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 tDCS Effects on Resisting Smoking: Dose Ranging Study (NCT02624284), a randomized na study. The primary outcome is Resisting Smoking - Time to First Cigarette in the Resist Smoking Paradigm.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT02624284 |
| Phase | NA |
| Condition | Nicotine Addiction |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Triple |
| Enrollment | 172 |
| Arms in the primary outcome | 3 |
| Lead sponsor | University of Pennsylvania |
| Results posted | Yes |
2. Clinical Question
Population
The registry lists nicotine addiction as the condition and records enrollment of 172 participants. The primary outcome was assessed in a laboratory session on day 5, after participants had been assigned to one of the three study arms. Further eligibility details and the primary analysis population are not reported in the registry record.
Intervention
The active interventions were 1mA and 2 mA transcranial direct current stimulation, abbreviated tDCS. The registry describes anodal stimulation to the left dorsolateral prefrontal cortex for the active-dose arms. The available arm descriptions are incomplete, so further details of the treatment procedures are not reported in the registry record.
Comparator
The comparator was sham tDCS. Its description states that a 1.0 mA to 2.0 mA current was delivered for approximately 30 seconds before being extinguished over a course of seconds. The registry record does not give complete procedural details for the sham arm.
Primary question
Did time to the first cigarette during a smoking-resistance paradigm differ across sham, 1mA, and 2 mA arms? The measure was recorded in minutes during a laboratory session on day 5 and assessed for up to 2 hours. The registry’s reported overall regression analysis has p = 0.94; pairwise recalculations from the posted arm summaries are not a substitute for that analysis.
The study is identified as NCT02624284 and titled tDCS Effects on Resisting Smoking: Dose Ranging Study. The registry lists random allocation, triple masking, and a parallel-group model. The posted results concern a laboratory measure of smoking resistance, not a long-term clinical outcome. The registry record does not report enough information to establish how the enrolled participants were selected, how masking was maintained, or how the three-arm allocation was implemented.
3. Trial Design
This was a randomized, triple-masked, parallel-group study with three arms: sham dose, 1mA dose, and 2 mA dose. The registry records enrollment of 172 and lists the study status as completed. It identifies the University of Pennsylvania as sponsor. The study’s phase is listed as NA. The recorded start is 2015-11, and primary completion is dated 2018-03-31.
The active arms used tDCS, with the available descriptions specifying anodal stimulation to the left dorsolateral prefrontal cortex. The sham description says that current was applied briefly and then extinguished. Those descriptions are truncated, however, and the full procedures, treatment schedule, and duration of active stimulation are not reported in the registry record. No additional intervention is listed.
The primary outcome was time to first cigarette during a validated smoking-lapse paradigm, assessed in a laboratory session on day 5 for up to 2 hours. The registry also posts two secondary outcomes: urge to smoke for negative affect relief during the same day-5 laboratory session, and days abstinent from cigarettes during a monitored abstinence period on study days 6–12. The registry identifies a linear regression analysis across the three groups for the primary outcome and for days abstinent. It reports no analysis method for the urge outcome.
Although the record gives the overall enrollment, the outcome summaries have separate arm counts. The primary outcome summaries list 35 participants for sham, 35 for 1mA, and 36 for 2 mA. The registry does not explain the difference between enrollment and the counts used in these posted outcome summaries. Eligibility criteria, participant flow, analysis-population definitions, and handling of missing outcomes are not reported in the registry record.
4. Participant Flow and Accounting
The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.
Overall Study
| Stage | Sham Dose | 1mA Dose | 2 mA Dose |
|---|---|---|---|
| STARTED | 49 | 53 | 47 |
| COMPLETED | 35 | 35 | 36 |
| NOT COMPLETED | 14 | 18 | 11 |
Reasons for not completing this period:
| Reason | Sham Dose | 1mA Dose | 2 mA Dose |
|---|---|---|---|
| Withdrawal by Subject | 3 | 6 | 3 |
| Protocol Violation | 9 | 10 | 7 |
| Revealed exclusionary condition | 2 | 2 | 0 |
| Adverse Event | 0 | 0 | 1 |
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.
