This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.
1. Trial at a Glance
This page covers the registry results for Mobile Health for Alcohol Use Disorders in Clinical Practice (NCT04011644), a randomized na study. The primary outcome is Percentage of Heavy Drinking Days, PHDD.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT04011644 |
| Phase | NA |
| Condition | Alcohol Drinking, Telemedicine |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | None (open label) |
| Enrollment | 558 |
| Arms in the primary outcome | 3 |
| Lead sponsor | University of Wisconsin, Madison |
| Results posted | Yes |
2. Clinical Question
Population
Patients with alcohol use disorder receiving care in clinical practice. The registry record lists alcohol drinking and telemedicine as conditions; further eligibility details are not reported in the registry record.
Intervention
Access to the A-CHESS mobile health smartphone application with peer support, or access with clinical integration. The clinically integrated approach included a health coach working within a healthcare system, according to the study summary.
Comparator
A-CHESS self-monitored access, alongside regular physician care. The study summary describes this group as receiving app access without monitoring.
Primary question
At 12 months, did mean percentage of heavy drinking days differ among the self-monitored, peer-supported, and clinically integrated groups?
The central statistical question concerns whether the degree and type of support accompanying a mobile health application are associated with a different reported percentage of heavy drinking days. The outcome captures the percentage of days meeting the study's definition of heavy drinking during the 7 days before assessment. Results are reported separately for each arm, while the sponsor's analysis compares all three groups in a mixed models analysis.
The posted arm summaries show mean percentages of 24.4 for self-monitoring, 21.4 for peer support, and 21.3 for clinical integration. Recalculations compare each supported group with self-monitoring, estimating the difference in group means. Those estimates are unadjusted and do not replace the sponsor's overall analysis. Neither the arm summaries nor the recalculations establish that one approach is equivalent to another; interpreting the estimates requires attention to their uncertainty and to the analysis actually reported by the sponsor.
The registry record does not report a threshold for a clinically important difference in percentage of heavy drinking days. It also does not report the trial's original sample-size rationale or a prespecified pairwise testing plan. These omissions limit conclusions about the intended precision and the role of individual pairwise comparisons.
3. Trial Design
The registry record describes a randomized, parallel-group behavioral study of A-CHESS for alcohol use disorder. It lists allocation as randomized and masking as none. The study status is completed, and enrollment is recorded as 558. The listed phase is NA. The sponsor is the University of Wisconsin, Madison.
Three intervention groups were compared: A-CHESS self-monitored, A-CHESS peer-supported, and A-CHESS clinically-integrated. The study summary describes a third of participants as receiving app access without monitoring, a third as receiving app access connected with a peer mentor, and a third as receiving app access connected with a health coach working within a healthcare system. The detailed arm descriptions in the registry record are incomplete, so additional features should not be inferred from them. The self-monitored group is described as continuing regular physician care.
The primary outcome is percentage of heavy drinking days, assessed at 12 months. The registry defines a heavy drinking day using self-reported drinking in the last 7 days: 5 or more standard drinks on any day for men under 65, or 4 or more standard drinks for women and men over 65. The primary endpoint is reported as a mean with standard deviation for each arm.
The record lists a start date of 2020-03-23 and primary completion of 2023-10-31. It also lists secondary outcomes covering hospital nights, implementation cost, alcohol screening and severity scores, willingness to share data, and measures of relatedness, competence, and autonomous motivation. The registry record does not report further details of the randomization procedure, concealment, the intervention delivery schedule, or the original statistical analysis plan.
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: The site staff were not enrolled in the clinical trial that is represented in the overall study flow diagram above and as such are not included in it. They were engaged in a post hoc interview to understand the study results for an exploratory analysis.
Overall Study
| Stage | Self Monitored | Peer Supported | Clinically Integrated |
|---|---|---|---|
| STARTED | 185 | 186 | 187 |
| COMPLETED | 139 | 132 | 102 |
| NOT COMPLETED | 46 | 54 | 85 |
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.
