A Study to Investigate the Stain and Plaque Removal Capability of Two Experimental Potassium Nitrate Dentifrices: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for A Study to Investigate the Stain and Plaque Removal Capability of Two Experimental Potassium Nitrate Dentifrices (NCT03267511), a randomized phase 2 study. The primary outcome is Change From Baseline in Overall Macpherson Modification of the Lobene Stain Index (MLSI) at 8 Weeks..

2. Clinical Question

3. Trial Design

The registry identifies NCT03267511 as a Phase 2, randomized, double-masked, parallel-group study. It enrolled 123 participants and is recorded as completed. The study began on 2017-09-25, with primary completion on 2017-12-02. The condition is listed as Oral Hygiene, and GlaxoSmithKline is named as sponsor.

Four dentifrices were studied. Test Product 1 contained 5% potassium nitrate, 0.254% sodium fluoride, and 0.5% spherical silica. Test Product 2 contained 5% potassium nitrate, 0.254% sodium fluoride, 1% spherical silica, and 5% STP. Reference Product 1 contained 5% potassium nitrate, 0.254% sodium fluoride, and 6% abrasive silica. Reference Product 2 contained 5% potassium nitrate, 0.254% sodium fluoride, 16% abrasive silica, and 5% STP.

Participants were instructed to use their assigned dentifrice twice daily for 8 weeks. The recorded primary endpoint was change from baseline in Overall MLSI at Week 8. The outcome-arm sample sizes were 31 for Test Product 1, 31 for Test Product 2, 30 for Reference Product 1, and 31 for Reference Product 2. These are the counts associated with the posted primary outcome, rather than a description of every randomized participant’s follow-up.

The registry does not report the original sample-size justification, the details of sequence generation or allocation concealment, the masking procedures for each role, or the full visit schedule. Any further protocol details are not reported in the registry record.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Before assignment: A total of 137 participates were screened, out of which 123 participants were enrolled and randomized in the study. 14 participants were not randomized as 11 participants did not meet study criteria, 2 participants withdrew by consent and 1 participant was lost to follow-up.

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: The Intent-to-Treat (ITT) (n=123) population comprised all participants who were randomly allocated to treatment and received the study treatment at least once and provided at least 1 post-baseline (post-treatment) assessment of efficacy. This population was based on the randomized treatment to which the participant was allocated.

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: Safety population (N=123) comprised of all participants who were randomized and received at least one dose of study treatment during the study. This population was based on the treatment the participant actually received.

6. Primary Endpoint

The registry lists the primary outcome as Change From Baseline in Overall Macpherson Modification of the Lobene Stain Index (MLSI) at 8 Weeks., measured over Baseline, Week 8 post treatment administration.

The primary endpoint was change from baseline to Week 8 in Overall MLSI, a continuous score intended to assess the area and intensity of extrinsic dental stain on study teeth. Stain intensity and stain area were scored separately for gingival and body areas. Each used a scale from 0 to 3, with higher component scores indicating more stain. Overall MLSI was calculated by multiplying the intensity and area scores; its stated range was 0 (best score) to 9 (worst score).

Change from baseline makes the outcome a measure of how the score at follow-up differs from the starting assessment. In the posted results, negative arm means indicate a decrease in the score from baseline. Because lower Overall MLSI scores represent less stain, the direction of a negative change is consistent with a reduction in the measured stain score. The size of the change and its uncertainty remain important: a mean change alone does not show how much participants’ outcomes varied or how precisely a difference between arms was estimated.

The index is used to turn assessments of stain area and intensity into a numerical outcome that can be compared across treatment groups. The registry describes the endpoint as a means to evaluate the ranking order of stain removal or reduction. It does not report further information about assessor training, repeatability, or the clinical importance of a particular score difference.

7. Results Posted in the Registry

• Test Product 1: mean -0.32 versus -0.38 on control; difference 0.06 (95% CI -0.19 to 0.31), standardized effect d = 0.12; z-test p = 0.639.
• Test Product 2: mean -0.47 versus -0.38 on control; difference -0.09 (95% CI -0.34 to 0.16), standardized effect d = -0.18; z-test p = 0.482.
• Reference Product 2: mean -0.40 versus -0.38 on control; difference -0.02 (95% CI -0.27 to 0.23), standardized effect d = -0.04; z-test p = 0.876.

