Treating Low-Income Smokers in the Hospital Emergency Department: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Treating Low-Income Smokers in the Hospital Emergency Department (NCT01328431), a randomized na study. The primary outcome is Biochemical Verification of Tobacco Abstinence.

2. Clinical Question

The registry record frames the study as a test of an emergency-department-initiated tobacco intervention that combined counseling and medication. Its primary hypothesis describes superiority over the control condition for reducing self-reported and biochemically verified 7-day tobacco abstinence at 3 months. The posted primary outcome is titled “Biochemical Verification of Tobacco Abstinence” and records the number of participants in each group. The registry describes biochemical verification as a breathalyzer reading for carbon monoxide.

This is a comparison of a package of intervention components with a quitline brochure, rather than a comparison of nicotine replacement therapy alone with no intervention. The posted results therefore describe the group contrast for the combined package as registered. They do not isolate the contribution of counseling, nicotine patches, nicotine gum, or referral individually.

3. Trial Design

The registry describes a randomized, triple-masked, parallel-group study. It records enrollment of 780 and marks the trial completed. The recorded phase is NA. Yale University is listed as the sponsor. The study start is recorded as 2010-10 and primary completion as 2013-04.

Participants were allocated to Standard Care or SBIRT+NRT. Standard Care is described as receipt of a brochure for the state's Smokers' Quitline only. SBIRT+NRT is described as a 6 week course of nicotine replacement therapy, a motivational Brief Negotiated Interview, and a facilitated referral to the same quitline. The brief summary additionally describes nicotine patches and gum initiated in the emergency department and a faxed referral to the quitline.

The word “triple” is the masking category recorded in the registry; which people or roles were masked is not reported in the registry record. The allocation sequence method, concealment procedures, participating sites, eligibility criteria, and recruitment details are also not reported in the registry record. The stated overall enrollment and the group denominators for the primary result are both retained as recorded; the registry does not explain the relationship between them.

The parallel-group structure means the registry presents results separately for the intervention and comparator groups. The primary outcome is assessed at 3 months after enrollment. The registry lists secondary outcome areas concerning self-reported tobacco reduction or abstinence and health care service utilization. It does not report further detail about the timing or definition of each secondary measure.

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

Reasons for not completing this period:

1 Month (1M)

Reasons for not completing this period:

3 Month (3M)

Reasons for not completing this period:

12 Month (12M)

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: This is the # of participants in each group.

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 Biochemical Verification of Tobacco Abstinence, measured over 3 months after enrollment.

The primary endpoint is titled “Biochemical Verification of Tobacco Abstinence.” It measures the number of participants in each group with abstinence verified using a breathalyzer reading for carbon monoxide, at 3 months after enrollment. The posted results list 19 participants in Standard Care and 47 in SBIRT+NRT.

Biochemical verification adds an objective measurement to an outcome that can otherwise rely on a participant's report. In general, a biological measure can complement self-report, but it represents the particular substance and threshold captured by that measure; the registry record does not report a carbon monoxide threshold or further verification procedures. It also does not explain how missing breathalyzer measurements were handled or whether participants with no measurement were counted as not abstinent.

The registry's brief summary frames the primary hypothesis around self-reported and biochemically verified 7-day abstinence at 3 months. The posted primary outcome, however, is the biochemical verification count. The listed secondary outcome areas include self-reported tobacco reduction or abstinence, but the record does not provide enough detail to assume that a specific self-report measure is part of the same primary endpoint. These distinctions matter when interpreting what the primary count captures: it is the recorded biochemical outcome, not every possible measure of tobacco use or longer-term abstinence.

7. Results Posted in the Registry

• SBIRT+NRT: 12.2% (47/386) versus 4.9% (19/388) on control; risk difference 7.3 percentage points (95% CI 3.4 to 11.2), risk ratio 2.49 (1.49–4.16); unadjusted two-proportion z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary result is a comparison of two groups on a binary outcome: whether a participant had biochemical verification of tobacco abstinence at the stated follow-up. The registry reports the number of participants with the event and the group denominator. For Standard Care, the count is 19 among 388; for SBIRT+NRT, it is 47 among 386. The measure is defined as a breathalyzer reading for carbon monoxide. In general, a binary outcome is summarized by the number of events, the number of participants assessed, and a measure comparing the groups.

What does the risk difference describe?