| Characteristic | Unit | Self Monitored | Peer Supported | Clinically Integrated | Total |
|---|---|---|---|---|---|
| Participants analysed | 185 | 186 | 187 | 558 | |
| Age, Continuous | years | 42.80 (SD 12.9) | 42.8 (SD 12.9) | 42.6 (SD 12.9) | 42.8 (SD 12.9) |
| Sex: Female, Male: Female | Participants | 120 | 122 | 123 | 365 |
| Sex: Female, Male: Male | Participants | 65 | 64 | 64 | 193 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 4 | 6 | 4 | 14 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 181 | 180 | 183 | 544 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 0 | 0 | 0 | 0 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 2 | 1 | 0 | 3 |
| Race (NIH/OMB): Asian | Participants | 5 | 2 | 4 | 11 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 0 | 1 | 1 | 2 |
| Race (NIH/OMB): Black or African American | Participants | 7 | 8 | 10 | 25 |
| Race (NIH/OMB): White | Participants | 170 | 167 | 170 | 507 |
| Race (NIH/OMB): More than one race | Participants | 0 | 3 | 1 | 4 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 1 | 4 | 1 | 6 |
| Education: < High school | Participants | 0 | 2 | 1 | 3 |
| Education: HS or GED | Participants | 16 | 19 | 32 | 67 |
| Education: Vocation or associate | Participants | 35 | 34 | 16 | 85 |
| Education: Bachelors | Participants | 76 | 83 | 76 | 235 |
| Education: Masters | Participants | 44 | 29 | 48 | 121 |
| Education: Doctorate | Participants | 14 | 19 | 14 | 47 |
| AUDIT Category: Low risk | Participants | 39 | 53 | 41 | 133 |
| AUDIT Category: Harmful drinking | Participants | 85 | 72 | 84 | 241 |
| AUDIT Category: Alcohol dependence | Participants | 61 | 61 | 62 | 184 |
| Percentage of heavy drinking days (PHDD) | percentage | 37.1 (SD 30.6) | 36.2 (SD 31.2) | 41.9 (SD 31.4) | 38.4 (SD 31.1) |
| Quality of life-physical health, QOL-PH | T-score | 48.4 (SD 6.3) | 48.1 (SD 6.7) | 48.3 (SD 6.5) | 48.3 (SD 6.5) |
| Quality of life-mental health, QOL-MH | T-scores | 45.5 (SD 6.9) | 45.5 (SD 7.5) | 45.4 (SD 6.9) | 45.4 (SD 7.1) |
6. Primary Endpoint
The registry lists the primary outcome as Percentage of Heavy Drinking Days, PHDD, measured over 12 months.
| Element | Registry entry |
|---|---|
| Result type | Mean |
| Measure of spread | Standard Deviation |
| Unit | percentage of heavy drinking days |
| Endpoint classification | Continuous Endpoint |
The primary endpoint is percentage of self-reported heavy drinking days at 12 months. It is calculated from the participant's report of heavy drinking days during the last 7 days, using the registry's sex- and age-specific drink thresholds. The outcome is a continuous measure expressed as a percentage; the registry reports arm means and standard deviations.
This endpoint describes the frequency of heavy drinking days over a recent period at the follow-up assessment. A percentage can be compared across groups on the same scale, and reporting the mean gives a summary of the central level in each group. The standard deviation describes variation in individual measurements around that mean. It is not the same as the uncertainty in the estimated group mean or the uncertainty in a difference between groups.
A single 7-day self-report is a short-window measure, rather than a record of every day throughout the full follow-up period. Self-report also depends on recall and on how participants understand and report drinking. These measurement features matter when interpreting small differences between group means. The registry record does not report a minimum clinically important difference for this endpoint, so the clinical importance of a particular numerical difference cannot be determined from the posted outcome alone.
7. Results Posted in the Registry
- Peer Supported: mean 21.40 versus 24.40 on control; difference -3.00 (95% CI -9.83 to 3.83), standardized effect d = -0.11; z-test p = 0.389.
- Clinically Integrated: mean 21.30 versus 24.40 on control; difference -3.10 (95% CI -10.68 to 4.48), standardized effect d = -0.11; z-test p = 0.423.
Mean difference: Peer Supported
95% CI: -9.83 to 3.83
Recalculated from the posted summary statistics
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.
| Secondary outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Number of Hospital Nights in the Past 6 Months | Continuous Endpoint | Mean difference | -0.01 (-0.10 to 0.09) | 52,544 per arm |
| Score of Alcohol Use Disorders Identification Test (AUDIT) Screening Tool | Continuous Endpoint | Mean difference | 0.31 (-1.02 to 1.64) | 4,877 per arm |
| Score of the Diagnostic and Statistical Manual- 5 Alcohol Use Disorder (AUD) Severity | Continuous Endpoint | Mean difference | -0.01 (-0.47 to 0.44) | 251,870 per arm |
Number of Hospital Nights in the Past 6 Months
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
- Result:
- Peer Supported: mean 0.05 versus 0.05 on control; difference -0.01 (95% CI -0.10 to 0.09), standardized effect d = -0.02; z-test p = 0.890.
