Evaluation of a Shelter-Based Diet and Physical Activity Intervention for Homeless Adults: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Evaluation of a Shelter-Based Diet and Physical Activity Intervention for Homeless Adults (NCT02427100), a randomized na study. The primary outcome is Automated Self-Administered 24-Hour Dietary Recall: Fruit/Vegetable, Cups.

2. Clinical Question

3. Trial Design

NCT02427100 is a completed, randomized, parallel-group pilot study of a behavioral intervention. Its title describes a shelter-based diet and physical activity intervention for homeless adults. The sponsor was the University of Texas Southwestern Medical Center. The registry lists the study as completed and gives enrollment as 32. The study is classified as not applicable for phase and as having no masking.

The registry summary describes a planned 4-week intervention and a follow-up assessment 4 weeks after the intervention ended. It describes random assignment to the intervention or to an assessment-only control group. The intervention combined newsletters, fruit and vegetable snacks, a pedometer, and walking goals or advice. The control group was paid for assessments and received newsletters and a pedometer with advice after the final follow-up visit. The registry summary's proposed sample was N = 50, with 25 participants in each group; actual registry enrollment is 32, so the proposed and recorded enrollment figures should not be conflated.

The primary outcome listed in the registry is fruit and vegetable intake in cups, measured using an automated self-administered 24-hour dietary recall at 4 weeks post-enrollment. The posted outcome estimates include 14 participants in each group. The outcome description says that one control participant attended but did not complete the recall, leaving 14 from a control group of 15. In the intervention group, two participants did not attend and one attendee did not complete a recall, leaving 14.

The registry lists a randomized allocation and a parallel model, but further details of the randomization procedure, concealment, and any stratification are not reported in the registry record. The trial's original sample-size justification, its planned statistical analysis details beyond the listed ANCOVA, and any interim analyses are also not reported in the registry record. This is a small pilot study, so its posted outcome should be read as an estimate with substantial uncertainty rather than as a definitive assessment.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: In the control group (n = 15), 1 participant who attended the visit did not complete a dietary recall (leaving a total of 14 participants). In the intervention group, 2 participants did not attend the visit, and 1 who attended did not complete a dietary recall (leaving a total of 14 participants).

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 Automated Self-Administered 24-Hour Dietary Recall: Fruit/Vegetable, Cups, measured over 4 weeks post-enrollment.

The primary endpoint is the least-squares mean of fruit and vegetable intake, measured in cups using an automated self-administered 24-hour dietary recall. The recorded timeframe is 4 weeks post-enrollment. A dietary recall asks participants to report what they ate over a defined period; expressing intake in cups makes the reported fruit and vegetable outcome quantitative and allows group averages to be compared.

Self-reported dietary intake is relevant to the intervention because the program included fruit and vegetable snacks and newsletters focused on diet. It offers an outcome directly related to the dietary component of the program, while the pedometer and walking advice address physical activity. The registry summary also describes objective pedometer or accelerometer activity measurement as a main study outcome, but the primary endpoint reported in the outcome results is the dietary recall measure.

A least-squares mean is a model-based group mean. It can account for variables included in the statistical model, unlike a simple arithmetic average. However, the covariates used in the registry's ANCOVA and the adjusted least-squares mean estimates are not reported in the registry record. The posted group values are 2.08 cups for control and 3.56 cups for intervention, each with a standard error of 0.74. These are group estimates, not individual participant values. Dietary recall depends on participants' reports, and the record does not describe validation procedures, recall completion conditions, or further details of measurement quality.

7. Results Posted in the Registry

• Intervention Group: mean 3.56 versus 2.08 on control; difference 1.48 (95% CI -0.57 to 3.53), standardized effect d = 0.53; z-test p = 0.157.

8. Statistical Interpretation

9. Statistical Methods Explained

The registry lists ANCOVA as the sponsor-reported method for the comparison of the control and intervention groups. ANCOVA, or analysis of covariance, compares group outcomes while adjusting for one or more covariates included in a model. In general, adjustment may improve precision or account for baseline differences when the selected covariates and model are appropriate. The covariates and model specification for this study are not reported in the registry record, and the adjusted group estimates and confidence interval are also not reported. Therefore, the reported sponsor p-value cannot be used to reconstruct the adjusted effect size from the information in the record.

