Blacks and Exacerbations on Long Acting Beta Agonists (LABA) vs. Tiotropium (BELT): Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Blacks and Exacerbations on Long Acting Beta Agonists (LABA) vs. Tiotropium (BELT) (NCT01290874), a randomized phase 3 study. The primary outcome is Time to Asthma Exacerbation (Mean Number of Exacerbations/Person-year).

2. Clinical Question

3. Trial Design

BELT was a phase 3 randomized, parallel-group study with no masking. The registry lists an enrollment of 1070 and marks the study as completed. The study start is recorded as 2011-03-30, and primary completion as 2013-07. Brigham and Women's Hospital is listed as the sponsor. These details describe the registered design and status, but the registry record does not give the full conduct history or explain any changes made during the study.

Participants were assigned to tiotropium or to salmeterol or formoterol. The posted arm records list 532.0 in the tiotropium group and 538.0 in the salmeterol-or-formoterol group. The comparator is pooled in the reported results; separate arm-level estimates for salmeterol and formoterol are not reported in the registry record. Because the study was unmasked, participants and study personnel were not kept unaware of assigned treatment, as reflected by the registry’s masking entry.

The study’s stated motivation was to examine asthma-treatment response among Black people, including the possible role of genes. The trial compared the asthma outcome between treatment groups; the posted primary result does not report a genetic subgroup analysis or a treatment-by-genotype estimate. Whether genetic testing was used in the analysis, and how any genetic measures were assessed, are not reported in the registry record.

The primary endpoint was evaluated monthly on average via questionnaire for 12 months. The primary population is described as intention-to-treat. The registry lists 7 secondary outcomes, including changes in lung function, asthma control, quality of life, symptoms, rescue medication use, and moderate asthma deterioration. Results for those secondary outcomes are not reported in the record summarized by the posted primary result. The trial’s detailed eligibility criteria, allocation procedures, treatment duration beyond the endpoint timeframe, adherence measures, and original design 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: Subjects on combination ICS/LABA were switched to equivalent-dose ICS monotherapy at the same time they were assigned to the Tiotropium vs. LABA arm of the study.

Overall Study

Analysis population for the primary outcome, as defined in the registry: intention-to-treat

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 Time to Asthma Exacerbation (Mean Number of Exacerbations/Person-year), measured over evaluated monthly (on average) via questionnaire for 12 months.

The primary endpoint is titled time to asthma exacerbation, with the result expressed as the mean number of exacerbations per person-year. A rate per person-year describes event frequency relative to time under observation, rather than simply counting how many participants had an event. The registry gives the unit as events per person-year and says the outcome was evaluated monthly on average via questionnaire for 12 months.

Time-to-event methods are used when the timing of an event matters and observation may end before every participant experiences that event. The registry says that survival experience was summarized using the mean exacerbation rate and compared using a log-rank test of Kaplan–Meier survival curves. These are related but not identical summaries: the rate describes event frequency per exposure time, while a survival curve describes the probability of remaining without the event over time. The registry record does not report the operational definition of an exacerbation, how recurrent events were handled in the survival analysis, or how follow-up ending for reasons other than an exacerbation was treated.

The endpoint is relevant to the stated comparison because it captures exacerbation occurrence over follow-up. It does not, by itself, describe every aspect of asthma control, symptoms, lung function, or quality of life. Those topics appear among the listed secondary outcomes, but their results are not reported in the primary result record.

7. Results Posted in the Registry

• Salmeterol or Formoterol: 0.42 versus 0.37 (event per person-year) on control; rate ratio 1.14 (95% CI 0.92–1.40, derived from the posted confidence limits); p ≈ 0.228.

8. Statistical Interpretation

9. Statistical Methods Explained

Different statistical summaries answer different questions, even when they use data from the same trial. BELT’s registry record describes a time-to-exacerbation endpoint and reports both mean event rates and a log-rank comparison. The rate ratio in the unadjusted recalculation compares the posted event rates; the log-rank test compares the groups’ survival experience over time. Keeping those estimands distinct helps explain why their numerical results need not match exactly.

What does an event rate per person-year describe?

An event rate uses both the number of events and the amount of time participants contribute to observation. It is useful when participants have different lengths of follow-up or when events can occur more than once. The registry reports the arm-level rates as 0.37 and 0.42 events per person-year. These are rates, not the proportions of participants who experienced at least one exacerbation. The registry record does not state whether the primary rate calculation counted recurrent exacerbations or how exposure time was accumulated.

