Pharmacist Intervention to Reduce Post-Hospitalization Utilization: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Pharmacist Intervention to Reduce Post-Hospitalization Utilization (NCT04071951), a randomized na study. The primary outcome is Rate (%) of 30-day Post-discharge Hospitalization and ED Visits (Based on EHR Data and CMS Claims).

2. Clinical Question

The study is a patient-level randomized, pragmatic, multicenter trial conducted in two large hospitals. Its scope also includes implementation barriers and facilitators and the costs of the intervention. Those aims broaden the study beyond the immediate event comparison, but the posted primary result concerns utilization in the claims-available subset. The central statistical issue is how to interpret a modest difference in observed event proportions alongside an interval that includes both lower and higher risk in the pharmacist arm. The result describes the comparison measured in the posted data; it does not, by itself, resolve every implementation, cost, or subgroup question named in the study description.

3. Trial Design

The registry describes a randomized, single-masked, parallel-group trial with patient-level allocation. The intervention is pharmacist-led discharge care; the comparator is usual care, in which clinically indicated services may still include pharmacist services. The trial is pragmatic and multicenter, and the study description says it is being conducted in two large hospitals. The registry does not identify who was masked, so the meaning of single masking beyond that label is not reported in the registry record.

The recorded enrollment is 6478. For the primary outcome, the analysis was limited to 4472 participants with fee-for-service Medicare, because claims data covering all hospitals were available for this group. Thus the enrollment figure and the primary-outcome analysis population describe different quantities. The record does not explain the disposition or primary-outcome data availability for participants outside that claims subset, and it does not specify the analysis population as intention-to-treat, per-protocol, or another named approach.

The primary outcome is a participant count for hospitalization or an emergency department visit within 30 days of discharge. Hospitalization includes observation, and foreseen admissions are excluded. The outcome description says events are checked at least across facilities in the same state, using EHR data and CMS claims. Secondary outcomes include same-hospital utilization and planned stratifications involving intervention components, congestive heart failure, high-risk medication use, medication count, study site, adherence and literacy, and socioeconomic status.

The registry lists a start date of 2019-12-23, a primary completion date of 2024-08-28, and an active, not recruiting status. It identifies Cedars-Sinai Medical Center as sponsor and the trial phase as NA. The record also describes qualitative work on implementation and cost analyses from the health-system perspective. Details of randomization sequence generation, allocation concealment, the masking procedure, and the original statistical analysis plan are not reported in the registry record.

4. Participant Flow and Accounting

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

Overall Study

Analysis population for the primary outcome, as defined in the registry: note that to obtain outside hospital data, analysis was restricted to 4472 patients with fee-for-service Medicare (for whom all-hospital claims data was available)

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 Rate (%) of 30-day Post-discharge Hospitalization and ED Visits (Based on EHR Data and CMS Claims), measured over Hospitalization to a hospital or ED visit within 30 days of discharge (checking at least all same state facilities).

The primary endpoint counts participants with a hospitalization or emergency department visit within 30 days after discharge. It is a composite utilization outcome: a participant qualifies through either component, and the primary description includes hospitalization at a hospital, including observation, or an emergency department visit. Foreseen readmissions are excluded, with examples including transplants, chemotherapy or radiotherapy, treatment follow-up, rehabilitation care, and planned operations. The outcome is based on EHR data and CMS claims, with the description specifying checks at least across facilities in the same state.

The study description makes post-discharge utilization its central clinical-service question. Combining hospital and emergency department use captures more than readmission alone, while the fixed 30-day period sets a defined window after discharge. A participant-level event count gives a binary outcome for the comparison: whether each participant had an event during that window. The registry also lists same-hospital utilization as a secondary outcome, which is narrower than the primary outcome's effort to include outside-hospital data.

Availability of all-hospital claims data determined the primary analysis subset: 4472 participants with fee-for-service Medicare. This restriction matters when interpreting the result, because the primary estimate describes that subset rather than automatically representing every enrolled participant. The registry does not report the individual event totals separately for hospitalization and emergency department visits, nor does it provide component-specific estimates in the posted primary comparison.