What does the unadjusted recalculation represent?

The separate recalculation compares the posted group means without covariate adjustment. It uses the intervention mean of 3.56 cups and control mean of 2.08 cups, with 14 participants in each group. The resulting mean difference is 1.48 cups. This is a simple unadjusted comparison of the reported summaries, not a replacement for the sponsor's ANCOVA. In general, an unadjusted comparison and an adjusted model may produce different estimates or uncertainty because they use different information and assumptions. The registry does not provide enough detail to reproduce the ANCOVA.

The recalculation uses the standard errors reported for the group means to obtain an approximate pooled standard deviation. That approximation is marked as such because the arm-level dispersion is reported as standard error rather than as a standard deviation. In general, a standard error describes uncertainty in an estimated mean, while a standard deviation describes variability among individual observations. They answer different questions. A calculation that derives an approximate standard deviation from standard errors depends on assumptions about the reported estimates and sample sizes; it should not be confused with a directly reported measure of participant-level variability.

How should the confidence interval and p-value be read?

A confidence interval gives a range of effect estimates compatible with the observed data under the method's assumptions. In general, a 95% confidence interval is generated by a procedure that would cover the true effect in 95% of repeated samples under those assumptions. It is not a statement that the particular interval has a 95% probability of containing the true effect. The recalculated interval includes zero, indicating that the unadjusted data do not sharply distinguish the observed difference from no difference. Its width also reflects substantial uncertainty in the effect estimate.

The unadjusted p-value is 0.157. In general, a p-value is calculated under a null hypothesis and describes how unusual results at least as extreme as the observed result would be if that null model and the analysis assumptions held. It is not a direct measure of the probability that the null hypothesis is true, and it does not quantify clinical or public health importance. The trial's own significance threshold is not reported in the registry record. The two-sided significance level of 0.05 listed for the planning illustration applies to that illustration and should not be assumed to be the prespecified threshold for the trial's sponsor analysis.

Why can over-dispersion matter?

For continuous outcomes, variability among participants affects the uncertainty of a group comparison. In general, greater dispersion makes it harder to estimate a mean difference precisely for a given sample size. Dietary intake can vary across people and across recall periods. The registry reports standard errors for the group estimates, but does not report the individual-level observations or a directly stated standard deviation for the endpoint. That restricts independent assessment of the distribution and of whether model assumptions, such as the form of residual variation, were suitable.

The endpoint is a continuous measure, so the mean difference describes the difference in average cups between groups. It does not describe how many participants increased intake, whether a change was sustained, or the distribution of individual responses. Those quantities are not reported in the registry record. The main outcome estimates also do not isolate the effects of newsletters, snacks, or walking support from one another.

Finally, the number of participants contributing an endpoint is not the same as the number originally assigned. The record describes missed visits and incomplete recalls in the intervention group, and an incomplete recall among control participants who attended. It does not report the full analysis population definition, imputation approach, sensitivity analyses, or whether analyses followed assignment regardless of intervention participation. These omissions limit assessment of how missing outcome data may affect the result. They do not justify assuming a particular analysis strategy.

10. Confidence Intervals and Precision

The unadjusted mean difference is 1.48 cups, with a recalculated 95% confidence interval from -0.571 to 3.531 cups. The interval includes zero and spans values on both sides of no difference. Thus, the estimate is not precise enough to exclude a null difference, and the data are also compatible with a range of nonzero differences. The interval should be interpreted as uncertainty around the unadjusted estimate, not as a range guaranteed to contain the true effect.

Only 14 participants in each group contributed to the reported primary outcome. With a small number of observations, estimates can be sensitive to participant-to-participant variation, and the resulting uncertainty can be substantial. The reported standard error for each least-squares mean is 0.74 cups. A standard error describes the precision of an estimated mean; it is not the spread of individual intake values. Individual-level dispersion is not directly reported for this endpoint.

