This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.
1. Trial at a Glance
This page covers the registry results for Financial Incentives for Smoking Cessation Among Disadvantaged Pregnant Women (NCT02210832), a randomized na study. The primary outcome is 7-day Point Prevalence Abstinence Levels at Final Antepartum Assessment.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT02210832 |
| Phase | NA |
| Condition | Cigarette Smoking |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | None (open label) |
| Enrollment | 257 |
| Arms in the primary outcome | 2 |
| Lead sponsor | University of Vermont |
| Results posted | Yes |
2. Clinical Question
Population
Pregnant women who smoked and entered the smoking-cessation trial. The registry describes the study as focused on disadvantaged pregnant women. A separate never-smoker comparison condition followed pregnant women matched to smokers on key sociodemographic and obstetrical characteristics; that group was intended for comparisons of birth and health outcomes, not the primary cessation comparison.
Intervention
Best practices plus financial incentives. Best practices included the Five As and referral to a pregnancy-specific tobacco quit line. Incentives were vouchers exchangeable for retail items, contingent on biochemically verified abstinence, and available through 12-weeks postpartum.
Comparator
Best practices alone: the Five As plus referral to the pregnancy-specific tobacco quit line. The primary comparison was between this group and the group offered financial incentives in addition to best practices.
Primary question
At the final antepartum assessment, did the proportion meeting the trial definition of seven-day abstinence differ between the two smoking-cessation groups? Abstinence meant reporting no smoking, not even a puff, in the past seven days, with self-report verified by urine cotinine testing.
The central statistical contrast is between two behavioral support strategies for pregnant smokers. It is not a randomized comparison with the never-smoker group: that group was matched for comparisons of birth and health outcomes. The primary endpoint concerns cessation during pregnancy at approximately 28-weeks gestation, rather than a longer-term measure of abstinence or infant health.
The registry’s background describes an additional economic and infant-health rationale for the study. It says investigators planned to examine whether incentives increased cessation and improved infant health, and hypothesized that later cost savings might offset higher upfront costs. Those aims provide context, but the primary endpoint reported for the main comparison is antepartum abstinence.
3. Trial Design
The registry describes a randomized, parallel-group trial with no masking. The intervention was behavioral, and the listed phase is NA. Enrollment was 257. The study status is completed; the recorded start date is 2014-01-31 and the primary completion date is 2019-01-31. The sponsor is the University of Vermont.
The two randomized smoking-cessation conditions were best practices for pregnant smokers and best practices plus financial incentives. Best practices consisted of the Five As and a referral to a pregnancy-specific tobacco quit line. The added incentives were vouchers exchangeable for retail items, contingent on biochemically verified abstinence, and available through 12-weeks postpartum. Because masking was absent, participants and study personnel were not masked to the assigned condition.
A third condition followed pregnant women who had never smoked. The registry says these women were matched to smokers on key sociodemographic and obstetrical characteristics for comparisons of birth and health outcomes at delivery and through 1 year postpartum. This matched comparison condition should be distinguished from the randomized comparison between the two smoking-cessation groups.
The primary assessment was collected once per woman at approximately 28-weeks gestation in each smoking arm. The primary outcome counts participants meeting the abstinence definition, rather than measuring a continuous quantity. The primary result includes 88 participants in the best-practices group and 81 in the incentives group. The registry record does not report the original sample-size justification, the allocation ratio specified in the protocol, or details of the randomization procedure. Information about protocol deviations and the analysis population is 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
| Stage | Best Practices for Pregnant Smokers | Best Practices Plus Financial Incentives | Never-smoker Comparison Condition |
|---|---|---|---|
| STARTED | 91 | 85 | 81 |
| COMPLETED | 62 | 49 | 63 |
| NOT COMPLETED | 29 | 36 | 18 |
Reasons for not completing this period:
| Reason | Best Practices for Pregnant Smokers | Best Practices Plus Financial Incentives | Never-smoker Comparison Condition |
|---|---|---|---|
| Pregnancy termination . | 3 | 4 | 1 |
| Lost to Follow-up | 26 | 32 | 17 |
Analysis population for the primary outcome, as defined in the registry: Comparison of women in two smoking-cessation arms
5. Baseline Characteristics
The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.