7. Results Posted in the Registry

• Pharmacist Arm: 25.6% (570/2230) versus 26.4% (593/2242) on control; risk difference -0.9 percentage points (95% CI -3.5 to 1.7), risk ratio 0.97 (0.88–1.07); unadjusted two-proportion z-test p = 0.498.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is binary at the participant level: a participant either experienced the qualifying 30-day utilization event or did not. For a binary outcome, the event proportion describes the share of participants with an event. The comparison reports 570 events among 2230 participants in the pharmacist arm and 593 among 2242 in usual care, with proportions 0.256 and 0.265. These are the posted counts and proportions for the claims-available population.

What does the risk difference represent?

General: a risk difference subtracts the event proportion in one group from that in the other. Its sign depends on the stated ordering. In this comparison, the risk difference is reported for the pharmacist arm relative to usual care and is -0.009. A negative estimate means the observed event proportion was lower in the pharmacist arm on this scale. The estimate alone does not establish that the underlying group risks differ; its uncertainty interval and the analysis method also matter.

General: risk differences are expressed on the absolute scale of the outcome, so they describe a difference in event proportions rather than a relative change. The registry also reports relative measures: the risk ratio is 0.966 and the odds ratio is 0.955. A risk ratio compares the proportions, while an odds ratio compares event odds. These measures use different scales and should not be read as interchangeable with the risk difference. Their intervals are reported as 0.875 to 1.067 for the risk ratio and 0.835 to 1.091 for the odds ratio.

How should the p-value be read?

General: a p-value describes how unusual data at least as discrepant as those observed would be under a specified null model and its assumptions. It is not the probability that the null hypothesis is true, and it does not measure the size or practical importance of an effect. The unadjusted p-value reported for this comparison is 0.498. The registry does not give a threshold for interpreting this primary result as statistically significant, nor does it report a full model specification in the posted result.

General: a confidence interval represents uncertainty around an estimate under the method used to construct it. For a risk difference, zero is the value corresponding to no difference between the groups. The reported interval, -0.035 to 0.017, crosses zero, so it includes estimates on either side of no difference. The registry does not identify the confidence level or the interval-construction method in the posted comparison. No confidence level should therefore be assumed from this record.

Why does the analysis population matter?

The primary endpoint relies on EHR data and CMS claims and is described as checking events at least statewide. The record says that obtaining outside-hospital data required restricting the analysis to 4472 participants with fee-for-service Medicare. The primary comparison uses 2230 participants in the pharmacist arm and 2242 in usual care. This gives the estimate broader hospital capture than a same-hospital-only outcome, as described by the registry, but the result pertains to this claims-available subset. It should not automatically be generalized to all 6478 enrolled participants or to groups for whom equivalent claims data were unavailable.

General: randomization is intended to make treatment groups comparable on average, but interpretation also depends on following the assigned groups appropriately, handling missing outcome information, and using a prespecified analysis. The registry identifies the trial as randomized at the patient level, but the posted record does not describe allocation concealment, the exact analysis population, missing-data methods, covariate adjustment, or whether the reported comparison follows intention-to-treat principles. Those details cannot be inferred from the event counts alone.

The endpoint combines hospitalization and emergency department use. A composite can capture either type of utilization, but it does not reveal whether the components moved in the same direction or which contributed more events. The posted primary result does not separate those components. Secondary outcomes include same-hospital utilization and several stratified analyses, but subgroup-specific primary estimates and interaction tests are not included in the posted comparison.

General: when a study evaluates several outcomes or subgroup comparisons, the chance of finding at least one apparently notable result can increase if each is tested independently without an appropriate multiplicity strategy. The registry lists 19 outcome measures and 18 posted secondary outcomes, but does not report a multiplicity adjustment or hierarchy for interpreting these measures. The primary comparison should therefore be distinguished from exploratory or secondary analyses, whose statistical interpretation depends on plans and methods not stated in the record.

