Heart Failure Medication Adherence: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Heart Failure Medication Adherence (NCT03402750), a randomized na study. The primary outcome is Adherence to Medication.

2. Clinical Question

The clinical question concerns whether providing medication in hand at hospital discharge differs from standard care in the number of participants meeting the registry’s Day 30 medication-adherence threshold. The study is described as a pilot investigation of a medication-in-hand intervention for patients with heart failure. Its stated aims also include evaluating physical health and hospital readmissions, and assessing intervention feasibility and acceptability.

The registry record identifies adherence as the primary outcome, while also naming physical health, medication receipt before discharge, and intervention acceptance among the study’s other interests. The posted results include numerical comparisons for medication receipt before discharge and intervention acceptance. Numerical results for the PROMIS physical-health outcome are not reported in the registry record.

3. Trial Design

This was a randomized, parallel-group study with no masking. The registry lists 40 participants as enrolled and the study status as completed. The study start date was 2018-05-28, and primary completion was 2019-04-08. The sponsor was the University of Miami.

Participants were assigned to Meds to Beds or Standard Care. In the Meds to Beds arm, medication was given to participants at hospital discharge. In Standard Care, participants received an electronic prescription and picked up medication at a pharmacy. The registry also lists Electronic Prescription as an intervention, while its arm description identifies this approach as Standard Care.

The primary outcome was assessed at Day 30. The registry describes it as the number of participants with an adherence questionnaire score of 12 or lower. Four participants in each condition did not complete this measure; the posted primary-outcome counts are based on 16 participants per arm. The medication-receipt outcome was assessed at Day 0, and intervention acceptance was assessed at Day 30.

The study is presented as a pilot intended to examine feasibility and acceptability as well as adherence and physical health. The registry record does not report the original sample-size justification, the planned statistical analysis, or the randomization procedure beyond identifying the study as randomized. A trial phase is listed as NA.

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: 4 participants in each condition did not complete this measure.

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 to Medication, measured over Day 30.

The primary endpoint is a count: the number of participants whose self-reported Adherence to Refills and Medications Scale score was 12 or lower at Day 30. The questionnaire has 12 items, each recorded on a four-point Likert scale. Its total score ranges from 12-48, with lower scores indicating better adherence. The registry defines the endpoint using the number meeting the stated cutoff, rather than reporting the full score distribution or a change from an earlier assessment.

Using a defined threshold turns questionnaire responses into a binary outcome for this comparison: each participant either meets the cutoff or does not. Counts can be compared between the randomized arms, but this form of reporting does not show how far scores lie from the cutoff or how scores vary among participants who do not meet it. It also does not describe individual changes over time.

The endpoint is relevant to the study’s stated focus on medication adherence. Its interpretation depends on the questionnaire responses and the registry’s threshold definition. Four participants in each condition did not complete this measure. The registry record does not report how missing responses were handled beyond identifying the number who did not complete it, nor does it provide individual questionnaire scores.

7. Results Posted in the Registry

• Meds to Beds: 12.5% (2/16) versus 18.8% (3/16) on control; risk difference -6.2 percentage points (95% CI -31.3 to 18.8), risk ratio 0.67 (0.13–3.47); unadjusted two-proportion z-test p = 0.626.

8. Secondary Efficacy Endpoints

The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.

Number of Participants That Received Their Medications Prior to Discharge.

• Endpoint type: Binary: the number of participants with the event, compared as proportions.
• Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
• Result:
  • Meds to Beds: 35.0% (7/20) versus 25.0% (5/20) on control; risk difference 10.0 percentage points (95% CI -18.2 to 38.2), risk ratio 1.40 (0.53–3.68); unadjusted two-proportion z-test p = 0.490.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Meds to Beds and the control. The interval gives the range of effects that remain compatible with the data.

Intervention Acceptance

• Endpoint type: Binary: the number of participants with the event, compared as proportions.
• Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
• Result:
  • Meds to Beds: 62.5% (10/16) versus 56.2% (9/16) on control; risk difference 6.2 percentage points (95% CI -27.7 to 40.2), risk ratio 1.11 (0.63–1.97); unadjusted two-proportion z-test p = 0.719.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Meds to Beds and the control. The interval gives the range of effects that remain compatible with the data.

The posted secondary results address two distinct questions: whether participants received medication before discharge and whether they accepted the intervention. The registry also names PROMIS-assessed physical health as a secondary outcome, but numerical results for it are not reported in the registry record. The study summary mentions hospital readmissions, but a posted readmission result is not reported in the registry record.

