Use of Nudges To Enhance Enrollment in Critical Care Research: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Use of Nudges To Enhance Enrollment in Critical Care Research (NCT03284359), a randomized na study. The primary outcome is Consent Rate.

2. Clinical Question

The simulated trial concerned two mechanical ventilation weaning protocols among mechanically ventilated patients. The trial therefore examined a recruitment process, rather than comparing the clinical effects of those protocols. Its focus was whether a behavioral intervention before the consent approach could alter enrollment behavior in a critical-care research setting. The registry also lists risk assessment as a secondary outcome, measured after the informed-consent process. Details of how that assessment was defined or analyzed are not reported in the registry record.

3. Trial Design

This was a completed, randomized, parallel trial with single masking recorded in the registry. The listed enrollment was 182. The study began on 2018-02-19, and primary completion was recorded as 2019-08-08. It was conducted in 10 intensive care units at the University of Pennsylvania, according to the study description. The record lists the condition as critical illness and the phase as not applicable.

Participants were critically ill patients’ surrogate decision makers. They engaged with recruitment procedures for a simulated randomized trial about mechanical ventilation weaning protocols. In the intervention arm, participants received the pre-consent nudge bundle, which incorporated behavioral interventions into a brief survey. In the control arm, participants received standard consent. The description does not specify further details of the survey content or the standard consent procedure.

The primary outcome was consent rate, described as a binary measure and assessed among the intention-to-treat population. The registry states a timeframe of up to 96 hours. The listed arm counts were 93.0 for the pre-consent nudge bundle and 89.0 for standard consent. The record lists risk assessment as a secondary outcome. A detailed protocol, recruitment workflow, masking procedures, and the original design assumptions are not reported in the registry record. The record does not identify which individuals were masked or how masking was maintained.

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

Analysis population for the primary outcome, as defined in the registry: Intention to treat

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.

Population: Intention to treat

6. Primary Endpoint

The registry lists the primary outcome as Consent Rate, measured over Up to 96 hours.

The primary endpoint was consent to a simulated randomized clinical trial. It was recorded as a binary outcome: whether a participant consented or did not consent. The registry describes the outcome as a count of participants, with the primary population specified as intention to treat and a timeframe of up to 96 hours.

Consent is relevant to this study because the intervention was intended to affect enrollment behavior. A binary endpoint directly represents whether a person proceeded to consent under the assigned recruitment procedure. The study did not assess enrollment into an actual trial of ventilation protocols; the consent decision concerned a simulated trial. That distinction defines what the endpoint can support: it describes responses to the study’s simulated recruitment process, not enrollment behavior in every clinical-trial setting.

The posted counts were 27.0 participants in the nudge-bundle arm and 30.0 in the standard-consent arm. The registry also lists risk assessment after the consent process as a secondary outcome, but further measurement details are not reported in the registry record. The endpoint’s value for recruitment research is that it captures a concrete decision rather than a stated intention alone. Interpretation still depends on the specific simulated setting, the approach used in each arm, and the uncertainty around the observed contrast.

7. Results Posted in the Registry

• Pre-Consent Nudge Bundle: 29.0% (27/93) versus 33.7% (30/89) on control; risk difference -4.7 percentage points (95% CI -18.1 to 8.8), risk ratio 0.86 (0.56–1.33); unadjusted two-proportion z-test p = 0.497.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is binary because each participant either consented to the simulated trial or did not. For binary outcomes, a group’s event count is interpreted in relation to the number of participants in that group. The posted outcome counts and group sizes allow the comparison to be expressed in several ways. The registry reports a risk difference, a risk ratio, and an odds ratio. These are related summaries of the same contrast, not separate endpoints.

What does a risk difference express?

A risk difference subtracts one group’s event probability from the other group’s event probability. In this comparison, the reported estimate is negative for the pre-consent nudge bundle relative to standard consent. The sign indicates the direction of the estimated contrast under the comparison’s stated ordering. A risk difference is measured on the probability scale, so zero represents no difference between groups. Its confidence interval includes zero, meaning the data remain compatible with no difference as well as with contrasts on either side of zero.

The risk difference can be useful because it describes an absolute contrast rather than a relative change. Its interpretation depends on the outcome and study context; here, the outcome is consent to a simulated trial. The result should not be translated into a claim about actual trial enrollment without evidence from that setting.

How do risk ratios and odds ratios differ?