Population: Women who aborted were removed from the study as per convention in this research area. A total of 8 women were removed for this reason, 3, 4, and 1 in Best practices for pregnant smokers, Best practices plus financial incentives, and Never-smoker comparison conditions.
| Characteristic | Unit | Best Practices for Pregnant Smokers | Best Practices Plus Financial Incentives | Never-smoker Comparison Condition | Total |
|---|---|---|---|---|---|
| Participants analysed | 88 | 81 | 80 | 249 | |
| Age, Continuous | years | 26.6 (SD 5.5) | 25.4 (SD 5.0) | 25.6 (SD 5.0) | 25.87 (SD 5.17) |
| Sex: Female, Male: Female | Participants | 88 | 81 | 80 | 249 |
| Sex: Female, Male: Male | Participants | 0 | 0 | 0 | 0 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 0 | 0 | 0 | 0 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 82 | 74 | 72 | 228 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 6 | 7 | 8 | 21 |
| Region of Enrollment: United States | participants | 88 | 81 | 80 | 249 |
| Cigarettes smoked per day pre-pregnancy | cigarettes/day | 18.27 (SD 9.42) | 19.25 (SD 9.87) | 0 (SD 0) | 12.51 (SD 6.43) |
| Cigarettes smoked per day at 1st antepartum visit | cigarettes/day | 9.92 (SD 6.18) | 8.99 (SD 5.21) | 0 (SD 0) | 6.30 (SD 3.80) |
| Age started smoking (yrs) | years | 15.47 (SD 2.96) | 15.10 (SD 2.92) | 0 (SD 0) | 10.19 (SD 1.96) |
| % living with other smokers | Participants | 68 | 64 | 18 | 150 |
| % with no smoking allowed in home | Participants | 62 | 55 | 73 | 190 |
| % with none or few family who smoke | Participants | 23 | 20 | 62 | 105 |
| % attempted to quit prepregnancy | Participants | 64 | 57 | 0 | 121 |
| # quit attempts during pregnancy | attempts | 0.73 (SD 2.35) | 0.57 (SD 0.97) | 0 (SD 0) | 0.43 (SD 1.11) |
| Minnesota Nicotine Withdrawal Scale total score; scale: 0 (none) to 4 (severe);average item scores | scores on a scale | 1.60 (SD 0.75) | 1.37 (SD 0.76) | 0 (SD 0) | 0.99 (SD 0.50) |
| Fagerstrom Test for Nicotine Dependence | 0-10 scale | 4.33 (SD 2.30) | 3.98 (SD 2.07) | 0 (SD 0) | 2.77 (SD 1.46) |
6. Primary Endpoint
The registry lists the primary outcome as 7-day Point Prevalence Abstinence Levels at Final Antepartum Assessment, measured over collected once per women at approximately 28-weeks gestation in each of the two smoking arms.
| Element | Registry entry |
|---|---|
| Result type | Count Of Participants |
| Measure of spread | not applicable |
| Unit | Participants |
| Endpoint classification | Binary Endpoint |
The primary endpoint is the number of participants meeting the trial’s definition of seven-day point-prevalence abstinence at the final antepartum assessment. It was collected once per woman at approximately 28-weeks gestation in each of the two smoking arms. A participant met the definition if she reported that she had not smoked, not even a puff, in the past seven days, and the self-report was biochemically verified by urine cotinine testing.
This outcome is binary at the participant level: each participant either meets the stated abstinence definition or does not. The reported counts were 8 of 88 in the best-practices group and 31 of 81 in the incentives group. The endpoint therefore describes abstinence at a specified assessment, not continuous abstinence throughout pregnancy or after delivery.
Point-prevalence abstinence is used to give a clearly timed measure of recent smoking status. Biochemical verification adds an objective check to self-report, although it does not change the endpoint’s seven-day time window. The endpoint aligns with the trial’s primary cessation question, but it does not by itself establish longer-term abstinence, explain why participants did or did not quit, or summarize infant health. Those are separate questions. The registry record does not report further details about the cotinine threshold or how an unavailable verification result was handled.