Across the two secondary outcomes with numerical comparisons, the point estimates favor Meds to Beds in the direction of more participants receiving medication before discharge and more participants reporting intervention acceptance. Both confidence intervals include zero, and both unadjusted p-values are not small. These results are therefore uncertain and do not establish a clear group difference. They do not add a decisive answer to the primary adherence comparison, because they measure different aspects of the intervention and do not substitute for the Day 30 adherence endpoint.

These outcomes can help describe how the intervention was delivered and received, which aligns with the study’s stated feasibility and acceptability aims. They should not be treated as independent confirmations of the primary result. A favorable direction in a secondary point estimate does not establish that a related primary outcome differs, and a secondary result cannot fill gaps in unreported outcomes such as PROMIS physical health.

Unadjusted secondary results carry less weight when several outcomes may be examined without a reported plan for controlling multiplicity. General statistical explanation: when many outcomes are tested, the chance of finding at least one apparently unusual result can rise, even if there are no true differences. The registry record does not report a multiplicity adjustment or a hierarchy for interpreting secondary outcomes. The secondary estimates are consequently best read as exploratory descriptions, alongside their uncertainty, rather than as confirmatory evidence.

Secondary outcomes registered for this trial, for reference (only those above were recalculated):

• Physical Health as Assessed by the Patient-Reported Outcome Measurement Information System (PROMIS) Questionnaire
• Number of Participants That Received Their Medications Prior to Discharge.
• Intervention Acceptance

9. Statistical Interpretation

10. Statistical Methods Explained

What does the endpoint count?

The primary endpoint is binary at the participant level. A participant is counted if the Day 30 self-reported Adherence to Refills and Medications Scale score is 12 or lower; the reported arm value is the number meeting that definition. The posted results are 2 participants in Meds to Beds and 3 in Standard Care, with 16 participants contributing in each arm. This count-based outcome is different from comparing average questionnaire scores. It retains the threshold classification but does not describe the full range or distribution of scores.

What does a risk difference mean?

General statistical explanation: a risk difference compares the proportion with an event in one group with the proportion in the other. A value below zero means the event proportion in the first group is lower; a value above zero means it is higher. For this primary comparison, the stated orientation is Meds to Beds relative to Standard Care, and the posted risk difference is -0.062. This is an unadjusted estimate from the posted summary counts, not an adjusted model result.

How should a confidence interval be read?

General statistical explanation: a confidence interval describes uncertainty around an estimate under the assumptions of the method used to construct it. A wider interval indicates less precision than a narrower interval. For a risk difference, an interval spanning zero includes values that correspond to either direction of difference, as well as no difference. The primary interval runs from -0.313 to 0.188. The confidence level and the precise interval-construction method are not reported in the registry record.

What does a p-value convey?

General statistical explanation: a p-value describes how unusual data at least as discrepant as those observed would be under a specified null model and its assumptions. It does not describe the probability that the null hypothesis is true, the probability that a result occurred by chance, or the size of an effect. The posted primary unadjusted p-value is 0.626. The original analysis plan and the test used for a sponsor analysis are not reported in the registry record, and no reported analyses are listed.

Why distinguish posted results from the calculated comparisons?

The arm counts are the registry’s posted outcome summaries. The risk differences, confidence intervals, and unadjusted p-values are simple unadjusted recalculations from the posted summary statistics. Such recalculations do not account for covariates, repeated measurements, or other features not represented in the summary counts. The registry record does not report an adjusted estimate for comparison. Since the posted record does not identify a discrepancy between a sponsor analysis and these recalculations, there is no stated disagreement to reconcile.

What does randomization contribute?

General statistical explanation: random assignment is intended to make treatment groups comparable on average at the point of assignment, including for factors that were not measured. It does not guarantee that small groups will have the same characteristics, and it cannot eliminate uncertainty in estimates. The registry identifies the study as randomized, but details of sequence generation, allocation concealment, and baseline balance are not reported in the registry record. The record also identifies no masking.

Why does a small number of observations matter?

General statistical explanation: estimates based on fewer observations are often less precise, particularly when the outcome is a count of participants meeting a threshold and only a small number meet it. The primary result has 16 observed participants per arm and only 2 and 3 participants meeting the threshold. The resulting confidence interval is broad and includes differences in either direction. This uncertainty should be considered alongside the point estimate and p-value rather than treating any one statistic as a complete summary.

The study’s registry description calls it a pilot and includes feasibility and acceptability aims. A pilot can provide descriptive evidence and inform later planning, but the registry record does not report that this trial was designed or powered to test a specific confirmatory hypothesis. Its original design assumptions are not reported in the registry record.

11. Confidence Intervals and Precision

The primary risk-difference estimate is -0.062 for Meds to Beds relative to Standard Care. Its confidence interval extends from -0.313 to 0.188. Because the interval includes zero and reaches values on both sides of it, the result does not pin down the direction of the difference. It also includes effects materially farther from zero than the point estimate. This is a sign of limited precision, not evidence that every value in the interval is equally plausible.

