Multiphase Optimization Trial of Incentives for Veterans to Encourage Walking: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Multiphase Optimization Trial of Incentives for Veterans to Encourage Walking (NCT04518943), a randomized na study. The primary outcome is Change in Average Steps Per Day From Baseline Week to Week 12.

2. Clinical Question

3. Trial Design

The trial is registered as a randomized, single-masked, factorial study. Its title identifies it as a multiphase optimization trial of incentives for Veterans to encourage walking. The registry reports enrollment of 102 and lists walking as the behavioral intervention. The recorded study status is completed. The study began on 2022-03-17, and primary completion is recorded as 2023-11-30.

The arm descriptions combine several design features. Incentives could be financial or non-financial; the descriptions also distinguish mixed-lottery incentives from loss incentives. Participants could receive pre-commitment postcard reminders, and some groups were asked to request physical-activity advice. This is a factorial structure in the broad sense that multiple intervention components are varied in combinations. The registry record does not report enough detail to reconstruct the allocation sequence, component-specific randomization procedures, or the exact planned contrasts.

The displayed primary-outcome arm summaries include 15 combinations, but the record says that one group was not assessed for this outcome because its baseline step counts were too high or too low. The outcome summaries therefore do not represent the full enrollment in a simple way. Individual group counts are small, and the record does not provide a participant flow account explaining the difference between enrollment and the counts contributing to each posted outcome summary.

The registry lists three secondary outcomes: self-efficacy, intrinsic or extrinsic motivation, and mental health. It also reports five outcome measures and 32 analyses, but the full analysis plan and detailed endpoint-to-analysis mapping are not reported in the registry record. Phase is recorded as not applicable. Masking beyond the single-masked designation, including who was masked, is not reported in the registry record.

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.

Only the first 6 of 16 groups are shown.

Consent Through Baseline

Reasons for not completing this period:

Baseline to Week 12

Week 12 to 24

Analysis population for the primary outcome, as defined in the registry: The participants in the N1L1P0R0 group were not assessed because they either walked too many or to few steps at the baseline period

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

Only the first 6 of 17 groups are shown.

6. Primary Endpoint

The registry lists the primary outcome as Change in Average Steps Per Day From Baseline Week to Week 12, measured over baseline to week 12.

The primary endpoint is change in average steps per day from baseline week to week 12, expressed in steps per day. It is a continuous outcome: each participant’s step count can take a range of numerical values, and the posted summaries describe means and standard deviations. The endpoint focuses on change across the study period rather than a single step-count reading.

Daily steps provide a direct measure of walking activity, the behavior targeted by the intervention. Comparing change from baseline can describe whether the average activity level shifted during follow-up, while accounting for where participants started. This is the outcome named in the registry as primary; the registry also lists self-efficacy, motivation, and mental health as secondary outcomes.

Interpretation requires attention to the population actually assessed. The record states that the non-financial, loss-incentive group without reminders or an advice request was not assessed for this endpoint because participants either walked too many or too few steps at baseline. It does not report the threshold used, how this decision was applied, or further detail about the resulting analysis population. The posted arm-level means are not themselves baseline-to-follow-up changes, and the registry’s model estimates should not be conflated with those raw summaries.

For a continuous outcome, the mean describes the average, while the standard deviation describes how much participant values vary around that mean. In groups with small counts, both summaries may be imprecise and sensitive to individual observations. The endpoint is therefore useful for describing average walking change, but the record’s exclusions, small arm counts, and unclear mapping of modeled estimates to specific contrasts constrain interpretation.

7. Why No Re-analysis Is Shown

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is continuous, and the registry reports group means and standard deviations alongside model-based mean differences. These quantities answer different questions. A group mean describes the average outcome among participants summarized in that group. A standard deviation describes the spread of participant values around the mean. A model-based mean difference estimates a contrast between groups or conditions, potentially accounting for features of the analysis model. The registry reports the latter as a net mean difference, but it does not clearly map each estimate to a specific comparison.

What does a confidence interval express?

