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HIV/AIDS NA Binary Endpoint NCT04088656

Systems Analysis and Improvement Approach for the Hypertension Care Cascade: Complete Statistical Analysis

This analysis examines a randomized evaluation of the Systems Analysis and Improvement Approach for hypertension screening and management among people living with HIV. It focuses on controlled hypertension across baseline, intensive implementation, and sustainment phases, alongside the posted secondary cascade outcomes and the limits of the registry results.

Trial start: 2020-07-01  ·  Enrollment: 305  ·  Sponsor: University of Washington
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 Systems Analysis and Improvement Approach for the Hypertension Care Cascade (NCT04088656), a randomized na study. The primary outcome is Controlled Hypertension.

305
Enrollment
NA
6
Arms
In the primary outcome
+2.1 pts
Risk difference
Intervention Arm - Baseline Phase
-3.7 to 8.0 pts
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT04088656
PhaseNA
ConditionHIV/AIDS, Hypertension
AllocationRandomized
Design modelParallel
MaskingNone (open label)
Enrollment305
Arms in the primary outcome6
Lead sponsorUniversity of Washington
Results postedYes

2. Clinical Question

Population

People living with HIV/AIDS attending the enrolled health facilities, with the primary outcome restricted to patients diagnosed with hypertension who picked up prescribed medication. The registry describes the primary outcome population as new and existing patients at participating facilities.

Intervention

The Systems Analysis and Improvement Approach for hypertension screening and treatment optimization, identified as SAIA-HTN. The intervention was intended to improve hypertension detection and management within HIV care services.

Comparator

Facilities assigned to control did not receive SAIA-HTN. The posted primary comparisons use the control baseline phase as the reference for intervention baseline, intensive implementation, sustainment, and control follow-up phases.

Primary question

Among patients diagnosed with hypertension who picked up medication after prescription, how did the count with controlled hypertension vary across the intervention and control phases? The registry reports phase-specific counts and unadjusted comparisons, but does not report an adjusted analysis directly comparing intervention and control during the same follow-up phase.

The clinical problem is framed as a care-cascade challenge: hypertension must be detected, diagnosed, treated, and managed within services that already provide HIV care. The study evaluates a service-improvement approach rather than a drug or other individual-level clinical treatment. The registry describes an intention to optimize screening and management for people living with HIV/AIDS and lists outcomes along several steps of the cascade.

The main posted result concerns controlled hypertension among patients who had reached the point of diagnosis and medication pickup. This is a selected group within the broader population attending the facilities. It does not describe blood pressure control among every person living with HIV at those facilities, nor does it by itself capture how many people moved successfully through every earlier step in the cascade. The secondary outcomes address screening, diagnosis, and treatment prescription; medication pickup is named among the outcomes, but its results are not reported in the registry record.

3. Trial Design

The registry describes a completed, randomized, parallel-group study with no masking. The sponsor was the University of Washington. The study enrolled 305 participants, and its listed conditions were HIV/AIDS and hypertension. The intervention is a health-service systems approach, with facilities rather than individual patients described as receiving or not receiving SAIA-HTN.

Eight health facilities were assigned to receive the Systems Analysis and Improvement Approach, and eight facilities were assigned to control. Intervention facilities received SAIA-HTN to optimize hypertension screening and management for people living with HIV/AIDS. Control facilities did not receive this approach. The registry does not report how randomization was carried out, whether allocation was stratified, or whether the facilities or participants were the formal randomization units in the statistical analysis. It also does not report masking procedures beyond the designation of no masking.

Outcomes are organized into a baseline phase, an intensive implementation phase, and a sustainment phase. The listed timeframe is up to 3 months for baseline, up to 2 years for intensive implementation, and up to 1 year for sustainment. The primary endpoint is a count of participants with controlled hypertension among those diagnosed with hypertension and picking up medication after prescription. The registry also lists blood pressure screening, hypertension diagnosis, hypertension treatment prescription, and hypertension medication pickup as secondary outcomes.

