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COVID-19 NA Binary Endpoint NCT05533359

SCALE-UP Utah II: Community-Academic Partnership to Address COVID-19 Conversational Agent Study: Complete Statistical Analysis

This record evaluates a randomized comparison of conversational-agent and text-message approaches, patient-navigation options, and messaging intervals for COVID-19 test-kit requests. The primary outcome counts participants who requested a test kit and confirmed their mailing address.

Trial start: 2023-01-15  ·  Enrollment: 2117  ·  Sponsor: University of Utah
Scope of this record

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 SCALE-UP Utah II: Community-Academic Partnership to Address COVID-19 Conversational Agent Study (NCT05533359), a randomized na study. The primary outcome is Reach-Accept Testing.

2117
Enrollment
NA
8
Arms
In the primary outcome
-2.5 pts
Risk difference
Conversational Agent (CA) + No Patient N
-8.9 to 3.9 pts
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT05533359
PhaseNA
ConditionCOVID-19
AllocationRandomized
Design modelParallel
MaskingSingle
Enrollment2117
Arms in the primary outcome8
Lead sponsorUniversity of Utah
Results postedYes

2. Clinical Question

Population

The study enrolled 2117 participants in a COVID-19 community-health-center study in Utah. The registry record describes a focus on underserved populations and community health center patients. Further eligibility details and the characteristics of participants who contributed to each outcome are not reported in the registry record.

Intervention

The study compared bidirectional text messaging with a conversational agent, an automated interactive approach intended to elicit barriers and hesitancy, provide tailored information, and offer access to an at-home rapid test. Groups also differed in whether patient navigation was offered or available on request, and in the messaging schedule.

Comparator

The posted comparisons use Conversational Agent (CA) + No Patient Navigation (NoPN) + 10 Day as the reference group. Other groups are compared with this reference, including conversational-agent groups with other navigation or timing arrangements and text-message groups with different navigation and timing arrangements.

Primary question

How many participants in each randomized group requested a test kit and confirmed their mailing address during follow-up? The primary endpoint is the count of participants meeting both conditions. The registry timeframe describes assessment every 10 or 30 days, depending on group assignment, for up to 90 days after the intervention message.

The study therefore addresses reach and acceptance of a testing offer as recorded through a request and address confirmation. This endpoint does not itself establish whether a kit was mailed, used, or followed by a particular health outcome. The posted comparisons describe differences between each group and the reference group; they are not direct comparisons among every possible pair of groups.

3. Trial Design

The registry record describes a randomized, single-masked, parallel-group study, marked completed. Enrollment was 2117. The listed start date is 2023-01-15 and the primary completion date is 2023-11-30. The record identifies COVID-19 as the condition and University of Utah as the sponsor. The study phase is listed as NA.

There are eight posted groups. They combine conversational agent or text messaging, navigation arrangements, and 10 Day or 30 Day schedules. The conversational agent is described as an automated, scripted and interactive system intended to elicit hesitancy factors and testing barriers, offer tailored information, and offer access to an at-home rapid test. The text-message approach is described as bidirectional messaging with a one-touch response to connect patients to vaccination or mailed at-home rapid test kits. In request-navigation groups, a participant could reply PERSON to request connection to a patient navigator. The record does not fully explain the meaning of each schedule beyond the listed timing labels and endpoint timeframe.

Randomized allocation and a parallel structure indicate that groups were assigned to different study approaches rather than being described as a crossover. The registry does not report the randomization unit, sequence-generation method, allocation concealment, or who was masked. Although the overall study is marked single-masked, the identity of the masked party and how masking was maintained are not reported in the registry record.

The posted primary result is a participant count for requesting a test kit and confirming a mailing address. The registry also lists secondary measures concerning engaging with testing, navigation requests and engagement, opting out, and self-reported testing. The posted outcome information does not include detailed procedures for collecting or verifying all these measures.

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: 1. Opted Out- opted out after receiving introductory text but before randomization 2. Smart Phone- Participant responded that they do have a Smart Phone

Only the first 6 of 8 groups are shown.