A risk ratio divides the event probability in one group by the event probability in another. A value of one represents equal probabilities, while values on either side represent a relative contrast. An odds ratio compares event odds rather than probabilities. Odds are the ratio of the chance of an event to the chance of no event. Although the two ratio measures can look similar in some settings, they are not interchangeable, and an odds ratio should not automatically be described as a risk ratio.

The posted confidence intervals for both ratio measures include one, the no-contrast value. They therefore do not resolve whether the nudge bundle was associated with a lower or higher consent outcome than standard consent. The measures offer alternative scales for the same comparison and do not add new participants or independent evidence.

What does the p-value contribute?

The reported unadjusted p-value is 0.497. In general, a p-value describes how compatible the observed data are with a specified null hypothesis, given the assumptions of the test. It is not the probability that the null hypothesis is true, and it is not a direct measure of the size, practical importance, or precision of the effect. The registry record does not report the full testing procedure or any adjusted p-value. The value should therefore be read as the posted unadjusted result, without assuming an unreported model or adjustment.

The word “unadjusted” distinguishes this value from a result adjusted for covariates or other considerations, but the record does not state whether additional analyses were conducted outside the posted results. No posted analyses are listed in the registry record. The p-value and confidence interval answer related but different questions: one summarizes compatibility with a null hypothesis under a test, while the interval describes a range of effect estimates compatible with the data and method.

Why does the analysis population matter?

The primary population is listed as intention to treat. In general, an intention-to-treat analysis aims to retain participants in the groups to which they were assigned, regardless of whether they followed the assigned procedure. This preserves the randomized comparison and estimates the effect of assignment to the recruitment procedure under the analysis approach. The registry does not report the operational rules used to implement that principle, including how missing outcome data, withdrawals, or deviations were handled. Those details should not be inferred from the population label alone.

The registry describes the outcome as a count of participants and the intervention as a behavioral nudge bundle. The posted comparison is an unadjusted arm-level result; adjustment variables, model specification, and a more detailed statistical analysis plan are not reported in the registry record. Consequently, the interpretation should stay close to the reported contrast and its uncertainty, rather than implying that a more elaborate model or subgroup analysis was used.

What can be learned from the planning calculations?

The planning illustrations use the observed effect as a reference and then consider specified fractions of that effect. They are not the original trial’s design calculations. General sample-size planning asks how many participants would be needed under assumptions about the target effect, significance level, allocation, and statistical method. Smaller effects are harder to distinguish from random variation and therefore require more participants under otherwise unchanged assumptions. The calculation assumptions and participant requirements are described with the sample-size discussion, but the trial’s original sample-size justification is not reported in the registry record.

Because the trial tested a recruitment procedure in a simulated setting, the practical meaning of any estimated contrast also depends on the context in which consent was requested. Statistical summaries quantify uncertainty in the posted comparison; they cannot by themselves establish how well that comparison generalizes to other sites, populations, or actual clinical trials.

10. Confidence Intervals and Precision

Precision describes how tightly an estimate is determined by the data and the analysis method. A confidence interval communicates that uncertainty by giving a range of values compatible with the observed data under the method’s assumptions. It does not guarantee that the true effect lies in the interval, nor does it describe the probability that any particular effect value is true.

For the risk difference, the reported confidence interval extends across zero. This means the posted estimate does not precisely distinguish no difference from effects in either direction. The point estimate is negative for the nudge bundle relative to standard consent, but the interval indicates that the estimate is uncertain. The interval should be considered alongside the arm counts and the unadjusted p-value of 0.497, rather than interpreting the point estimate alone.

The confidence intervals for the risk ratio and odds ratio also span their no-contrast value of one. This is consistent with the uncertainty described by the risk-difference interval. The three measures express the same underlying comparison on different scales, so their uncertainty should not be treated as three independent findings.

The registry does not report a prespecified precision target or the original sample-size assumptions. The listed enrollment and posted group sizes describe the study that was conducted; they do not, by themselves, show how precisely the investigators intended to estimate the primary effect. The interval’s breadth is important when considering whether the result rules out effects that could matter in a recruitment context. It does not support a precise claim of equivalence between the procedures.

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 participant counts per arm, not total events. They are illustrations computed from the observed effect, not the trial’s own design justification. The stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. For each assumed effect size, the 80% power column gives the number of participants per arm associated with an 80% chance of detecting that effect under those assumptions; the 90% power column gives the corresponding number for a 90% chance. These are planning targets, not observed results.

