Mirabegron as Medical Expulsive Therapy (MET) for Ureteral Stones and Ureteral Stent Pain: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Mirabegron as Medical Expulsive Therapy (MET) for Ureteral Stones and Ureteral Stent Pain (NCT02744430), a randomized phase 2 study. The primary outcome is Spontaneous Stone Passage Using Fisher's Exact Test.

2. Clinical Question

The clinical question is whether participants with a CT scan-proven ureteral stone between 4 to 10 mm who were undergoing expectant management had different rates of spontaneous stone passage when assigned mirabegron or placebo. The registry identifies ureteral obstruction and flank pain as the conditions studied. The primary outcome was assessed at 30 days.

This is a question about a binary outcome: each participant either met the registry's definition of passage or did not. The comparison concerns the observed passage counts and their uncertainty; the registry record does not establish that any observed difference was caused by treatment. Pain levels using the Wong-Baker Pain Rating Scale are listed as a secondary outcome, but the record does not post a numerical result for that outcome.

3. Trial Design

The registry describes a prospective, randomized, double-blind, placebo-controlled Phase 2 trial. It also classifies the masking as triple and the allocation model as parallel. These labels describe the registered design; the registry record does not explain which roles were included in the triple masking or give further details about how randomization and masking were implemented.

The active group received mirabegron 50 mg orally once every 24 hours starting immediately. The comparison group received placebo orally once every 24 hours starting immediately. The posted primary outcome was spontaneous stone passage at 30 days. Passage could be identified by CT or Renal Ultrasound/KUB imaging, or by finding the stone using a straining device.

The registry reports enrollment of 33 and a completed study. The recorded start date is 2017-07-22, and the primary completion date is 2019-10-31. The outcome counts are 8 of 17 in the mirabegron group and 5 of 16 in the placebo group. These are the group counts associated with the posted primary outcome, not a description of every participant’s follow-up or analysis status.

The registry lists a comparison of pain levels between groups using the Wong-Baker Pain Rating Scale as a secondary outcome. It records two outcome measures and one posted secondary outcome. There are no registry analysis entries listed. The original statistical analysis plan, details of the random sequence, concealment procedures, and the trial's own sample-size assumptions 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.

Before assignment: 33 met inclusion criteria and were randomized to treatment.

Overall Study

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 Spontaneous Stone Passage Using Fisher's Exact Test, measured over 30 days.

The primary endpoint is spontaneous stone passage by 30 days. The registry defines passage using either imaging—CT or Renal Ultrasound/KUB—or identification of the stone with a straining device. The outcome is recorded as a count of participants meeting this definition, so it represents a binary event rather than a measurement on a continuous scale.

A passage endpoint is used to assess whether the stone has passed during the stated follow-up period. Using the registered definition makes clear what counted as an event, while permitting more than one way to identify passage. The record does not report how often each method was used, whether the methods were applied uniformly, or how cases with unavailable or inconclusive assessments were handled.

The posted counts are 8 participants in the mirabegron group and 5 in the placebo group. Counts alone do not express the difference in relation to the number assessed in each group, so comparative statistics also describe the event proportions and their uncertainty. The registered primary-outcome title identifies Fisher's exact test, but the registry record does not include a sponsor analysis entry or a detailed account of the test implementation.

The registry also names pain levels on the Wong-Baker Pain Rating Scale as a secondary outcome. A numerical result for that outcome is not reported in the registry record.

7. Results Posted in the Registry

• Arm 1 - Active: 47.1% (8/17) versus 31.2% (5/16) on control; risk difference 15.8 percentage points (95% CI -17.0 to 48.7), risk ratio 1.51 (0.62–3.65); unadjusted two-proportion z-test p = 0.353.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is binary: a participant either met the registered definition of stone passage by 30 days or did not. The registry reports the number of participants with passage in each group and identifies Fisher's exact test in the primary outcome title. The listed counts are 8 of 17 for mirabegron and 5 of 16 for placebo. This kind of outcome can be described with group event proportions and compared using measures of absolute or relative association.