7. Results Posted in the Registry
- Best Practices Plus Financial Incentives: 38.3% (31/81) versus 9.1% (8/88) on control; risk difference 29.2 percentage points (95% CI 17.0 to 41.4), risk ratio 4.21 (2.06–8.62); unadjusted two-proportion z-test p = <0.001.
Risk difference: Best Practices Plus Financial Incentives
95% CI: 17.0 to 41.4 percentage points
Recalculated from the posted summary statistics
8. Secondary Efficacy Endpoints
The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.
| Secondary outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Birth Outcome: Gestational Age at Delivery | Continuous Endpoint | Mean difference | -0.49 (-1.11 to 0.13) | 272 per arm |
| Cost Per Participant | Continuous Endpoint | Mean difference | -634.76 (-4,648 to 3,378) | 7,036 per arm |
Birth Outcome: Gestational Age at Delivery
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard errors.
- Result:
- Best Practices Plus Financial Incentives: mean 38.69 versus 39.18 on control; difference -0.49 (95% CI -1.11 to 0.13), standardized effect d = -0.24; z-test p = 0.124.
- Never-smoker Comparison Condition: mean 39.35 versus 39.18 on control; difference 0.17 (95% CI -0.44 to 0.78), standardized effect d = 0.08; z-test p = 0.585.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Best Practices Plus Financial Incentives and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Never-smoker Comparison Condition and the control. The interval gives the range of effects that remain compatible with the data.
Cost Per Participant
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard errors.
- Result:
- Best Practices: mean 22,372 versus 23,007 on control; difference -634.76 (95% CI -4,648 to 3,378), standardized effect d = -0.05; z-test p = 0.757.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Best Practices and the control. The interval gives the range of effects that remain compatible with the data.
The registry lists a broad range of secondary topics, including postpartum abstinence, breastfeeding, nicotine craving and withdrawal, infant growth, and birth outcomes. Fourteen secondary outcomes are posted, and 14 secondary outcomes are not individually described in the registry record for this analysis. The detailed results cover gestational age at delivery and cost per participant. Taken together, these entries do not form a uniform pattern of clear differences across outcomes: the unadjusted estimates for the continuous comparisons have confidence intervals that include zero, while the registry also reports an ANCOVA result for gestational age with p < 0.05.
These secondary measures address questions related to, but distinct from, the primary cessation endpoint. Gestational age at delivery concerns a birth outcome; cost per participant concerns resource use over a defined follow-up period. Neither is a direct replication of the primary measure of seven-day abstinence around 28-weeks gestation. The primary result should therefore not be treated as proof of a corresponding effect on every secondary outcome, and the secondary findings should not be used to replace the primary question.
Unadjusted secondary results generally carry less weight when many outcomes or comparisons are examined, because the chance of at least one apparently notable result can rise as the number of tests increases. This is a general statistical concern. The registry record lists 16 outcome measures and 15 analyses but does not report a multiplicity adjustment or a hierarchy for interpreting secondary outcomes. Without that information, isolated secondary p-values should be read cautiously, especially where the estimate and interval are not fully reported.
The reported ANCOVA p-value for gestational age is an across-group analysis, while the unadjusted recalculations are pairwise contrasts. They answer different statistical questions and should not be combined as though they were one test. The cost result has a posted unadjusted comparison but no reported sponsor analysis. The record does not provide enough detail to determine how all secondary analyses were selected, adjusted, or interpreted in relation to one another.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- 7-day Point Prevalence Abstinence Postpartum
- Breastfeeding in the Three Trial Arms
- Breastfeeding While Abstinent From Smoking
- Craving Item From the Minnesota Nicotine Withdrawal Scale (MNWS).
- Nicotine Withdrawal Total Scores for the Two Smoking-cessation Trial Conditions.