The arm counts underlying the primary comparison are 2 of 16 and 3 of 16. With so few participants meeting the threshold, a small change in the observed counts could have a substantial influence on the estimated group contrast. The record does not report a confidence level or the method used to construct the interval, so those details cannot be evaluated from the registry record.

The secondary risk-difference intervals are also broad and include zero: -0.182 to 0.382 for medication receipt before discharge, and -0.277 to 0.402 for intervention acceptance. These intervals do not provide a precise basis for distinguishing the groups on those outcomes. They concern different endpoints and should not be combined into a single conclusion.

Precision is distinct from bias and from statistical significance. An interval can be wide even when the study is randomized, and an estimate close to zero does not establish equivalence. The primary result is best understood as an uncertain estimate from the participants with completed measures, rather than a precise description of the difference that would be expected in a broader population.

12. 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 for the binary outcomes in this study; they are not total event counts. The registry’s planning illustration uses a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. It bases the effect to detect on the stated fraction of the observed effect: 100%, 75%, or 50%. The original trial’s own sample-size assumptions and justification are not reported in the registry record.

The 80% power column describes the planned number of participants per arm for a design that would have an 80% chance of detecting the specified effect under the planning assumptions, if that effect and those assumptions were correct. The 90% power column describes the corresponding target for a 90% chance. These are design targets, not guarantees about the result of a future study. They depend on the selected effect size and the statistical assumptions.

Planning for a smaller effect requires more participants than planning for a larger effect, because smaller differences are harder to distinguish from random variation. Accordingly, the illustration gives separate estimates for detecting the full observed effect and smaller fractions of it. The estimates vary by endpoint because the observed event counts and group rates differ.

The calculations are planning illustrations based on the observed effect, not observed power. They should not be read as evidence that the completed pilot had a particular probability of finding a statistically significant result. They also do not replace a prospective design calculation based on a justified target effect and the trial’s intended analysis.

13. 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 = 0.188; treatment proportion p₁ = 0.125; average p̄ = 0.156.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.5135 = 1.0064.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.5116 = 0.4306.
4. n = (1.0064 + 0.4306)² / (-0.0625)² = 528.6, rounded up to 529 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 <- 0.1875                          # control proportion
p1 <- 0.125                          # 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(3402750)
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 = 529 (80% power), 708 (90% power)
 75% of observed effect: n per arm = 979 (80% power), 1,310 (90% power)
 50% of observed effect: n per arm = 2,287 (80% power), 3,061 (90% power)
power.prop.test: 528.6 
Simulated power at n = 529 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.

14. Multiplicity, Missing Data and Analysis Populations

The registry record lists five outcome measures and three secondary outcomes, while the posted results include numerical comparisons for the primary adherence endpoint and two secondary outcomes. No reported analyses are listed. The registry record does not report a statistical analysis plan, a prespecified hierarchy among outcomes, or an approach to multiplicity. It is therefore not possible to determine from the record whether the reported p-values were intended as confirmatory tests or how the investigators planned to interpret multiple outcomes.

General statistical explanation: testing several outcomes can increase the chance of at least one apparently notable result. A multiplicity strategy may define a primary outcome, adjust thresholds, or specify an order for testing. Without such a strategy reported, unadjusted secondary p-values should be interpreted cautiously. This limitation does not change the numerical estimates, but it affects how much confirmatory weight they can carry.

Missingness is explicit for the primary measure: four participants in each condition did not complete it. The posted primary counts use 16 participants per arm. The registry record does not report reasons for noncompletion, whether the missingness differed by participant characteristics, or how the investigators handled missing data in any analysis. It does not report imputation, sensitivity analyses, or a missing-data assumption.

The analysis population is also not defined in the posted record. The registry identifies randomization and provides the number with completed primary measures, but does not state whether the primary comparison followed an intention-to-treat, per-protocol, or other population definition. The handling of participants after randomization and any exclusions beyond the stated noncompletion are not reported in the registry record. These omissions limit assessment of whether the analyzed participants represent all randomized participants and how missing outcomes might affect the comparison.

For these reasons, the primary result can be described using its observed denominators, but the record does not support a detailed evaluation of the missing-data process or the full analysis strategy.

15. 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.

Most frequent serious adverse event terms

Serious events with the highest arm-level rate: death (5.0%).

The registry reports serious adverse events for 20 participants at risk in each arm. One participant in Meds to Beds and one participant in Standard Care were reported as affected by a serious adverse event. The top serious adverse-event term is Death, listed as 5.0%. The registry reports one death in each group.