A confidence interval gives a range of estimates compatible with the observed data and the assumptions of the statistical model, at the stated confidence level. The registry reports 90% intervals for the posted model estimates. A narrower interval represents greater precision than a wider interval, all else equal. These intervals do not show the spread of individual step counts; that is what the standard deviation describes. Nor does an interval establish that every value inside it is equally plausible.

For a mean difference, zero represents no difference on the scale being estimated. If an interval includes zero, the data do not distinguish the estimate from zero at the interval’s stated confidence level. If an interval excludes zero, it indicates a nonzero estimate under that model and contrast. This interpretation remains conditional on the analysis assumptions, and it does not establish practical importance. The registry does not report a threshold for a meaningful change in steps per day.

How should the p-values be read?

A p-value describes how unusual the observed data, or data more extreme, would be under a specified null model and its assumptions. It is not the probability that the null hypothesis is true, and it does not measure the size or importance of an effect. The posted p-values range across the four model-based results, and the corresponding estimates and intervals should be considered together rather than interpreting a p-value alone.

The registry identifies a linear mixed model for one result and mixed models analysis for the others. Mixed models are commonly used for data with repeated observations or other correlated structure, because observations from the same participant or related units may not be independent. This is a general explanation of the method; the registry record does not report the specific model terms, covariance structure, adjustment variables, or handling of repeated measurements. Consequently, the exact assumptions behind the posted estimates cannot be independently assessed from this record.

Why do small groups and variability matter?

The displayed arm summaries have small counts, and the standard deviations vary substantially across arms. With few observations, an average can be strongly affected by individual values, and the uncertainty around a group estimate may be considerable. A large standard deviation relative to a group’s mean signals considerable dispersion in the observed values, though it does not by itself reveal the shape of the data. When counts are small, standard deviations can also be unstable. Some reported spreads are zero, which may occur when values in the summarized group do not vary or when the summary is based on very few observations; the registry does not provide participant-level data to distinguish these possibilities.

General statistical context: over-dispersion means that observed variability is greater than a model expects. It can make standard errors too small and confidence intervals too narrow if the analysis does not account for it. The record does not state that over-dispersion was identified or how model diagnostics were conducted, so this is a general consideration rather than a claim about this trial.

What does the factorial structure add?

In a factorial trial, intervention components are varied in combinations so their effects can be examined across more than one feature. This can be efficient for studying several design choices, but interpretation depends on the prespecified contrasts and how interactions between components are handled. For example, a component’s association with outcome could depend on which other components accompany it. The registry identifies a factorial model and lists combinations of incentive type, lottery or loss framing, reminders, and advice requests. It does not report the planned component contrasts, interaction terms, or multiplicity strategy. The posted net mean differences therefore cannot be confidently assigned to particular components using this record alone.

Finally, the registry’s group summaries are descriptive and its model estimates are inferential. They should not be substituted for one another. The former show means and standard deviations in the listed outcome groups; the latter reflect model-based comparisons. In the absence of detailed model specifications and explicit contrast labels, interpretation should stay close to the reported estimates and acknowledge the limits of what the record establishes.

10. Analyses Reported by the Sponsor

The registry reports four sponsor analyses for the primary outcome, including one described as a linear mixed model and three described as mixed models analyses. Their mean differences, confidence intervals, and p-values are the official posted inferential results. The record does not clearly identify the precise intervention contrast associated with each estimate, which limits a direct interpretation of the estimates as effects of individual design features.

No discrepancy is flagged between the sponsor results and a recalculated result. The sponsor’s own analysis therefore remains the appropriate posted analysis to cite; no alternate recalculated estimate is presented as a replacement. The arm-level means and standard deviations are descriptive summaries, not a substitute for the sponsor’s model-based contrasts. Reconstructing an unadjusted contrast from those summaries would not necessarily reproduce a mixed-model estimate, particularly when the relevant contrast, model structure, and analysis population are not fully specified.

