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The assumed effect to detect is the stated fraction of the observed effect.

For planning at 100% of the observed effect, the illustration gives 267 participants per arm for 80% power and 357 participants per arm for 90% power. At 75% of the observed effect, the corresponding figures are 475 and 635 participants per arm. At 50% of the observed effect, they are 1,064 and 1,424 participants per arm.

In plain language, the 80% power column describes the planned number per arm under which the specified calculation has an 80% chance of detecting the assumed effect at the stated significance level, if the assumptions hold. The 90% column uses a higher chance of detection and therefore requires more participants per arm for each listed effect assumption. The figures are not total sample sizes; they are per-arm planning counts. The record says that time-to-event calculations, when used, would instead report total events, but this endpoint is not a time-to-event measure.

The smaller assumed effects require more participants because they are harder to distinguish from random variation. The planning figures are not observed power and do not describe what the completed trial was originally designed to achieve. The trial’s own original sample-size assumptions are not reported in the registry record. No additional numerical values for the planning curve are stated.

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 = 0.574; treatment proportion p₁ = 0.453; average p̄ = 0.513.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.7069 = 1.3854.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.7017 = 0.5905.
4. n = (1.3854 + 0.5905)² / (-0.1210)² = 266.8, rounded up to 267 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 <- 0.573529411764706                          # control proportion
p1 <- 0.452554744525547                          # 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(635570)
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 = 267 (80% power), 357 (90% power)
 75% of observed effect: n per arm = 475 (80% power), 635 (90% power)
 50% of observed effect: n per arm = 1,064 (80% power), 1,424 (90% power)
power.prop.test: 266.8 
Simulated power at n = 267 per arm: 0.804 (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. Analyses Reported by the Sponsor

The registry reports the sponsor’s primary comparison as a corrected chi-squared test with p=0.05. A separate unadjusted recalculation from the posted group counts gives a risk difference of -0.121 and an unadjusted p-value of 0.046. The record flags a discrepancy between the reported analysis and recalculation. Under the stated interpretation rule for this record, the sponsor’s own analysis takes precedence.

The recalculation is useful as a transparent comparison based on the posted summary counts, but it is not a replacement for the sponsor’s reported test. The record does not give enough detail to identify the source of the difference. It does not report the sponsor’s full statistical analysis plan, an explanation of the corrected test, or a confidence interval for the sponsor’s result. The recalculated interval should therefore be understood as belonging to the recalculation only.

Both results should be kept in their proper roles: p=0.05 is the registry’s reported sponsor result, and p=0.046 is the unadjusted recalculated result. The latter should not be used to override the former or to suggest that the sponsor reached a different conclusion. Neither p-value, by itself, conveys the size of the adherence difference or its importance to participants.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists four outcome measures and four analyses. It identifies the adherence rate as the primary outcome and lists satisfaction rate and continuation rate as secondary outcomes. However, the results described for this analysis do not provide a complete account of all outcomes or analyses. The registry record does not report a multiplicity adjustment or explain how the primary and secondary comparisons were prioritized for statistical inference.

Multiplicity is a general concern when several outcomes or statistical tests are examined. The more tests conducted, the greater the chance that at least one may appear unusual under a null model by chance. Adjustments or a prespecified hierarchy can help control how results are interpreted. Without a reported plan, it is not possible to determine whether multiplicity was addressed, or how it might affect interpretation of the reported primary p-value.

The record also does not report the analysis population for the adherence outcome. It is not clear whether the reported percentages include all randomized participants, only participants with observed adherence information, or another defined group. The number of missing primary endpoint observations and the rules used to classify incomplete reports are not reported in the registry record. No assumption should be made about whether missing observations were excluded, imputed, or counted as failures to meet the definition.

Other important analysis details are also absent from the registry record: the randomization procedure, allocation concealment, the full statistical analysis plan, baseline-adjusted analyses, subgroup analyses, and any interim analyses. The record does not say whether the sponsor’s test was prespecified or whether any changes were made after the study began. These missing details limit the ability to assess how closely the posted analysis follows an original plan.

The four analyses and four outcome measures should not be taken to mean that every result is fully reported in the record. Only the adherence result is described in the primary comparison details, while the listed secondary outcomes do not have accompanying estimates in this account. The status of multiplicity control, missing-data handling, and analysis-population selection remains not reported in 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 5% reporting threshold.

Most frequent non-serious adverse event terms

The registry reports serious adverse events in 0 participants among 136 at risk in the contraceptive vaginal ring group and 0 participants among 137 at risk in the oral contraceptive pill group. These are the serious-event counts recorded for the groups. The record does not provide serious adverse-event terms, and it does not report death counts; the death entries are not available as numerical values. An unreported death count should not be read as a count of zero.

The record also lists other adverse events affecting 100 participants in the ring group and 105 participants in the pill group. These are separate figures from the serious-event counts. The available information does not specify the event terms, severity categories, duration, or observation window for these other events, so their nature and clinical importance cannot be characterized from these counts alone.

As a general statistical point, zero recorded serious events in a group does not prove that the risk is zero. Event counts describe what was observed and recorded during the study’s reporting period, and the record does not provide further detail about safety follow-up or ascertainment. These figures should be read as registry-recorded counts, not as a complete comparison of all possible safety outcomes.

