Behavioral Economics to Improve Antihypertensive Therapy Adherence: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Behavioral Economics to Improve Antihypertensive Therapy Adherence (NCT04029883), a randomized na study. The primary outcome is Electronically Measured Mean Medication Adherence During Intervention.

2. Clinical Question

The study focuses on adherence behavior rather than a clinical event. Its primary measure uses electronic monitoring of one antihypertensive medication and compares the timing of actual bottle openings with the prescribed once-a-day openings during the intervention. The registry lists Hypertension Control as a secondary outcome, but its results are not reported in the registry record.

3. Trial Design

This was a randomized, single-masked, parallel-group study sponsored by Cedars-Sinai Medical Center. The registry lists the study as completed, with enrollment of 60. The study began on 2022-04-19, and primary completion was recorded as 2024-02-01. The phase is listed as NA.

Participants were assigned to a Control Group, a Message Group, or an Incentive Group, with 20 participants in each group in the posted primary-outcome results. The Control Group received care as usual, a MEMS-cap, and a leaflet explaining the importance of pill-taking routines and how to establish them. A coordinator reviewed the leaflet and answered questions during an approximately ten-minute session. The Message Group received the same session and daily text messages reinforcing its information for 3 months. The Incentive Group received the same information and text messages, along with a chance of winning small, intermittent rewards linked to taking medication at the time associated with an anchoring strategy.

The registry identifies the design as parallel and single-masked, but does not report who was masked, how randomization was generated or implemented, or whether allocation was concealed. The record does not report the trial’s original sample-size assumptions, detailed eligibility criteria, or further operational details for the intervention. Those design details should not be inferred from the outcome summaries.

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 Electronically Measured Mean Medication Adherence During Intervention, measured over 3 months.

The primary endpoint was electronically measured mean medication adherence during the 3-month intervention. It was expressed as the percentage of timely medication adherence. The registry defines timely adherence as actual bottle openings within 1 hour of the participant’s anchor time. The numerator was the number of actual once-a-day bottle openings within that interval during the intervention; the denominator was the number of prescribed once-a-day bottle openings during the same period. Only one antihypertensive medication was used to measure adherence.

Electronic monitoring was used to record bottle openings continuously over the intervention. This measure is intended to capture whether medication-taking occurred at the chosen time, rather than relying only on a participant’s retrospective report. The registry’s rationale describes anchoring medication-taking to daily routines as a behavioral approach, so the timing component is relevant to the intervention being studied.

The measure is still a record of bottle openings, not direct confirmation that a dose was swallowed. The registry defines the endpoint using openings and does not report an additional measure verifying ingestion. The posted group values are means, with standard deviations describing variation among participants. The results therefore characterize average measured adherence and its observed spread in each group, not adherence for every participant.

7. Results Posted in the Registry

• Message Group: mean 95.00 versus 87.00 on control; difference 8.00 (95% CI -9.75 to 25.75), standardized effect d = 0.28; z-test p = 0.377.
• Incentive Group: mean 92.00 versus 87.00 on control; difference 5.00 (95% CI -14.24 to 24.24), standardized effect d = 0.16; z-test p = 0.611.

8. Statistical Interpretation

9. Statistical Methods Explained

What kind of outcome is being analyzed?

Mean medication adherence is a continuous outcome: each participant’s adherence is represented by a numerical percentage, and the group result is the mean of those participant-level measurements. A mean gives a concise description of the group’s average, while the standard deviation describes how spread out individual measurements are around that average. The group means were 87.0 for Control, 95.0 for Message, and 92.0 for Incentive. Their standard deviations were 22.0, 34.0, and 38.0, respectively.

What does a mean difference express?

A mean difference describes the distance between two group averages in the outcome’s units. For the Message-versus-Control comparison, the posted mean difference is 8.0; for Incentive versus Control, it is 5.0. These are unadjusted recalculations from posted summary statistics. A positive value in these comparisons means that the intervention-group mean is higher than the Control mean. The difference is an estimate from the study sample, not a guarantee that the underlying population difference has that exact value.

How should the p-values be read?

A p-value is a measure of how compatible the observed data are with a specified null hypothesis, under the assumptions of the statistical procedure. It is not the probability that the null hypothesis is true, and it does not measure the size or importance of a difference. The posted unadjusted p-values are 0.377 for Message versus Control and 0.611 for Incentive versus Control. The registry record does not report a sponsor analysis for these comparisons; the posted comparisons are simple, unadjusted recalculations from the group summaries. The exact test used in an original sponsor analysis is not reported in the registry record.

