MOTIVATE: Moving to Improve Outcomes for Older Adults: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for MOTIVATE: Moving to Improve Outcomes for Older Adults (NCT03914469), a randomized na study. The primary outcome is Recruitment Rates.

2. Clinical Question

3. Trial Design

MOTIVATE was registered as a randomized, parallel-group pilot trial. The record lists single masking. It does not identify which parties were masked; the brief study description does say that a blinded research assistant conducted outcome assessments. The study status is terminated. The registry lists a start date of 2019-08-01 and a primary completion date of 2022-11-07. A reason for termination is not reported in the registry record.

The trial aimed to evaluate the feasibility of a telephone-based behavioral change intervention for older adults with chronic low back pain and depression. Trained health coaches were to deliver the intervention using motivational interviewing. The waitlist control group was to continue usual care for chronic back pain and depression. The registry describes outcome assessments at baseline, mid-point, and final follow-up for both groups; arm descriptions also mention pre-screening assessments.

The enrollment entry is 12, and the primary outcome description states that 12 participants were enrolled, with 6 in each arm, after 371 participants were pre-screened. The arm records also contain denominators of 185 and 186 in the comparison data. The registry does not explain how those denominators relate to the enrollment narrative, so they should not be treated as a clarified count of randomized or analyzed participants. The record lists four secondary outcome categories: Pain Scale, Roland Morris Disability Questionnaire (RMDQ), Depression, and Step Counts. It also records six outcome measures, without identifying all six measures individually. The trial's phase is listed as NA.

The original sample-size justification, the intended analysis population, and the detailed analysis plan are not reported in the registry record. The posted comparison is an unadjusted comparison of the recorded recruitment counts, rather than a reported analysis of the secondary clinical outcomes.

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: We pre-screened 371 participants and enrolled 12 (6 in each study arm)

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 Recruitment Rates, measured over Through study completion, up to 6 months.

The primary endpoint is titled “Recruitment Rates.” Its unit is participants, and its description defines it as the total number of pre-screened patients who enrolled through study completion, up to 6 months. The outcome narrative reports 371 pre-screened participants and 12 enrolled, with 6 assigned to each study arm. The registry does not report a recruitment proportion or a rate per unit of time; the posted endpoint is a count.

For a pilot intervention study, recruitment is a feasibility measure: it describes whether the study enrolled participants from the population it sought to reach. It addresses a different question from whether pain, disability, or depressive symptoms changed. A recruitment count alone does not establish how acceptable the intervention was, whether participants completed it, or whether clinical outcomes improved. Those questions would require their own reported measures and results.

The registry lists Pain Scale, RMDQ, Depression, and Step Counts among secondary outcomes, but it does not post results for those measures. The primary endpoint should therefore be read as an account of enrollment, not as evidence about the intervention's clinical effects. The record does not explain the relationship between the narrative enrollment count and the larger denominators included in the arm comparison data.

7. Results Posted in the Registry

• Behavioral Intervention Group: 3.2% (6/186) versus 3.2% (6/185) on control; risk difference -0.0 percentage points (95% CI -3.6 to 3.6), risk ratio 0.99 (0.33–3.03); unadjusted two-proportion z-test p = 0.992.

8. Statistical Interpretation

9. Statistical Methods Explained

What kind of comparison is posted?

The primary endpoint is a count of enrolled participants, and the posted comparison expresses the arm results as a risk difference. The comparison lists 6 events in each arm, with denominators of 185 and 186. The event in this setting is enrollment as represented in the comparison data. The registry's outcome narrative separately says that 12 people were enrolled, with 6 in each arm, from 371 pre-screened participants. Since the record does not explain the denominators in the comparison, the two descriptions should not be silently combined or treated as interchangeable.

General statistical context: a risk difference subtracts one group's event proportion from the other group's event proportion. A value near zero indicates that the observed proportions are close on this scale. The sign indicates which group has the larger recorded proportion under the comparison's coding, but interpretation depends on the order of the groups. Here, the posted risk-difference estimate is close to zero. Its numeric estimate and interval have more than three decimal places in the registry-derived comparison, so they are not repeated in prose; the qualitative interpretation is that the interval includes values on either side of zero.

How should the p-value be understood?

The comparison reports an unadjusted p-value of 0.992. General statistical context: a p-value assesses how unusual data at least as different as those observed would be under a specified null model and the test's assumptions. It does not give the probability that the null model is true, the probability that a treatment works, or the probability that a result occurred “by chance.” A large p-value means the comparison does not provide a clear statistical distinction under the test; it is not proof that the groups are equivalent.

The registry record does not state the test procedure or the assumptions used for this comparison. The numerical p-value should therefore be understood as the posted unadjusted result, without assuming additional adjustment or a particular model beyond what the record describes. The record does not report an adjusted p-value.