10. Confidence Intervals and Precision

The risk-difference estimate is -0.009, with an interval from -0.035 to 0.017. The interval includes zero and values on both sides of it. In practical statistical terms, the point estimate is not the only plausible description of the group difference: the posted interval allows for a lower event proportion in the pharmacist arm as well as a higher one. The interval therefore conveys uncertainty that cannot be summarized by the point estimate alone.

General: a confidence interval is a range generated by a statistical procedure to express uncertainty about an estimate. Narrower intervals indicate greater precision under that procedure, while wider intervals indicate less precision. The registry does not state the confidence level or construction method for the posted interval, so those features cannot be specified. The interval should not be read as a range in which the true value is guaranteed to lie.

The relative measures show similar uncertainty. The risk-ratio interval is 0.875 to 1.067, and the odds-ratio interval is 0.835 to 1.091; each includes its no-difference value. These scales provide a complementary view, but they do not remove the uncertainty apparent in the risk-difference interval. The unadjusted p-value is 0.498 and does not replace the interval as a description of the range of estimates compatible with the comparison.

Precision is tied to the analysis population and outcome definition. The estimate uses 4472 participants with fee-for-service Medicare, not all 6478 enrolled participants, and combines hospitalization with emergency department visits within 30 days. The record does not provide component-specific intervals or interval estimates for the listed subgroups. As a result, precision for those distinct questions cannot be inferred from the primary interval.

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 sample-size figures are planning illustrations based on the observed effect, not the original design assumptions for this trial. They give participants per arm, not total participants. The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each scenario uses the stated fraction of the observed effect as the effect to detect. The registry does not report the trial's original sample-size justification or design assumptions.

The 80% power column gives the number of participants per arm in a hypothetical design that would have 80% power under those assumptions and for the specified effect. The 90% power column gives the corresponding number per arm for 90% power. Power describes the probability of detecting the chosen effect under the planning model if that effect is the true one; it is not a guarantee that a study will produce a particular finding.

For planning at 100% of the observed effect, the figures are 38,214 participants per arm for 80% power and 51,158 for 90% power. At 75% of the observed effect, they are 68,125 and 91,200 participants per arm. At 50% of the observed effect, they are 153,703 and 205,764 participants per arm. These are planning scenarios, not observed trial results. Smaller effects require more participants under the stated assumptions, which is why the required figures rise as the assumed effect becomes a smaller fraction of the observed effect.

This is not observed power. The figures do not describe the power achieved by the completed comparison, and they should not be used to reinterpret the posted p-value or interval. The stated calculation applies a simplified planning model and does not establish that the trial itself was designed using these assumptions.

12. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n is the number of participants in each arm, p₀ and p₁ are the control and treatment proportions, and p̄ is their average.

Worked calculation for this trial

1. Control proportion p₀ = 0.264; treatment proportion p₁ = 0.256; average p̄ = 0.260.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6204 = 1.2159.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.6203 = 0.5221.
4. n = (1.2159 + 0.5221)² / (-0.0089)² = 38,213.9, rounded up to 38,214 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 <- 0.264495985727029                          # control proportion
p1 <- 0.255605381165919                          # 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(4071951)
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 = 38,214 (80% power), 51,158 (90% power)
 75% of observed effect: n per arm = 68,125 (80% power), 91,200 (90% power)
 50% of observed effect: n per arm = 153,703 (80% power), 205,764 (90% power)
power.prop.test: 38213.9 
Simulated power at n = 38,214 per arm: 0.800 (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 19 outcome measures and 18 posted secondary outcomes, in addition to the primary utilization endpoint. Secondary measures include same-hospital 30-day utilization and stratifications by intervention components, congestive heart failure, high-risk medication use, medication count, site, adherence and literacy, and socioeconomic status. The number of analyses reported is 0. This does not establish that no analyses were conducted; it describes the registry record. The record does not report a testing hierarchy, a multiplicity adjustment, or an approach for distinguishing confirmatory from exploratory secondary results.