Why does variation matter?

General statistical explanation: greater variability among participants makes a group mean less precisely estimated when sample size is held fixed. If participants’ measurements vary widely, the observed average can be less informative about the population average. Here, the standard deviations are sizeable relative to the mean differences, and the confidence intervals span a broad range. This combination illustrates why the direction of a point estimate alone is not enough to characterize the strength of the evidence.

General statistical explanation: over-dispersion refers to variation greater than a statistical model expects. A model that does not allow for such extra variation can understate uncertainty. The registry record does not identify a model-based analysis or report an assessment of over-dispersion for this continuous endpoint, so no claim can be made that such a model was used or required. The standard deviations nevertheless make the observed spread visible.

What do confidence intervals contribute?

A confidence interval expresses uncertainty around an estimated difference. In repeated use of a method under its assumptions, intervals constructed at the stated confidence level are intended to cover the fixed target parameter at that rate. For an individual study, the interval is best read as a range of values reasonably compatible with the data and method, not as a range guaranteed to contain the true value. The interval also communicates precision: a narrower interval indicates a more precise estimate than a wider one, all else equal.

For Message versus Control, the 95% confidence interval runs from -9.748 to 25.75. For Incentive versus Control, it runs from -14.24 to 24.24. Both intervals include zero and extend to positive and negative differences. The posted estimates therefore have limited precision for distinguishing the direction and size of the population difference. No confidence interval for a direct Message-versus-Incentive contrast is reported.

What analysis details are missing?

The registry record does not report whether the original analysis adjusted for baseline measurements or other participant characteristics, how missing endpoint data were handled, or which analysis population was used. It does not report a statistical analysis plan, the exact method used for any sponsor analysis, or an approach to repeated or interim analyses. The randomized, parallel design is recorded, but the method of assigning participants and the identity of the masked party are not reported. Consequently, the recalculated unadjusted comparisons should be distinguished from any original analysis that may have been conducted outside the registry record.

10. Confidence Intervals and Precision

The estimates are uncertain. The Message Group mean was 95.0, compared with 87.0 in Control, giving a posted mean difference of 8.0. Its 95% confidence interval extends from -9.748 to 25.75. The Incentive Group mean was 92.0, and its posted difference from Control was 5.0, with a 95% confidence interval from -14.24 to 24.24. Each interval includes zero, and each also includes values on both sides of zero.

In practical statistical terms, the data do not pin down a single direction or a narrow range of plausible differences. The intervals allow for no difference as well as differences favoring either group. The point estimates are positive, but they should not be read without their uncertainty. The unadjusted p-values, 0.377 and 0.611, likewise do not provide a precise estimate of effect size and do not prove that there is no difference.

The standard deviations were 22.0 in Control, 34.0 in Message, and 38.0 in Incentive, while each group included 20 participants in the posted results. The observed spread and the limited group sizes contribute to uncertainty in the group comparisons. The registry record does not report a confidence interval for the direct comparison between Message and Incentive, or intervals for the secondary outcome.

A confidence interval quantifies sampling uncertainty under the method used; it does not address every potential source of uncertainty, such as missing data or measurement limitations. Details of missing endpoint data and their handling are not reported in the registry record. The intervals should therefore be interpreted as precision summaries for the posted unadjusted comparisons, not as a complete account of all possible sources of bias or uncertainty.

11. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

The planning figures are participants per arm for 80% power and participants per arm for 90% power. They are not total events. The calculations use two-sided significance level 0.05, equal allocation between the two arms, and a normal approximation. Each planning scenario uses a stated fraction of the observed effect. The effect fractions are 100%, 75%, and 50% of the observed effect for each comparison.

For the Message-versus-Control comparison, planning for 100% of the observed effect gives 202 participants per arm for 80% power and 270 participants per arm for 90% power. Planning for 75% of the observed effect gives 358 and 479 participants per arm, respectively. Planning for 50% of the observed effect gives 805 and 1,078 participants per arm, respectively.

For the Incentive-versus-Control comparison, planning for 100% of the observed effect gives 606 participants per arm for 80% power and 811 participants per arm for 90% power. Planning for 75% of the observed effect gives 1,077 and 1,441 participants per arm, respectively. Planning for 50% of the observed effect gives 2,422 and 3,242 participants per arm, respectively.