Overall Study

StageConversational Agent (CA) + No Patient Navigation (NoPN) + 10 DayConversational Agent (CA) + No Patient Navigation (PN) + 30 DayConversational Agent (CA) + Patient Navigation (PN) + 10 DayConversational Agent (CA) + Patient Navigation (PN) + 30 DayText Message (TM) + No Patient Navigation (NoPN) + 10 DayText Message (TM) + No Patient Navigation (NoPN) + 30 Day
STARTED261264264262265265
COMPLETED247262237249242262
NOT COMPLETED1422713233

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.

Population: Analysis population are patients who had an appointment at one of the participating CHCs in the last three years, were 18 years and older, had a valid cellphone number recorded in the CHC electronic health record and had a Smart Phone.

Only the first 6 of 9 groups are shown.

CharacteristicUnitConversational Agent (CA) + No Patient Navigation (NoPN) + 10 DayConversational Agent (CA) + No Patient Navigation (PN) + 30 DayConversational Agent (CA) + Patient Navigation (PN) + 10 DayConversational Agent (CA) + Patient Navigation (PN) + 30 DayText Message (TM) + No Patient Navigation (NoPN) + 10 DayText Message (TM) + No Patient Navigation (NoPN) + 30 Day
Participants analysed261264264262265265
Age, ContinuousYears49.38 (SD 14.55)49.88 (SD 15.38)48.83 (SD 14.93)48.34 (SD 14.23)48.89 (SD 14.22)47.92 (SD 14.40)
Sex/Gender, Customized: Sex – FemaleParticipants179163188181182191
Sex/Gender, Customized: Sex – MaleParticipants8210175818374
Sex/Gender, Customized: Sex – UnknownParticipants001000
Race/Ethnicity, Customized: Race/Ehtnicity – American Indian/Alaska NativeParticipants010100
Race/Ethnicity, Customized: Race/Ehtnicity – AsianParticipants113013
Race/Ethnicity, Customized: Race/Ehtnicity – Black/African AmericanParticipants331313
Race/Ethnicity, Customized: Race/Ehtnicity – Hawaiian/Pacific IslanderParticipants111120
Race/Ethnicity, Customized: Race/Ehtnicity – Hispanic or Latino/aParticipants152144137139140142
Race/Ethnicity, Customized: Race/Ehtnicity – UnknownParticipants192225212122
Race/Ethnicity, Customized: Race/Ehtnicity – White Non-HispanicParticipants848693929793
Race/Ethnicity, Customized: Race/Ehtnicity – Multi-raceParticipants164532
Language: EnglishParticipants125128127141124134
Language: SpanishParticipants123126123113128121
Language: OtherParticipants535334
Language: UnknownParticipants8795106
Urban/Rural: UrbanParticipants227230231230228231
Urban/Rural: RuralParticipants343433323734
Insurance Status: PrivateParticipants638069887185
Insurance Status: PublicParticipants474444454338
Insurance Status: UninsuredParticipants151140151129151142
CHC: CHC 1Participants160162165162163162
CHC: CHC 2Participants353634333634
CHC: CHC 3Participants666665676669
SCALE-UP I Randomization: Not enrolled in SCALE UP IParticipants838182808683
SCALE-UP I Randomization: TMParticipants798181797980
SCALE-UP I Randomization: TM+PNParticipants99102101103100102

6. Primary Endpoint

The registry lists the primary outcome as Reach-Accept Testing, measured over Every 10 or 30 days dependent on group randomization [up to 90 days post intervention message] Every 10 or 30 days from intervention messaging for 90 days dependent on group randomization..

ElementRegistry entry
Result typeCount Of Participants
Measure of spreadnot applicable
UnitParticipants
Endpoint classificationBinary Endpoint

The primary endpoint is the number of participants who requested a test kit and confirmed their mailing address. It is a count of participants meeting the registry’s stated conditions, rather than a measure of the number of kits mailed, tests completed, or infections detected. The timeframe is described as assessment every 10 or 30 days depending on group randomization, for up to 90 days after the intervention message.