| Characteristic | Unit | Sham Dose | 1mA Dose | 2 mA Dose | Total |
|---|---|---|---|---|---|
| Participants analysed | 35 | 35 | 36 | 106 | |
| Age, Continuous | years | 44.7 (SD 11.2) | 45.6 (SD 9.4) | 45.4 (SD 9.2) | 45.3 (SD 9.9) |
| Sex: Female, Male: Female | Participants | 15 | 13 | 10 | 38 |
| Sex: Female, Male: Male | Participants | 20 | 22 | 26 | 68 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 0 | 1 | 0 | 1 |
| Race (NIH/OMB): Asian | Participants | 0 | 0 | 1 | 1 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 0 | 0 | 0 | 0 |
| Race (NIH/OMB): Black or African American | Participants | 24 | 25 | 28 | 77 |
| Race (NIH/OMB): White | Participants | 10 | 8 | 7 | 25 |
| Race (NIH/OMB): More than one race | Participants | 1 | 1 | 0 | 2 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 0 | 0 | 0 | 0 |
| Region of Enrollment: United States | participants | 35 | 35 | 36 | 106 |
| Nicotine dependence (FTND score) | units on a scale | 5.3 (SD 1.5) | 5.1 (SD 1.6) | 5.1 (SD 1.8) | 5.2 (SD 1.6) |
6. Primary Endpoint
The registry lists the primary outcome as Resisting Smoking - Time to First Cigarette in the Resist Smoking Paradigm, measured over During laboratory session on day 5, assessed for up to 2 hours.
| Element | Registry entry |
|---|---|
| Result type | Mean |
| Measure of spread | Standard Deviation |
| Unit | minutes |
| Endpoint classification | Continuous Endpoint |
The primary endpoint is time to first cigarette, measured in minutes during a laboratory smoking-resistance paradigm. Participants were assessed during a laboratory session on day 5, for up to 2 hours. The registry describes the measure as an assessment of smoking behavior using a validated smoking-lapse paradigm. It is a continuous outcome: larger reported means represent a longer average time before the first cigarette during the observation period.
This kind of endpoint is used to quantify behavior under a defined laboratory challenge. It offers a direct, timed measure of how long participants refrain from smoking in that setting, rather than relying only on a report of intention or urge. As a general statistical point, a continuous measure can retain distinctions among observed values rather than reducing the outcome to a simple yes-or-no classification. That does not by itself establish that the measure predicts smoking behavior outside the laboratory.
The endpoint must also be interpreted within its assessment window. The record states that the paradigm was assessed for up to 2 hours; it does not report how values at the end of that window were handled, whether anyone did not smoke during the full assessment, or the analysis method used to account for such observations. Those details are not reported in the registry record. The posted arm summaries use means and standard deviations, while the registry’s reported overall analysis is linear regression. The record does not state whether the regression included covariates or how its assumptions were checked.
7. Results Posted in the Registry
- 1mA Dose: mean 63.40 versus 60.30 on control; difference 3.10 (95% CI 0.62 to 5.58), standardized effect d = 0.58; z-test p = 0.014.
- 2 mA Dose: mean 63.20 versus 60.30 on control; difference 2.90 (95% CI 0.59 to 5.21), standardized effect d = 0.59; z-test p = 0.014.
Mean difference: 1mA Dose
95% CI: 0.62 to 5.58
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 |
|---|---|---|---|---|
| Urge to Smoke for Negative Affect Relief | Continuous Endpoint | Mean difference | -0.70 (-3.40 to 2.00) | 1,062 per arm |
| Number of Days Abstinent From Cigarettes During Monitored Abstinence Period | Continuous Endpoint | Mean difference | 0.30 (0.10 to 0.50) | 34 per arm |
Urge to Smoke for Negative Affect Relief
- 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 deviations.
- Result:
- 1mA Dose: mean 10.80 versus 11.50 on control; difference -0.70 (95% CI -3.40 to 2.00), standardized effect d = -0.12; z-test p = 0.611.
- 2 mA Dose: mean 8.60 versus 11.50 on control; difference -2.90 (95% CI -5.30 to -0.50), standardized effect d = -0.56; z-test p = 0.018.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between 1mA Dose and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval excludes no difference, so the mean is statistically lower for 2 mA Dose than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Number of Days Abstinent From Cigarettes During Monitored Abstinence Period
- 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 deviations.