A rate ratio compares one group’s event rate with the other group’s rate. The reported recalculation is oriented as salmeterol or formoterol relative to tiotropium, with an estimate of 1.135. A ratio of 1.0 corresponds to equal rates. Values on either side represent different relative directions, but the estimate should be read together with its interval, not as a stand-alone conclusion. The recalculation is described as unadjusted and is based on posted summary statistics; it is not a substitute for an adjusted or participant-level analysis.

What does the log-rank test compare?

The log-rank test is a general method for comparing time-to-event experience between groups. It uses the ordering of event times and the participants still at risk over follow-up, rather than reducing the data to a single event rate. Kaplan–Meier curves are a general way to display estimated event-free experience over time while accounting for censoring, when the method’s assumptions are appropriate. The registry says the survival experience was summarized using mean exacerbations per person-year and compared with a log-rank test of Kaplan–Meier curves. It reports p = 0.31 for that analysis. The record does not provide the curves’ numerical estimates, a log-rank effect estimate, or a confidence interval for the comparison.

In general, a p-value describes how incompatible the observed data are with a specified null hypothesis under the test’s assumptions. It does not measure the probability that the null hypothesis is true, nor does it show the size or clinical importance of a difference. A p-value should therefore be read alongside the effect estimate, its interval, the analysis method, and the design. In this case, the sponsor’s log-rank p-value is distinct from the unadjusted recalculation’s p-value of 0.228 because the analyses use different statistical summaries.

Why does over-dispersion matter for event rates?

In general, a simple Poisson model assumes that the event-count variability follows a particular relationship with the expected count. Clinical event data can be more variable than that assumption allows, a feature called over-dispersion. When over-dispersion is present but not accommodated, standard errors and intervals from a simple model may be too narrow, making uncertainty appear smaller than it is. The recalculation is marked as Poisson-based, but the registry record does not report a dispersion assessment or an adjustment for over-dispersion. The posted arm-level intervals and the recalculated comparison should therefore be understood in light of the methods used, not as a guarantee that all sources of variability were modeled.

What can the posted intervals tell a reader?

A confidence interval gives a range of estimates that are reasonably compatible with the data under the statistical procedure and its assumptions. It communicates precision as well as direction. The posted arm-level intervals are 95% confidence intervals. The rate-ratio interval extends from 0.924 to 1.395; it includes 1.0, the value corresponding to equal rates. The registry does not state the confidence level for the recalculated ratio interval, so it is best described as the posted interval rather than assigning it a confidence level not stated in the record.

Intervals are not guarantees that the true value lies within a particular range, and they do not incorporate every possible source of bias. Randomization supports a comparison of assigned groups, but the registry’s no-masking entry, the endpoint measurement process, missing-data handling, and outcome definition remain relevant to interpretation. The details of those procedures are not reported in the registry record.

What analysis population is named?

The primary population is listed as intention-to-treat. In general, an intention-to-treat analysis compares participants according to their assigned groups, regardless of subsequent treatment changes, as defined by the analysis plan. The registry does not provide further details about how the intention-to-treat population was constructed, how missing outcome information was handled, or whether additional analysis populations were used. These omissions limit how fully the posted result can be reproduced or evaluated.

The registry identifies one reported primary comparison, while listing 7 secondary outcomes. It does not report a multiplicity strategy describing how the chance of false-positive findings across outcomes or analyses was addressed. The absence of that information does not invalidate the primary result, but it means readers cannot determine from the record whether or how multiplicity influenced the analysis plan or interpretation. The statistical plan, interim analyses, model adjustments, and original sample-size justification are not reported in the registry record.

10. Confidence Intervals and Precision

Precision concerns how narrowly the data locate an effect estimate. The posted 95% confidence interval for the tiotropium rate is 0.32 to 0.43 events per person-year; for salmeterol or formoterol it is 0.36 to 0.48 events per person-year. These intervals convey uncertainty around each arm’s rate. Their overlap is not a formal test of the between-group comparison, so the comparison should be evaluated using its own estimate and analysis.

The unadjusted rate ratio is 1.135, with a posted interval from 0.924 to 1.395. The interval includes 1.0, the value representing equal rates. It also covers values on either side of that reference, so the recalculated comparison does not isolate a single direction with high precision. The point estimate is one summary of the data; the interval indicates that estimates meaningfully different from that point remain compatible with the calculation.