- Clinically Integrated: mean 0.22 versus 0.05 on control; difference 0.16 (95% CI -0.11 to 0.43), standardized effect d = 0.18; z-test p = 0.232.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Peer Supported and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Clinically Integrated and the control. The interval gives the range of effects that remain compatible with the data.
Score of Alcohol Use Disorders Identification Test (AUDIT) Screening Tool
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
- Result:
- Peer Supported: mean 9.34 versus 9.03 on control; difference 0.31 (95% CI -1.02 to 1.64), standardized effect d = 0.06; z-test p = 0.649.
- Clinically Integrated: mean 8.83 versus 9.03 on control; difference -0.20 (95% CI -1.58 to 1.18), standardized effect d = -0.04; z-test p = 0.774.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Peer Supported and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Clinically Integrated and the control. The interval gives the range of effects that remain compatible with the data.
Score of the Diagnostic and Statistical Manual- 5 Alcohol Use Disorder (AUD) Severity
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
- Result:
- Peer Supported: mean 2.52 versus 2.54 on control; difference -0.01 (95% CI -0.47 to 0.44), standardized effect d = -0.01; z-test p = 0.953.
- Clinically Integrated: mean 2.92 versus 2.54 on control; difference 0.38 (95% CI -0.22 to 0.99), standardized effect d = 0.20; z-test p = 0.216.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Peer Supported and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Clinically Integrated and the control. The interval gives the range of effects that remain compatible with the data.
The registry lists a range of secondary outcomes, including hospital nights, alcohol screening and severity scores, implementation cost, willingness to share data, and measures related to motivation, competence, and relatedness. The posted secondary results cover multiple outcomes and analyses, with the number of posted secondary outcome measures recorded as 14. The pattern is not a single consistent signal across measures: group summaries and overall tests vary by outcome, and the registry does not report a unified secondary-outcome estimate.
These outcomes provide additional perspectives on health service use, alcohol-related measures, and engagement with the intervention. They can help describe what was assessed alongside the primary endpoint, but they do not replace it. The primary outcome addresses percentage of heavy drinking days at 12 months; a secondary measure has its own scale, measurement properties, and analysis question. Agreement or disagreement across distinct measures is not, by itself, a direct replication of the primary result.
Several secondary comparisons are accompanied by unadjusted recalculated contrasts, while the registry also reports sponsor analyses such as ANCOVA for listed outcomes. Those approaches answer different questions and may use different adjustment. The details of covariate selection and handling of missing observations are not reported in the registry record.
Unadjusted secondary results carry less weight because many outcomes and contrasts create more opportunities for chance findings. The registry record does not report a multiplicity adjustment or a prespecified hierarchy for secondary testing. In the absence of that information, individual secondary p-values should be treated as exploratory signals rather than isolated confirmatory evidence. The secondary findings can contextualize the primary result, but they do not resolve the uncertainty in the primary pairwise estimates or establish an overall treatment effect.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Number of Patients Who Are Willing to Share Data
- Number of Hospital Nights in the Past 6 Months
- Cost of Implementation of Each Intervention Arm in US Dollars
- Score of Alcohol Use Disorders Identification Test (AUDIT) Screening Tool
- Score of the Diagnostic and Statistical Manual- 5 Alcohol Use Disorder (AUD) Severity
- Score of Relatedness as Assessed by the CHESS Bonding Scale
- Score of Competence as Assessed by the Perceived Competence Scale (PCS)
- Score of Autonomous Motivation as Assessed by Revised Treatment Self Regulation Questionnaire
9. Statistical Interpretation
At 12 months, the posted mean percentage of heavy drinking days was 24.4 in the self-monitored group, 21.4 in the peer-supported group, and 21.3 in the clinically integrated group. The standard deviations were 28.2, 28.9, and 30.4, respectively. These summaries describe the observed outcome distributions and show substantial variation within each arm relative to the differences between their means.