- Result:
- 1mA Dose: mean 4.10 versus 3.80 on control; difference 0.30 (95% CI 0.10 to 0.50), standardized effect d = 0.69; z-test p = 0.004.
- 2 mA Dose: mean 3.60 versus 3.80 on control; difference -0.20 (95% CI -0.39 to -0.01), standardized effect d = -0.48; z-test p = 0.043.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically higher for 1mA Dose than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
- The 95% confidence interval excludes no difference, so the mean is statistically lower for 2 mA Dose than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The secondary outcomes provide a mixed pattern rather than a consistent confirmation of the primary endpoint. Across the two outcomes, recalculated pairwise estimates vary in direction, and the registry’s reported overall analysis for days abstinent has p = 0.78. The urge outcome has no reported overall analysis. The results therefore do not supply a single coherent pattern that resolves the primary-analysis discrepancy.
Secondary measures can add useful context by examining related but distinct aspects of smoking behavior. They are not interchangeable with the primary laboratory measure: urge during the day-5 session and abstinent days during the monitored period on study days 6–12 capture different outcomes and timeframes. Their association with the primary endpoint is not established by the registry record, and the data do not show that one measure explains another.
Unadjusted secondary results carry less weight as confirmatory evidence when the number of tests and multiplicity strategy are not reported. In general, testing multiple outcomes and contrasts increases the opportunity for results to appear notable by chance. The registry does not state whether the secondary analyses were prespecified, whether any adjustment was applied, or how secondary missing data were handled. Their estimates should therefore be treated as descriptive or exploratory rather than as independent confirmation of a primary effect.
The broad pattern is not enough to establish a dose-response relationship. The record contains three dose-group summaries, but does not report a formal dose-trend analysis. Nor does it report longer-term outcomes that would connect the laboratory and monitored-abstinence measures to smoking behavior beyond the recorded periods. The secondary findings can inform questions for further study, but they cannot settle the result of the sponsor’s primary analysis.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Urge to Smoke for Negative Affect Relief
- Number of Days Abstinent From Cigarettes During Monitored Abstinence Period
9. Statistical Interpretation
For the primary endpoint, the posted means are 60.3 minutes in the sham arm, 63.4 minutes in the 1mA arm, and 63.2 minutes in the 2 mA arm. The corresponding standard deviations are 5.2, 5.4, and 4.7 minutes. These descriptive summaries show higher observed mean times in both active-dose arms than in the sham arm. They do not, on their own, establish a treatment effect or its statistical significance.
The registry’s reported analysis is a linear regression comparing all three groups, with p = 0.94. This is the sponsor’s reported overall analysis. The pairwise recalculations from the posted summary statistics give mean differences of 3.1 minutes for 1mA versus sham and 2.9 minutes for 2 mA versus sham, each with an unadjusted p = 0.014. Because the registry analysis and the recalculations give a substantial discrepancy, the sponsor’s own analysis takes precedence. The pairwise results should be read as unadjusted recalculations, not as the trial’s reported primary analysis.
The reported overall p-value and the pairwise recalculations address analyses with different forms. An overall test across three groups is not identical to two separate comparisons against sham. A p-value is not an estimate of the size of an effect, and it does not measure the probability that a hypothesis is true. The reported p = 0.94 means the registry’s overall regression analysis did not identify a statistically detectable group difference under that analysis. The posted arm means still describe the observed data, but their pattern should not override the reported overall result.
There are two posted secondary outcomes. Their recalculated pairwise results vary in direction and strength, while the registry also reports an overall regression p-value for days abstinent. These secondary findings should be considered exploratory because the record does not report a multiplicity adjustment or a complete prespecified analysis plan. They do not resolve the discrepancy in the primary analysis.
The summaries are limited to the observed measures and their stated timeframes. They do not establish effects beyond the laboratory task or monitored abstinence period. The registry does not report longer-term smoking outcomes, the exact analysis population, or how missing observations were treated. Any broader interpretation therefore goes beyond what the posted results establish.
10. Statistical Methods Explained
What does the reported overall test address?