The record marks the trial completed. It does not report the original statistical analysis plan, the planned sample size, the allocation procedure in further detail, or the trial’s own assumptions for design and power. There are no analyses listed as reported analyses. The posted comparisons are unadjusted and use the control baseline phase as their reference, rather than presenting a direct adjusted contrast between intervention and control in each follow-up phase. That structure matters when interpreting the results: phase-specific changes from a baseline reference are not identical to a concurrent randomized-group comparison.

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.

Baseline Period

StageHypertension Systems Analysis and ImprovementControl
STARTED1230710042
Patients1230710042
COMPLETED1230710042
NOT COMPLETED00

Intensive Implementation Period

StageHypertension Systems Analysis and ImprovementControl
STARTED2078817909
Healthcare Workers1710
Patients2061717909
COMPLETED2078817909
NOT COMPLETED00

Sustainment Implementation Period

StageHypertension Systems Analysis and ImprovementControl
STARTED23172567
Healthcare Workers1340
Patients21832567
COMPLETED23172567
NOT COMPLETED00

Analysis population for the primary outcome, as defined in the registry: Number of new and existing HIV-infected patients attending enrolled facilities who were diagnosed with hypertension and picked up their medications after receiving a prescription

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: Enrolled and consented 305 healthcare workers in intervention sites and none in control sites. Data captured from 35107 patients in intervention sites and 30518 control sites.

CharacteristicUnitHypertension Systems Analysis and ImprovementControlTotal
Participants analysed354123051865930
Age, Categorical: Healthcare Workers – <=18 yearsParticipants000
Age, Categorical: Healthcare Workers – Between 18 and 65 yearsParticipants3050305
Age, Categorical: Healthcare Workers – >=65 yearsParticipants000
Age, Categorical: Patients – <=18 yearsParticipants000
Age, Categorical: Patients – Between 18 and 65 yearsParticipants334652987163336
Age, Categorical: Patients – >=65 yearsParticipants6765951271
Sex: Female, Male: Healthcare Workers – FemaleParticipants1320132
Sex: Female, Male: Healthcare Workers – MaleParticipants1520152
Sex: Female, Male: Patients – FemaleParticipants227181882141539
Sex: Female, Male: Patients – MaleParticipants123611168724048
Race (NIH/OMB): Healthcare Workers – American Indian or Alaska NativeParticipants000
Race (NIH/OMB): Healthcare Workers – AsianParticipants000
Race (NIH/OMB): Healthcare Workers – Native Hawaiian or Other Pacific IslanderParticipants000
Race (NIH/OMB): Healthcare Workers – Black or African AmericanParticipants3050305
Race (NIH/OMB): Healthcare Workers – WhiteParticipants000
Race (NIH/OMB): Healthcare Workers – More than one raceParticipants000
Race (NIH/OMB): Healthcare Workers – Unknown or Not ReportedParticipants000
Race (NIH/OMB): Patients – American Indian or Alaska NativeParticipants000
Race (NIH/OMB): Patients – AsianParticipants000
Race (NIH/OMB): Patients – Native Hawaiian or Other Pacific IslanderParticipants000
Race (NIH/OMB): Patients – Black or African AmericanParticipants351073051865625
Race (NIH/OMB): Patients – WhiteParticipants000
Race (NIH/OMB): Patients – More than one raceParticipants000
Race (NIH/OMB): Patients – Unknown or Not ReportedParticipants000
Region of Enrollment: MozambiqueHealthcare workers and Patients354123051865930

6. Primary Endpoint

The registry lists the primary outcome as Controlled Hypertension, measured over Per Phase: up 3 months for Baseline Phase, up to 2 years for Intensive Implementation Phase, up to 1 year for Sustainment Phase..