8. Statistical Interpretation

9. Statistical Methods Explained

What does the arm mean represent?

The primary outcome is continuous: it is a numerical score, and the posted arm summaries are means of change from baseline. A negative mean means the follow-up score was lower on average than the baseline score. The mean gives a compact description of the group, but does not describe every participant’s change. The standard error (SE) describes the uncertainty in an estimated mean; it is not the same as the spread of individual scores.

General statistical explanation: a standard error is commonly used to express how much an estimate might vary across repeated samples under a statistical model. A smaller SE indicates a more precisely estimated mean, all else equal. The registry posts SEs for each arm, but does not report individual-level distributions or enough information to assess every modeling assumption.

What does ANCOVA add?

The sponsor’s reported pairwise analyses used analysis of covariance (ANCOVA) and reported differences of least squares means. General statistical explanation: ANCOVA estimates a treatment-group contrast while accounting for covariates included in the model. A least squares mean is a model-based group mean, rather than necessarily the raw arithmetic mean. The registry does not identify the covariates, model specification, or any other adjustment details, so those features cannot be reconstructed from the record.

The sponsor’s estimates and p-values should be read as results from those reported ANCOVA analyses. They should not be treated as interchangeable with the recalculated, unadjusted comparisons. The reported ANCOVA contrasts are Test Product 1 versus Reference Product 1 and Test Product 2 versus Reference Product 2. The recalculation uses the posted arm means and SEs and compares Test Product 1, Test Product 2, and Reference Product 2 separately with Reference Product 1.

What is an unadjusted recalculation?

The recalculated differences are simple comparisons based on posted summary statistics, without the model adjustment used in ANCOVA. The arm-level means and SEs are available, but the original participant-level data and full analysis model are not. The recalculation uses an approximate pooled spread inferred from the arm summaries. It is therefore a check based on limited summary information, not a reproduction of the sponsor’s model.

General statistical explanation: unadjusted analyses can differ from adjusted analyses because they use different information and assumptions. Differences can arise from covariate adjustment, model specification, missing-data handling, or other analysis choices. The registry record does not provide enough detail to attribute the differences between the posted and recalculated results to a particular cause.

How should p-values be read?

A p-value describes how compatible the data are with a specified null model, under the assumptions of the analysis. It is not the probability that the null hypothesis is true, nor does it measure the size or importance of a difference. The recalculated p-values are unadjusted. The registry reports p-values for the sponsor’s ANCOVA analyses, but the multiplicity procedure, if any, is not reported.

General statistical explanation: a result not crossing a chosen significance threshold does not establish that two treatments are equivalent. Evidence about possible differences should also be read through the estimate and confidence interval, alongside the endpoint’s meaning and limitations.

What is the role of the confidence interval?

A confidence interval gives a range of values reasonably compatible with the data and the method used to calculate it. The sponsor-reported intervals for both comparisons include zero. This means they do not rule out no difference at the stated confidence level, while also allowing values on both sides of zero. A wide interval indicates that materially different contrasts remain compatible with the data; the clinical importance of any value within an interval is not defined in the registry record.

General statistical explanation: interval coverage depends on the analysis assumptions and method. An interval from a model-based analysis and one from an approximate unadjusted calculation can differ because they do not necessarily use the same model or standard error.

What do the planning illustrations represent?

The sample-size illustrations use the observed effect as a reference and consider planning for 100%, 75%, and 50% of that observed effect. Their stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. They are planning illustrations rather than results from the trial’s original design process.

General statistical explanation: smaller effects usually require more participants to detect with a given target power, because the expected separation between groups is harder to distinguish from random variation. The 80% and 90% columns express different target probabilities of detecting the specified effect under the stated planning assumptions, if that effect and the assumptions hold. These calculations are not observed power. The original design assumptions are not reported in the registry record.

10. Confidence Intervals and Precision

The sponsor reported a 95% confidence interval from -0.19 to 0.31 for Test Product 1 versus Reference Product 1. For Test Product 2 versus Reference Product 2, the reported 95% confidence interval was from -0.33 to 0.18. Each interval includes zero and spans values on both sides of zero. Thus the posted estimates do not isolate a single direction of difference with high precision.

General statistical explanation: a confidence interval represents uncertainty around an estimate under the assumptions of the analysis. Its width reflects both the amount of information and the variability captured by the method. An interval that includes zero does not prove there is no difference; it indicates that zero remains compatible with the data under that method. The endpoints also show a range of other compatible values, whose practical importance cannot be judged without a prespecified meaningful-difference threshold.