In plain language, 80% power means that, under the stated assumptions and for the selected effect size, a study of that planned size would have an 80% chance of detecting an effect at the chosen significance level if that effect were the true one. The 90% column describes the corresponding planning target at 90% power. Smaller effects require more participants because they are harder to distinguish from random variation. These calculations are illustrations based on the observed effects, not the trial’s original design assumptions; the original assumptions are not reported in the registry record. This is 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, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = 8.000; pooled standard deviation σ = 28.636.
2. n = 2 × (1.96 + 0.842)² × 28.636² / 8.000² = 201.1, rounded up to 202 participants per arm for 80% power.

The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
delta <- 8                      # observed difference in means
sigma <- 28.6356421265527                     # pooled standard deviation
n_per_arm <- function(power, frac = 1) {
  ceiling(round(2 * (z_a + qnorm(power))^2 * sigma^2 / (delta * frac)^2, 6))
}
for (f in c(1, 0.75, 0.5))
  cat(sprintf("%3.0f%% of observed effect: n per arm = %s (80%% power), %s (90%% power)\n", 100 * f,
              format(n_per_arm(0.80, f), big.mark = ","), format(n_per_arm(0.90, f), big.mark = ",")))

# Check against R's built-in function (t-based, so very slightly larger)
cat("power.t.test:", round(power.t.test(delta = delta, sd = sigma, power = 0.80)$n, 1), "\n")

# Simulation: exact two-sample t-test using simulated means and variances
set.seed(4029883)
n    <- n_per_arm(0.80)
reps <- 20000
m_diff <- rnorm(reps, delta, sigma * sqrt(2 / n))             # difference in sample means
s2     <- sigma^2 * rchisq(reps, 2 * (n - 1)) / (2 * (n - 1))   # pooled sample variance
tstat  <- m_diff / sqrt(s2 * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(tstat) > qt(0.975, 2 * (n - 1))), reps))

Output from running the code

100% of observed effect: n per arm = 202 (80% power), 270 (90% power)
 75% of observed effect: n per arm = 358 (80% power), 479 (90% power)
 50% of observed effect: n per arm = 805 (80% power), 1,078 (90% power)
power.t.test: 202.1 
Simulated power at n = 202 per arm: 0.802 (20000 replicates)

The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

13. Multiplicity, Missing Data and Analysis Populations

The registry reports two posted primary-outcome comparisons against Control: Message versus Control and Incentive versus Control. The comparisons are unadjusted recalculations from summary statistics. The record does not report whether a multiplicity adjustment was planned or applied in an original sponsor analysis, or whether one primary contrast was designated as the principal comparison. The reported p-values should therefore be read as unadjusted values for their individual comparisons rather than as evidence that any family-wide error rate was controlled.

Multiplicity arises when several hypotheses are examined. As the number of comparisons increases, the chance of at least one small p-value arising by chance can increase if each test is interpreted separately. General statistical explanation: adjustment methods can control a chosen error rate across a defined family of tests, but they can also change the threshold or interpretation used for each comparison. The necessary analysis plan and family of hypotheses are not reported in the registry record, so an adjustment method cannot be attributed to this study.

The registry lists Hypertension Control as a secondary outcome, but its result is not reported in the registry record. The record also lists four outcome measures, but does not provide enough details to characterize every measure or analysis. Interim analyses, stopping rules, and any planned hierarchy of outcomes are not reported in the registry record.

Missing-data handling and analysis populations are also not reported in the registry record. The posted primary outcome summaries include 20 participants per group, but this alone does not establish how many participants had complete data, whether all randomized participants were analyzed, or how any missing measurements were treated. The record does not report whether the analysis followed an intention-to-treat approach, a per-protocol approach, or another definition. These omissions matter because analysis choices can influence both the estimate and its uncertainty, especially when data are missing or groups are defined after randomization.

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 20 participants at risk in each group and zero serious adverse events affecting participants in each group. The death count is zero in Control, Message, and Incentive. The other adverse event figures likewise list 20 participants at risk and zero affected participants in each group.

These are the counts recorded for the groups in the registry. A zero count means that no events of the listed type are recorded as affecting participants in those figures; it does not establish that the underlying risk is zero. With 20 participants in each group, the data provide limited information about uncommon events. The registry record does not report further details about adverse-event definitions, collection procedures, severity grading, or follow-up windows beyond the displayed figures, so those aspects cannot be characterized.

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

The posted primary outcome means are higher in both intervention groups than in Control: 95.0 for Message and 92.0 for Incentive, compared with 87.0 for Control. The unadjusted recalculated mean differences are 8.0 for Message versus Control and 5.0 for Incentive versus Control. Their confidence intervals include zero and extend in both directions, so the observed estimates do not precisely establish the direction or size of a population difference.