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

The primary endpoint counts participants with controlled hypertension among HIV-infected patients who had been diagnosed with hypertension and picked up medication after receiving a prescription. The registry gives phase-specific counts for the intervention and control arms. It describes the relevant population as new and existing patients attending the enrolled facilities who met those diagnosis and medication-pickup conditions.

This endpoint addresses blood pressure control at a later point in the care cascade than screening or diagnosis. It is relevant to the stated goal of improving hypertension management in HIV services because it focuses on whether hypertension is controlled among people who have entered treatment. It should not be read as the proportion of all facility attendees, or all patients living with HIV, whose hypertension was controlled. The denominator is restricted to the stated group that had been diagnosed and picked up medication.

The endpoint is posted as a participant count, with the number counted and the number in the phase-specific denominator. Counts make the observed data concrete, but do not alone establish whether a difference is attributable to the intervention. Interpretation also depends on how the comparison groups were defined, how repeated or phase-specific observations were handled, and whether facility clustering was incorporated. Those analytic details are not reported in the registry record. The outcome timeframe is specified separately for each phase, and the record does not provide further detail about when blood pressure was assessed or how control was defined.

7. Results Posted in the Registry

Risk difference: Intervention Arm - Baseline Phase

+2.1

95% CI: -3.7 to 8.0 percentage points

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals0.06.813.520.327.133.8Intervention Arm - Baseline P… (n=74)Intervention Arm - Intensive … (n=1447)Intervention Arm - Sustainmen… (n=157)Control Arm - Baseline Phase (n=52)Control Arm - Intensive Imple… (n=1430)Control Arm - Sustainment Pha… (n=161)% of participants (95% CI)
Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Intervention Arm - Baseline P…Intervention Arm - Intensive …Intervention Arm - Sustainmen…Control Arm - Intensive Imple…Control Arm - Sustainment Pha…-6.351.308.95172432risk 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
Blood Pressure ScreeningBinary EndpointRisk difference+1.4 pts (0.1 to 2.6)18,878 per arm
Hypertension DiagnosisBinary EndpointRisk difference-1.2 pts (-2.4 to 0.1)8,664 per arm
Hypertension Treatment PrescriptionBinary EndpointRisk difference+8.7 pts (1.2 to 16.3)467 per arm

Blood Pressure Screening

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Intervention Arm - Baseline P…Intervention Arm - Intensive …-5.311025415672risk difference (percentage points) vs control (95% CI)

Hypertension Diagnosis

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Intervention Arm - Baseline P…Intervention Arm - Intensive …-2.86-1.50-0.131.232.593.95risk difference (percentage points) vs control (95% CI)

Hypertension Treatment Prescription

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Intervention Arm - Baseline P…Intervention Arm - Intensive …-1.593.017.62121721risk difference (percentage points) vs control (95% CI)

The secondary outcomes follow several steps in the hypertension care cascade: blood pressure screening, diagnosis, treatment prescription, and medication pickup. Their conceptual role is to help interpret the primary outcome, which concerns control among patients who had been diagnosed and picked up medication. A pattern across upstream and downstream steps can give context about where service delivery may have changed, but the posted outcomes do not establish that any change in one step caused a change in a later step.

The available phase-specific counts suggest that screening activity was high during intensive implementation in both arms, while the diagnosis and prescription outcomes show different patterns across the posted phases. These summaries are descriptive and are not a substitute for a direct, design-appropriate randomized comparison. The registry lists medication pickup as a secondary outcome, but its results are not reported in the registry record. Secondary comparisons are also not posted for every outcome and phase; for example, the reported comparison entries do not cover sustainment for the screening, diagnosis, or prescription outcomes.

Unadjusted secondary results carry less weight than a prespecified, appropriately adjusted primary analysis because they may involve multiple comparisons, incomplete phase coverage, and potentially correlated observations. The registry does not report a multiplicity procedure or a statistical analysis plan, so the degree to which these outcomes and contrasts were selected in advance is unknown. In addition, the outcomes concern changing denominators along a care pathway. The patients eligible for diagnosis are those counted at screening, and those eligible for prescription or control are successively more selected groups. Differences between cascade steps should not be treated as independent confirmation of a single effect.