The registry's ANCOVA result is reported as p = .18, but its adjusted effect estimate and confidence interval are not reported in the registry record. The unadjusted interval therefore cannot be taken as the uncertainty interval for the sponsor's adjusted analysis. The lack of an adjusted interval also prevents a direct assessment of the range of values compatible with that specific model.

In general, confidence intervals are more informative than a binary declaration based only on whether a p-value crosses a threshold: they show the estimated effect and the range of uncertainty at the same time. Here, the interval's inclusion of zero means that a no-difference value remains compatible with the unadjusted data. The broad range also means the result does not tightly determine the magnitude or direction of the group difference. Further studies would be needed to estimate the effect more precisely; the registry does not report a confirmatory trial or additional outcome data.

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, not total event counts. They are illustrations based on the observed unadjusted effect, not the original trial's design assumptions. The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The assumed effect to detect is a stated fraction of the observed effect. The trial's original sample-size justification and its original planning assumptions are not reported in the registry record.

The 80% power column gives the illustrative number of participants per arm for a design with an 80% chance of detecting the assumed effect under the stated planning assumptions, if that effect and those assumptions were correct. The 90% power column gives the corresponding illustration for a 90% chance. These are prospective planning concepts: power describes a design's ability to detect an effect under specified assumptions. The figures do not indicate the probability that the observed study result is true, and they are not estimates of the study's observed power.

The rows use 100%, 75%, and 50% of the observed effect. The figures show that smaller assumed effects require more participants per arm to attain the same target power. This is a general feature of study planning: a smaller difference is harder to distinguish from random variation unless the study has more information, such as a larger sample or lower outcome variability. The observed effect in a small pilot can itself be uncertain, so planning around it should not be interpreted as a guarantee that a later study will see the same effect.

For example, the listed planning figures for 100% of the observed effect are 55 participants per arm for 80% power and 74 participants per arm for 90% power. For 75% of the observed effect, the corresponding figures are 98 and 131 participants per arm; for 50%, they are 220 and 295. These are planning illustrations only. They are not observed enrollment targets from the trial and do not establish the sample size that would be appropriate for a future study, which would depend on its objectives and assumptions.

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 = 1.480; pooled standard deviation σ = 2.769.
2. n = 2 × (1.96 + 0.842)² × 2.769² / 1.480² = 54.9, rounded up to 55 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 <- 1.48                      # observed difference in means
sigma <- 2.76882646621272                     # 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(2427100)
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 = 55 (80% power), 74 (90% power)
 75% of observed effect: n per arm = 98 (80% power), 131 (90% power)
 50% of observed effect: n per arm = 220 (80% power), 295 (90% power)
power.t.test: 55.9 
Simulated power at n = 55 per arm: 0.796 (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. Analyses Reported by the Sponsor

The registry reports an ANCOVA comparison between the intervention and control groups with p = .18. It does not report the ANCOVA's adjusted effect estimate, confidence interval, covariates, or fuller model specification. The unadjusted recalculation from the posted group summaries gives a mean difference of 1.48 cups and an unadjusted p-value of 0.157. Because the two analyses differ, their estimates and p-values should be kept distinct.

The sponsor's own analysis takes precedence over the recalculation for describing the study's reported analysis. The recalculation is a simple, unadjusted comparison of the posted summary statistics; it is not a reproduction of the ANCOVA. In general, covariate adjustment can change an estimate or its standard error, depending on the model and covariates. The registry record does not provide enough information to explain the relationship between the two p-values or to verify the ANCOVA independently.

Both reported p-values are compatible with substantial uncertainty, but neither should be interpreted as a measure of the probability that an effect exists. The ANCOVA p-value does not give the size or direction of the adjusted effect, and the unadjusted result does not substitute for that missing information. The available record therefore supports a description of the posted group means and the two analysis reports, while leaving the adjusted magnitude and precision unresolved.

14. Multiplicity, Missing Data and Analysis Populations

The registry describes several study aims. In addition to dietary intake and physical activity, the summary mentions indicators of physical health, including blood pressure, weight, body mass index, waist circumference, and other dietary variables. The posted results include two outcome measures and two analyses in the registry record, but no secondary outcome analyses are posted. The registry record does not report whether a formal multiplicity strategy was planned or applied, such as prioritizing outcomes, adjusting significance thresholds, or treating additional analyses as exploratory.