General: evaluating several outcomes and subgroup comparisons creates multiple opportunities for apparently unusual findings. A prespecified hierarchy or adjustment can help control how results are interpreted across multiple tests. Without a reported plan, the primary comparison should be kept distinct from any separate subgroup findings, and isolated secondary results should not be treated as equivalent to a single prespecified primary result. The registry does not provide posted subgroup estimates in the information describing the primary comparison.

Missing-data procedures are not reported in the registry record. The primary outcome uses EHR data and CMS claims, and the stated restriction to participants with fee-for-service Medicare was made to obtain outside-hospital data. The record does not say how missing or incomplete outcome data within that subset were handled, whether any imputation was used, or how participants without claims availability were treated in analyses other than the described primary subset.

The record identifies patient-level randomization but does not specify whether the primary analysis followed intention-to-treat, per-protocol, or another population definition. It also does not report adjustment for baseline variables, the exact model, handling of protocol deviations, or whether subgroup analyses included formal interaction tests. These omissions limit assessment of how the posted estimates were generated and how secondary comparisons should be interpreted. The available counts and estimates can be described, but they do not reveal the full analysis plan.

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.

Most frequent serious adverse event terms

Serious events with the highest arm-level rate: 90-day post-discharge utilization (35.7%), 30-day post-discharge utilization (same hospital) (20.6%).

The registry's serious-event reporting lists 3239 participants at risk in each arm. It records 1485 serious events affected in the pharmacist arm and 1438 in usual care. For other events, it lists 3239 at risk in each arm and 0 affected in each. Deaths are recorded as 330 in the pharmacist arm and 334 in usual care. These are the registry's reported figures; the record does not specify in this summary whether affected counts represent unique participants or event episodes.

The listed top serious-event terms are 90-day post-discharge utilization at 35.7% and 30-day post-discharge utilization (same hospital) at 20.6%. The denominator and calculation details for these percentages are not reported in the registry record, so they should not be interpreted as participant-level risks or compared directly with the primary 30-day outcome proportions. The terms describe utilization outcomes and are not, by themselves, evidence that an event was caused by the intervention.

These figures do not establish a treatment-related safety difference. The record does not provide attribution details, event definitions, or a statistical comparison for these safety entries. The death counts are reported separately and should not be assumed to be intervention-related or included among serious events without further information.

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

The posted primary comparison describes 30-day hospitalization or emergency department use among participants with fee-for-service Medicare. The event counts are 570 of 2230 in the pharmacist arm and 593 of 2242 in usual care. The reported risk difference is -0.009, with an interval from -0.035 to 0.017, and the unadjusted p-value is 0.498. The point estimate favors a lower observed event proportion in the pharmacist arm, but the uncertainty interval includes zero and extends to a possible higher event proportion in that arm.

This result does not demonstrate that the two groups are identical, and it does not establish that any difference is clinically important. A non-definitive comparison can arise when the data are compatible with effects in more than one direction. The interval and point estimate should be read together: the estimate indicates the direction and size of the observed difference, while the interval indicates that meaningful uncertainty remains around it. The p-value is not a probability that the treatment has no effect.

The finding is specific to the composite utilization endpoint, the 30-day period, and the 4472-person claims-available subset. It does not tell whether hospitalizations or emergency department visits accounted for more of the events, and the primary comparison does not report separate component results. It also does not answer whether effects differ by the secondary subgroups listed in the registry. Although the study description includes implementation and cost aims, those questions are not answered by the posted primary comparison.

The record does not report the full analysis plan, missing-data methods, or the primary analysis population definition beyond the claims-data restriction. These details matter when assessing the robustness and generalizability of an estimate. The primary result should therefore be interpreted as the posted comparison for the analyzed subset, rather than as a complete account of all trial aims or of every enrolled participant's outcome.