The registry’s log-rank result, p = 0.31, has no accompanying estimate or interval in the record. A p-value alone does not show the range of plausible effect sizes or the precision of the group contrast. The registry’s reported method and the rate-based recalculation are different, so the rate-ratio interval should not be treated as the interval for the log-rank analysis.

These intervals reflect statistical uncertainty under the respective methods. They do not quantify uncertainty from all possible design limitations, such as outcome measurement or missing data. The registry record does not report the event definition, missing-data procedures, or further details of the models, which limits a fuller assessment of precision.

11. Planning a Similar Trial: Sample Size

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

The planning figures are illustrations based on the observed effect, not the trial’s own original design assumptions. They use 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 original sample-size justification or design assumptions.

For this time-to-event planning illustration, the figures refer to the total number of events, not participants per arm. The listed scenarios show the event totals associated with planning for 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect. For each scenario, the 80% power column means the event total targeted to give an 80% chance of detecting the specified effect under the stated assumptions, if that effect were present. The 90% power column uses a higher target chance of detection under the same planning framework. These are planning targets, not observed trial outcomes.

The figures increase as the assumed effect becomes smaller: detecting a smaller difference generally requires more information, which in this illustration means more events. The columns should not be read as numbers of participants per arm, because the time-to-event planning rule reports total events. Follow-up duration and event occurrence affect how many participants would be needed to accumulate those events; that participant total is not specified by these event figures.

This is not observed power. It is a forward-looking planning illustration using the effect estimated from the trial, and it cannot establish how likely the observed result was to be detected under the trial’s actual design. The trial’s own design assumptions and original justification are not reported in the registry record.

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, λ₀ and λ₁ are event rates per patient-year, and T is follow-up per participant in years. This assumes Poisson counts and equal follow-up.

Worked calculation for this trial

1. Control rate λ₀ = 0.3700; treatment rate λ₁ = 0.4200 events per patient-year; follow-up T = 1.00 years.
2. n = (1.96 + 0.842)² × (1/0.3700 + 1/0.4200) / (1.00 × [ln(1.135)]²) = 2,483.6, rounded up to 2,484 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
lambda0 <- 0.37                      # control rate, events per patient-year
lambda1 <- 0.42                      # treatment rate
tt      <- 1                       # follow-up per participant, years
n_per_arm <- function(power, frac = 1) {
  l1 <- lambda0 * (lambda1 / lambda0)^frac   # smaller effect = fraction of the observed log rate ratio
  ceiling(round((z_a + qnorm(power))^2 * (1 / lambda0 + 1 / l1) / (tt * log(l1 / lambda0)^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 = ",")))

# Simulation 1: Poisson counts. Simulation 2: over-dispersed counts (variance = 1.5 x mean), analysed with the matching variance.
set.seed(1290874)
n    <- n_per_arm(0.80)
reps <- 20000
m0 <- lambda0 * n * tt; m1 <- lambda1 * n * tt
x0 <- rpois(reps, m0); x1 <- rpois(reps, m1)
z  <- log(x1 / x0) / sqrt(1 / x0 + 1 / x1)
cat(sprintf("Simulated power, Poisson counts, n = %s per arm: %.3f\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE)))
phi <- 1.5
y0 <- rnbinom(reps, mu = m0, size = m0 / (phi - 1)); y1 <- rnbinom(reps, mu = m1, size = m1 / (phi - 1))
z2 <- log(y1 / y0) / sqrt(phi * (1 / y0 + 1 / y1))
cat(sprintf("Simulated power, over-dispersed counts (phi = 1.5), same n: %.3f\n", mean(abs(z2) > z_a, na.rm = TRUE)))

Output from running the code

100% of observed effect: n per arm = 2,484 (80% power), 3,325 (90% power)
 75% of observed effect: n per arm = 4,482 (80% power), 6,000 (90% power)
 50% of observed effect: n per arm = 10,239 (80% power), 13,707 (90% power)
Simulated power, Poisson counts, n = 2,484 per arm: 0.805
Simulated power, over-dispersed counts (phi = 1.5), same n: 0.628

The first simulation draws Poisson counts and should land close to the target power. The second allows extra variability (variance 1.5 times the mean, a purely illustrative value), which lowers the power at the same sample size, so rate trials usually need more participants than the Poisson formula suggests.

13. Analyses Reported by the Sponsor

The registry’s reported analysis is a log-rank test comparing the Kaplan–Meier survival experience of the two groups, with p = 0.31. No numerical effect estimate or interval for that analysis is reported. This is the sponsor’s own posted analysis and should be distinguished from the unadjusted recalculation based on the posted arm-level rates.