The registry does not report enough detail to independently reproduce the fitted models. In particular, model terms, covariance assumptions, adjustment variables, and the mapping of each estimate to a contrast are not reported in the registry record. The interpretation should therefore distinguish the reported model results from the raw group summaries and avoid assigning a particular result to one incentive component without an explicit contrast definition.

11. Multiplicity, Missing Data and Analysis Populations

The record lists 32 analyses, five outcome measures, and three posted secondary outcomes. It does not report a multiplicity adjustment strategy, a hierarchy of confirmatory tests, or which analyses were designated primary beyond naming the primary outcome. When many outcomes or contrasts are examined, the chance of at least one apparently notable result can increase. This is a general statistical issue, not evidence that any particular result is false. The p-values should be interpreted in light of the breadth of analyses and the absence of a reported multiplicity plan.

Missing-data procedures are not reported in the registry record. The primary outcome was not assessed in the non-financial, loss-incentive group without reminders or an advice request because participants either walked too many or too few steps at baseline. The record does not give the qualifying threshold, how many participants were affected, or whether that exclusion was planned. It also does not describe other missing observations, reasons for missingness, imputation, or sensitivity analyses. Those omissions make it difficult to judge how the analyzed participants represent the enrolled group.

The registry reports enrollment of 102, while the primary outcome arm summaries show small group counts. The record does not provide a participant flow account that explains which participants contributed to each analysis or how the outcome analysis population was defined. It also does not report whether all randomized participants were analyzed in their assigned groups. The primary outcome population is therefore not fully characterized by the posted information.

These reporting gaps matter for the factorial design as well. Without the planned contrasts and analysis-population definitions, it is unclear how the analyses account for the multiple component combinations or whether interaction questions were included. The statistical analysis plan, sample-size justification, interim analyses, and detailed missing-data strategy are not reported in the registry record. Absence of those details from the registry record should not be taken as evidence that a procedure was or was not used.

12. 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 registry reports serious adverse events, other adverse events, and deaths by listed group. In each displayed group, the count affected by serious adverse events is zero, the count affected by other adverse events is zero, and deaths are zero. The record’s at-risk counts differ across groups. These figures describe the adverse-event reporting in the registry; they do not establish that no events occurred outside the recorded definitions, observation period, or reporting process.

Zero reported events should be interpreted in context. Group counts are small, and an absence of observed events in a small group does not demonstrate that an event cannot occur. The registry does not provide event-term detail for serious events, and it reports no top serious-event terms. It also does not give further information in this record about surveillance methods, event collection windows, severity grading, or causal attribution.

The adverse-event groups and the primary-outcome summaries have different reported group counts, so the safety figures should not be treated as a complete account of the primary outcome analysis population. The registry lists no deaths in the reported groups. These descriptive safety counts are not a comparative safety analysis, and they do not establish that one incentive combination is safer than another.

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

The results concern average steps per day from baseline week to week 12 in a trial testing combinations of incentives and behavioral supports for walking among Veterans. The registry presents four model-based mean differences with 90% confidence intervals and p-values. One estimate has an interval that excludes zero, while the others include zero; the point estimates also differ in direction. These findings describe the posted analyses, not a settled ranking of the incentive designs.

The outcome summaries show variation in the average step changes across groups, but raw arm summaries do not identify the causal effect of any single component. The study has a factorial structure, and the registry record does not clearly label which feature contrast corresponds to each model result. It is therefore not possible from the posted record alone to say which specific combination or component accounts for a particular estimate.

The estimates are imprecise enough that their intervals cover a range of possible differences. The record does not report a threshold for judging whether a change in steps per day would be important in practical terms. Statistical evidence of a difference and the practical value of that difference are separate questions. The posted p-values cannot answer the latter.

The results also do not establish whether findings generalize beyond the participants studied. Eligibility details, participant characteristics, and complete analysis-population information are not reported in this record. In addition, one group was not assessed for the primary endpoint because of baseline step-count criteria, and the missing-data approach is not reported.

Accordingly, the registry supports a cautious description of model-specific estimates and their uncertainty. It does not support medical advice, a claim that an incentive works or fails, or a definitive conclusion about which intervention component should be selected. Those conclusions would require clearer contrast definitions, fuller analysis details, and context about the size of change that matters.