In general, a risk difference subtracts the event proportion in one group from the event proportion in the other. It expresses the contrast on an absolute scale: how far apart the group event proportions are. The registry reports a risk difference with a confidence interval. The interval's endpoints are both above zero, indicating that the range displayed for this contrast is on the side favoring a higher event proportion in SBIRT+NRT. The interval is the relevant uncertainty summary for the absolute contrast; the p-value alone does not convey its magnitude.

What do the relative measures describe?

The registry also reports a relative risk of 2.487 and an odds ratio of 2.693. In general, the relative risk compares event proportions, whereas the odds ratio compares event odds. These measures use different scales and need not have the same numerical value. Their confidence intervals are 1.487 to 4.157 for the relative risk and 1.549 to 4.68 for the odds ratio. Because the intervals are above the relative-measure null value of one, they indicate a contrast in the same direction as the posted counts. Relative measures should be considered alongside the group counts and absolute difference; they do not replace them.

How should the p-value be read?

The posted p-value is unadjusted and reported as <0.001. In general, a p-value describes how compatible the data are with a specified null model, under the assumptions of the statistical test. It is not a measure of the probability that the null hypothesis is true, and it does not measure the probability that the finding will be repeated. The registry does not report the test name, its detailed assumptions, or whether the analysis included covariate adjustment. Those details should not be inferred from the p-value alone.

What can randomization and masking tell us?

The design is recorded as randomized, triple-masked, and parallel. In general, randomization is intended to make treatment-group assignment independent of participants' baseline characteristics, while masking can reduce the influence of knowledge of assignment on care, measurement, or assessment. The registry does not state how the allocation sequence was generated or concealed, nor does it identify the masked roles. The design labels alone therefore do not establish exactly how these procedures operated.

The intervention is a package: a Brief Negotiated Interview, nicotine patches and gum, and facilitated quitline referral. A comparison of the package with brochure-only Standard Care estimates the contrast between those assigned groups as represented in the posted analysis. It cannot identify the separate contribution of each component. The registry does not report a factorial or component-specific comparison.

The outcome timing is 3 months after enrollment, and the endpoint is a participant count. The record does not state the handling of missing measurements, the analysis population, a protocol-defined estimand, or adjustment variables. It also does not report the statistical analysis plan or methods for any interim analyses. These are distinct from the displayed estimates: the outcome counts and comparison are posted, but several methodological details needed to fully reconstruct the analysis are not reported in the registry record.

10. Confidence Intervals and Precision

The confidence intervals show a range of effect estimates compatible with the posted data under the analysis used. In general, a narrower interval indicates greater statistical precision, while a wider interval indicates more uncertainty. An interval is not a guarantee that the true effect lies within its endpoints, and its interpretation depends on the method and assumptions used to construct it. The registry record does not identify the interval method.

For the primary comparison, the risk-difference interval is entirely above zero. The relative risk interval, 1.487 to 4.157, and the odds-ratio interval, 1.549 to 4.68, are entirely above one. These intervals support the same direction of contrast as the posted group counts. Their widths also show that a range of effect sizes remains compatible with the data; the relative estimates in particular are not represented by a single precise value.

The unadjusted p-value is <0.001, but statistical significance and precision are not interchangeable. A small p-value does not by itself make an estimate precise, nor does it describe the range of plausible effect sizes. Reading the intervals alongside the counts and estimates gives a more complete picture of the uncertainty than reading the p-value alone.

The registry reports endpoint denominators of 388 and 386. The record does not explain whether all randomized participants had endpoint data, how unmeasured outcomes were treated, or whether the confidence intervals reflect any adjustment. These missing details are relevant to interpreting precision because uncertainty about missing observations and analysis choices is not necessarily captured by a conventional confidence interval. No sensitivity analyses are reported to show how the result might vary under alternative assumptions.

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 table and curve are planning illustrations based on the posted observed effect, not a report of the trial's original design calculation. For this binary outcome, the figures are participants per arm, not total event counts. The registry's original sample-size justification and design assumptions are not reported in the registry record.

The planning illustration uses a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. It considers effects equal to 100%, 75%, and 50% of the observed effect. For planning for 100% of the observed effect, The table shows 231 participants per arm for 80% power and 308 participants per arm for 90% power. For planning for 75% of the observed effect, it lists 370 participants per arm for 80% power and 495 participants per arm for 90% power. For planning for 50% of the observed effect, it lists 742 participants per arm for 80% power and 992 participants per arm for 90% power.