The recalculation gives a rate ratio of 1.135 for salmeterol or formoterol relative to tiotropium, with an interval from 0.924 to 1.395 and an unadjusted p-value of 0.228. It is a simple rate-based comparison from posted summary statistics, not a reconstruction of the log-rank test. The two p-values need not agree because the tests summarize the outcome differently.

The discrepancy indicator is false, but that does not make the recalculation interchangeable with the registry analysis. The registry’s log-rank result remains the result of the reported primary analysis. The recalculated rate ratio offers a separate descriptive comparison and should be interpreted with its own interval and unadjusted status. The registry record does not report additional information that would allow the log-rank analysis to be reproduced.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists a primary outcome and 7 secondary outcomes. The primary result record includes one reported analysis, the log-rank comparison between tiotropium and salmeterol or formoterol. The secondary outcomes cover changes in FEV1, asthma control, asthma quality of life, symptom utility, symptom-free days, rescue medication use, and moderate asthma deterioration. Their results are not reported in the primary result record.

Multiplicity arises when several outcomes, comparisons, or analyses are examined. In general, conducting many statistical tests can increase the chance that at least one result appears notable by chance. A prespecified testing hierarchy or other multiplicity strategy can address that issue, but the registry record does not report whether such a strategy was planned or used. No multiplicity adjustment should be assumed from the single reported analysis alone, because the record also lists secondary outcomes.

The primary analysis population is described as intention-to-treat. The registry record does not report further details about the analysis population, such as how participants with missing primary outcome information were handled, whether analyses followed assignment after treatment discontinuation, or whether other populations were examined. The extent and reasons for missing data, imputation methods, and sensitivity analyses are not reported in the registry record.

The record also does not report the full statistical analysis plan, interim analyses, covariate adjustments, or the original sample-size rationale. These details matter when assessing whether analyses were prespecified, how uncertainty was handled, and how planned comparisons relate to the results reported. Their absence from the registry record should be treated as missing information rather than evidence that a particular procedure was or was not used.

15. Safety Results

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

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 5% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: asthma (5.6%), chest pain (1.5%), pneumonia (1.3%), cardiac failure congestive (0.6%), acute myocardial infarction (0.4%).

The registry reports serious adverse events by group, with 532 at risk in the tiotropium group and 538 at risk in the salmeterol-or-formoterol group. It records 84 affected participants in the tiotropium group and 69 in the salmeterol-or-formoterol group for serious adverse events. For other adverse events, the affected counts are 338 and 342, respectively. These are posted counts, not a comparison adjusted for follow-up time or other factors.

The listed leading serious adverse event terms and their reported percentages are Asthma, 5.6%; Chest Pain, 1.5%; Pneumonia, 1.3%; Cardiac Failure Congestive, 0.6%; Acute Myocardial Infarction, 0.4%; and Non-cardiac chest pain, 0.4%. The record does not specify in this summary whether participants could appear under multiple terms, or how the listed terms relate to the group-level affected counts. The categories should not be added together or treated as mutually exclusive without that information.

Deaths are not reported in the registry record. The safety figures describe events recorded during the study and do not, by themselves, establish that a treatment caused an event or provide a complete account of comparative safety. The registry record does not give further detail about event severity definitions, exposure duration, or statistical comparisons for adverse events.

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

The posted results describe a randomized comparison of tiotropium with salmeterol or formoterol for asthma exacerbations in a study focused on Black participants. The observed mean rates were 0.37 and 0.42 events per person-year, respectively. The unadjusted rate ratio was 1.135, with an interval from 0.924 to 1.395. That interval includes 1.0, and the registry’s log-rank analysis reports p = 0.31. Together, these results do not provide clear evidence of a difference in the posted primary comparison, but they also do not establish that the groups have identical rates.

The results are estimates with uncertainty, not guarantees about what would occur in another population or under different conditions. The trial’s focus on Black people is important context, but the posted primary result does not report a genetic subgroup comparison or demonstrate how genetic characteristics relate to treatment response. The registry’s stated interest in genes is a rationale for the study, not itself a finding from the primary result.

The endpoint captures exacerbations as a rate over person-time and is not a complete measure of asthma experience. Lung function, control, quality of life, symptoms, and other outcomes are listed as secondary outcomes, but their results are not reported in the primary result record. The result therefore cannot be used to characterize all benefits and harms or all aspects of disease management.