The registry reports linear regression for the primary outcome across the sham, 1mA, and 2 mA groups, with p = 0.94. An overall comparison asks whether the outcome pattern across the groups is compatible with a common mean, under the assumptions of the specified model. It is not the same question as separately comparing each active dose with sham. The registry record does not report the regression coefficient, confidence interval, covariates, exact test statistic, or model diagnostics. It also does not explain whether the reported p-value is adjusted for any other analyses.
In general, linear regression models a continuous outcome in relation to group membership and, when specified, other explanatory variables. Its interpretation depends on how the model was built and on assumptions about the outcome and residual variation. The registry names the method but does not give enough information to assess the full model specification. The posted arm means and standard deviations are descriptive summaries rather than a replacement for that model.
What are the pairwise recalculations?
The pairwise results compare each active dose with sham using the posted group means and standard deviations. They are simple, unadjusted recalculations, not the sponsor’s reported regression analysis. For time to first cigarette, the recalculated mean difference is 3.1 minutes for 1mA versus sham and 2.9 minutes for 2 mA versus sham. Both recalculations have unadjusted p = 0.014. Their intervals exclude zero using the posted estimates, but the precision of those results does not remove the discrepancy with the registry’s overall analysis.
In general, a mean difference expresses the contrast between two group averages in the outcome’s original units. Here, the unit is minutes. A confidence interval conveys a range of values compatible with the estimate and the statistical procedure used, subject to the model assumptions. A p-value measures how unusual data at least as discrepant as those observed would be under a specified null hypothesis and model. It is not an effect size and does not tell whether a result is clinically important.
The pairwise contrasts are unadjusted: they do not account for making multiple comparisons. When several tests are performed, the chance of at least one apparently notable result can rise. The record does not report a multiplicity strategy for these comparisons. This is one reason not to treat the recalculated pairwise p-values as interchangeable with the sponsor’s overall result.
Why can over-dispersion matter?
Over-dispersion is a general concern when observed variability is greater than a statistical model expects. If a model underestimates the true variability, standard errors can be too small and confidence intervals too narrow, making apparent evidence stronger than it should be. The posted endpoint is continuous and is summarized with standard deviations; the record does not report an over-dispersion assessment or any particular adjustment for it. This general concept should not be taken to mean that over-dispersion was observed in this trial.
How should the secondary analyses be understood?
The registry reports a linear regression analysis across groups for days abstinent, with p = 0.78. It does not report a corresponding overall analysis for urge to smoke. The pairwise values for both secondary outcomes are recalculations from their posted summaries and are unadjusted. A collection of secondary measures can provide context, but each result is less secure as confirmatory evidence when the analysis plan and multiplicity handling are not reported.
General statistical practice distinguishes prespecified primary analyses from exploratory analyses because choices made after looking at results can make apparent evidence less reliable. The registry record does not report whether these secondary analyses were prespecified, how missing data were handled, or whether the analysis population differed by outcome. The unreported details should not be inferred from the posted means and standard deviations.
What is not documented?
The original sample-size justification, target effect, interim analyses, and complete statistical analysis plan are not reported in the registry record. The record also does not describe allocation concealment, outcome-assessment procedures, model diagnostics, or treatment of values at the end of the two-hour smoking-resistance assessment. These are not minor details for reconstructing an analysis: they can affect the meaning and precision of estimates. General statistical explanations describe how methods work, but they cannot fill in undocumented trial procedures.
11. Confidence Intervals and Precision
Precision describes how much uncertainty surrounds an estimated effect. For the primary pairwise recalculations, the mean differences are 3.1 minutes for 1mA versus sham and 2.9 minutes for 2 mA versus sham. Their recalculated confidence intervals are above zero, but the registry’s overall linear regression analysis reports p = 0.94. Because the discrepancy is true, the sponsor’s own analysis takes precedence over these simple recalculations.
A confidence interval is generally a range generated by a statistical procedure to describe uncertainty in an estimate. It is not a guarantee that the true effect lies within the particular interval, nor does it describe the range of individual participant outcomes. A narrower interval indicates greater precision under the chosen method; a wider interval indicates more uncertainty. Precision depends on factors such as sample size and variability, as well as the assumptions used to calculate the interval.
The arm-level standard deviations for the primary endpoint range from 4.7 to 5.4 minutes, and the arm counts are 35, 35, and 36. These summaries help describe the amount of variation and information in the observed groups, but they do not resolve the mismatch between the overall reported analysis and the pairwise recalculations. The registry does not provide a confidence interval for the overall regression analysis, nor its estimated regression coefficients. As a result, the precision of the sponsor’s overall comparison cannot be assessed from the reported analysis alone.