- Infant Growth in First Year of Life
- Birth Outcomes (% Small for Gestational Age Deliveries)
- Birth Outcomes (Percent Preterm [<37 Weeks] Deliveries)
9. Statistical Interpretation
At the final antepartum assessment, the posted counts were 8 of 88 participants meeting the abstinence definition in the best-practices group and 31 of 81 in the group offered financial incentives as well. The registry’s reported comparison used a chi-squared test and gave p < 0.001. The unadjusted recalculation also gives p < 0.001. The posted risk-difference interval lies above zero, so the observed contrast is not compatible with no difference under that interval estimate. This is evidence of a difference in the observed primary outcome between the two randomized groups, not a guarantee that the same contrast would appear in every setting or population.
The outcome concerns abstinence at one assessment around 28-weeks gestation. It does not directly describe abstinence after delivery, sustained quitting, or infant health. The trial also included a never-smoker comparison condition for birth and health outcomes, but that matched group is not the primary cessation comparator. Keeping these questions distinct prevents the cessation result from being read as a finding about every aim described in the registry’s background.
The number of participants meeting the outcome differs between groups, but the estimate remains subject to sampling uncertainty. A confidence interval communicates a range of effect sizes compatible with the data and analysis; a small p-value does not make that range disappear. The primary interval excludes zero, while the estimates for the reported secondary continuous comparisons have intervals that include zero. Those secondary comparisons should therefore not be interpreted as showing a clearly established difference on the basis of their unadjusted estimates alone.
The primary result is an unadjusted comparison of two randomized groups. Randomization supports a causal interpretation of the assigned strategies in principle, but the registry record does not report the full analysis population, missing-data handling, or adjustment details. Those omissions limit assessment of how the analysis addressed all randomized participants and other design features. The absence of masking is also relevant for a behavioral intervention, even though the primary endpoint included biochemical verification.
Statistical evidence about the primary endpoint does not resolve the broader economic hypothesis. Cost per participant is also posted, but the registry record does not report a sponsor analysis for that outcome. Nor does the primary cessation comparison establish that later cost savings offset upfront costs. The findings should be read as a comparison of the posted outcomes and their precision, rather than as a clinical recommendation or a conclusion about every proposed benefit.
10. Statistical Methods Explained
The primary outcome is binary: each participant either meets the seven-day abstinence definition or does not. For this kind of endpoint, group counts and the number assessed in each group describe the data directly. The primary results report 8 participants meeting the definition among 88 in the best-practices group and 31 among 81 in the incentives group. The reported analysis is a chi-squared test of the two groups, with p < 0.001.
What does the risk difference describe?
A risk difference compares the proportions meeting the endpoint in two groups by subtracting one group’s proportion from the other’s. It expresses the contrast on an absolute scale: how far apart the observed proportions are, rather than how many times one proportion is the other. The posted risk-difference estimate is positive, and its confidence interval lies above zero. The interval is a measure of uncertainty around the estimate; its exclusion of zero is consistent with the reported test result. The estimate remains an unadjusted comparison based on the posted group summaries.
Other common measures for binary outcomes include a risk ratio and an odds ratio. A risk ratio compares the proportions directly as a relative measure, whereas an odds ratio compares the odds of the outcome. These measures use different scales and need not have the same numerical value. They describe the same group contrast in different ways and do not remove uncertainty or establish that the observed association will recur. The registry also posts relative measures for the primary comparison, but the main interpretation emphasizes counts, the absolute contrast, and its interval.
What does the chi-squared test assess?
In general, a chi-squared test assesses whether the observed group counts are compatible with a null model of no association between group and outcome. Its p-value measures how unusual data at least as discrepant as those observed would be under that model and its assumptions. It is not the probability that the null hypothesis is true, nor does it measure the size or importance of an effect. The sponsor-reported primary test is chi-squared, with p < 0.001; the unadjusted recalculation gives the same reported p-value threshold.
The registry identifies the primary analysis as a superiority comparison. In general, a superiority test asks whether the data support a difference in a specified direction or any difference, depending on the test’s setup. The detailed hypothesis wording and any prespecified analysis choices are not reported in the registry record. The estimated contrast and its confidence interval help describe the direction and range of the result; the p-value alone does not provide that information.