The unadjusted recalculation for peer support versus self-monitoring estimates a mean difference of -3.0 percentage points, with a 95% confidence interval from -9.831 to 3.831 and p = 0.389. For clinical integration versus self-monitoring, the estimated mean difference is -3.1 percentage points, with a 95% confidence interval from -10.68 to 4.481 and p = 0.423. Both intervals include zero, so the recalculations do not distinguish the observed differences from no mean difference at the stated interval level. They are not evidence that the groups are equivalent.
The sponsor's reported mixed models analysis compares the three groups together and gives p = 0.688. This is an overall analysis, rather than either of the two separate recalculated pairwise contrasts. The registry record does not report a model estimate or confidence interval for that overall analysis, so its result cannot be described in terms of the magnitude or precision of an adjusted overall effect.
The direction of the two unadjusted mean differences favors lower observed percentages in the supported groups relative to self-monitoring, but their confidence intervals are broad and span values in either direction. The estimates therefore do not establish a precise difference. The sponsor's overall p-value also does not show a difference among the groups in that analysis, but it does not demonstrate that any two approaches are the same.
Interpretation should separate descriptive arm means, recalculated unadjusted pairwise estimates, and the sponsor's overall model result. The record does not report a clinical threshold for meaningful change, a detailed account of missing primary outcomes, or the prespecified strategy for multiple comparisons. Those gaps prevent a stronger conclusion about clinical importance, robustness, or the intended inferential emphasis.
10. Statistical Methods Explained
The primary endpoint is continuous, so the registry presents a mean and standard deviation for each arm. A mean is an average of the measured percentages within a group. A standard deviation describes how dispersed individual measurements are around that group mean. A large standard deviation relative to differences between means indicates that individual observations vary widely within groups; it does not, by itself, tell whether the estimated difference is precise.
What does a mean difference express?
The recalculated pairwise estimates subtract the self-monitored arm mean from the relevant supported-arm mean. A negative estimate means the supported arm's observed average was lower on the endpoint's percentage scale. The peer-supported comparison is -3.0, and the clinically integrated comparison is -3.1. These are simple unadjusted calculations from posted summary statistics. They do not incorporate adjustment for baseline values or other covariates, and they should not be confused with the sponsor's reported model.
What does a confidence interval add?
A confidence interval gives a range of estimates compatible with the data under the calculation's assumptions. For a mean difference, values below zero indicate a lower mean in the supported arm, while values above zero indicate a higher mean. When an interval includes zero, the data do not clearly distinguish the estimated contrast from no difference using that interval. This does not establish equivalence or rule out effects that could matter. The width of the interval is important: wider intervals indicate less precision.
How should p-values be read?
A p-value describes how unusual data at least as extreme as those observed would be under a specified null model and its assumptions. It is not the probability that the null hypothesis is true, nor does it measure the size or importance of an effect. The pairwise recalculations report unadjusted p-values of 0.389 and 0.423. The sponsor reports p = 0.688 for the overall mixed models analysis. These values refer to different analyses and should not be treated as interchangeable.
Why are the sponsor and recalculated analyses different in purpose?
The sponsor's reported analysis uses mixed models and evaluates the three groups together. The registry record does not provide its model estimates, model specification, or details of how repeated observations were handled. The recalculations are separate, unadjusted contrasts based on arm-level means and standard deviations. They offer interpretable pairwise estimates, but they cannot reproduce an adjusted model without the relevant individual-level data and analysis details. The registry record reports no discrepancy flag, but the recalculations remain supplementary rather than a substitute for the sponsor's own analysis.
Why can variation affect precision?
When outcomes vary substantially among participants, a mean difference may be estimated less precisely unless the available information is sufficient to offset that variability. In this trial, the primary-outcome standard deviations are large compared with the observed mean differences. This helps explain why the recalculated intervals are broad. General statistical principle: when a continuous outcome has a long-tailed or highly uneven distribution, a mean and standard deviation can be influenced by unusual values. The registry record does not provide distribution plots or enough detail to assess this feature directly.
What is over-dispersion, in general?
For count or binary outcomes, over-dispersion means that observed variability exceeds what a simple model assumes. Methods that ignore it can give standard errors that are too small and intervals that are too narrow. This is a general concept, not a claim that over-dispersion occurred in the primary analysis. The primary endpoint is continuous, and the registry record does not report a specific over-dispersion assessment.
The primary sponsor analysis is identified as a mixed models analysis, but its model formula, covariance structure, adjustment variables, handling of incomplete follow-up, and analysis population are not reported in the registry record. These details matter because they determine what estimate the model targets and how uncertainty is calculated. The posted summary alone does not support reconstructing those choices.