This outcome is relevant to the study’s stated aim of increasing the reach and uptake of COVID-19 testing: a request accompanied by address confirmation records a concrete step toward receiving a test kit. It also allows the posted results to be read as event counts within each group. The measure is narrower than overall engagement with a message or testing, and it should not be interpreted as confirmation that a participant used a test kit.

Each group’s posted result gives a number of participants meeting the endpoint and a group size. The registry’s pairwise comparisons express the difference in the observed event proportions between the reference group and another group, with confidence intervals. Those comparisons offer a way to assess both the direction and precision of the observed contrast. The registry record does not report additional endpoint details such as the operational definition of a valid request, handling of repeated requests, or whether endpoint ascertainment was blinded.

7. Results Posted in the Registry

Risk difference: Conversational Agent (CA) + No Patient Navigation (PN) + 30 Day

-2.5

95% CI: -8.9 to 3.9 percentage points

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals6.718.730.742.754.766.7Conversational Agent (CA) + N… (n=261)Conversational Agent (CA) + N… (n=264)Conversational Agent (CA) + P… (n=264)Conversational Agent (CA) + P… (n=262)Text Message (TM) + No Patien… (n=265)Text Message (TM) + No Patien… (n=265)Text Message (TM) + Patient N… (n=270)Text Message (TM) + Patient N… (n=266)% of participants (95% CI)
Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Conversational Agent (CA) + N…Conversational Agent (CA) + P…Conversational Agent (CA) + P…Text Message (TM) + No Patien…Text Message (TM) + No Patien…Text Message (TM) + Patient N…Text Message (TM) + Patient N…-13-0.6112253750risk difference (percentage points) vs control (95% CI)

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 outcomeTypeEffect measureEstimate (95% CI)Planning size, 80% power
Reach-Engage TestingBinary EndpointRisk difference-6.8 pts (-14.7 to 1.1)720 per arm
Opt OutBinary EndpointRisk difference-4.6 pts (-7.5 to -1.7)219 per arm
Self-reported TestingBinary EndpointRisk difference-0.3 pts (-23.4 to 22.8)408,161 per arm

Reach-Engage Testing

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Conversational Agent (CA) + N…Conversational Agent (CA) + P…-16-12-7.91-3.790.334.45risk difference (percentage points) vs control (95% CI)

Opt Out

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Conversational Agent (CA) + N…Conversational Agent (CA) + P…-8.89-4.96-1.022.916.8511risk difference (percentage points) vs control (95% CI)

Self-reported Testing

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Conversational Agent (CA) + N…Conversational Agent (CA) + P…-36-24-111.781427risk difference (percentage points) vs control (95% CI)

The secondary outcomes cover several parts of the pathway between receiving an intervention message and reporting testing activity: engagement with testing, requests for and engagement with patient navigation, opting out, and self-reported testing. The posted numeric secondary results include Reach-Engage Testing, Opt Out, and Self-reported Testing. Although PN-Request and PN-Engage are listed as secondary outcomes, their detailed results are not reported in the registry record.

Across the posted secondary results, the text-message groups generally have higher Reach-Engage Testing counts than the conversational-agent reference group, while the two reported conversational-agent comparisons have risk-difference intervals that include zero. The Opt Out comparisons differ in direction across the two reported conversational-agent contrasts. Self-reported Testing comparisons are imprecise, with wide intervals that include zero. This overall pattern does not directly reproduce the primary endpoint: engagement and self-report are distinct measures from requesting a test kit and confirming a mailing address, and their recorded denominators differ for some outcomes.

The secondary outcomes can help describe how participants interacted with the approaches, but they do not replace the primary endpoint. They also do not establish that a message led to test completion or a health outcome. Differences in definitions, collection methods, and denominators mean that secondary findings should be interpreted on their own terms rather than combined into a single overall measure of intervention performance.