What does Fisher's exact test assess?

As a general statistical explanation, Fisher's exact test evaluates how compatible a two-group table of event and non-event counts is with a null hypothesis of no association between group assignment and outcome. It is often used for categorical data, particularly when event counts are limited. The test produces a p-value under its assumptions; it does not estimate the clinical importance of a difference or establish that the null hypothesis is true. The registry record does not report the exact test settings or a sponsor-reported test result.

What does the risk difference mean?

As a general statistical explanation, a risk difference subtracts the event proportion in one group from the event proportion in the other. It expresses an absolute contrast in the outcome proportions. The posted unadjusted risk difference is 0.158, with mirabegron as the active group and placebo as the comparator. Its positive direction corresponds to a higher observed passage proportion in the active group. This statistic describes the posted observations; it does not adjust for other participant characteristics.

How should relative measures be understood?

A risk ratio compares the event proportions by division, while an odds ratio compares the odds of the event between groups. These are relative measures and answer a different descriptive question from the absolute risk difference. Relative estimates can be difficult to interpret when there are few events, and their uncertainty matters as much as their point estimates. The registry-based comparison includes relative measures, but the central interpretation should remain grounded in the observed group counts and their limited precision. No additional numbers for those measures are needed to understand the main result.

What does a p-value say?

As a general statistical explanation, a p-value measures how unusual data at least as incompatible with a specified null model would be if that model and the test assumptions were correct. It is not the probability that the null hypothesis is true, nor the probability that the result occurred by chance. The unadjusted p-value reported for this comparison is 0.353. Considered with the effect estimate and interval, it does not establish either a treatment difference or equivalence.

Why does the interval matter?

As a general statistical explanation, a confidence interval gives a range of estimates compatible with the data under the procedure used to construct it. A narrow interval indicates greater precision than a wide interval. The reported interval for the risk difference includes values on both sides of zero, so it is compatible with either direction of the group contrast. Its width reflects substantial uncertainty in the estimate. The confidence level and the precise interval-construction method are not reported in the registry record.

Interpretation also depends on how outcome data were collected and analyzed. The registry defines passage through imaging or stone identification with a straining device, but does not report the frequency of each ascertainment method, the handling of missing outcomes, the analysis population, or whether any adjustment was planned. Those omissions limit assessment of the complete analysis process. No registry analysis entries are listed, so the posted comparison should not be mistaken for a documented full sponsor analysis.

10. Confidence Intervals and Precision

The risk difference estimate is 0.158, but the reported interval is broad and crosses zero. In practical statistical terms, the interval includes both a negative contrast and a positive contrast. Therefore, the posted data do not precisely determine the direction or magnitude of the underlying difference in passage proportions.

As a general statistical explanation, a confidence interval represents uncertainty around an estimate under a specified statistical procedure. Greater precision is usually reflected by a narrower interval, while a wider interval leaves more possible values compatible with the data. Here, the limited number of observed passage events is consistent with substantial uncertainty. The interval should not be read as a set of equally likely values or as proof that the true effect lies within a particular range with certainty.

The registry record does not state the confidence level or detailed interval method. The interval's endpoints are not repeated in this explanation; its direction and breadth are the relevant features for interpreting precision. The unadjusted p-value of 0.353 is also consistent with the data not clearly distinguishing the observed contrast from no difference under the test's null model. A non-small p-value does not establish that the treatment groups are equivalent, and it does not erase the range of effects compatible with the interval.

Precision is separate from clinical importance. The record does not specify a threshold for a meaningful difference in passage, so the estimates cannot be classified against such a threshold. The observed counts and uncertainty are the appropriate basis for describing what this comparison can establish.

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 trial's original design assumptions. They are stated as participants per arm for 80% power and participants per arm for 90% power; they are not total event counts. 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 as a stated fraction of the observed effect.