The secondary outcomes include continuous measures and other outcome types, and the registry lists analyses using ANCOVA for several secondary comparisons. General statistical principle: ANCOVA estimates group differences while accounting for specified covariates, often including a baseline measurement. Which covariates were used in these analyses is not reported in the registry record, so the model details should not be assumed. The sponsor's posted overall tests for the named secondary outcomes should be read as analyses distinct from the simple recalculations based on arm summaries.
11. Confidence Intervals and Precision
Precision is the degree to which an estimate is constrained by the data. The recalculated 95% confidence interval for peer support versus self-monitoring runs from -9.831 to 3.831 percentage points. For clinical integration versus self-monitoring, it runs from -10.68 to 4.481 percentage points. Each interval includes zero and spans both a lower and a higher mean in the supported arm. The data therefore leave uncertainty about the direction and size of either pairwise difference.
The interval limits also show why a point estimate alone is insufficient. The estimates, -3.0 and -3.1, are both lower observed means in the supported groups, but the intervals extend beyond zero. The point estimates should not be read as exact effects, and interval inclusion of zero should not be translated into proof of no effect. Nor do these intervals establish equivalence: that would require an appropriate equivalence framework and a prespecified margin, neither of which is reported in the registry record.
These recalculated intervals are unadjusted and are based on summary statistics. The sponsor's mixed models analysis is reported with a p-value but no estimate or confidence interval in the registry record. Consequently, its precision cannot be evaluated from a reported interval, and the pairwise intervals should not be presented as if they came from that model.
The registry record does not state a threshold for a clinically important difference. Statistical uncertainty can therefore be described, but the range cannot be classified against a registry-defined clinical benchmark. General statistical principle: precision depends on variability, information available, and the analysis method; it is not captured by a p-value alone.
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.
| Effect to detect | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 1,421 | 1,902 |
| 75% of the observed effect | 2,526 | 3,382 |
| 50% of the observed effect | 5,683 | 7,608 |
The planning figures are illustrations based on the observed effect in each recalculated comparison, not the trial's original design calculation. They give participants per arm, rather than total events. The assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, a normal approximation, and an effect to detect set at the stated fraction of the observed effect. The trial's own original sample-size assumptions are not reported in the registry record.
The 80% power column describes the number of participants per arm that the illustration estimates would be needed to have an 80% chance of detecting the specified effect under those assumptions, if that effect were the true one. The 90% power column uses a higher probability of detection and therefore calls for more participants per arm under the same framework. Power is a property of a proposed design under assumptions; it is not a probability that the observed result is true.
Each planning row uses a different fraction of the observed effect. Planning for 75% of the observed effect means targeting a smaller effect than the full observed estimate; planning for 50% means targeting a still smaller one. Smaller effects are harder to distinguish from random variation, so they require more participants per arm under otherwise unchanged assumptions. Where an observed effect is very close to zero, these calculations can become extremely large and should be treated as unstable illustrations rather than practical recommendations.
These figures are not observed power. They do not explain why the trial used its enrolled sample, and they should not be used to infer what the trial was designed to detect. They also do not account for features not included in the stated assumptions, such as adjustment, attrition, or a multiplicity strategy.
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 z1−α/2 = 1.960) and the desired power (z1−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
- Observed difference Δ = -3.000; pooled standard deviation σ = 28.540.
- n = 2 × (1.96 + 0.842)2 × 28.5402 / -3.0002 = 1,420.7, rounded up to 1,421 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 <- -3 # observed difference in means
sigma <- 28.5403459739823 # 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(4011644)
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 = 1,421 (80% power), 1,902 (90% power)
75% of observed effect: n per arm = 2,526 (80% power), 3,382 (90% power)
50% of observed effect: n per arm = 5,683 (80% power), 7,608 (90% power)
power.t.test: 1421.7
Simulated power at n = 1,421 per arm: 0.797 (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.
14. Analyses Reported by the Sponsor
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| Mixed Models Analysis | not reported | 0.688 |
The sponsor reports a mixed models analysis across the three groups for the primary outcome, with p = 0.688. The reported result is an overall test; it is not a pairwise estimate of peer support versus self-monitoring or clinical integration versus self-monitoring. The registry record gives no model estimate or confidence interval for this test.