14. Why This Trial Matters Statistically

This trial is statistically interesting because the intervention is not a single treatment compared with a single control. It combines incentive format, loss or lottery framing, postcard reminders, and requests for physical-activity advice. A factorial approach can be used to investigate multiple design features in the same study, but the meaning of the estimates depends on how component effects and interactions are specified. Clear contrast labels are especially important when a registry reports several net mean differences.

The primary outcome is a continuous measure of walking behavior, and the registry reports both descriptive group summaries and mixed-model estimates. That creates a useful opportunity to distinguish observed averages from adjusted or model-based comparisons. The distinction is essential: a raw mean is not automatically an estimate of a component’s effect, and a model estimate cannot be interpreted correctly without knowing the contrast it represents.

The record also illustrates why uncertainty and analysis populations belong alongside point estimates. The outcome arm counts are small, variability differs across groups, and one group was excluded from primary assessment based on baseline step counts. Confidence intervals communicate uncertainty, but they do not resolve the underlying questions about who contributed data or how missingness was handled.

Finally, the listed number of analyses makes transparent reporting of multiplicity and planned contrasts important. The registry does not give those details, so findings should be read as exploratory in the sense that their confirmatory status cannot be determined from this record. That is a limitation of the available reporting, not proof that the study lacked a plan. The case shows how statistical interpretation depends not only on numerical results but also on precise definitions of comparisons, populations, and analytic decisions.

15. 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.

Several limitations are specific to the registry record for this trial. The model-based results are not mapped clearly to specific component contrasts. Because the study combines financial versus non-financial rewards, mixed lottery versus loss incentives, reminders, and advice requests, an estimate cannot be attributed to one design feature without that mapping. The registry also does not report the planned interaction analyses or the model terms used to separate component effects.

The primary endpoint was not assessed in one described group because baseline step counts were considered too high or too low. The record does not report the threshold, the number affected, or whether this exclusion was prespecified. This makes the analysis population difficult to reconstruct and limits assessment of how the exclusion could influence the estimates. The small counts in the posted arm summaries and the variable standard deviations further constrain precision and stability.

Although enrollment is recorded as 102, the registry does not provide a participant flow explanation connecting enrollment with the small outcome-summary counts. It does not report detailed participant characteristics, eligibility criteria, missing-data handling, or whether the primary analysis followed randomized assignment. These details are needed to assess representativeness and possible selection effects.

Other unreported items include a sample-size justification, a detailed statistical analysis plan, interim analyses, multiplicity procedures, model diagnostics, and the identity of the masked parties. The record also does not define a practically important change in steps per day. These omissions prevent a fuller evaluation of precision, robustness, and practical meaning; they do not establish what procedures were or were not carried out.

16. Related Tutorials

17. Related Statistical Calculators

18. Sources

• ClinicalTrials.gov: Multiphase Optimization Trial of Incentives for Veterans to Encourage Walking — NCT04518943.
• Registry record last updated 2025-04-30; status last verified 2025-04.
• Results first posted 2025-04-30.
• 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.

19. Record Summary

NCT04518943 is a completed randomized, single-masked factorial trial of incentive and behavioral-support combinations intended to encourage walking among Veterans. Enrollment was 102. The primary endpoint was change in average steps per day from baseline week to week 12. One group was not assessed for that endpoint because participants had baseline step counts considered too high or too low.

The registry reports four mixed-model mean-difference results with 90% confidence intervals and p-values. Their estimates point in different directions, and the record does not clearly identify the specific component contrast for each result. Three secondary outcomes are listed: self-efficacy, intrinsic or extrinsic motivation, and mental health.

All displayed adverse-event groups report zero affected by serious or other adverse events and zero deaths. The record does not report detailed analysis plans, multiplicity handling, missing-data procedures, or a sample-size justification. Overall interpretation is limited by unclear contrast definitions, small outcome-summary counts, and incomplete reporting of analysis populations and methods.