These results are about electronically measured timely bottle openings for one antihypertensive medication during the 3-month intervention. They do not directly establish whether participants swallowed each dose, whether adherence persisted after the intervention, or whether hypertension control changed. Although Hypertension Control is listed as a secondary outcome, its results are not reported in the registry record. No clinical-event result is presented in the primary outcome summaries.

The findings also do not establish whether incentives add benefit beyond text messages: the posted primary comparisons are each against Control, and a direct comparison between the two intervention groups is not reported. The randomized parallel design is relevant to interpreting group comparisons, but details such as the randomization procedure, masked party, missing-data handling, and analysis population are not reported in the registry record. The confidence intervals and unadjusted p-values should be read with those limitations in mind.

Overall, the posted data show group averages and uncertain between-group estimates in a study with 20 participants per group. They neither establish that the interventions changed adherence nor demonstrate that the groups were equivalent. They are best treated as estimates with substantial uncertainty, not as a definitive statement about clinical benefit, harm, or longer-term outcomes.

16. Why This Trial Matters Statistically

This trial illustrates a central issue in interpreting behavioral intervention studies: a difference between group averages can look straightforward, while uncertainty around that difference remains substantial. The Message and Incentive groups had higher observed mean timely adherence than Control, but the confidence intervals are wide and include zero. Looking at both the estimate and its precision gives a more complete account than focusing on the direction of the means alone.

The endpoint also makes the target behavior explicit. It is not simply whether a bottle was opened at some point; the measure concerns openings within 1 hour of an anchor time. That definition aligns the outcome with the study’s focus on routines and timely medication-taking. At the same time, it makes clear what the electronic record can and cannot capture: the endpoint is based on bottle openings, rather than direct confirmation of ingestion.

The planning illustrations show how sample size depends on the effect a future study aims to detect. Their values differ between the two comparisons because the observed differences and variability differ. Planning around an observed effect is an illustration, not evidence that the original study was designed with those assumptions. The original sample-size rationale is not reported in the registry record, and the observed study included 20 participants per group.

Finally, the record leaves important analysis details unreported, including missing-data procedures and multiplicity handling. Those omissions do not change the reported group summaries, but they limit how fully the analysis strategy can be evaluated. The example is statistically useful because it separates observed averages, uncertainty, planning assumptions, and unreported design details instead of treating them as interchangeable.

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 outcome is based on electronic bottle openings for one antihypertensive medication. It therefore describes a specific measured behavior and does not directly verify that medication was taken. The registry record does not report whether adherence to other antihypertensive medications was measured or how the selected medication was chosen.

The study enrolled 60 participants, with 20 in each group in the posted primary outcome results. The estimates are imprecise, as reflected by the broad confidence intervals and the standard deviations of 22.0, 34.0, and 38.0 across Control, Message, and Incentive. The registry record does not report the original sample-size justification, so the planned ability to detect a particular effect cannot be assessed from that record.

The endpoint covers the 3-month intervention. The registry record does not report adherence results after the intervention, so persistence of any observed pattern cannot be assessed. Hypertension Control is listed as a secondary outcome, but its results are not reported in the registry record. Thus the primary adherence summaries alone do not describe a clinical outcome.

Further limitations in evaluating the analysis include unreported eligibility and participant-characteristic details, randomization procedures, the identity of the masked party, missing-data handling, and analysis-population definitions. The posted comparisons are unadjusted recalculations, and the registry record does not report whether an original sponsor analysis used additional adjustment or a multiplicity procedure. These limitations qualify interpretation of the estimates without changing the numerical summaries recorded for the primary endpoint.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Behavioral Economics to Improve Antihypertensive Therapy Adherence — NCT04029883.
• Registry record last updated 2024-09-19; status last verified 2024-08.
• Results first posted 2023-11-18.
• 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

NCT04029883 is a completed, randomized, single-masked, parallel-group study sponsored by Cedars-Sinai Medical Center. The registry records enrollment of 60 and a study period beginning on 2022-04-19, with primary completion on 2024-02-01. Participants were assigned to Control, Message, or Incentive groups.

The primary outcome was mean electronically measured timely medication adherence during 3 months. The group means were 87.0 for Control, 95.0 for Message, and 92.0 for Incentive. The unadjusted recalculated comparisons against Control were 8.0 for Message and 5.0 for Incentive; both confidence intervals included zero. Hypertension Control is listed as a secondary outcome, but its result is not reported in the registry record. Serious adverse events and deaths were recorded as zero in each group.