No other adverse events were reported among the 20 participants at risk in either group. These are descriptive safety counts; they do not establish whether an event was caused by the intervention or whether the groups differ in safety. The record does not report event timing, individual circumstances, relatedness assessments, or further details about the serious events. The figures should be interpreted within the study’s limited size and the information available in the registry record.

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

The primary result gives a direct description of the Day 30 threshold outcome among participants who completed the measure: 2 participants in Meds to Beds and 3 in Standard Care met the stated adherence cutoff. The unadjusted estimated risk difference is -0.062, with a confidence interval from -0.313 to 0.188. The estimate is uncertain and compatible with differences in either direction. The result does not establish equivalence or determine what would happen in a larger or different population.

The study was described as a pilot with aims extending beyond adherence to feasibility, acceptability, physical health, and readmissions. The posted information provides some results on medication receipt and intervention acceptance, but numerical PROMIS and readmission results are not reported in the registry record. The posted evidence therefore addresses only part of the study’s stated interests.

The result also does not describe the full adherence-score distribution. It reports how many participants met one cutoff, not average scores, individual changes, or the range of responses within each arm. Four participants per condition did not complete the primary measure, and the registry record does not explain the reasons or analysis of those missing responses.

These data are a limited, uncertain comparison from a randomized pilot. They may be useful for understanding the observed outcomes and identifying questions for further study, but they do not by themselves establish a definitive comparative effect. No medical recommendation follows from these registry results alone.

17. Why This Trial Matters Statistically

This study illustrates why effect estimates and their precision matter alongside counts and p-values. The primary counts are small, and the risk-difference interval includes both negative and positive values. Reporting only which arm had the numerically larger count would miss the uncertainty in the comparison. Reporting only the p-value would also omit the range of differences compatible with the data.

The endpoint is a thresholded self-report measure. That definition makes the outcome straightforward to count, but does not convey the full pattern of questionnaire scores. The distinction between a count meeting a cutoff and the underlying scale is important when interpreting what the outcome represents.

The pilot’s other aims highlight the value of separating outcome types. Adherence, medication receipt before discharge, intervention acceptance, physical health, and readmissions are not interchangeable measures. Results on one do not automatically answer questions about the others. The record’s unreported PROMIS and readmission results leave part of the stated study purpose unevaluated from the posted data.

Finally, sample-size planning depends on a target effect and stated assumptions. The posted planning illustrations are tied to fractions of the observed effects, while the original trial’s design justification is not reported. This makes clear why an observed estimate can be useful for planning discussion without serving as a definitive target for a later study. The central statistical lesson is to read the estimate, its uncertainty, the endpoint definition, missing data, and the study’s pilot context together.

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 primary endpoint is based on self-reported questionnaire responses and a single threshold. Self-report may be affected by how participants understand or answer the questions, and thresholding does not preserve the full score information. The record does not provide score distributions or repeated adherence measurements that would clarify how responses varied beyond the count meeting the cutoff.

The primary comparison has 16 participants per arm with completed measures, and only 2 and 3 participants met the threshold. Its confidence interval is broad. Four participants in each arm did not complete the measure, but reasons for noncompletion and the handling of missing data are not reported in the registry record. No analysis-population definition is reported.

The study had no masking, as recorded in the registry. For self-reported outcomes, awareness of assignment could potentially influence responses; the record does not provide information that would quantify or resolve that possibility. Details of randomization, baseline characteristics, adherence to the assigned approaches, and intervention delivery beyond the arm descriptions are not reported in the registry record.

The registry identifies a pilot purpose, but the original sample-size rationale and statistical analysis plan are not reported. A multiplicity strategy is also not reported. Numerical results for the named PROMIS physical-health outcome and readmissions are not reported in the registry record. These limitations constrain the interpretation of both the primary comparison and the broader study aims.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Heart Failure Medication Adherence — NCT03402750.
• Registry record last updated 2019-11-07; status last verified 2019-11.
• Results first posted 2019-11-07.
• 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 University of Miami-sponsored Heart Failure Medication Adherence Study was a completed randomized, unmasked, parallel-group pilot with 40 participants. It compared medication in hand at hospital discharge through Meds to Beds with Standard Care, consisting of an electronic prescription and pharmacy pickup.

The primary Day 30 outcome counted participants with an Adherence to Refills and Medications Scale score of 12 or lower. The posted counts were 2 of 16 for Meds to Beds and 3 of 16 for Standard Care; four participants in each arm did not complete the measure. The unadjusted risk difference was -0.062, with a confidence interval from -0.313 to 0.188 and an unadjusted p-value of 0.626. Secondary numerical results were posted for medication receipt before discharge and intervention acceptance. Numerical PROMIS and readmission results, the original design assumptions, and the analysis plan are not reported in the registry record.