In plain terms, the 80% column gives the illustrated number of participants per arm for a design with an 80% chance of detecting the selected effect under the stated assumptions. The 90% column gives the corresponding planning figure for a 90% chance. These are hypothetical design calculations, not a measure of the probability that this completed trial found a true effect; this is not observed power. The rows also illustrate that smaller effects need more participants under the same assumptions. The curve should be read as another display of this planning relationship, not as additional outcome data.

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 = 0.049; treatment proportion p₁ = 0.122; average p̄ = 0.085.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.3952 = 0.7745.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.3918 = 0.3297.
4. n = (0.7745 + 0.3297)² / (0.0728)² = 230.1, rounded up to 231 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 <- 0.0489690721649485                          # control proportion
p1 <- 0.121761658031088                          # 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(1328431)
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 = 231 (80% power), 308 (90% power)
 75% of observed effect: n per arm = 370 (80% power), 495 (90% power)
 50% of observed effect: n per arm = 742 (80% power), 992 (90% power)
power.prop.test: 230.1 
Simulated power at n = 231 per arm: 0.814 (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 7 outcome measures, 5 posted secondary outcomes, and 0 analyses. The secondary outcome descriptions include self-reported tobacco reduction or abstinence and health care service utilization, with repeated entries in the listed outcome areas. The record does not provide enough detail to identify every measure, time point, or analysis represented by those counts.

When a study examines multiple outcomes or multiple analyses, the chance of at least one result appearing noteworthy by chance can increase. In general, multiplicity procedures may address this by adjusting the interpretation or testing threshold. The posted primary comparison is labeled unadjusted, and no multiplicity adjustment is reported in the registry record. It is therefore not possible to determine from this entry whether the analysis plan specified a hierarchy, correction, or other control for multiple comparisons. The posted p-value should be read as unadjusted, not as evidence that any such adjustment was made.

The record does not report how missing primary-outcome measurements were handled. It does not state whether participants without a breathalyzer reading were counted as abstinent, counted as not abstinent, excluded, or addressed using another method. The relationship between the overall enrollment of 780 and the primary-outcome denominators of 388 and 386 is also not explained. Without a reported participant flow or analysis population, it is not possible to establish from this record how many randomized participants contributed to the primary comparison or why the denominators differ from the enrollment figure.

The analysis population is not reported in the registry record. In particular, the record does not say whether the primary analysis followed an intention-to-treat approach, included only participants with outcome data, or used another population definition. No details are reported about covariate adjustment, sensitivity analyses, subgroup analyses, or interim analyses. These absences do not invalidate the posted comparison, but they limit assessment of how the analysis was selected and how robust it might be to missing data or other analytical choices.

14. 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.

The serious adverse event figures list 0 participants affected in Standard Care among 390 at risk and 0 participants affected in SBIRT+NRT among 388 at risk. No serious adverse event terms are listed. The registry record therefore reports no participants affected by serious adverse events in either group in these entries.

These figures should be read as the registry's recorded serious adverse event summary, not as proof that no adverse events of any kind occurred. The record distinguishes serious adverse events from other adverse events and lists 0 affected in the other-adverse-event fields as well, with the same respective at-risk group sizes. The deaths entries are null, so deaths are not reported in the registry record. The registry does not provide event definitions, collection procedures, follow-up duration for safety, or explanatory detail about the at-risk denominators.

The safety denominators, 390 and 388, differ from the primary-outcome denominators, 388 and 386. The registry does not explain this distinction. The adverse event entries should not be used to infer the frequency of non-serious symptoms beyond what is listed, or to compare safety in a way that assumes details about collection and follow-up that are not reported.

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

The posted primary result shows 19 participants with biochemically verified tobacco abstinence in Standard Care and 47 in SBIRT+NRT at 3 months after enrollment. The group denominators are 388 and 386. The reported risk difference and relative measures, together with their confidence intervals, describe a contrast in the direction of a higher recorded endpoint count in SBIRT+NRT. The unadjusted p-value is <0.001.

This result pertains to the intervention package as a whole: counseling through a Brief Negotiated Interview, nicotine replacement therapy, and a facilitated quitline referral. It does not show which component contributed to the group contrast. Nor does the primary endpoint, as described in the record, establish tobacco abstinence beyond the stated assessment time or across other definitions of abstinence. The registry's summary mentions a hypothesis involving self-reported as well as biochemically verified 7-day abstinence, while the posted primary outcome is the biochemical verification count.