The recalculated comparisons use the posted arm means and standard deviations to estimate unadjusted pairwise mean differences. They report -3.0 for peer support versus self-monitoring and -3.1 for clinical integration versus self-monitoring, each with a confidence interval that includes zero. These calculations are useful as descriptive contrasts, but they do not reproduce the sponsor's mixed model or its potential adjustments and assumptions.
The registry record does not indicate a discrepancy between the sponsor's reported result and the recalculations. Even so, the sponsor's own analysis takes precedence for the trial's reported inferential result. The recalculations should be regarded as supplementary, transparent comparisons from the posted summaries, not as a replacement analysis or an alternative definitive test.
15. Multiplicity, Missing Data and Analysis Populations
Multiplicity arises when multiple hypotheses are tested. Testing several outcomes, groups, or pairwise contrasts can increase the chance that at least one result appears notable by chance, even when no true difference exists. This trial has three arms, a primary outcome, and numerous secondary measures. The registry record does not report a multiplicity adjustment, a confirmatory testing hierarchy, or which secondary tests were designated exploratory.
The sponsor's primary analysis is an overall test of the three groups. The recalculated contrasts are two unadjusted pairwise comparisons with self-monitoring. The record does not say whether those pairwise comparisons were prespecified, whether a correction was planned, or how they fit into the original analysis plan. Their p-values and confidence intervals therefore need to be interpreted as unadjusted summaries, not as multiplicity-controlled confirmatory findings.
Missing data can also affect interpretation when outcome observations are unavailable or differ across groups. The primary outcome summaries have reported arm-specific sample sizes, but the registry record does not explain why those numbers differ from one another or from the enrollment figure. It does not report the amount or pattern of missing primary outcome data, reasons for missingness, imputation methods, or sensitivity analyses. The impact of missingness on estimates cannot be assessed from the registry summaries alone.
The registry record identifies a mixed models analysis but does not state the analysis population, whether participants were analyzed according to randomized assignment, or how post-randomization exclusions were handled. It does not report the full statistical analysis plan, model specification, or assumptions about incomplete repeated measurements. These are not details to infer from the method label. They matter for evaluating whether the reported comparison is robust to departures from model assumptions and missing-data patterns.
Without those details, the posted results support a description of the reported estimates and their uncertainty, but not a complete audit of the planned inferential strategy. General statistical principle: prespecification and transparent reporting help distinguish planned tests from analyses selected after seeing results.
16. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Self Monitored | 0 | 185 | 0.0% |
| Peer Supported | 0 | 186 | 0.0% |
| Clinically Integrated | 0 | 187 | 0.0% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Self Monitored | 0 of 185 |
| Peer Supported | 0 of 186 |
| Clinically Integrated | 0 of 187 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 0% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Self Monitored | 0 of 185 |
| Peer Supported | 0 of 186 |
| Clinically Integrated | 0 of 187 |
The adverse-event record reports serious adverse events affecting 0 participants in each listed group, and other adverse events affecting 0 participants in each listed group. Deaths are also reported as 0 in each group. The registry lists 185 participants at risk for each adverse-event category in the self-monitored group, 186 in the peer-supported group, and 187 in the clinically integrated group.
These figures describe what was recorded in the registry for the stated at-risk groups. They do not establish that no adverse experiences occurred outside the registry's reporting definitions or observation procedures. The registry record does not list serious adverse-event terms, and the event counts alone do not provide information about event monitoring, attribution, duration, or completeness of follow-up.
Safety counts should be read separately from the primary outcome analysis. They do not measure the effect on heavy drinking days and cannot resolve the uncertainty in the primary endpoint comparisons. The record's zero counts are a description of posted adverse-event reporting, not a broad conclusion about safety.
17. What the Result Does, and Does Not, Mean
The posted primary results describe three groups with mean percentage of heavy drinking days of 24.4 for self-monitoring, 21.4 for peer support, and 21.3 for clinical integration at 12 months. The sponsor's overall mixed models analysis reports p = 0.688. The unadjusted recalculations estimate lower means in each supported group relative to self-monitoring, but their confidence intervals include zero and are broad.
These results do not establish that peer support or clinical integration produces a different primary outcome from self-monitoring. They also do not establish that the approaches are equivalent or that any difference is absent. The sponsor's overall test, the recalculated pairwise comparisons, and the descriptive arm means are distinct pieces of evidence and should not be merged into one claim.