In general, intervals and p-values should be interpreted alongside the estimate, the analysis method, and the question being tested. The pairwise intervals concern particular contrasts; the overall regression test concerns all three groups. The registry’s incomplete analytic details and the discrepancy between results limit the confidence that can be placed in a single numerical summary.
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 | 46 | 62 |
| 75% of the observed effect | 82 | 110 |
| 50% of the observed effect | 184 | 246 |
The sample-size figures are planning illustrations based on the observed pairwise effect, not the trial’s original design calculation. For continuous outcomes, the figures are participants per arm. The general planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set to the stated fraction of the observed effect. These assumptions describe the illustration only; the trial’s original sample-size assumptions are not reported in the registry record.
The 80% power column gives the illustrative number of participants per arm that would yield an 80% chance of detecting the specified effect under those assumptions, if the effect and model assumptions were correct. The 90% power column uses a higher target chance of detection and therefore generally calls for more participants. These are design-planning quantities, not observed power. They do not state the probability that the trial’s result is correct or that an effect exists.
Rows for 100%, 75%, and 50% of the observed effect show how the planning result changes when the target effect is smaller than the observed estimate. Smaller effects require more participants to detect at the same nominal power and significance level. This behavior is a general consequence of needing more information to distinguish a smaller signal from random variation.
The table and curve should be read as planning aids for two-arm contrasts, not as a reconstruction of this three-arm study’s design. They are calculated separately for comparisons based on the posted summaries. The figures do not account for unreported design features, missing data, multiplicity, or the discrepancy between the sponsor’s overall analysis and the pairwise recalculations. No time-to-event outcome is being planned in these continuous-outcome illustrations, so the figures are participants per arm, not total events.
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, Δ is the difference in means to detect and σ is the common standard deviation.
Worked calculation for this trial
- Observed difference Δ = 3.100; pooled standard deviation σ = 5.301.
- n = 2 × (1.96 + 0.842)2 × 5.3012 / 3.1002 = 45.9, rounded up to 46 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
delta <- 3.1 # observed difference in means
sigma <- 5.30094331227943 # pooled standard deviation
n_per_arm <- function(power, frac = 1) {
ceiling(round(2 * (z_a + qnorm(power))^2 * sigma^2 / (delta * frac)^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 (t-based, so very slightly larger)
cat("power.t.test:", round(power.t.test(delta = delta, sd = sigma, power = 0.80)$n, 1), "\n")
# Simulation: exact two-sample t-test using simulated means and variances
set.seed(2624284)
n <- n_per_arm(0.80)
reps <- 20000
m_diff <- rnorm(reps, delta, sigma * sqrt(2 / n)) # difference in sample means
s2 <- sigma^2 * rchisq(reps, 2 * (n - 1)) / (2 * (n - 1)) # pooled sample variance
tstat <- m_diff / sqrt(s2 * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(tstat) > qt(0.975, 2 * (n - 1))), reps))
Output from running the code
100% of observed effect: n per arm = 46 (80% power), 62 (90% power)
75% of observed effect: n per arm = 82 (80% power), 110 (90% power)
50% of observed effect: n per arm = 184 (80% power), 246 (90% power)
power.t.test: 46.9
Simulated power at n = 46 per arm: 0.790 (20000 replicates)
The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-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 |
|---|---|---|---|
| Regression, Linear | not reported | 0.940 |
The sponsor’s reported analysis for the primary endpoint is linear regression across all three groups, with p = 0.94. The pairwise recalculations use the posted arm means and standard deviations to compare 1mA with sham and 2 mA with sham separately. They yield mean differences of 3.1 and 2.9 minutes, respectively, and unadjusted p = 0.014 for each contrast. These are not the same analysis, and the recalculations do not reproduce the registry’s overall model.
The recorded discrepancy is substantive: the pairwise recalculations suggest contrasts that differ from the reading of the reported overall test. In this situation, the sponsor’s own analysis takes precedence. The pairwise figures can be useful as descriptive, unadjusted calculations from posted summaries, but they should not be described as the trial’s reported primary result or used to replace it.