What does a confidence interval add?

General statistical context: a confidence interval conveys uncertainty around an estimate. Its endpoints describe a range of values compatible with the data under the interval method and its assumptions; they are not a guarantee that the true value lies within that particular interval. A confidence interval is useful because it shows both the direction and the range of effects that remain plausible, rather than reducing the evidence to a threshold judgment based on a p-value alone.

For this comparison, the interval for the risk difference includes zero and reaches to both negative and positive values. It therefore does not rule out no difference, and it also does not rule out differences in either direction. The relatively sparse enrollment narrative limits how much can be learned from this comparison. The unclear relationship between the comparison denominators and the enrollment count adds a further interpretive constraint.

What do the relative measures represent?

The posted comparison also contains risk-ratio and odds-ratio results. General statistical context: a risk ratio compares event proportions by division, while an odds ratio compares event odds. These measures use different scales from a risk difference, so their values are not directly interchangeable. Ratios near one correspond to similar group values on their respective scales; intervals spanning one are compatible with no relative difference under the interval assumptions. The registry comparison includes intervals for both ratio measures, but their endpoints are not repeated in prose because they are recorded to more than three decimal places. No model adjustment is reported for these values.

Because the outcome is enrollment and the arm denominator entries are not explained, the relative measures should not be read as a clinical treatment effect. Their meaning is limited to the binary comparison represented in the registry data.

What cannot be determined from the analysis record?

The record lists zero posted analyses beyond the primary comparison represented in the results data. It does not report the statistical analysis plan, the exact test specification, missing-data procedures, handling of protocol deviations, or an analysis population definition. It also does not report analyses of pain, RMDQ disability, depression, or step counts. The presence of outcome names in the registry does not establish that results were collected, analyzed, or omitted for a particular reason.

General statistical context: sparse data can produce unstable estimates and wide uncertainty, especially when event counts are small. The estimates may be sensitive to a small number of observations. That general limitation is relevant to the recorded counts, but it does not establish that a specific model assumption was violated. No over-dispersion adjustment is indicated or described; over-dispersion is generally a concern when observed variability exceeds what a model assumes, particularly for count models, but the posted endpoint comparison is represented as a binary event comparison rather than a count-model analysis.

Overall, the available methods information supports a cautious reading of a simple unadjusted recruitment comparison. It does not permit reconstruction of the trial's original statistical plan or a broader assessment of treatment outcomes.

10. Confidence Intervals and Precision

The posted risk-difference estimate is close to zero, while its confidence interval extends to both negative and positive values and includes zero. The interval therefore reflects uncertainty about the direction as well as the size of any difference in the compared recruitment proportions. Its endpoints are recorded with more than three decimal places, so they are not reproduced in this discussion.

General statistical context: a confidence interval is a range generated by a statistical procedure that, over repeated use under its assumptions, would contain the underlying parameter at the stated confidence level at the procedure's long-run frequency. It is not a probability statement about this one fixed interval. The interval is often more informative than a p-value alone because it shows the range of effect sizes that remain compatible with the data and method.

Here, the interval does not narrowly identify an effect near zero: it permits values in either direction. That means the result is not precise enough to establish that the groups had the same recruitment experience, nor to establish a meaningful difference. The recorded counts are limited, and the comparison denominators of 185 and 186 are not explained in relation to the narrative enrollment total. Both points constrain interpretation. The p-value of 0.992 does not remove that uncertainty; it summarizes a test under its assumptions and does not establish equivalence.

The registry does not state the confidence level or interval construction method in the record. No greater precision should be inferred than the posted estimate and interval support. In particular, the near-zero point estimate should not be read in isolation as proof that there was no difference.

11. Planning a Similar Trial: Sample Size

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

The planning figures are participants per arm for 80% power and participants per arm for 90% power. They are planning illustrations based on the observed effect, not the trial's own original design assumptions. The stated 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 to the stated fraction of the observed effect. The original trial's sample-size assumptions are not reported in the registry record.

For planning at 100% of the observed effect, the figures are 16,159,779 participants per arm for 80% power and 21,633,359 participants per arm for 90% power. For planning at 75% of the observed effect, they are 28,747,208 participants per arm for 80% power and 38,484,355 participants per arm for 90% power. For planning at 50% of the observed effect, they are 64,723,318 participants per arm for 80% power and 86,646,158 participants per arm for 90% power. These are participants per arm, not total event counts.

In general, power is the chance that a study will detect an effect of a specified size under the assumed model and significance threshold if that effect is truly present. The 80% and 90% columns represent different planning targets: the higher target generally requires a larger sample for the same assumed effect. Smaller effects are harder to distinguish from random variation and therefore require more participants. The posted values are extremely large because the observed risk-difference estimate is close to zero; planning from such an estimate yields very large requirements.