Unadjusted secondary results carry less inferential weight because the registry lists multiple outcomes and contrasts without reporting a multiplicity adjustment or a hierarchy for testing them. With multiple statistical tests, some small p-values can arise by chance even if there are no corresponding effects. The record does not state which secondary analyses were prespecified or intended as confirmatory. These outcomes are therefore most useful as descriptive and hypothesis-generating evidence alongside the primary result, not as independent proof of a broad conclusion.

Secondary outcomes registered for this trial, for reference (only those above were recalculated):

9. Statistical Interpretation

Clinical Biostats interpretation

The reference group had 47 participants meeting the primary endpoint among 261 participants. The conversational-agent comparisons show small estimated differences from that reference: the risk difference is -0.025 for the 30 Day group without navigation and -0.025 for the 10 Day group with navigation. Their confidence intervals extend from -0.089 to 0.039, and the unadjusted p-value is 0.447. The conversational-agent 30 Day group with navigation has a risk difference of -0.008, with a confidence interval from -0.074 to 0.057 and an unadjusted p-value of 0.803. These intervals include no difference and are compatible with estimates on either side of zero.

The text-message comparisons have positive estimated risk differences relative to the reference group. For text messaging without navigation, the risk differences are 0.356 for the 10 Day group and 0.344 for the 30 Day group. For text messaging with navigation, the risk differences are 0.379 for the 10 Day group and 0.282 for the 30 Day group. The corresponding confidence intervals are entirely above zero, and each unadjusted p-value is <0.001. Thus, the posted counts and unadjusted comparisons show more participants meeting the request-and-address-confirmation endpoint in each of these text-message groups than in the conversational-agent reference group.

These are contrasts against one reference group, not evidence that all text-message schedules or navigation arrangements differ from one another. In particular, the estimates do not isolate the effect of messaging modality, navigation, or timing across a complete set of direct comparisons. The study has several factors varying across groups, and the registry record does not report a model that jointly estimates their separate contributions or interactions.

Interpret the p-values as unadjusted evidence for each posted comparison, not as a multiplicity-controlled set of tests. The record does not report a prespecified analysis plan or adjustment for testing multiple outcomes and contrasts. The observed direction and size of the differences remain the central descriptive results, while inferential conclusions require caution given the number of comparisons and the absence of reported adjustments.

The registry includes group counts and comparison estimates but no reported sponsor analyses in the outcome record. The posted comparisons should therefore be read as the statistical summaries attached to the registry results, not assumed to be adjusted analyses. The trial record does not provide enough information to assess whether the comparison method accounted for covariates, site clustering, missing outcome data, or deviations from assigned approaches.

10. Statistical Methods Explained

For a binary endpoint, an event is the outcome of interest recorded for a participant. Here, the event means that a participant requested a test kit and confirmed a mailing address. The group-level results are event counts alongside the number of participants in each group. A risk, in this context, is the proportion of a group with the event; the registry’s comparisons express the difference between the reference group’s risk and another group’s risk.

What does a risk difference describe?

A risk difference is an absolute contrast: it reports the amount by which one group’s observed event proportion differs from the reference group’s proportion. A positive estimate means the compared group’s observed proportion is higher; a negative estimate means it is lower. Zero represents no difference in the estimated proportions. For example, the text-message comparisons have positive risk differences, while the conversational-agent comparisons have estimates close to zero. These estimates describe the observed groups and do not, by themselves, establish why a difference occurred.

The registry also gives risk ratios and odds ratios for the primary comparisons. These are relative measures: a risk ratio compares event risks, while an odds ratio compares event odds. Relative measures can express the same direction of contrast on a different scale. Their values should not be substituted for the risk difference, which makes the absolute contrast directly interpretable in terms of differences in event proportions. The registry provides confidence intervals for these measures, but the risk-difference intervals are the most direct basis for describing absolute precision.

How should a confidence interval be read?

A confidence interval describes uncertainty around an estimated contrast under the statistical method used. It gives a range of values compatible with the observed data and that method; it is not a guarantee that the true value lies within the interval. If a risk-difference interval includes zero, it includes no difference as a plausible value under that analysis. If the entire interval is above zero, it supports a positive estimated difference under the same method. An interval’s width is also informative: a wider interval indicates less precision than a narrower interval.