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

The result describes how often participants met a specific definition of perfect use during the first 3 months: 57.0% in the vaginal-ring arm and 45.0% in the oral-pill arm. The unadjusted recalculation places the pill group below the ring group for this endpoint, with a risk difference of -0.121. The sponsor’s own corrected chi-squared analysis reports p=0.05 and takes precedence over the recalculated p-value of 0.046.

This is an adherence finding, not a pregnancy-outcome comparison. The endpoint does not measure whether a participant became pregnant, whether the method prevented pregnancy, or whether participants preferred one method. Satisfaction and continuation are listed as secondary outcomes, but their results are not reported in the registry record for this comparison. The primary result therefore should not be extended to those outcomes.

The endpoint captures whether participants met the study’s definition throughout days 1-21 of all three monthly cycles. It does not show the frequency, timing, or reasons for lapses among participants who did not meet the definition. The registry record does not explain how missing or incomplete reports were handled, or which analysis population was used. Those limitations affect how fully the proportions can be understood.

The trial was open-label, and the study focused on female undergraduate or graduate students. The result should be interpreted within that setting and follow-up period. The registry record does not provide enough information to judge how the result might apply to people with different characteristics or in other settings.

Statistical results are not medical advice and do not, by themselves, determine which method is appropriate for an individual. The posted figures give a comparative description of reported adherence in this trial. They do not establish an overall ranking of the methods, and the registry record does not report enough information to draw conclusions about every outcome of interest.

17. Why This Trial Matters Statistically

This trial illustrates why an endpoint must be interpreted according to its operational definition. “Perfect use” is not an abstract or interchangeable measure: the study specified different behaviors for pills and the vaginal ring, then assessed whether participants met the relevant rule across the first 3 months. A comparison of adherence rates is meaningful only with that definition and time window in view.

It also illustrates the difference between an arm-level percentage, an effect estimate, and a test result. The percentages describe each group. The risk difference gives a direct unadjusted comparison using an explicit ordering of groups. The p-values address compatibility with a statistical null model under different analyses. These quantities answer related but distinct questions, and one should not be substituted for another.

The registry record also makes the distinction between a sponsor-reported result and a recalculation important. The sponsor’s corrected chi-squared test reports p=0.05, while the unadjusted recalculation reports p=0.046. Since the record flags a discrepancy, the sponsor’s analysis takes precedence. This is a reminder that a recalculation from summary counts may not reproduce every detail of an analysis that is not fully described.

Finally, planning calculations based on an observed effect are not a retrospective measure of how well a trial was designed or conducted. Their assumptions make them useful as illustrations of how smaller effects call for larger planned samples, but the original design assumptions are not reported. Keeping that distinction clear prevents planning figures from being mistaken for observed trial results.

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.
• Participant counts were reconstructed from posted percentages and arm sizes, so small rounding differences are possible.

Several trial-specific limitations follow from the registry record. The study was unmasked, so participants knew which method they used. Because the primary endpoint depends on reported use behavior, the absence of masking is relevant context, although the record does not quantify whether it affected reporting. The method-specific definitions also differ: pill adherence is described in terms of missed pills, while ring adherence concerns removal for more than 2 hours. The record does not report any validation of self-reported use.

The endpoint covers the first 3 months, and the record does not provide a longer-term primary adherence result. It does not report pregnancy outcomes in the primary comparison. Satisfaction and continuation are listed as secondary outcomes, but their estimates are not reported in the registry record for this analysis. These omissions restrict conclusions to the posted adherence measure rather than broader effectiveness, acceptability, or continuation.

The analysis population and missing-data handling are not reported in the registry record. Consequently, it is unclear whether the arm percentages represent all randomized participants or only those with outcome information. The registry record also does not describe randomization sequence generation, allocation concealment, baseline characteristics, or covariate adjustment. The absence of these details does not establish that procedures were not used; it means they are not reported in the registry record.

The sponsor’s corrected chi-squared result and the unadjusted recalculation differ, and the record does not explain why. The sponsor’s own analysis takes precedence, but the lack of detail limits independent assessment of the test and its assumptions. The confidence level for the recalculated interval is not reported, and no interval is given for the sponsor’s analysis.

Lastly, the study’s focus was female undergraduate or graduate students. The record does not establish how broadly the findings apply outside that population. The primary result is also limited to a specific pair of methods and the stated follow-up period; it cannot resolve comparisons with other methods or outcomes not reported for this trial.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Acceptability of the NuvaRing Among Students — NCT00635570.
• Registry record last updated 2021-02-03; status last verified 2013-06.
• Results first posted 2012-11-07.
• 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

The registry describes a completed, randomized, open-label Phase IV parallel-group trial focused on acceptability among female undergraduate or graduate students. Participants were assigned to a contraceptive vaginal ring, NuvaRing, or an oral contraceptive pill, Ortho Tri-cyclen Lo. The primary outcome was the percentage meeting the definition of perfect method use during the first 3 months.

Posted adherence rates were 57.0% for the ring and 45.0% for the pill. The sponsor’s corrected chi-squared analysis reports p=0.05. The unadjusted recalculation gives a risk difference of -0.121 and p=0.046; because the record flags a discrepancy, the sponsor’s analysis takes precedence.

The record lists satisfaction and continuation as secondary outcomes, but their results are not reported in the registry record for this analysis. Details on missing data, analysis populations, multiplicity, the original sample-size rationale, and several design procedures are not reported in the registry record.