16. Why This Trial Matters Statistically

Statistically, this trial illustrates the distinction between the observed effect and the precision with which that effect is estimated. The risk-difference point estimate is -0.009, while the interval from -0.035 to 0.017 spans zero. The point estimate alone might invite a directional reading, but the interval shows that the data do not pin down a single direction. The relative measures also have intervals that include their no-difference value. Together, these summaries make uncertainty central to interpreting the result.

The endpoint and data source are also consequential. The primary outcome seeks to capture utilization beyond the hospital where discharge occurred, using EHR data and CMS claims and checking at least statewide facilities. The registry says that complete outside-hospital claims information was available for the 4472 participants with fee-for-service Medicare, leading to a restricted analysis population. This creates a clear distinction between total enrollment and the group supporting the primary estimate, which readers need to keep in view.

The pragmatic design connects a clinical workflow intervention with outcomes that matter to health-system use, while the record also names implementation and cost-effectiveness aims. Yet the statistical interpretation of the primary outcome does not substitute for the implementation or economic evaluations. In addition, the many listed secondary outcomes make a reported multiplicity plan important for assessing subgroup and secondary findings; such a plan is not reported in the registry record.

Finally, the trial highlights why event counts, effect estimates, intervals, and analysis-population details answer different questions. Counts describe what was observed in each arm; the risk difference summarizes the absolute comparison; intervals describe uncertainty; and the claims restriction clarifies who contributed to the primary analysis. None of these alone establishes an intervention effect across every enrolled participant or resolves the broader aims.

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 primary-outcome comparison covers 4472 participants with fee-for-service Medicare rather than all 6478 enrolled participants, because all-hospital claims data were available for that subset. This improves capture of outside-hospital utilization for the analyzed group, as described by the registry, but limits direct interpretation for participants outside it. The record does not provide a separate primary estimate for those without the specified claims availability.

The endpoint combines hospitalization and emergency department visits, so the posted primary result does not show which component contributed to the counts or whether their patterns differed. It also excludes specified foreseen readmissions. The registry's secondary outcome list includes same-hospital utilization, but the primary comparison does not provide a component breakdown or a comparison of the broader outcome against the same-hospital measure.

Important statistical details are not reported in the registry record: the confidence-interval level and construction, the complete model specification, missing-data handling, the primary analysis population definition, and the original sample-size justification. The record also does not report a multiplicity strategy for the many outcome and subgroup measures, or identify who was masked in the single-masked trial. These omissions constrain evaluation of analysis choices and secondary findings.

The posted outcome comparison does not answer the study's implementation or cost aims, and no subgroup-specific results are included in the primary comparison. The record's safety summary does not state event attribution or clarify the denominator behind the listed serious-event percentages. These are limits on what can be concluded from the registry record, not evidence that the study did not collect the relevant information.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Pharmacist Intervention to Reduce Post-Hospitalization Utilization — NCT04071951.
• Registry record last updated 2026-04-02; status last verified 2026-03.
• Results first posted 2024-10-29.
• 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

NCT04071951 is a randomized, single-masked, parallel-group pragmatic trial of pharmacist-directed transitional care compared with usual care. The intervention includes medication reconciliation, regimen review, and adherence and literacy assessment and counseling. The registry lists 6478 enrolled participants and identifies Cedars-Sinai Medical Center as sponsor. The study is recorded as active, not recruiting, with a start date of 2019-12-23 and a primary completion date of 2024-08-28.

The primary outcome is a participant count for hospitalization or emergency department use within 30 days after discharge, excluding specified foreseen readmissions. The posted primary comparison uses 4472 participants with fee-for-service Medicare. It reports 570 events among 2230 participants in the pharmacist arm and 593 among 2242 in usual care. The risk difference is -0.009, with an interval from -0.035 to 0.017 and an unadjusted p-value of 0.498.

The study description also names implementation and cost aims. The registry record does not report the original sample-size justification, missing-data methods, or a multiplicity plan.