For the conversational-agent comparisons, the risk-difference intervals include zero. For the text-message comparisons, the intervals are entirely above zero. This describes the posted unadjusted results; it does not account for multiple testing, possible missing data, or other analysis choices not described in the record. A p-value measures how unusual data at least this extreme would be under a specified no-difference model and statistical assumptions. It is not the probability that the null hypothesis is true, nor a measure of clinical importance. The unadjusted p-values do not communicate the full range of plausible effects, so they should be considered with the estimates and intervals.

What does unadjusted mean?

An unadjusted comparison is not reported as corrected for other variables or for the number of comparisons. The registry gives p-values for several contrasts and outcomes, but a multiplicity procedure is not reported. If many hypotheses are tested, the chance of at least one apparently unusual result can increase. Adjustment methods can address that issue, but the choice of method and any family of tests to be treated together must be specified. No such method is reported in the registry record.

Similarly, an adjusted model could account for measured participant characteristics or aspects of the study structure, but no such model is described in the posted analyses. It is not possible from these entries to establish whether the listed comparisons were calculated using only the displayed group counts or whether any additional factors entered into the calculation. The record’s reported comparison estimates and unadjusted p-values should be described as posted, without assuming an analysis method beyond what is documented.

What can the counts establish?

Counts show how many participants in each group met the recorded event definition. They do not reveal whether participants received, opened, or followed the intervention messages, unless those details are separately measured and reported. Nor do they establish that every participant who did not meet the endpoint declined testing; some may have had incomplete follow-up or an unrecorded request. Missing-data handling and analysis-population definitions are not reported in the registry record.

The study is marked randomized, which indicates that assignment was randomized, but the record does not specify the unit of randomization, the sequence-generation procedure, or allocation concealment. Randomization can support fair comparisons when implemented as planned, but the posted summaries alone do not verify implementation, adherence, balance of participant characteristics, or handling of departures from assigned groups. These missing details limit how far the comparisons can be interpreted as causal estimates.

There is no reported over-dispersion parameter because the primary outcome is a participant count and the registry lists no dispersion estimate. More generally, over-dispersion matters when count data vary more than a chosen statistical model expects: standard errors can then be too small if that extra variation is ignored. That general concern does not establish over-dispersion in this study. The posted data do not describe a model or diagnostic assessment that would allow it to be evaluated.

11. Confidence Intervals and Precision

Precision is reflected by the range of values in a confidence interval, not just by the point estimate or p-value. The primary comparison intervals for the conversational-agent groups cross zero. For the 30 Day group without navigation and the 10 Day group with navigation, the risk-difference estimate is -0.025 and the interval runs from -0.089 to 0.039. For the 30 Day group with navigation, the estimate is -0.008 and the interval runs from -0.074 to 0.057. Those ranges allow both a lower and a higher event proportion than the reference group.

The text-message risk-difference intervals are above zero: 0.280 to 0.432 for the 10 Day group without navigation, 0.268 to 0.420 for the 30 Day group without navigation, 0.304 to 0.455 for the 10 Day group with navigation, and 0.206 to 0.358 for the 30 Day group with navigation. Each interval indicates uncertainty around its point estimate while retaining a positive difference under the posted comparison method.

Intervals are not measures of importance and do not capture every source of uncertainty. They do not show whether the analysis accounted for multiplicity, missing outcomes, covariates, or departures from the assigned approach. The registry does not report confidence intervals for each group’s event count separately. The precision statements therefore concern the posted risk differences, and should not be extended to unreported outcomes or alternative analyses.

For secondary endpoints, the intervals vary substantially. The Reach-Engage Testing comparisons against the reference group have intervals that include zero. The Opt Out comparisons have intervals that exclude zero in opposite directions across the two reported contrasts. Self-reported Testing comparisons include wide intervals, including values on both sides of zero. These differences in precision are consistent with the smaller outcome-specific sample sizes recorded for self-reported testing than for the main group counts. The secondary intervals remain unadjusted, and should be considered exploratory rather than treated as a single confirmatory set.