Taken together, the secondary outcomes provide process context for the primary result, but the record does not post a unified estimate of cascade completion or a model relating the steps. Nor does it explain how phase counts relate to the enrolled participant total. Their value is therefore primarily descriptive: they indicate which aspects of screening and management were recorded, while leaving important questions about analysis, comparability, and the flow of individuals through the cascade unresolved.

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

9. Statistical Interpretation

Clinical Biostats interpretation

The primary outcome counts are higher during intensive implementation and sustainment in the intervention arm than in its baseline phase and the control baseline reference. The posted unadjusted risk-difference comparison for intervention intensive implementation is 0.199, with a confidence interval from 0.155 to 0.241 and p < 0.001. For intervention sustainment, the risk difference is 0.216, with a confidence interval from 0.140 to 0.293 and p < 0.001. In contrast, the intervention baseline comparison has a risk difference of 0.021, a confidence interval from -0.037 to 0.080, and p = 0.502.

These figures compare each phase with the control baseline phase. They should not be described as direct randomized comparisons of intervention versus control during the same phase. The control arm’s intensive implementation comparison with its baseline has a risk difference of 0.038, a confidence interval from -0.001 to 0.077, and p = 0.24. The control sustainment comparison has a risk difference of 0.068, a confidence interval from 0.010 to 0.125, and p = 0.097. The posted results therefore show different patterns across the phase-specific comparisons, but do not provide an adjusted estimate of the intervention effect relative to a concurrent control group.

The phase-specific participant counts also need context. In the primary outcome, the reported denominator is 74 in intervention baseline, 1,447 in intervention intensive implementation, and 157 in intervention sustainment; the corresponding control counts are 52, 1,430, and 161. The study enrollment is 305. The registry record does not explain the relationship between enrollment and the much larger phase-specific outcome denominators, including whether observations represent repeated measurements, facility-level aggregates, or another counting structure. That distinction is important for assessing independence and uncertainty.

A small p-value indicates that the observed comparison would be unusual under a specified null model, but it does not establish that the intervention caused the difference. The registry does not report an adjusted analysis, a model accounting for facility clustering, or a prespecified statistical plan. The unadjusted comparisons are therefore descriptive evidence from the posted counts, with causal interpretation limited by the comparison structure and unavailable analytic details. The baseline comparison is not statistically distinguishable from no risk difference by its reported interval and p-value; this should not be taken as proof that the arms were equivalent. Likewise, the reported intensive implementation and sustainment comparisons do not on their own establish the size of a causal intervention effect.

The outcome itself is conditional on diagnosis and medication pickup. Changes in who reaches that group could affect the composition of the people counted for blood pressure control. The secondary cascade outcomes help describe earlier steps, but do not resolve this selection issue or replace a direct analysis of the full randomized comparison. The registry also does not report missing-data handling, analysis populations, or multiplicity procedures. These omissions leave uncertainty about how complete and comparable the phase-specific records are and how to interpret multiple outcome comparisons.

10. Statistical Methods Explained

General: A binary outcome records whether an event occurred for each person or unit counted. The registry’s primary outcome is posted as a count of participants with controlled hypertension, alongside a denominator for each arm and phase. A proportion can be analyzed from such data, but the posted comparisons are expressed as risk differences. The risk difference is the difference between two event proportions, expressed on the proportion scale. A positive value means the first proportion in the comparison is higher; a value of zero represents no difference on that scale.

What does the risk difference compare?

The primary comparisons use control baseline as the reference. Intervention baseline, intervention intensive implementation, intervention sustainment, control intensive implementation, and control sustainment are each compared with that reference. This is different from comparing intervention with control within the intensive implementation phase or within the sustainment phase. A phase-versus-baseline comparison can describe change relative to the reference, but a direct intervention-versus-control contrast at the same phase is more closely aligned with the randomized group question. Such a direct adjusted analysis is not reported in the registry record.