Multiplicity matters in general when many outcomes, timepoints, or comparisons are tested. The more questions examined, the greater the chance that at least one result appears notable by chance if each is judged separately. This general concern does not establish that the study conducted unreported tests. The registry does not provide a complete statistical analysis plan or a full account of all analyses considered, so the extent of multiplicity cannot be assessed from this record.

The primary outcome description reports 14 participants per group with a completed recall. It states that one control participant who attended did not complete the recall, leaving 14 from a control group of 15. In the intervention group, two participants did not attend and one attendee did not complete a recall, also leaving 14. The registry record does not report why visits were missed, whether missingness was related to intake or intervention participation, or how missing outcomes were handled analytically.

In general, missing data can bias a group comparison if the likelihood of an outcome being missing is related to the outcome itself or to other relevant participant characteristics. The direction and size of any such effect cannot be inferred from counts alone. The record does not report imputation, sensitivity analyses, or an analysis population definition such as intention-to-treat. It also does not report how adherence to the intervention was handled. These reporting gaps limit evaluation of the robustness of the primary result, without proving that any particular bias occurred.

Interim analyses and stopping rules are not reported in the registry record. The trial's own multiplicity and missing-data plans are likewise not reported in the registry record. These should be treated as unavailable information, not as evidence that no such procedures existed.

15. Safety Results

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

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 zero serious adverse events among 15 control participants at risk and zero among 17 intervention participants at risk. It also reports zero other adverse events among 15 control participants at risk and zero among 17 intervention participants at risk. These figures describe the counts recorded in the registry for the stated groups and at-risk populations.

A zero recorded event count means that no events of the listed type were reported for those participants in this record. It does not establish that the true risk is zero or that no unrecorded events occurred. In general, when the number of participants observed is limited, absence of recorded events gives only limited information about how frequently an event might occur in a larger or different population.

The registry does not list serious adverse event terms, deaths, event severity details, timing, or additional information about surveillance and attribution. Death counts are not reported in the registry record. The safety counts should therefore be read narrowly as posted event totals, rather than as a comprehensive account of safety or proof about causation. These figures also do not establish that an event was or was not related to the intervention.

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

The posted result describes a difference in average fruit and vegetable intake between groups at 4 weeks post-enrollment. The intervention group estimate was 3.56 cups and the control group estimate was 2.08 cups, with a reported mean difference of 1.48 cups. The unadjusted confidence interval includes zero and is broad, so the estimated difference is uncertain. The registry's ANCOVA result is p = .18, but the adjusted effect size and its confidence interval are not reported in the registry record.

This result does not establish that the intervention caused a change in intake, nor does it establish that there was no effect. It is a small pilot-study result based on 14 completed recalls in each group. The uncertainty is consistent with a range of possible differences. A single p-value cannot resolve that range or indicate whether any difference would be important to participants or to public health.

The intervention combined several elements: newsletters, fruit and vegetable snacks, and pedometer-based walking advice. The posted primary endpoint concerns diet, not physical activity. Because the components were delivered as a package, the result cannot identify which component may have contributed to the observed group estimates. Physical activity results and the other health outcomes described in the study summary are not posted as secondary analyses in the registry record.

The record also does not establish whether any intake difference persisted after the study period. It describes a follow-up assessment after the intervention, but the reported primary endpoint timeframe is 4 weeks post-enrollment, and no later dietary result is included in the posted outcome data. Nor can results from this shelter-based pilot automatically be generalized to homeless adults in other settings or to people with different circumstances.

The most defensible interpretation is descriptive: the posted group estimates differ, but the estimate is imprecise, the sponsor's adjusted effect magnitude is unavailable, and the registry's outcome reporting is limited. The result can inform questions for further research, but it is not a standalone answer about the intervention's effectiveness across populations or outcomes.

17. Why This Trial Matters Statistically

This study illustrates several important statistical issues in pilot trials. First, a group difference is an estimate, not a certainty. The reported 1.48-cup unadjusted difference is accompanied by a confidence interval that includes zero and extends across a wide range. Reading the effect estimate together with its uncertainty avoids treating the direction of the point estimate as a settled finding.