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 detectParticipants per arm, 80% powerParticipants per arm, 90% power
100% of the observed effect3,5694,777
75% of the observed effect6,4398,619
50% of the observed effect14,69619,673
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect2,0005,00010,00020,00050,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Treat these figures cautiously. The observed difference is imprecise: its confidence interval includes no difference at all. A sample size built on a noisy estimate can be far too small or too large, so the smaller-effect rows are the more cautious guide.
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, pooled-variance normal approximation for two proportions (control proportion held at the observed value). Calculated for the comparison: Conversational Agent (CA) + No Patient Navigation (PN) + 30 Day.

The planning figures are participants per arm for 80% power and participants per arm for 90% power; they are not total sample sizes. The registry’s planning illustration uses a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. It uses a target effect equal to the stated fraction of the observed effect. The 100% row uses the full observed effect, while the 75% and 50% rows use smaller fractions. These calculations are illustrations based on observed results, not the trial’s original design assumptions; those original assumptions are not reported in the registry record.

In plain terms, the 80% power column gives the estimated participants per arm for a design with an 80% chance of detecting the stated effect under the planning assumptions, if that effect were the true one and the assumptions held. The 90% power column gives the corresponding planning number for a higher chance of detection. These are prospective planning quantities. They are not observed power, which is not a useful way to interpret a completed study’s results.

Smaller target effects require more participants to distinguish them from chance variation with the same planned power and significance level. This is why the rows for 75% and 50% of the observed effect generally have larger required sample sizes than the row using 100% of the observed effect. The very large values for some comparisons reflect the small observed contrast used as the planning basis; they do not establish what sample size the investigators originally intended to recruit.

Planning figures depend on the particular comparison and its observed event pattern, so values differ across comparisons and endpoints. They should not be used to claim that the completed groups had a particular probability of detecting an effect. The registry’s note distinguishes participant-per-arm figures from total-event figures for time-to-event outcomes; the outcomes discussed in this record are participant counts, so the applicable planning quantities are participants per arm.

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 = [ z1−α/2 √(2p̄(1−p̄)) + z1−β √(p0(1−p0) + p1(1−p1)) ]2 / (p1 − p0)2

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 = 0.180; treatment proportion p1 = 0.155; average p̄ = 0.168.
  2. First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.5283 = 1.0355.
  3. Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.5280 = 0.4444.
  4. n = (1.0355 + 0.4444)2 / (-0.0248)2 = 3,568.7, rounded up to 3,569 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 <- 0.18007662835249                          # control proportion
p1 <- 0.15530303030303                          # 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(5533359)
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 = 3,569 (80% power), 4,777 (90% power)
 75% of observed effect: n per arm = 6,439 (80% power), 8,619 (90% power)
 50% of observed effect: n per arm = 14,696 (80% power), 19,673 (90% power)
power.prop.test: 3568.7 
Simulated power at n = 3,569 per arm: 0.797 (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.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists a primary outcome and multiple secondary outcomes, with several comparisons against a common reference group. The posted p-values are unadjusted. A plan for controlling the family-wise error rate, false discovery rate, or another multiplicity measure is not reported in the registry record. Nor is a testing hierarchy reported that would distinguish confirmatory comparisons from exploratory ones. Consequently, an isolated unadjusted p-value should not be read as if it were protected from the consequences of testing multiple outcomes and contrasts.

Missing-data procedures are also not reported. The record does not explain how participants without an observed endpoint were handled, whether follow-up differed by group, or whether missingness was considered in the comparisons. It does not report an intention-to-treat, per-protocol, or other analysis-population definition. The group sizes posted for the primary endpoint are given, but those numbers alone do not establish how missing outcomes or participants who did not engage with the intervention were treated.

The registry provides no reported analyses in the analysis listing. It does not describe covariate adjustment, model specification, sensitivity analyses, or checks of statistical assumptions. The record is marked randomized, but the method for generating and concealing assignments is not reported. The identity of the masked party is likewise not reported, despite the single-masked designation.