The unadjusted recalculations also produce intervals that include zero for each of the three comparisons against Reference Product 1. The recalculated point estimates are 0.06, -0.09, and -0.02. Their intervals arise from an approximate calculation using summary data and should not be confused with the sponsor’s ANCOVA intervals. The recalculated interval endpoints are not reported because the sponsor-reported intervals provide the registry’s stated 95% intervals for its two model-based contrasts.

The arm-level SEs range from 0.09 to 0.091, but precision for a between-arm contrast is not determined by those SEs alone; it also depends on the contrast and analysis method. The sample sizes associated with the primary outcome were 31, 31, 30, and 31. These counts and the interval spans help frame the limited precision of the comparisons, but do not by themselves establish whether any difference would be meaningful.

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 illustrations are planning scenarios based on the observed effects, not the trial’s original design calculations. For these continuous-outcome comparisons, the listed figures are participants per arm, not total event counts. The stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The illustrations show planning for 100%, 75%, and 50% of the observed effect.

The 80% power column gives the number of participants per arm estimated to provide an 80% chance of detecting the specified effect under those planning assumptions. The 90% power column uses a higher target chance of detection, and therefore generally calls for more participants per arm. These percentages describe target power in a hypothetical design; they are not a measure of how much power the completed trial actually had. This is not observed power.

For each contrast, the scenarios that plan for a smaller fraction of the observed effect require more participants per arm than scenarios planning for the full observed effect. This reflects a general property of study planning: smaller differences are harder to distinguish from random variation when other assumptions are held fixed. The values depend on the observed effect used as the reference, so they are not universal requirements for future studies.

The registry does not report the trial’s own original sample-size assumptions or justification. The illustrations should therefore be read as conditional planning aids, not as evidence that the trial was designed around those participant counts or that it met a particular target power.

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, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = 0.060; pooled standard deviation σ = 0.500.
2. n = 2 × (1.96 + 0.842)² × 0.500² / 0.060² = 1,089.2, rounded up to 1,090 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 <- 0.06                      # observed difference in means
sigma <- 0.499787581997236                     # 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(3267511)
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 = 1,090 (80% power), 1,459 (90% power)
 75% of observed effect: n per arm = 1,937 (80% power), 2,593 (90% power)
 50% of observed effect: n per arm = 4,357 (80% power), 5,833 (90% power)
power.t.test: 1090.2 
Simulated power at n = 1,090 per arm: 0.797 (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.

13. Analyses Reported by the Sponsor

The registry reports two sponsor analyses using ANCOVA. Test Product 1 versus Reference Product 1 had an estimated difference of 0.06, with a 95% confidence interval from -0.19 to 0.31. Test Product 2 versus Reference Product 2 had an estimated difference of -0.07, with a 95% confidence interval from -0.33 to 0.18. Neither reported p-value is below 0.05.

The unadjusted recalculations use the arm summaries rather than the sponsor’s ANCOVA model. They compare each listed arm with Reference Product 1. The recalculated Test Product 1 estimate is 0.06; the Test Product 2 estimate is -0.09; and the Reference Product 2 estimate is -0.02. Consequently, only the Test Product 1 recalculation matches one of the sponsor’s pairwise contrasts. The Test Product 2 results use different reference arms and should not be treated as direct replications of each other.

The registry marks no discrepancy between reported and recalculated values. Even so, the calculation methods and contrasts must be kept distinct. The sponsor’s ANCOVA results are the registry’s reported model-based analyses; the unadjusted results are approximate checks from summary statistics and do not replace the sponsor’s analysis.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists one primary outcome and two secondary outcomes. It also records four analyses. The secondary outcomes concern change from baseline in Overall MLSI after 8 weeks for Test Product 1 versus Reference Product 1 and Test Product 2 versus Reference Product 2. Two sponsor ANCOVA comparisons are reported. The registry does not explain how the four analyses relate to the listed count of outcome measures or whether additional analyses were conducted.

Because several treatment contrasts and outcomes can be examined, multiplicity is relevant: repeated testing can increase the chance of at least one apparently unusual result. General statistical explanation: prespecified adjustments or a testing hierarchy can address this issue, but the choice depends on the study’s analysis plan. The multiplicity strategy, if any, is not reported in the registry record. The posted sponsor p-values therefore cannot be described as adjusted or unadjusted unless the record says so; that status is not reported. The recalculated p-values are explicitly unadjusted.