The registry does not give the regression estimates, confidence intervals, covariates, or full analysis plan needed to investigate why the results differ. It is therefore not possible from the registry record to identify the cause of the discrepancy. The responsible interpretation is to report both sources distinctly, acknowledge the discrepancy, and avoid selecting whichever result appears more favorable.
15. Multiplicity, Missing Data and Analysis Populations
Multiplicity arises when more than one statistical hypothesis is tested. This study has a three-group primary analysis, pairwise recalculations against sham, and two secondary outcomes with posted comparisons. Without a prespecified strategy for controlling or interpreting multiple tests, isolated unadjusted p-values can overstate the strength of evidence. The registry record does not report a multiplicity adjustment or state which analyses were confirmatory.
The registry reports a primary linear regression analysis across the three groups and another overall linear regression analysis for days abstinent. It does not report an overall analysis for urge to smoke. The pairwise results are unadjusted recalculations and should not be mistaken for a multiplicity-controlled analysis. The original statistical analysis plan and the roles of any planned secondary or exploratory tests are not reported in the registry record.
Missing-data methods and analysis populations are also not reported in the registry record. The record does not explain why the primary endpoint summaries include 35 participants in sham, 35 in 1mA, and 36 in 2 mA when the overall enrollment is 172. It does not specify whether all randomized participants were included in the analyses, how participants with missing outcomes were handled, or whether any imputation method was used. The handling of participants who did not smoke during the full assessment window is also not reported.
These omissions limit assessment of bias and uncertainty. General statistical methods can describe how multiplicity adjustments or missing-data approaches work, but the choice and implementation in this trial cannot be reconstructed from the registry record. No interim analyses or stopping rules are reported. The absence of reported details should not be interpreted as proof that a procedure was or was not used.
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 |
|---|---|---|---|
| Sham Dose | 0 | 49 | 0.0% |
| 1mA Dose | 0 | 53 | 0.0% |
| 2 mA Dose | 0 | 47 | 0.0% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Sham Dose | 0 of 49 |
| 1mA Dose | 0 of 53 |
| 2 mA Dose | 0 of 47 |
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 |
|---|---|
| Sham Dose | 0 of 49 |
| 1mA Dose | 1 of 53 |
| 2 mA Dose | 3 of 47 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Sham Dose | 1mA Dose | 2 mA Dose |
|---|---|---|---|---|
| Leg pain | Musculoskeletal and connective tissue disorders | 0 of 49 | 1 of 53 | 0 of 47 |
| high blood pressure | Vascular disorders | 0 of 49 | 0 of 53 | 1 of 47 |
| Bike accident | Injury, poisoning and procedural complications | 0 of 49 | 0 of 53 | 1 of 47 |
| Tingling and burning sensation | Nervous system disorders | 0 of 49 | 0 of 53 | 1 of 47 |
The safety summaries use group-specific numbers at risk that differ from the outcome-summary counts. For serious adverse events, the record lists 49 participants at risk in sham, 53 in 1mA, and 47 in 2 mA. It reports zero serious adverse events in each group and zero deaths in each group.
For other adverse events, the same at-risk counts are listed: 49, 53, and 47, respectively. The record reports zero in sham, 1 in 1mA, and 3 in 2 mA. These are the posted event counts; the registry record does not provide further event descriptions in the serious-event terms list.
These figures describe what was recorded in the listed safety groups. They do not establish that no unrecorded event occurred, and they do not by themselves show whether groups differ in safety. The registry does not report the safety collection period, definitions, severity grading, or the relationship of the safety groups to the outcome analysis populations. The different at-risk counts should not be combined with the outcome counts without further information.
17. What the Result Does, and Does Not, Mean
The results describe a specific laboratory assessment of resistance to smoking after assignment to sham, 1mA, or 2 mA tDCS. The primary endpoint was time to first cigarette during a day-5 laboratory session assessed for up to 2 hours. The posted group means are higher in both active-dose arms than in sham, but the sponsor’s reported overall regression analysis gives p = 0.94. The pairwise recalculations differ from that overall result and must be treated as unadjusted calculations rather than as the primary reported analysis.