For planning for 100% of the observed effect, the figures are 1,545 participants per arm for 80% power and 2,068 participants per arm for 90% power. For planning for 75% of the observed effect, they are 2,775 participants per arm for 80% power and 3,714 participants per arm for 90% power. For planning for 50% of the observed effect, they are 6,304 participants per arm for 80% power and 8,439 participants per arm for 90% power. The pattern illustrates the general principle that smaller effects need more participants to detect under otherwise fixed assumptions.

The curve expresses the same planning relationship between the effect being targeted and the participant requirement. It should be read as a set of assumption-dependent planning illustrations, not as a prediction of what a future trial will find. This is not observed power. The original trial’s own design assumptions and sample-size justification are not reported in the registry record.

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 = 0.337; treatment proportion p₁ = 0.290; average p̄ = 0.314.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6562 = 1.2861.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.6554 = 0.5516.
4. n = (1.2861 + 0.5516)² / (-0.0468)² = 1,544.8, rounded up to 1,545 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 <- 0.337078651685393                          # control proportion
p1 <- 0.290322580645161                          # 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(3284359)
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 = 1,545 (80% power), 2,068 (90% power)
 75% of observed effect: n per arm = 2,775 (80% power), 3,714 (90% power)
 50% of observed effect: n per arm = 6,304 (80% power), 8,439 (90% power)
power.prop.test: 1544.8 
Simulated power at n = 1,545 per arm: 0.800 (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 a primary consent-rate outcome and one secondary outcome, risk assessment. The record also reports two outcome measures, but it does not describe a multiplicity plan or state whether confirmatory testing was adjusted for considering more than one outcome. When multiple outcomes or analyses are examined, the chance of obtaining at least one apparently notable result can change. In general, a prespecified hierarchy or adjustment can guide interpretation, but the registry record does not report such a plan. The posted primary result is identified as unadjusted.

Missing outcome data can affect estimates when the outcome is unavailable for some assigned participants. The registry record does not report how many primary outcomes were missing, whether any participants withdrew, or how missing observations were handled. The primary population is labeled intention to treat, but that label alone does not specify an imputation method, a rule for classifying missing consent outcomes, or a sensitivity analysis. Such procedures are not reported in the registry record.

The record does not provide a detailed statistical analysis plan, covariate-adjusted estimates, subgroup analyses, or interim-analysis details. It lists zero posted analyses. This does not establish whether analyses were considered during the research process; it means that these details are not reported in the registry record. No protocol-specific multiplicity correction, missing-data assumption, or model choice should be inferred from the arm-level result alone.

Randomization supports a comparison by assigned group, and the stated intention-to-treat population signals the intended analysis population. However, a complete assessment of how assignment, adherence, missingness, and multiple outcomes were handled requires details beyond those reported. The available result is most safely interpreted as the registry’s posted unadjusted comparison for the primary consent endpoint, with the secondary risk-assessment outcome noted but not described in detail.

14. Safety Results

The registry reports serious adverse events as affected participants divided by participants at risk.

Deaths

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 0% reporting threshold.

The serious adverse event figures list zero affected participants in the pre-consent nudge-bundle group, with 93 at risk, and zero affected participants in the standard-consent group, with 89 at risk. Deaths are listed as zero in both groups. The other adverse-event counts are also listed as zero in both groups. No serious adverse-event terms are listed.

These figures describe the adverse-event entries posted in the registry. A zero count means that no affected participants are recorded in those entries; it does not prove that an event is impossible or that the procedures have no risks. The record does not provide further detail on adverse-event collection, definitions, monitoring, or completeness. The study involved a simulated recruitment process, and the serious adverse-event counts should be interpreted as registry reporting for this trial, not as evidence about the safety of ventilation protocols in clinical care.

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

The result describes consent to a simulated randomized trial among surrogate decision makers approached in critical-care settings. The posted counts were 27.0 in the pre-consent nudge-bundle group and 30.0 in the standard-consent group. The reported risk-difference estimate is negative for the nudge bundle relative to standard consent, but its confidence interval includes zero. The unadjusted p-value is 0.497. These data do not establish a statistically clear difference between the recruitment procedures, and the uncertainty does not justify treating the procedures as equivalent.

The result does not show whether either recruitment procedure increases enrollment in actual clinical trials. Participants were asked about joining a simulated trial involving ventilation weaning protocols, rather than being enrolled in a clinical comparison of those protocols. Responses in a simulated process may not capture all decisions, pressures, or practical constraints associated with real trial enrollment. The record does not report evidence on whether the findings generalize to other institutions, clinical contexts, or participant groups.