General: A confidence interval expresses uncertainty around an estimated effect under the statistical method used. Its width reflects precision: narrower intervals indicate more precise estimates, while wider intervals indicate greater uncertainty. For a risk difference, an interval that includes zero is compatible with no difference under the interval procedure; an interval entirely above or below zero indicates a difference in that direction at the corresponding confidence level. The registry comparisons include intervals that cross zero for intervention baseline and control intensive implementation, while the intervals for intervention intensive implementation, intervention sustainment, and control sustainment are above zero. These are unadjusted comparisons and should be interpreted in light of the comparison definitions and missing analysis details.

What does the p-value add?

General: A p-value describes how incompatible the observed data are with a null hypothesis under a particular model and its assumptions. It is not the probability that the null hypothesis is true, and it does not measure clinical importance. The posted primary comparison for intervention intensive implementation and intervention sustainment each has p < 0.001; the intervention baseline comparison has p = 0.502. The control intensive implementation and sustainment comparisons have p = 0.24 and p = 0.097. The values are unadjusted. Because multiple phases and outcomes are posted, individual p-values should not be interpreted as if they were the only analysis undertaken.

General: Randomization can support a causal comparison when the analysis preserves the assigned groups and appropriately accounts for the design. In a facility-randomized setting, people treated at the same facility may have correlated outcomes because they share staff, workflows, and service conditions. This is called clustering. If correlation within facilities is ignored, standard errors and confidence intervals can be too optimistic. The registry states that the trial was randomized and that eight facilities received the intervention while eight were control, but the statistical analysis accounting for facility clustering is not reported. It is therefore not possible to determine from the record whether the posted intervals and p-values reflect the facility-level design.

General: Over-dispersion arises when observed variability is greater than a model expects, often because outcomes are more heterogeneous or correlated than assumed. Accounting for over-dispersion can affect uncertainty estimates. The primary outcome is a binary participant count and no dispersion estimate is posted. The registry does not report whether over-dispersion was assessed or whether a model allowing extra variability was used. This is especially relevant when outcomes are grouped within facilities or measured across phases.

How should the phases be understood?

The baseline, intensive implementation, and sustainment phases have different stated maximum durations: up to 3 months, up to 2 years, and up to 1 year, respectively. Counts collected over phases with different durations do not by themselves convey event rates over a common time interval. The record does not describe whether analyses account for duration, repeated observations, changing facility populations, or possible changes in the denominator over time. The comparison displays should therefore be read as phase-specific summaries, not as standardized time-to-event rates.

The primary outcome is conditional on diagnosis and medication pickup. These conditions describe a subset of the broader facility population and may change as screening, diagnosis, prescribing, and pickup practices change. Comparing control of hypertension within that subset can be informative about management among people who reached treatment, but it does not alone quantify the full effect across the cascade. The secondary outcomes are relevant to the steps that precede control; however, the registry does not report a combined cascade analysis linking each individual’s progress through those steps.

The record lists zero reported analyses and does not report a statistical analysis plan, missing-data approach, analysis population definitions, or adjustment strategy. General: Prespecification helps distinguish planned analyses from exploratory comparisons and reduces the risk that results are selected after examination. Without the plan, it is not possible to know which contrasts were primary to the analysis, whether any interim looks occurred, how multiplicity was handled, or whether the posted calculations align with the intended model. Those items are not reported in the registry record.

11. Confidence Intervals and Precision

The posted primary confidence intervals indicate different levels of certainty across phase comparisons. The interval for intervention baseline extends across zero, and the corresponding p-value is 0.502. The control intensive implementation interval also extends across zero, with p = 0.24. These results are compatible with a range of risk differences that includes no difference under the unadjusted interval method. They do not establish equivalence or prove that there was no change.