For planning based on 100% of the observed effect, the illustration gives 149 participants per arm for 80% power and 199 participants per arm for 90% power. For planning for 75% of the observed effect, it gives 260 participants per arm for 80% power and 348 participants per arm for 90% power. For planning for 50% of the observed effect, it gives 572 participants per arm for 80% power and 766 participants per arm for 90% power.

In general, power is the chance that a planned study will meet its statistical decision rule if a particular effect is truly present and the planning assumptions hold. The 80% and 90% columns therefore describe different target chances of detecting the assumed effect. A higher target power requires a larger planned group size under otherwise unchanged assumptions. Smaller effects also require more participants to distinguish them from random variation, which is why the illustrations increase as the target fraction of the observed effect decreases.

The curve should be read as a visual expression of this planning relationship, not as an observed trial result. These figures are not observed power. The registry does not report the trial's own original sample-size justification or planning 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 = 0.312; treatment proportion p₁ = 0.471; average p̄ = 0.392.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6903 = 1.3529.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.6812 = 0.5733.
4. n = (1.3529 + 0.5733)² / (0.1581)² = 148.5, rounded up to 149 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 <- 0.3125                          # control proportion
p1 <- 0.470588235294118                          # 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(2744430)
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 = 149 (80% power), 199 (90% power)
 75% of observed effect: n per arm = 260 (80% power), 348 (90% power)
 50% of observed effect: n per arm = 572 (80% power), 766 (90% power)
power.prop.test: 148.5 
Simulated power at n = 149 per arm: 0.803 (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 the primary endpoint as spontaneous stone passage at 30 days and names pain levels between treatment groups using the Wong-Baker Pain Rating Scale as a secondary outcome. It records two outcome measures and one posted secondary outcome. The numerical result for the pain outcome is not reported in the registry record.

When a study evaluates multiple outcomes or multiple comparisons, the chance of obtaining at least one apparently notable result can increase. As a general statistical point, methods for addressing multiplicity may include prioritizing outcomes or adjusting the decision criteria. The registry record does not report whether any multiplicity strategy was planned or used. It also does not provide enough information to determine whether there were additional analyses beyond the outcomes listed.

Missing data handling is not reported in the registry record. The posted group counts do not establish whether every randomized participant had an outcome assessment, whether any participants were excluded from the analysis, or how an unavailable passage assessment was treated. The analysis population—such as whether all randomized participants were included—is also not reported.

The record contains no registry analysis entries and does not provide a detailed statistical analysis plan, interim-analysis information, or a complete description of adjustment procedures. These omissions prevent a full evaluation of outcome hierarchy, multiplicity, missing-data assumptions, and analysis populations. They do not change the description of the posted counts, but they limit how fully the inferential process can be assessed.

14. Safety Results

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

Deaths

Other (non-serious) adverse events

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

The registry reports zero serious adverse events in the placebo group, with 16 at risk, and zero in the mirabegron group, with 17 at risk. It also reports zero other adverse events in the placebo group, with 16 at risk, and zero in the mirabegron group, with 17 at risk. Deaths are reported as zero in both groups.

These figures are counts recorded in the registry, not estimates of the likelihood of an event beyond the participants and observation represented in the record. Zero recorded events does not prove that an event cannot occur, and the counts do not establish whether events were related to treatment. The registry does not report further definitions, event-specific descriptions, or the adverse-event observation period in the registry record for these results. No serious adverse event terms are listed.

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

The posted primary-outcome data show that stone passage by 30 days was recorded for 8 of 17 participants assigned mirabegron and 5 of 16 assigned placebo. The unadjusted risk difference is 0.158, and the reported interval includes values below and above zero. The unadjusted p-value is 0.353. Together, these results describe a higher observed passage proportion in the mirabegron group while leaving substantial uncertainty about the underlying difference.

The result does not establish that mirabegron increases passage, and it does not establish that the groups have the same passage rate. A non-small p-value is not proof of no effect. Conversely, a positive point estimate does not by itself establish a causal effect or demonstrate that the estimate is clinically important. The registry record does not specify a threshold for clinical importance.