The outcome is a concrete consent decision, which is useful for studying recruitment, but the observed contrast remains imprecise. The confidence interval allows effects in either direction. A non-significant unadjusted result is not proof of no effect, and it cannot show that the intervention has no practical value. Conversely, the study does not establish that the nudge bundle improves recruitment. Further claims would require evidence beyond the posted estimate and its uncertainty.

The registry’s secondary outcome is risk assessment after consent, but detailed results and methods for that outcome are not reported in the registry record. Interpretation should therefore focus on the primary consent outcome and avoid conclusions about risk perceptions. The trial contributes evidence about one behavioral intervention and one simulated recruitment setting; it does not settle the broader question of how to improve enrollment in critical-care research.

16. Why This Trial Matters Statistically

Recruitment is part of the design and conduct of clinical research: if studies do not enroll enough participants, their ability to answer research questions can be limited. The study description identifies under-enrollment and selective enrollment as concerns in intensive-care trials and examines a nonmonetary behavioral approach to recruitment. Statistically, this makes the trial a test of a process that can influence whether later research is feasible, rather than a test of a clinical treatment.

The comparison illustrates why estimates and uncertainty should be read together. The posted counts differ across arms, and the estimated risk difference points in one direction, but the confidence interval includes zero and the unadjusted p-value is 0.497. A point estimate alone could make the observed direction seem more conclusive than the data warrant. The interval makes clear that the magnitude and direction remain uncertain.

The planning illustrations also highlight the relationship between effect size and required sample size. Detecting smaller effects generally requires more participants under the stated planning assumptions. That matters for recruitment-intervention research because the intervention is intended to affect enrollment itself, while a trial comparing recruitment strategies must still enroll enough participants to estimate that effect with useful precision.

The study’s simulated setting gives a focused way to examine a consent process, but it also constrains what the result can establish. The findings are relevant to the described recruitment procedure and population; whether they transfer to actual trials or other settings remains an open question. The record’s limited detail on analysis procedures, missing data, and design assumptions further supports a cautious, estimate-centered interpretation.

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 primary limitation for interpretation is that consent was measured for a simulated randomized trial. The result is not a direct comparison of enrollment into an actual clinical trial. How surrogate decision makers respond in this setting may not represent recruitment decisions under different circumstances, and the registry does not report evidence establishing generalizability beyond the study context.

The record describes the intervention as a bundle of behavioral interventions delivered within a brief survey, but it does not detail the components or their separate contributions. Consequently, the result cannot identify which component, if any, influenced consent. The control description states that participants received standard consent; further detail about how recruitment was conducted in each arm is not reported in the registry record.

The confidence interval for the primary risk difference includes zero, so the estimate does not precisely distinguish a difference from no difference. The posted p-value is unadjusted. The registry record does not report the full analysis plan, missing-data procedures, interim analyses, covariate adjustment, or multiplicity handling. The intention-to-treat label is reported, but implementation details are not.

The original sample-size justification and the trial’s design assumptions are not reported in the registry record. The planning figures are illustrations based on the observed effect and stated assumptions, not evidence that the original trial had a particular power target. The record also does not describe the detailed measurement or results for the secondary risk-assessment outcome. These limits make the primary result useful as an estimate from a particular recruitment experiment, while restricting stronger claims about mechanism, precision, and transportability.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Use of Nudges To Enhance Enrollment in Critical Care Research — NCT03284359.
• Registry record last updated 2021-03-03; status last verified 2021-02.
• Results first posted 2021-03-03.
• 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

NCT03284359 is a completed randomized, parallel trial sponsored by the University of Pennsylvania. It evaluated a pre-consent nudge bundle against standard consent for recruitment to a simulated trial among critically ill patients’ surrogate decision makers. The listed enrollment was 182, and the primary outcome was consent within up to 96 hours.

The posted consent counts were 27.0 among 93.0 participants in the nudge-bundle group and 30.0 among 89.0 in the standard-consent group. The estimated risk difference was negative, its confidence interval included zero, and the unadjusted p-value was 0.497. The record also lists risk assessment as a secondary outcome and reports zero serious adverse events and zero deaths in both groups. Further details on the analysis plan, missing data, and original sample-size rationale are not reported in the registry record.