These calculations are not observed power. They are illustrations under stated assumptions and do not show how likely the completed trial was to detect an effect. They should not be interpreted as evidence about the feasibility of a future study without considering whether its population, outcome definition, allocation, and assumptions would match this illustration.

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, p₀ and p₁ are the control and treatment proportions, and p̄ is their average.

Worked calculation for this trial

1. Control proportion p₀ = 0.032; treatment proportion p₁ = 0.032; average p̄ = 0.032.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.2502 = 0.4904.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.2502 = 0.2106.
4. n = (0.4904 + 0.2106)² / (-0.0002)² = 16,159,778.7, rounded up to 16,159,779 participants per arm for 80% power.

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

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
p0 <- 0.0324324324324324                          # control proportion
p1 <- 0.032258064516129                          # treatment proportion
n_per_arm <- function(power, frac = 1) {
  q1 <- p0 + (p1 - p0) * frac               # smaller effect = fraction of the observed difference
  pbar <- (p0 + q1) / 2
  z_b <- qnorm(power)
  ceiling(round((z_a * sqrt(2 * pbar * (1 - pbar)) + z_b * sqrt(p0 * (1 - p0) + q1 * (1 - q1)))^2 / (q1 - p0)^2, 6))
}
for (f in c(1, 0.75, 0.5))
  cat(sprintf("%3.0f%% of observed effect: n per arm = %s (80%% power), %s (90%% power)\n", 100 * f,
              format(n_per_arm(0.80, f), big.mark = ","), format(n_per_arm(0.90, f), big.mark = ",")))

# Check against R's built-in function (unrounded n per arm)
cat("power.prop.test:", round(power.prop.test(p1 = p0, p2 = p1, power = 0.80)$n, 1), "\n")

# Simulation: how often does the z-test reject at the 80%-power sample size?
set.seed(3914469)
n    <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z  <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))

Output from running the code

100% of observed effect: n per arm = 16,159,779 (80% power), 21,633,359 (90% power)
 75% of observed effect: n per arm = 28,747,208 (80% power), 38,484,355 (90% power)
 50% of observed effect: n per arm = 64,723,318 (80% power), 86,646,158 (90% power)
power.prop.test: 16159779 
Simulated power at n = 16,159,779 per arm: 0.795 (20000 replicates)

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

13. Multiplicity, Missing Data and Analysis Populations

The registry lists Pain Scale, Roland Morris Disability Questionnaire (RMDQ), Depression, and Step Counts as secondary outcomes. It also records six outcome measures, but does not identify all six measures individually in the record. No results for these secondary measures are posted in the trial information summarized by the registry entry.

The registry record does not report whether the investigators adjusted for multiple outcomes or multiple comparisons, or how any such adjustment would have been applied. General statistical context: when many outcomes or comparisons are tested, the chance of obtaining at least one apparently notable result can increase. A prespecified approach to multiplicity helps readers understand how to interpret a collection of tests. In the absence of a reported approach, no adjustment should be assumed and no unadjusted result should be treated as a complete account of all possible analyses.

Missing-data procedures are not reported in the registry record. The record does not explain whether participants had missing assessments, how incomplete measurements were handled, or whether any sensitivity analyses were planned. The primary enrollment count is reported, but that does not establish completeness for the secondary outcome assessments.

The analysis population is also not reported in the registry record. It does not specify whether any analysis was intended to include all randomized participants, only participants who received the assigned intervention, or another defined group. The record's enrollment narrative states that 12 participants were enrolled, with 6 in each arm, while the comparison data list denominators of 185 and 186. Their relationship is not explained. No population definition should be inferred from those entries.

The registry records zero posted analyses. This does not explain why secondary outcome results or analysis details are absent, and it does not establish that the outcomes were not collected. The absence of reported methods leaves uncertainty about multiplicity, missingness, and which participants contributed to each analysis.

14. Safety Results

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

Deaths

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 0% reporting threshold.

The serious adverse event entries report zero affected participants among 6 at risk in the Waitlist Control Group and zero among 6 at risk in the Behavioral Intervention Group. The entries for other adverse events also report zero affected participants among 6 at risk in each group. Deaths are recorded as zero in both groups. No serious adverse event terms are listed.

These are the event counts recorded in the registry, not a complete account of all possible harms or symptoms. The record does not specify the adverse-event reporting window in the information, and it does not describe how events were collected or classified. A zero count in a small group does not establish that an event is impossible or that the intervention is safe in other settings. Nor do these entries show that no participant experienced any symptom; they report zero events in the listed categories.

The registry status is terminated, but the reason for termination is not reported in the registry record. The adverse-event counts do not explain that status, and no causal interpretation should be attached to it.