The interpretation is limited to the registered endpoint definition and 30-day timeframe. It does not resolve longer-term outcomes, the secondary pain-scale comparison, or outcomes in populations beyond the participants represented in this trial. The registry record does not report numerical pain results, the handling of missing outcome data, or the analysis population, so conclusions about those matters cannot be drawn from the posted primary counts.

The most defensible reading is that the observed data are compatible with a range of possible underlying differences, including differences in either direction. The event counts are modest, and the interval is wide. The results are therefore more useful as an estimate with substantial uncertainty than as a definitive answer about the comparative treatment effect.

16. Why This Trial Matters Statistically

This trial illustrates why a treatment comparison should not be reduced to a single p-value. The primary outcome is a participant-level event, and the registry reports both group counts and an unadjusted estimate of the absolute contrast. The counts show what happened in the observed groups; the estimate describes the direction of the contrast; and the interval conveys how uncertain that estimate remains.

Here, the point estimate favors a higher observed passage proportion in the mirabegron group, but the interval spans both sides of zero and the unadjusted p-value is 0.353. These features make the result a useful example of the difference between an observed direction and a precise conclusion. Statistical nonsignificance does not demonstrate equivalence, while a favorable point estimate does not prove a treatment effect.

The trial also highlights the value of distinguishing observed results from planning calculations. The sample-size illustrations are derived from the observed effect under stated assumptions; they are not a reconstruction of the trial's original design or evidence about its observed power. Planning for a smaller target effect requires more participants under the stated framework.

Finally, a registry record can report outcome counts without supplying the full analysis context. Missing-data procedures, analysis populations, multiplicity handling, and detailed test settings are not reported. Recognizing these gaps helps readers keep conclusions aligned with the information documented rather than filling in an undocumented statistical plan.

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 comparison is based on a limited number of observed passage events: 8 in the mirabegron group and 5 in the placebo group. The resulting risk-difference interval is wide and includes values on both sides of zero, so the estimate is imprecise. The trial is registered as Phase 2, and its recorded enrollment is 33; the posted outcome group counts are 17 and 16.

The endpoint could be established through imaging or identification of a stone using a straining device. The registry does not report how often each method was used, whether the assessment approach differed between groups, or how discordant or unavailable assessments were handled. The primary outcome timeframe is 30 days, which does not describe later passage or other longer-term outcomes.

The registry record does not report the trial's original sample-size assumptions or justification, a complete statistical analysis plan, analysis populations, missing-data handling, multiplicity procedures, or detailed implementation of the primary test. It lists a pain-scale comparison as a secondary outcome but does not report its numerical result. There are no registry analysis entries.

These limitations do not change the posted counts, but they constrain interpretation of the comparison and the completeness of the analysis. The record does not permit conclusions about unreported outcomes or about procedures that are not documented.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Mirabegron as Medical Expulsive Therapy (MET) for Ureteral Stones and Ureteral Stent Pain — NCT02744430.
• Registry record last updated 2022-04-26; status last verified 2022-04.
• Results first posted 2022-04-26.
• 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

The registry record describes a completed, randomized, parallel, triple-masked Phase 2 trial sponsored by Baylor College of Medicine. The study compared mirabegron 50 mg orally once every 24 hours with placebo, each starting immediately, for medical expulsive therapy in participants with a CT scan-proven ureteral stone between 4 to 10 mm undergoing expectant management.

Enrollment is recorded as 33. The study start date is 2017-07-22, and the primary completion date is 2019-10-31. The primary endpoint was spontaneous stone passage at 30 days, defined using imaging or identification with a straining device. Passage was recorded in 8 of 17 participants in the mirabegron group and 5 of 16 in the placebo group.

The registry lists a secondary pain-scale outcome but does not report its numerical result. Details on missing data, analysis populations, multiplicity, and the original sample-size plan are not reported in the registry record.