The intervals for intervention intensive implementation and intervention sustainment are above zero, and both comparisons have p < 0.001. The control sustainment interval is also above zero, while its p-value is 0.097. The widths differ across comparisons, reflecting differences in the estimates and the available denominators. The registry posts unadjusted intervals, and the analysis method used to calculate them is not reported in the registry record. Their precision should therefore be considered alongside the unknown handling of facility clustering, repeated or phase-specific observations, and changing denominators.

General: A confidence interval is not a guarantee that the true effect lies within its limits. It describes uncertainty under the assumptions of the statistical procedure. If those assumptions do not account for correlated outcomes or other features of the study design, the apparent precision may not reflect all relevant uncertainty. The registry does not report whether the intervals account for the facility allocation structure.

The primary outcome counts vary substantially across phases, while the study enrollment is 305. The registry does not explain the relationship between those denominators and enrollment. Without that explanation, readers cannot fully assess the amount of independent information represented by the phase counts. The posted intervals quantify uncertainty according to the method used for the displayed comparisons, but the record does not provide enough analytic detail to evaluate the method’s fit to the data structure.

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 effect1,0021,340
75% of the observed effect1,6272,177
50% of the observed effect3,3124,433
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect1,0002,0005,00010,00040%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: Intervention Arm - Baseline Phase.

The planning figures are illustrations based on the observed effect, not the trial’s original design justification. For the binary outcomes, the figures are participants per arm, not total participants across both arms and not total events. The planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set to the stated fraction of the observed effect. The registry record does not report the trial’s own original sample-size assumptions or justification.

The 80% power column gives the estimated number of participants per arm under those assumptions for an analysis to have an 80% chance of detecting the selected effect, if that effect and the planning assumptions were correct. The 90% power column uses a higher target chance of detection and consequently generally requires more participants per arm. These are design-planning quantities, not descriptions of the probability that the completed study found a true effect. This is not observed power.

Rows that use a smaller fraction of the observed effect represent a more modest effect to detect. Smaller effects are harder to distinguish from random variation, so they require more participants per arm under otherwise identical assumptions. The planning values can differ sharply across outcomes because the observed event patterns and baseline frequencies differ. They should not be read as guaranteed requirements for a future study: the illustration uses an effect estimated from these posted data and simplified assumptions, and the record does not state that it accounts for facility clustering, changes over phases, missingness, or any other design feature.

For time-to-event outcomes, the stated convention is different: the planning figures are total event counts. That distinction does not apply to the posted primary endpoint, which is a participant-count binary outcome. The sample-size assumptions described in the record identify a normal approximation and equal allocation, but do not provide enough detail to reconstruct the trial’s original design or establish that these planning illustrations match its actual analytic approach.

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 = 0.019; treatment proportion p1 = 0.041; average p̄ = 0.030.
  2. First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.2408 = 0.4720.
  3. Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.2403 = 0.2023.
  4. n = (0.4720 + 0.2023)2 / (0.0213)2 = 1,001.0, rounded up to 1,002 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 <- 0.0192307692307692                          # control proportion
p1 <- 0.0405405405405405                          # 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(4088656)
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 = 1,002 (80% power), 1,340 (90% power)
 75% of observed effect: n per arm = 1,627 (80% power), 2,177 (90% power)
 50% of observed effect: n per arm = 3,312 (80% power), 4,433 (90% power)
power.prop.test: 1001 
Simulated power at n = 1,002 per arm: 0.809 (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 several secondary outcomes, with comparisons across phases. It reports no analyses as reported analyses and does not describe a multiplicity adjustment. When many outcomes or contrasts are examined, the chance of at least one apparently notable result can increase. General: Multiplicity procedures are methods for controlling or interpreting that risk, depending on the analytic goal. Without a stated plan, the posted unadjusted p-values should be treated as individual comparisons rather than as a family-wise confirmatory conclusion.