How should continuous outcomes be read?
Gestational age at delivery and cost per participant are continuous outcomes. A mean summarizes the average observed value in a group. A standard error describes uncertainty in the estimated mean, rather than the spread of individual observations. For gestational age, the posted group means were 39.18 weeks in the best-practices group, 38.69 weeks in the incentives group, and 39.35 weeks in the never-smoker comparison condition. The registry reports a standard error for each mean. The sponsor analysis listed for gestational age is ANCOVA across the three groups, with p < 0.05; the registry record does not provide the adjusted estimate or its confidence interval.
For cost per participant, the posted mean was U.S. dollars 23010.0 for best practices plus incentives and U.S. dollars 22370.0 for best practices. The unadjusted recalculated mean difference has an interval that includes zero and a p-value of 0.757. No sponsor-reported analysis for this outcome is listed. Cost is measured from trial entry through 24-weeks postpartum, approximately one year following the smoking-cessation quit date. Mean cost alone does not establish cost-effectiveness, which would require an economic comparison that relates costs to outcomes.
Why does over-dispersion matter in general?
Over-dispersion is a general concern when count data vary more than a model assumes. If the model understates variability, standard errors can be too small and intervals too narrow, making evidence appear more precise than it is. The primary outcome is a binary participant count, not a rate model with a stated dispersion parameter; dispersion is not reported for the primary endpoint. No adjustment for over-dispersion is described in the registry record, and the registry entries do not establish that one was needed.
More generally, methods should be matched to outcome type and design. A binary outcome is naturally expressed through participant counts and proportions; continuous outcomes are often described with group means and contrasts. Adjusted models can account for prespecified covariates, but their interpretation depends on the model, covariates, and analysis population. The registry names ANCOVA for the gestational-age analysis but does not report its covariate specification. The primary result is reported as a chi-squared comparison, not as an adjusted model.
11. Confidence Intervals and Precision
Precision concerns the uncertainty around an effect estimate, not simply whether a test crosses a significance threshold. For the primary outcome, the posted estimate is a positive risk difference and its confidence interval lies above zero. This indicates that the interval is inconsistent with a zero difference at the stated confidence level, while still allowing a range of positive effect sizes. The interval does not mean that every value inside it is equally likely, and it does not guarantee that a future study will produce an estimate inside that range.
The primary groups included 88 participants assigned to best practices and 81 assigned to best practices plus incentives. The observed abstinence counts were 8 and 31, respectively. These sample sizes and event counts are the basis for the uncertainty in the group comparison. A confidence interval is generally wider when information is limited and narrower when the estimate is more precise; it reflects both the amount of information and the variability in the outcome.
The secondary estimates illustrate why a p-value should be considered alongside an interval. The unadjusted interval for the gestational-age contrast between the two smoking groups includes zero, as does the interval for the contrast with the never-smoker group. The cost-per-participant interval also includes zero. These estimates therefore allow both directions of difference under their intervals, rather than pinning down a clear contrast. The registry’s adjusted ANCOVA result for gestational age is reported only as p < 0.05, without an adjusted estimate or interval, so its precision cannot be assessed from that analysis entry.
All these intervals are estimates from the posted data and methods, not guarantees about the true effect. The registry does not report further details about confidence-interval construction for the primary outcome, and the precision of the results should be understood in light of that reporting limit.
12. Planning a Similar Trial: Sample Size
This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.
| Effect to detect | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 33 | 43 |
| 75% of the observed effect | 52 | 69 |
| 50% of the observed effect | 100 | 134 |
The planning figures are illustrations based on the observed effect, not a record of the trial’s original sample-size design. The stated 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 original trial’s own design assumptions and sample-size justification are not reported in the registry record.
For the binary primary comparison, the figures are participants per arm, not total events. The planning entries for detecting 100% of the observed effect are 33 participants per arm for 80% power and 43 participants per arm for 90% power. For 75% of the observed effect, the corresponding figures are 52 and 69 participants per arm. For 50% of the observed effect, they are 100 and 134 participants per arm.