As a randomized, unmasked parallel-group trial, the study provides a comparison by assigned groups, but no masking can leave some outcome assessment or behavior susceptible to knowledge of treatment. The registry record does not provide enough detail to assess every potential influence on the estimates. The result should be read as the posted evidence for the specified primary outcome and population, rather than a universal conclusion about either medicine.

17. Why This Trial Matters Statistically

This trial raises several statistical issues that are especially relevant when an outcome is described both as a time-to-event endpoint and as an event rate. The registry reports a mean number of exacerbations per person-year and describes a log-rank comparison of Kaplan–Meier curves. Those methods focus on different features of the observed data. Distinguishing them prevents the rate ratio from being mistaken for the registry’s log-rank estimate.

The comparison also illustrates why effect estimates and uncertainty should be read together. The arm-level rates and rate ratio have a numerical direction, but the rate-ratio interval includes 1.0. A point estimate alone can make an uncertain comparison seem more decisive than it is, while a p-value alone gives no direct measure of the size or precision of the effect. Reporting and interpreting both the estimate and its interval provides a fuller account.

The registry describes a study motivated by possible variation in response and the role of genes, but the posted primary comparison does not report a genetic analysis. This distinction matters: a study’s rationale and its statistical findings are not the same. To establish how response varies across genetic characteristics would require results addressing that question, which are not reported in the registry record.

Finally, the planning illustration depends on an observed effect and stated assumptions, whereas the original design rationale is not reported. That makes it useful for understanding how assumed effect size relates to information requirements, but not for judging the trial’s design as originally planned or its observed power. The record’s missing details on multiplicity, missing outcomes, and analysis procedures also show why registry results must be interpreted alongside what is and is not documented.

18. 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.
• Rate comparisons use a Poisson approximation unless the sponsor posted confidence limits; real event counts are often over-dispersed.

The registry record leaves several trial-specific details unavailable. It does not report the operational definition of an asthma exacerbation, the approach to recurrent events, or the procedures for censoring and follow-up termination in the time-to-event analysis. Although the outcome was evaluated monthly on average via questionnaire for 12 months, the record does not explain the questionnaire’s event ascertainment or validation. These omissions make it difficult to assess precisely what counted as an event and how the rate and survival summaries were constructed.

The trial was unmasked. The registry does not describe whether outcome assessment was independently verified or whether safeguards were used to reduce possible effects of treatment awareness. It also does not give detailed eligibility criteria, adherence information, treatment changes, or follow-up completeness. The primary population is identified as intention-to-treat, but missing-data handling and sensitivity analyses are not reported in the registry record.

The comparator combines salmeterol or formoterol, and separate results for the two medicines are not reported. The primary result therefore cannot be used to compare those comparator medicines with each other. The study’s stated interest in genetic influences is not accompanied by a posted genetic subgroup result in the primary record. Secondary outcomes are listed, but their results are not reported in the primary result record.

The registry reports a log-rank p-value without an accompanying effect estimate or interval. The rate-ratio recalculation is unadjusted, based on posted summary statistics, and marked as Poisson-based; the registry does not report an assessment of over-dispersion or details of any alternative model. The original sample-size justification, analysis plan, multiplicity handling, and interim analyses are also not reported. These limitations do not by themselves determine the validity of the findings, but they restrict what can be independently evaluated from the registry record.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Blacks and Exacerbations on Long Acting Beta Agonists (LABA) vs. Tiotropium (BELT) — NCT01290874.
• Registry record last updated 2018-03-30; status last verified 2018-03.
• Results first posted 2018-03-30.
• 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.

22. Record Summary

BELT was a completed phase 3 randomized, unmasked, parallel-group study sponsored by Brigham and Women's Hospital. It compared tiotropium with salmeterol or formoterol in a study focused on Black people with asthma. The registry lists enrollment of 1070, a start date of 2011-03-30, and primary completion in 2013-07.

The primary outcome was time to asthma exacerbation, summarized as mean events per person-year and evaluated monthly on average via questionnaire for 12 months. The posted rates were 0.37 for tiotropium and 0.42 for salmeterol or formoterol. The registry reports a log-rank p-value of 0.31; an unadjusted rate-based recalculation gives a ratio of 1.135, with an interval from 0.924 to 1.395 and p = 0.228. The registry record does not report a genetic subgroup result, detailed missing-data methods, or the original sample-size justification.