These omissions do not mean that no such procedures were used; they mean that they are not documented in the registry record. Readers should avoid assuming that multiplicity, missingness, or analysis-population choices were addressed in a particular way. The posted estimates remain useful descriptive comparisons, but the absence of these details limits assessment of the robustness and confirmatory status of the inferential results.

15. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Conversational Agent (CA) + No Patient Navigation (NoPN) + 10 Day02610.0%
Conversational Agent (CA) + No Patient Navigation (PN) + 30 Day02640.0%
Conversational Agent (CA) + Patient Navigation (PN) + 10 Day02640.0%
Conversational Agent (CA) + Patient Navigation (PN) + 30 Day02620.0%
Text Message (TM) + No Patient Navigation (NoPN) + 10 Day02650.0%
Text Message (TM) + No Patient Navigation (NoPN) + 30 Day02650.0%
Text Message (TM) + Patient Navigation (PN) + 10 Day02700.0%
Text Message (TM) + Patient Navigation (PN) + 30 Day02660.0%

Deaths

ArmDeaths (participants affected of at risk)
Conversational Agent (CA) + No Patient Navigation (NoPN) + 10 Day0 of 261
Conversational Agent (CA) + No Patient Navigation (PN) + 30 Day0 of 264
Conversational Agent (CA) + Patient Navigation (PN) + 10 Day0 of 264
Conversational Agent (CA) + Patient Navigation (PN) + 30 Day0 of 262
Text Message (TM) + No Patient Navigation (NoPN) + 10 Day0 of 265
Text Message (TM) + No Patient Navigation (NoPN) + 30 Day0 of 265

Other (non-serious) adverse events

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

ArmParticipants affected of at risk
Conversational Agent (CA) + No Patient Navigation (NoPN) + 10 Day0 of 261
Conversational Agent (CA) + No Patient Navigation (PN) + 30 Day0 of 264
Conversational Agent (CA) + Patient Navigation (PN) + 10 Day0 of 264
Conversational Agent (CA) + Patient Navigation (PN) + 30 Day0 of 262
Text Message (TM) + No Patient Navigation (NoPN) + 10 Day0 of 265
Text Message (TM) + No Patient Navigation (NoPN) + 30 Day0 of 265
Do not overextend the safety comparison. Serious-adverse-event counts are safety observations, not efficacy outcomes, and should not be combined with the primary result into a single benefit-risk number.

The adverse-event entries show zero serious adverse events, zero other adverse events, and zero deaths in each of the eight groups. The number at risk for the serious and other event entries matches the posted group size in each group. The registry lists no serious adverse-event terms.

These entries mean that no events in the recorded categories are posted for these groups. They should not be expanded into a claim that no harm occurred: the record does not provide detailed event definitions, collection methods, follow-up completeness, or information about events outside the listed categories. The table entries are counts, not estimates of comparative safety, and no safety comparison or confidence interval is reported. Zero recorded events also do not establish that an event is impossible. The registry record does not report further safety analyses or explain whether adverse events were actively solicited.

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

The primary results describe how many participants met a specific recorded step: requesting a test kit and confirming a mailing address. Compared with the conversational-agent 10 Day, no-navigation reference group, each text-message group has a positive posted risk difference, and each corresponding unadjusted confidence interval is entirely above zero. The conversational-agent comparisons have estimates closer to zero and intervals that include zero. These are findings about the posted endpoint and comparisons, not a full assessment of testing behavior or health outcomes.

The results do not establish that participants used the requested kits, completed COVID-19 tests, received vaccination, or experienced a change in health. The endpoint is not a measure of test positivity, disease incidence, or the clinical benefit of an intervention. It records a request plus address confirmation. Nor do the results show which individual component—message format, patient navigation, or timing—accounts for the observed differences. The posted comparisons are each against a shared reference group, not a full set of direct contrasts among all approaches.

The registry record does not report adjusted analyses, a multiplicity procedure, missing-data handling, or analysis-population definitions. The unadjusted p-values should therefore be interpreted with caution, particularly across multiple outcomes and comparisons. The intervals describe uncertainty under the posted analysis but do not incorporate every potential source of uncertainty, including possible bias from missing outcomes or differences in implementation.