In plain language, the 80% power column gives the illustrative number of participants per group needed, under the stated assumptions, for an 80% chance of detecting the specified effect if that effect were the true one. The 90% column uses a higher target chance and therefore calls for more participants under the same assumptions. Smaller effects are harder to distinguish from chance variation, so the planning figures rise as the assumed effect becomes a smaller fraction of the observed effect. This is not observed power: it is a planning calculation, not a measure of the trial’s probability of having detected an effect after its results were known.
For time-to-event outcomes, the stated convention is total events; for all other outcomes, it is participants per arm. The primary outcome is not time-to-event, so its figures use participants per arm. These planning values depend on the observed effect used as their starting point, and a different true effect or analysis plan could lead to different requirements.
13. How the Sample Size Is Derived
Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z1−α/2 = 1.960) and the desired power (z1−β = 0.842 for 80% and 1.282 for 90%).
Formula
n 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
- Control proportion p0 = 0.091; treatment proportion p1 = 0.383; average p̄ = 0.237.
- First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6012 = 1.1784.
- Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.5647 = 0.4753.
- n = (1.1784 + 0.4753)2 / (0.2918)2 = 32.1, rounded up to 33 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 <- 0.0909090909090909 # control proportion
p1 <- 0.382716049382716 # 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(2210832)
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 = 33 (80% power), 43 (90% power)
75% of observed effect: n per arm = 52 (80% power), 69 (90% power)
50% of observed effect: n per arm = 100 (80% power), 134 (90% power)
power.prop.test: 32.1
Simulated power at n = 33 per arm: 0.838 (20000 replicates)
The simulation draws many pairs of event counts at the planned sample size and counts how often the two-proportion z-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.
14. Analyses Reported by the Sponsor
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| Chi-squared | not reported | < 0.001 |
For the primary abstinence comparison, the registry reports a chi-squared analysis with p < 0.001. The unadjusted recalculation from the posted group counts also gives p < 0.001, and the record identifies no discrepancy between the reported and recalculated result. The sponsor’s reported test is therefore consistent with the simple unadjusted comparison in the posted summaries.
The methods and results are not identical for every outcome. For gestational age, the sponsor analysis is listed as ANCOVA across the three groups, with p < 0.05. The unadjusted recalculations compare pairs of posted group means and are not a substitute for the adjusted three-group analysis. The registry record does not report the ANCOVA estimate, confidence interval, covariates, or further details needed to reproduce that analysis.
For cost per participant, no sponsor-reported analysis is listed. The posted unadjusted recalculation compares the two smoking-cessation groups, but it should not be treated as a sponsor analysis or a full economic evaluation. When a discrepancy exists, the sponsor’s own analysis takes precedence; no discrepancy is flagged for the primary result in this record.
15. Multiplicity, Missing Data and Analysis Populations
Multiplicity arises when several hypotheses are tested. Even if each test uses a conventional significance threshold, examining many outcomes can increase the chance that at least one result appears statistically notable by chance. The registry lists 16 outcome measures and 15 analyses. It does not report whether the investigators adjusted secondary tests for multiplicity, designated a hierarchy among secondary outcomes, or treated these analyses as exploratory. The registry record does not report a multiplicity plan, so the secondary p-values should not be read as if they were the sole prespecified test.
The primary endpoint is clearly identified, and the reported primary comparison is a chi-squared test with p < 0.001. However, the record does not report a complete statistical analysis plan or details such as whether any planned covariate adjustment was considered for this endpoint. It also does not report how the analysis handled participants with missing outcome or verification data, whether all randomized participants were analyzed in their assigned groups, or how exclusions after randomization were addressed. These omissions make it difficult to assess the consequences of missingness or deviations from the planned analysis.
Missing data can matter when the chance of an unavailable endpoint differs between groups or is related to the outcome. In general, complete-case results describe participants with observed data, while other approaches may use assumptions about unobserved outcomes. The registry record does not identify which approach was used for the primary endpoint. The reported denominators are 88 and 81 for the two smoking groups, but those numbers alone do not explain whether all randomized participants were included or why other participants may not appear in the endpoint counts.