These data do not establish what happens outside the study’s assessment periods. The primary outcome is a laboratory behavior measure; the secondary outcomes cover urge during the laboratory session and abstinent days during a monitored period on days 6–12. The registry does not report longer-term smoking outcomes. It also does not establish whether the laboratory measure predicts later behavior.
A statistical result does not by itself establish clinical importance, mechanism, or causation beyond the randomized comparison and measures documented. The registry’s incomplete methods information, unreported missing-data handling, and discrepancy between the primary analysis and recalculations constrain interpretation. The observed means and p-values should not be read as a guarantee of a particular outcome for an individual participant.
In general, randomized assignment can support comparisons between study groups when conduct, follow-up, and analysis preserve the intended comparison. The registry does not report enough detail to assess all of those conditions. The posted results are therefore best understood as evidence about the recorded group summaries and reported analyses, not as a definitive statement about effects on smoking behavior in other settings or over longer periods.
18. Why This Trial Matters Statistically
This study illustrates why a statistical interpretation should distinguish descriptive summaries, pairwise calculations, and the trial’s reported primary analysis. The arm means show a pattern, and recalculations from those summaries produce pairwise p-values. Yet the registry’s overall regression result is p = 0.94. When analyses do not align, transparent reporting of the discrepancy matters more than choosing the result that seems easiest to interpret.
The design also raises general questions about dose-ranging studies. A study with sham and two active dose groups can describe outcomes across those arms, but a formal claim about a dose trend requires an analysis that is reported and interpretable. No such analysis is reported in the registry record. The pattern of three means should not be treated as a dose-response test on its own.
Secondary outcomes and safety summaries add context, but they have their own limitations. The registry reports incomplete analysis details, no multiplicity strategy, and no missing-data approach. Those omissions make it harder to know how much weight to place on isolated secondary comparisons or how the analysis populations were formed.
The trial is statistically instructive because it demonstrates the importance of reporting estimates, uncertainty, model specification, analysis populations, and planned comparisons together. A p-value without its analysis context is difficult to reconcile with other calculations. Complete reporting would help readers understand whether discrepancies arise from different estimands, model choices, populations, or other factors. The record does not identify the reason in this case.
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 endpoint is a laboratory measure assessed on day 5 for up to 2 hours. The registry does not report longer-term smoking outcomes, so the results cannot establish whether the recorded behavior persisted beyond that assessment or translated to other settings. The secondary abstinence measure covers a monitored period on study days 6–12, not longer-term follow-up.
The registry provides incomplete intervention descriptions. The active arms are described as anodal stimulation to the left dorsolateral prefrontal cortex, but full treatment procedures and duration are not reported. The sham description is also truncated. That limits the ability to reproduce the intervention or assess how well masking may have been maintained, despite the record’s triple-masking designation.
The reported overall primary analysis conflicts with the pairwise recalculations from posted summaries. The registry does not provide regression coefficients, confidence intervals, covariates, diagnostics, or enough detail to explain the discrepancy. The pairwise results are unadjusted, and multiplicity handling is not reported. Missing-data methods, analysis-population definitions, participant flow, and the original sample-size rationale are also not reported in the registry record.
The safety groups’ at-risk counts differ from the arm counts for outcome summaries, and the record does not explain the relationship between those sets. The safety collection period and event definitions are not described in the posted information. These limits do not invalidate the listed figures, but they narrow what can responsibly be inferred from them.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: tDCS Effects on Resisting Smoking: Dose Ranging Study — NCT02624284.
- Registry record last updated 2019-03-19; status last verified 2019-02.
- Results first posted 2019-03-19.
- 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
NCT02624284 is a completed, randomized, triple-masked, parallel-group study sponsored by the University of Pennsylvania. It enrolled 172 participants and compared sham tDCS with 1mA and 2 mA tDCS. The primary endpoint was time to first cigarette in a day-5 laboratory smoking-resistance paradigm, assessed for up to 2 hours.
The registry reports an overall linear regression result for the primary endpoint of p = 0.94. Pairwise recalculations from posted arm summaries give unadjusted p = 0.014 for each active-dose comparison with sham, creating a discrepancy; the sponsor’s analysis takes precedence. Two secondary outcomes are posted, but their analysis and multiplicity details are incomplete. The registry does not report the original sample-size justification, missing-data methods, or full statistical analysis plan.