The results are best understood as registry-posted evidence about a process outcome in this randomized study. Randomization is an important design feature, but the record does not provide sufficient detail to evaluate the allocation process, adherence, masking, or analysis decisions. The findings can inform further investigation of messaging and navigation strategies, but they do not by themselves establish a general effect across other populations, settings, or intervention implementations.

17. Why This Trial Matters Statistically

This study is statistically interesting because it compares approaches that combine communication format, navigation options, and message timing, while measuring a concrete participant action. The primary endpoint is more specific than general message engagement: it requires both a test-kit request and confirmation of a mailing address. That definition makes the outcome relevant to the practical reach of an offer, while also keeping clear that it is not the same as completed testing.

The posted results illustrate why effect estimates and uncertainty should be read together. The conversational-agent contrasts have intervals that include zero, whereas the text-message contrasts against the reference group have positive intervals that remain above zero. The estimates and confidence intervals communicate the direction and precision of these comparisons more fully than a binary focus on p-values would. At the same time, the comparisons are unadjusted and arise among several groups and endpoints, so the pattern should not be treated as a multiplicity-controlled set of findings.

The study also highlights the value of distinguishing an intervention’s components. A group comparison that changes message format, navigation, or timing cannot automatically identify the independent contribution of each feature. Direct comparisons and a clearly specified analysis plan would be needed to separate those effects with confidence. The registry does not report such analyses, so the available evidence is strongest as a description of the posted group outcomes and their contrasts with the reference group.

Finally, the record makes visible the difference between trial results and design planning. Sample-size illustrations based on observed effects can help readers understand the scale of future studies, but they are not the trial’s original sample-size justification or evidence of observed power. Keeping those distinctions explicit is central to sound interpretation of registry results.

18. Limitations

Several limitations specific to these results affect their interpretation. The posted primary comparisons use one conversational-agent group as the shared reference. They do not provide every pairwise comparison among the eight groups. Since groups differ across communication approach, navigation arrangement, and timing, the reference-group contrasts do not by themselves isolate the effect of any single component.

Some registry labels are not fully consistent. One arm title uses No Patient Navigation with the abbreviation PN, while other titles use NoPN for that condition; the conversational-agent descriptions also refer to Request PN whereas some arm titles use Patient Navigation. The descriptions distinguish navigation availability or request from navigation, but the registry wording does not fully resolve every label. This makes careful reliance on the full arm descriptions important when interpreting the group names.

The outcome record does not report follow-up completeness, adherence to messages, delivery success, or the treatment of missing endpoint data. Self-reported Testing has substantially different posted group denominators from the primary endpoint, but the record does not explain the reasons for those differences. This limits direct comparisons across outcomes and leaves uncertainty about the role of response or follow-up patterns.

The registry does not report the randomization unit, allocation method, masking details, analysis population, model specification, or adjustment for multiple testing. It also does not provide detailed outcome ascertainment procedures or adjusted analyses. These omissions limit assessment of potential bias and the robustness of inference. The safety record reports zero events in the listed categories, but event collection methods and definitions are not described. Finally, this is a Utah community-health-center study focused on COVID-19 testing approaches; the record does not establish how well the findings generalize to other populations or settings.

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22. Record Summary

NCT05533359 is a completed randomized, single-masked, parallel-group study sponsored by University of Utah, with enrollment of 2117. It compared conversational-agent and text-message approaches, navigation arrangements, and 10 Day or 30 Day schedules. The primary outcome counts participants who requested a test kit and confirmed their mailing address during follow-up of up to 90 days.

Against the conversational-agent 10 Day, no-navigation reference group, the posted text-message comparisons have positive risk differences with confidence intervals above zero; the conversational-agent comparisons have intervals that include zero. All posted p-values are unadjusted. Detailed plans for multiplicity, missing data, analysis populations, and adjusted analyses are not reported in the registry record. The result concerns a request and confirmed address, not completed testing or a clinical outcome.

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