The record also does not report interim analyses, stopping rules, or details of the original sample-size justification. Those design and analysis details should not be inferred from the completed status or the posted p-values. The stated planning illustrations based on the observed effect are separate from the trial’s original design assumptions.
16. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Best Practices for Pregnant Smokers | 3 | 91 | 3.3% |
| Best Practices Plus Financial Incentives | 4 | 85 | 4.7% |
| Never-smoker Comparison Condition | 1 | 81 | 1.2% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Best Practices for Pregnant Smokers | 0 of 91 |
| Best Practices Plus Financial Incentives | 0 of 85 |
| Never-smoker Comparison Condition | 0 of 81 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 0% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Best Practices for Pregnant Smokers | 0 of 91 |
| Best Practices Plus Financial Incentives | 0 of 85 |
| Never-smoker Comparison Condition | 0 of 81 |
Most frequent serious adverse event terms
| Event term | Organ system | Best Practices for Pregnant Smokers | Best Practices Plus Financial Incentives | Never-smoker Comparison Condition |
|---|---|---|---|---|
| Pregnancy termination/fetal demise | Pregnancy, puerperium and perinatal conditions | 3 of 91 | 4 of 85 | 1 of 81 |
Serious events with the highest arm-level rate: pregnancy termination/fetal demise (4.7%).
The registry reports serious adverse event information for all three conditions. The serious-event affected counts are 3 among 91 at risk in the best-practices group, 4 among 85 at risk in the incentives group, and 1 among 81 at risk in the never-smoker comparison condition. Deaths are reported as 0 in each group. Other adverse events affected are reported as 0 in each group. These figures describe the registry’s reported counts and should be interpreted alongside the group-specific numbers at risk.
The registry identifies “Pregnancy termination/fetal demise” as the top serious adverse event term, at 4.7%. The record does not specify in the registry record how that percentage was calculated or give a group-specific breakdown for the term. The serious-event counts should not be conflated with the primary abstinence outcome, and the never-smoker condition is a matched comparison group rather than one of the randomized smoking-cessation conditions.
Adverse-event counts alone do not establish whether an event was caused by an assigned intervention. The registry record does not provide further details about event definitions, severity beyond the serious classification, timing, or causal attribution. These safety figures are therefore descriptive; they do not by themselves determine the comparative safety of the strategies.
17. What the Result Does, and Does Not, Mean
The primary result describes a difference in the observed proportion meeting a specific abstinence definition at one antepartum assessment. The group counts were 8 of 88 for best practices and 31 of 81 for best practices plus incentives. The reported chi-squared test gave p < 0.001, and the unadjusted recalculation agrees. The interval for the primary risk difference lies above zero, indicating that the posted estimate is not merely an imprecise contrast centered around no difference.
That result is limited to the outcome and timing that were measured. It does not show whether participants remained abstinent after delivery, whether abstinence continued throughout pregnancy, or whether infant health improved. It also does not establish that financial incentives were economically justified. Cost per participant is a separate outcome, and the registry record does not report an economic analysis linking costs to the primary or infant-health outcomes.
The never-smoker comparison condition has a different role. It followed women matched to smokers for comparisons of birth and health outcomes. It is not the randomized comparator for the primary cessation analysis, so contrasts involving that condition should not be interpreted as randomized estimates of the effect of incentives.
Statistical evidence is not the same as certainty. The interval represents uncertainty around the estimated contrast, and the estimates remain specific to this study’s participants, procedures, and endpoint definition. No masking was used, and the outcome combines self-report with urine cotinine verification. The registry record does not give details of missing-data handling, the full analysis population, or the original sample-size justification; these limits affect how fully the findings can be assessed.
These results are statistical findings, not medical advice. They do not establish an individual participant’s likely outcome or settle every question about smoking cessation in pregnancy. They describe the posted comparison and its uncertainty, while leaving broader questions about sustained abstinence, infant outcomes, and cost-effectiveness to other analyses.