The registry record does not report a threshold for a clinically meaningful difference. As a result, the numerical estimates cannot be classified as clinically important or unimportant on the basis of a registered benchmark. The outcome is self-reported for the last 7 days at a 12-month assessment, and its interpretation should remain tied to that measurement window rather than being treated as a continuous record of drinking throughout follow-up.
The secondary outcomes broaden the questions addressed but do not substitute for the primary endpoint. Their multiplicity and the absence of a reported testing hierarchy make isolated secondary results less definitive. Similarly, zero posted adverse-event counts are limited to the adverse-event reporting in the registry record and do not support a comprehensive safety conclusion.
Overall, the posted data offer descriptive comparisons and estimates with substantial uncertainty. They do not support a definitive claim about a meaningful advantage, equivalence, or absence of effect. The registry record's missing details about analysis populations, missing data, model specification, and multiplicity further constrain interpretation.
18. Why This Trial Matters Statistically
This trial illustrates why the statistical question should be defined before interpreting group summaries. Three randomized arms allow comparison of different ways to accompany a mobile health application, but a set of means is not itself a test of the overall group pattern. The sponsor's mixed models analysis addresses the three groups together, while the recalculated contrasts focus on each supported approach against self-monitoring.
It also illustrates the difference between effect magnitude and precision. The observed pairwise mean differences are modest in relation to the variability in the endpoint, and their confidence intervals include values on both sides of zero. A p-value alone would conceal that range of plausible effects. Reading estimates and intervals alongside arm summaries gives a more informative account of what the posted results can and cannot distinguish.
Another statistical lesson is that a small observed effect can imply very large planning illustrations when used as the target for a future study. Such figures depend on assumptions and should not be mistaken for the original trial's design rationale or an estimate of observed power. Here, the original sample-size justification is not reported in the registry record.
Finally, a broad set of secondary outcomes creates interpretive challenges. Without a reported multiplicity plan, isolated findings deserve caution, even when they may be useful for generating future questions. Transparent reporting of model details, missing-data handling, analysis populations, and prespecified testing priorities would make it easier to assess how robustly the trial answers its statistical questions.
19. 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 self-report about the last 7 days at the 12-month assessment. This captures a defined recent period, but it is not a continuous measure of drinking across the full follow-up. Recall and reporting may affect the measured value; the registry record does not describe procedures used to assess or address those measurement concerns.
The detailed descriptions of the three interventions are incomplete in the registry record. The study summary distinguishes self-monitoring, peer connection, and clinical integration with a health coach, but the record does not provide enough complete detail to characterize all intervention components, delivery intensity, or adherence. Differences in exposure to the app or support cannot be evaluated from the posted results alone.
Primary outcome sample sizes differ across arms, and the registry does not report the reasons. It does not provide a missing-data summary, an analysis population definition, or sensitivity analyses. The extent to which unavailable measurements could influence the comparisons is therefore unclear.
The sponsor reports an overall mixed models p-value without an estimate or confidence interval, while the recalculated pairwise estimates are unadjusted. The registry record does not provide the model specification, covariates, or the relationship between the pairwise contrasts and the prespecified analysis plan. No threshold for a clinically important difference or multiplicity strategy is reported.
These limitations apply to interpretation of the registry record; they do not establish that the original trial lacked procedures or analyses. They identify information that is not reported in the registry record and therefore cannot be assessed from these results.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Mobile Health for Alcohol Use Disorders in Clinical Practice — NCT04011644.
- Registry record last updated 2025-01-23; status last verified 2025-01.
- Results first posted 2025-01-23.
- 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.
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23. Record Summary
NCT04011644 is a completed randomized, parallel-group behavioral study sponsored by the University of Wisconsin, Madison. It evaluated A-CHESS in self-monitored, peer-supported, and clinically integrated groups, with no masking listed in the registry record. Enrollment is recorded as 558.
The primary outcome was mean percentage of self-reported heavy drinking days at 12 months. The sponsor reports a mixed models analysis across the three groups with p = 0.688. Unadjusted recalculations estimate mean differences of -3.0 for peer support versus self-monitoring and -3.1 for clinical integration versus self-monitoring; both confidence intervals include zero.
The registry record does not report the original sample-size rationale, detailed analysis plan, multiplicity strategy, or missing-data methods. The results are best read as descriptive arm summaries and uncertain comparisons, rather than evidence of equivalence or a definitive difference.