The record does not report the missing-data approach, analysis population, detailed statistical methods, or adjustments for multiple analyses. It also does not provide results for every outcome measure in the information. Those gaps limit how broadly the posted estimate can be interpreted. They do not change what the listed count and comparison say, but they mean that this registry entry alone cannot resolve every question about analysis choices, durability, or other outcomes.

This description is not medical advice and does not determine what any individual should do. It is a statistical reading of the registry record: a randomized comparison with a higher posted count in the intervention group for the defined biochemical endpoint at the stated follow-up, accompanied by an interval and an unadjusted p-value.

16. Why This Trial Matters Statistically

This trial illustrates how an outcome definition shapes a statistical comparison. The primary endpoint is not simply a report of smoking status; it is the count of participants with abstinence verified through a breathalyzer reading for carbon monoxide. The registry also frames its hypothesis in terms of self-reported and biochemically verified 7-day abstinence. Keeping those outcome descriptions distinct helps readers avoid treating every measure of tobacco use as interchangeable.

It also demonstrates the value of presenting several effect scales. The group counts show the underlying event totals, the risk difference describes an absolute contrast, and the relative risk and odds ratio describe relative contrasts. Confidence intervals add information about uncertainty, while the unadjusted p-value addresses a different question. Looking at these together is more informative than relying on a single significance label.

The intervention is a multicomponent package compared with a brochure-only condition. Statistically, this defines a group-level contrast but does not identify the effect of each package component. That distinction is important when interpreting what a trial result can answer. The randomized parallel design provides the framework for comparing assigned groups, while limited reporting on allocation, masking roles, missing data, and analysis populations constrains assessment of the full analytic process.

Finally, the sample-size display is a planning illustration derived from the posted effect, not the trial's own design justification. Its rows make visible the relationship between the target effect and required participants under stated assumptions. Keeping planning calculations separate from observed trial results prevents the planning display from being mistaken for an additional finding.

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 registry record gives a concise result but leaves several trial and analysis details unreported. Eligibility criteria, recruitment procedures, number of sites, allocation-sequence generation, and concealment are not reported in the registry record. Although the design is labeled triple-masked, the people or roles who were masked are not identified. These omissions limit assessment of who entered the trial and how assignment and masking were implemented.

The primary outcome is described as a breathalyzer reading for carbon monoxide, but no threshold, measurement protocol, or missing-measurement rule is reported. The record does not state how participants without a measurement were handled, define the analysis population, or explain the difference between overall enrollment and the primary-outcome denominators. The statistical test and confidence-interval method are also not reported.

The registry lists secondary outcome areas, but detailed results for those measures are not included in the registry record. The number of analyses is recorded as 0, and no analysis plan, multiplicity procedure, interim-analysis information, or sensitivity analysis is reported. The original sample-size justification is not reported; the displayed sample-size figures are planning illustrations based on the observed effect.

The primary endpoint is assessed at 3 months after enrollment. The record does not provide evidence about outcomes beyond that follow-up. Because the intervention combines counseling, nicotine replacement therapy, and quitline referral, the group comparison cannot separate the effect of any single component. These limits define what can be concluded from this registry entry; they do not imply that unreported procedures were or were not used.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Treating Low-Income Smokers in the Hospital Emergency Department — NCT01328431.
• Registry record last updated 2014-08-04; status last verified 2014-07.
• Results first posted 2014-08-04.
• 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, triple-masked, parallel-group trial sponsored by Yale University, with enrollment of 780 and a recorded phase of NA. The intervention combined a Brief Negotiated Interview, nicotine replacement therapy, and facilitated referral to the state's Smokers' Quitline; Standard Care consisted of a quitline brochure.

The primary outcome was the number of participants with biochemical verification of tobacco abstinence by breathalyzer reading for carbon monoxide at 3 months after enrollment. The posted counts are 19 in Standard Care and 47 in SBIRT+NRT, with denominators of 388 and 386. The unadjusted p-value is <0.001, and the posted effect measures include confidence intervals.

Key details—including the missing-data approach, analysis population, detailed analysis methods, and original sample-size justification—are not reported in the registry record. The sample-size figures shown elsewhere are planning illustrations, not the trial's original design calculation.