Second, a small study can be useful for examining a behavioral program in a real shelter context while still producing an imprecise estimate of an outcome difference. The registry summary identifies feasibility and effectiveness as aims. Those aims are not interchangeable: feasibility concerns whether an intervention can be delivered and evaluated, while effectiveness asks about outcomes. The record does not post a full set of feasibility results, so the primary dietary outcome should not be treated as a complete report of the pilot's objectives.

Third, the comparison highlights the distinction between an adjusted sponsor analysis and a transparent unadjusted recalculation. ANCOVA may incorporate covariates, but without the model details, adjusted estimate, and confidence interval, readers cannot assess the adjusted effect's magnitude and precision. A recalculation based on group summaries can help describe the unadjusted data, but cannot reproduce the sponsor's model.

Finally, the planning illustrations show how assumptions about the effect size shape sample-size requirements. Smaller effects require more participants per arm to reach the same planned power under the stated assumptions. Because the observed effect from a small pilot is itself uncertain, those figures are not a prescription for a future design. They illustrate the relationship between effect size, sample size, and power, while emphasizing the need to choose planning assumptions for a new study deliberately.

18. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.

The primary endpoint is based on self-reported dietary recall. Such a measure can be affected by recall and reporting, and the registry does not describe procedures for checking or validating the recall data. The outcome is a least-squares mean, but the covariates used to obtain that estimate are not reported in the registry record. Participant-level observations and a directly reported standard deviation are also not available.

Only 14 participants per group contributed a completed recall. The outcome description identifies missed visits and incomplete recalls, but the reasons for missingness and the analytic handling of missing data are not reported in the registry record. The record does not state whether all randomized participants were included in the analysis or whether any imputation or sensitivity analyses were used. This makes it difficult to evaluate possible effects of incomplete outcome data.

The sponsor's ANCOVA result is reported without its adjusted estimate or confidence interval. The model covariates, diagnostics, and fuller statistical plan are not reported in the registry record. As a result, the adjusted effect's direction and size cannot be evaluated from the reported p-value alone. The unadjusted recalculation is informative about the posted group summaries, but it cannot fill that reporting gap.

The study summary describes a package of dietary and physical activity strategies, so the primary dietary comparison cannot distinguish the contributions of individual components. Although the summary mentions physical activity and several health measures, no secondary outcome analyses are posted. The reported primary outcome is at 4 weeks post-enrollment, and the record does not provide an outcome trajectory or establish persistence beyond that assessment.

Finally, this is a pilot study in a specific transitional shelter context, with actual registry enrollment of 32. The registry summary's proposed N = 50 is a planning description, not the recorded enrollment. The record does not report enough information to assess representativeness or generalizability beyond the study setting. These limitations constrain interpretation; they do not establish that the intervention was ineffective or that the study procedures failed.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Evaluation of a Shelter-Based Diet and Physical Activity Intervention for Homeless Adults — NCT02427100.
• Registry record last updated 2019-05-06; status last verified 2019-02.
• Results first posted 2019-05-06.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

22. Record Summary

NCT02427100 is a completed randomized, parallel-group pilot study of a shelter-based diet and physical activity intervention for homeless adults. The registry lists actual enrollment as 32 and describes a planned 4-week intervention with a later follow-up assessment. The intervention included newsletters, fruit and vegetable snacks, and pedometer-based walking advice; the control group received assessment payments and later access to newsletters and a pedometer with advice.

The primary posted outcome is fruit and vegetable intake in cups by automated self-administered 24-hour dietary recall at 4 weeks post-enrollment. Fourteen participants per group contributed a completed recall. The group estimates were 3.56 cups for intervention and 2.08 cups for control. The unadjusted mean difference was 1.48 cups, with an interval that includes zero. The registry reports an ANCOVA p-value of .18 but does not report the adjusted effect estimate or its confidence interval.

The posted result is imprecise and should be interpreted in light of the small endpoint groups and incomplete reporting of model and missing-data details. The registry record does not post secondary outcome analyses or the original sample-size justification.