The registry record does not report how missing outcome data were handled, whether participants with incomplete information were excluded, or whether any imputation was used. It also does not report the analysis populations, such as whether analyses followed assignment regardless of intervention uptake or were restricted to participants with complete records. Those details affect how the estimates relate to the randomized design and how representative each phase denominator is.

The relationship between the enrollment of 305 and the much larger phase-specific outcome counts is not explained in the record. It is not possible to determine whether the posted counts reflect repeated observations, encounters, aggregated facility records, or another structure. The analysis does not report how dependence within a participant or facility was handled, or whether the facility-level allocation was reflected in standard errors. This limits assessment of the validity of the intervals and p-values.

The record also does not report interim analyses, stopping rules, a protocol-defined hierarchy for secondary outcomes, or a detailed statistical analysis plan. These items are not reported in the registry record; their absence from the record should not be interpreted as evidence that a particular procedure was or was not used. Without them, readers cannot establish whether the posted outcomes and comparisons were prespecified, how missingness was evaluated, or how the many possible contrasts were intended to be interpreted.

15. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Hypertension Systems Analysis and Improvement03050.0%

Deaths

ArmDeaths (participants affected of at risk)
Hypertension Systems Analysis and Improvement0 of 305
Control0 of 0

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
Hypertension Systems Analysis and Improvement0 of 305
Control0 of 0
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 serious adverse event figures report zero serious events among 305 people listed at risk in the intervention group. The control group lists zero people at risk and zero serious events. Therefore, the control figures do not provide an observed safety experience for a group with a reported at-risk denominator; they should not be interpreted as evidence that no serious events occurred among control participants.

The registry reports zero other adverse events in the intervention group among 305 listed at risk, and zero deaths. The control group has zero listed at risk, zero other adverse events, and zero deaths. No serious adverse event terms are listed. These are registry safety counts, not a detailed account of event definitions, collection procedures, follow-up time, or adjudication.

General: Zero recorded events do not establish that an event is impossible or that risk is absent. Interpretation depends on how events were sought, the duration and completeness of follow-up, and the population included. Those details are not reported in the registry record. The safety figures should be read narrowly as the counts posted, with the missing control at-risk denominator and absent collection details limiting comparison between arms.

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

The posted primary data show higher counts of controlled hypertension in intervention intensive implementation and sustainment comparisons than in the control baseline reference, with unadjusted p-values below 0.001 for both. The corresponding confidence intervals are above zero. The intervention baseline comparison is not statistically distinguishable from zero by its reported interval and p-value. These are statements about the posted phase-specific comparisons, not a definitive estimate of the causal effect of assigning facilities to SAIA-HTN.

The distinction matters because the comparator used in the posted calculations is the control baseline phase. The results do not provide a direct adjusted contrast between intervention and control during the same implementation or sustainment phase. While the trial is described as randomized, the record does not report the analysis methods needed to determine whether the facility allocation, within-facility correlation, and phase structure were accounted for. The reported comparisons therefore cannot be interpreted as though they were necessarily the planned randomized treatment-effect analysis.

The primary endpoint is also conditional on diagnosis and medication pickup. It describes control among people who reached that point of care, rather than the whole population attending the facilities. Screening, diagnosis, prescription, and pickup patterns could change who qualifies for the primary outcome over time. The secondary outcomes offer some process information, but medication-pickup results are not reported, and there is no posted analysis connecting individual steps across the full cascade.

Counts and unadjusted comparisons do not establish why the observed patterns arose. The registry does not report an analysis plan, missing-data approach, analysis populations, multiplicity handling, or a facility-clustered model. It also does not explain how phase-specific outcome denominators relate to the enrollment total. These limitations make it difficult to assess the robustness and generalizability of the estimates.