18. Why This Trial Matters Statistically
This trial poses a useful statistical question because it compares an added behavioral and financial component with an active support condition rather than with no support. The primary contrast is therefore about the incremental value of adding incentives to best practices, as represented by the randomized groups and the endpoint reported. Keeping the comparison explicit helps avoid attributing the whole cessation program’s effects to one component.
The endpoint also illustrates how outcome definition shapes interpretation. Abstinence was defined over the past seven days at approximately 28-weeks gestation and required both self-report and biochemical verification. That definition is more specific than a general statement that participants quit smoking, but it remains a snapshot rather than a measure of sustained abstinence. Statistical descriptions need to preserve that distinction.
Several kinds of evidence appear in the registry: a primary binary outcome, secondary birth and health measures, and a cost measure. They answer different questions and have different analysis methods. The primary chi-squared result, the across-group ANCOVA result for gestational age, and the unadjusted cost comparison cannot be treated as interchangeable evidence. Separating them clarifies both what the data support and what remains uncertain.
The record also demonstrates why reporting the estimate and its interval matters alongside a p-value. A p-value addresses compatibility with a null model under assumptions, while the interval communicates a range of effect sizes consistent with the data and method. The primary estimate’s interval lies above zero; secondary unadjusted intervals that include zero convey a different level of precision. Neither statistical significance nor its absence, by itself, answers questions about clinical importance or economic value.
Finally, details such as multiplicity, missing-data handling, analysis populations, and the original design assumptions affect how confidently results can be evaluated. Their absence from the registry record is an important reporting limitation, not a reason to fill in undocumented choices.
19. 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 observed at one antepartum time point, approximately 28-weeks gestation. It does not directly measure sustained abstinence through delivery or postpartum. Although the abstinence definition includes urine cotinine verification, the registry record does not report the verification threshold or how missing self-report or cotinine results were handled.
The trial was not masked. For a behavioral intervention involving vouchers, participants would know whether incentives were available; the record does not report any masking of outcome assessors. Biochemical verification can complement self-report, but it does not resolve every potential source of bias or uncertainty in the endpoint.
The primary outcome counts are based on 88 participants in the best-practices group and 81 in the incentives group. The registry reports total enrollment of 257, but does not explain in the available record how the enrollment total relates to the primary analysis population, or whether all randomized participants contributed to the endpoint analysis. Missing-data methods, exclusions, and the analysis population are not reported in the registry record.
The never-smoker condition was matched to smokers for birth and health comparisons; it was not the randomized comparator for the primary cessation question. Comparisons involving that group may therefore have different interpretive limits from the randomized comparison. The registry does not report details of matching implementation or adjustment for any remaining differences.
For secondary outcomes, the registry lists 16 outcome measures and 15 analyses, but multiplicity procedures and a hierarchy of secondary aims are not reported. The adjusted gestational-age analysis is named as ANCOVA, but its covariates and adjusted estimate are not reported. Cost per participant is posted without a sponsor-reported analysis or an economic evaluation linking cost and health outcomes. The original sample-size justification and interim-analysis plan are also not reported in the registry record.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Financial Incentives for Smoking Cessation Among Disadvantaged Pregnant Women — NCT02210832.
- Registry record last updated 2023-08-24; status last verified 2023-05.
- Results first posted 2023-08-24.
- 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.
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23. Record Summary
The record describes a completed, randomized, parallel-group, unmasked behavioral trial sponsored by the University of Vermont, with enrollment of 257. It compared best practices for pregnant smokers with best practices plus financial incentives. A matched never-smoker condition was included for birth and health comparisons, not for the primary cessation comparison.
The primary endpoint was biochemically verified seven-day abstinence at approximately 28-weeks gestation. The posted counts were 8 of 88 for best practices and 31 of 81 for best practices plus incentives. The sponsor-reported chi-squared test and the unadjusted recalculation both give p < 0.001.
Secondary information includes gestational age at delivery and cost per participant, alongside a broader set of listed outcomes. The record does not report the original sample-size justification, missing-data handling, analysis populations, or multiplicity procedures. The primary finding describes a specific outcome at a specific time; it does not by itself settle longer-term abstinence, infant-health, or cost-effectiveness questions.