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

The result describes enrollment into a pilot study: the registry reports 12 enrolled from 371 pre-screened participants, with 6 participants in each arm. It also posts an unadjusted comparison with equal event counts, a risk-difference estimate near zero, and a p-value of 0.992. The confidence interval includes zero and values on either side of it. Taken together, the comparison does not provide a clear distinction between the recorded arm recruitment proportions, while leaving substantial uncertainty about the possible difference.

The record does not explain the comparison denominators of 185 and 186 in relation to the enrollment narrative. That unresolved detail limits interpretation of the comparison. The posted primary outcome is a count of enrollment, not an assessment of changes in low back pain, disability, depression, or physical activity. Although the registry names Pain Scale, RMDQ, Depression, and Step Counts as secondary outcomes, it does not post their results.

These findings do not establish that the intervention improved or failed to improve a clinical outcome. They also do not establish that the groups were equivalent, that recruitment was successful by a predefined criterion, or that the intervention was acceptable or feasible for participants. The registry record does not report a recruitment target or a criterion for judging feasibility, and the trial's original analysis plan is not reported.

The trial is marked terminated, but the reason is not reported in the registry record. The status alone cannot show whether termination was related to recruitment, intervention delivery, safety, funding, or another issue. The narrow conclusion supported by the posted information is that enrollment counts and a simple comparison are recorded, while the clinical outcomes and the reason for termination remain unreported.

16. Why This Trial Matters Statistically

This trial raises an important statistical distinction between a feasibility endpoint and a clinical effectiveness endpoint. Recruitment is relevant to whether a study can enroll the population it intends to study. It does not answer whether an intervention changes pain, disability, depression, or activity. Keeping those questions separate prevents an enrollment result from being mistaken for a clinical outcome.

The record also illustrates how essential clear denominators are. The narrative reports 371 pre-screened participants and 12 enrolled, with 6 in each arm, while the comparison entries list denominators of 185 and 186. Without an explanation, readers cannot confidently connect the comparison proportions to the enrollment account. Clear descriptions of the analysis population and of what each denominator represents are necessary for reproducible interpretation.

The near-zero estimate and high p-value are not evidence of equivalence. Their meaning depends on the uncertainty interval, the outcome definition, and the data used in the comparison. The interval includes values on both sides of zero, and the small enrollment narrative offers limited precision. Treating a nonsignificant result as proof of no difference would overstate what the data establish.

Finally, this record demonstrates why registry reporting of the analysis plan, missing-data procedures, outcome results, and termination reason matters. Without those details, it is difficult to distinguish an outcome that was measured but not reported from one that was not collected, or to understand how the comparison was constructed. These are reporting and interpretation limits, not evidence for a particular explanation of the study's status or findings.

17. Limitations

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

The most immediate limitation is that the primary endpoint is an enrollment count, while the registry does not post results for the clinical outcomes named in the study description. The status is terminated, but the reason for termination is not reported in the registry record. The record therefore does not establish whether the study completed its planned recruitment or follow-up goals.

The enrollment narrative and comparison denominators are not reconciled. The narrative reports 12 enrolled, with 6 in each study arm, whereas the comparison entries list denominators of 185 and 186. The record does not explain what those denominators represent or how they relate to participants assigned to the study arms. This makes the comparison's denominator basis uncertain.

The registry does not report the original sample-size rationale, detailed statistical plan, exact analysis population, missing-data handling, multiplicity approach, or analysis of the secondary outcomes. It also does not provide a recruitment benchmark against which to judge the count. The number of outcome measures is recorded as six, but all of them are not identified individually.

Safety entries report zero serious events, other adverse events, and deaths in the listed groups, but the reporting window and collection procedures are not described in the record. Zero recorded events should not be interpreted as proof of no risk. More broadly, the pilot's limited enrollment narrative and the unresolved denominator information constrain precision and generalizability. These limitations do not establish why the study was terminated or why particular results are absent.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: MOTIVATE: Moving to Improve Outcomes for Older Adults — NCT03914469.
• Registry record last updated 2025-03-14; status last verified 2025-02.
• Results first posted 2024-08-12.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

21. Record Summary

MOTIVATE is a randomized, parallel-group pilot trial listed as single masked and terminated. The registry identifies a telephone-based behavioral intervention delivered by health coaches trained in motivational interviewing, compared with usual care in a waitlist group. The target population was adults aged 50 years and older with chronic low back pain and depression.

The primary outcome is recruitment, described as the number enrolled among pre-screened patients through study completion, up to 6 months. The record reports 371 pre-screened participants and 12 enrolled, with 6 in each arm. The posted comparison has equal event counts, an unadjusted p-value of 0.992, and a confidence interval for the risk difference that includes zero. Comparison denominators are listed as 185 and 186, but their relationship to the enrollment narrative is not explained.

Secondary outcomes include Pain Scale, RMDQ, Depression, and Step Counts; their results are not posted. The reason for termination, the original sample-size justification, and key analysis details are not reported in the registry record.