Accordingly, the results are best understood as descriptive registry findings that warrant careful attention to phase definitions and analysis structure. They do not establish that SAIA-HTN caused the observed differences, and they do not establish that the approach was ineffective. They describe posted outcomes and their statistical uncertainty under unadjusted comparisons, while leaving important design and analysis questions unresolved.

17. Why This Trial Matters Statistically

This trial is statistically informative because it evaluates a service-level intervention in a setting where patients’ outcomes are linked to the facilities and care systems they use. That structure raises questions beyond the usual comparison of independent patient-level outcomes. If patients within a facility share processes and staff, their outcomes may be correlated; a valid uncertainty estimate needs to reflect the design. The registry documents facility assignment but does not report how facility-level clustering was incorporated into the analyses.

The study also organizes results across baseline, intensive implementation, and sustainment phases. This makes temporal context central to interpretation. The posted comparisons reference control baseline rather than presenting a direct adjusted comparison of intervention and control within each follow-up phase. A reader must distinguish a phase change relative to baseline from an intervention contrast under concurrent follow-up. They answer different questions and can carry different causal meaning.

The cascade framing is another important statistical feature. Screening, diagnosis, prescription, pickup, and blood pressure control are connected stages, and the population counted at each stage may differ. Reporting several stage-specific outcomes can help locate where care processes change, but multiple outcomes also raise questions about multiplicity and the dependence between stages. The registry does not describe a combined cascade model or a multiplicity strategy.

Finally, the enrollment count and phase-specific denominators are not reconciled in the record. Clarifying how these quantities relate would help readers understand the observational unit, repeated measurement structure, and effective amount of independent information. The example illustrates why clear reporting of randomization units, denominators, analysis populations, clustering, missing data, and prespecified contrasts is essential when interpreting complex implementation trials.

18. Limitations

Several limitations specific to the registry record affect interpretation. The primary comparisons use the control baseline phase as a common reference, rather than reporting a direct intervention-versus-control comparison at each follow-up phase. The record gives no adjusted treatment-effect analysis, so the displayed differences cannot be assumed to represent the effect of randomized assignment.

The study assigns facilities to intervention or control, but the analysis method and handling of facility-level clustering are not reported. The record does not explain whether repeated observations or facility-level records contribute to the phase counts. This is particularly important because the phase-specific denominators exceed the enrollment count, and the relationship between those quantities is not described.

The phases have different stated maximum durations, and no information is reported about whether the analysis accounts for duration, participant turnover, or changes in denominators. The primary endpoint is restricted to participants who were diagnosed and picked up medication, so the eligible group may change across phases. The registry does not report how blood pressure control was defined or when it was assessed.

Secondary outcome results are incomplete in the record: medication pickup is named, but its results are not reported, and posted comparisons do not cover every phase for the other secondary outcomes. The registry also does not report missing-data methods, analysis populations, a multiplicity procedure, an interim-analysis plan, or the trial’s own sample-size justification. These omissions do not determine what methods were used, but they prevent readers from evaluating those aspects of the evidence.

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22. Record Summary

NCT04088656 is a completed randomized parallel-group study of the Systems Analysis and Improvement Approach for hypertension screening and treatment optimization among people living with HIV/AIDS. Eight facilities received SAIA-HTN and eight were assigned to control. The registry lists 305 enrolled participants and outcome phases of baseline, intensive implementation, and sustainment.

The primary outcome is controlled hypertension among diagnosed patients who picked up prescribed medication. The posted unadjusted comparisons show positive risk differences for intervention intensive implementation and sustainment relative to control baseline, each with p < 0.001. The registry does not report a direct adjusted comparison of intervention and control during the same follow-up phase. Secondary outcomes cover screening, diagnosis, treatment prescription, and medication pickup, although medication-pickup results are not reported.

The record does not describe the statistical analysis plan, missing-data methods, analysis populations, multiplicity handling, or whether facility clustering was accounted for. It also does not explain how phase-specific denominators relate to enrollment. These details are important for judging the precision and causal interpretation of the posted results.

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