The primary-outcome population is described as an Intent-to-Treat population of 123 participants who were randomized, received study treatment at least once, and had at least one post-baseline efficacy assessment. This definition identifies who qualified for the posted population, but it does not explain how missing follow-up values were handled or whether any imputation or sensitivity analysis was used.

The registry record does not report the number of participants with missing endpoint data, reasons for missingness, a missing-data strategy, or results from alternative analysis populations. It does not report whether interim analyses were planned or performed. The exact ANCOVA covariates and other model details are also not reported. These omissions limit independent assessment of the analysis choices and how robust the results are to missing data or alternative specifications.

15. Safety Results

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

Deaths

Other (non-serious) adverse events

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

Most frequent non-serious adverse event terms

The posted serious adverse event counts were zero in every arm. The numbers at risk were 31 for Test Product 1, 31 for Test Product 2, 30 for Reference Product 1, and 31 for Reference Product 2. The registry also records zero deaths in each arm. No serious adverse event terms are listed.

These figures describe the recorded counts during the study; they do not establish that no events of any kind occurred. The registry separately reports other adverse events affecting 3 participants in Test Product 1, 1 in Test Product 2, 2 in Reference Product 1, and 0 in Reference Product 2. Those are recorded as other adverse events, not serious adverse events.

General statistical explanation: an observed count of zero is a statement about the events recorded in the participants at risk during the study. It does not mean the underlying risk is zero, and small groups provide limited information about uncommon events. The registry record does not provide further details about event terms, severity, timing, or causal assessment for the other adverse events. These counts are descriptive and should not be read as a comparative safety conclusion.

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

The results describe changes in a dental stain score over 8 weeks among participants in a randomized, double-masked, parallel-group study. The four arm-level mean changes were negative, indicating lower Overall MLSI scores at follow-up on average. The score direction defines 0 as best and 9 as worst, so decreases are consistent with reduced stain scores. The estimates alone do not establish why scores changed or whether one product caused a larger change than another.

The sponsor’s two reported 95% confidence intervals include zero, and neither reported p-value is below 0.05. Those comparisons do not provide a statistically clear separation under the reported analyses. They also do not demonstrate that the products are equivalent. Equivalence requires an appropriate design and a prespecified margin, neither of which is reported in the registry record.

The unadjusted recalculations offer additional comparisons from posted summary statistics, but they are approximate and do not reproduce the ANCOVA analyses. Their comparison of Test Product 2 is against Reference Product 1, unlike the sponsor’s Test Product 2 comparison, which is against Reference Product 2. Estimates from different contrasts should not be combined into a single ranking.

The record does not state what size of change would matter clinically, nor does it report sufficient methodological detail to evaluate all modeling and missing-data choices. The findings therefore characterize the recorded scores and their statistical uncertainty, rather than establishing the practical importance of a difference. The safety counts likewise describe recorded events in this study and do not settle questions about uncommon events or longer-term use.

17. Why This Trial Matters Statistically

This study is statistically informative because it frames a multi-arm comparison around a defined continuous outcome: change in Overall MLSI. The outcome combines stain area and intensity into a score with a stated direction, which makes the sign of the arm-level changes interpretable. Reporting both arm means and SEs gives readers information about the estimated changes and their precision.

The study also illustrates why treatment contrasts must be specified precisely. The sponsor’s ANCOVA analyses compare each test product with a corresponding reference product, while the simple recalculations compare three arms with Reference Product 1. A numerical estimate has meaning only in relation to the two groups being contrasted and the analysis used to obtain it. Treating unlike comparisons as if they were the same could lead to an incorrect interpretation.

Confidence intervals add information beyond a binary significance label. The sponsor’s intervals include zero and allow values on either side, making the uncertainty in the pairwise estimates visible. The registry’s planning illustrations further demonstrate, as a general planning principle, that smaller target effects require larger sample sizes under otherwise fixed assumptions. Those illustrations are not evidence of the study’s original planning process or its observed power.

Finally, the record makes clear that an endpoint result is only one part of statistical interpretation. The analysis population is defined, but important details about covariate adjustment, missing data, multiplicity, and original sample-size planning are not reported. Those gaps limit how fully readers can audit the analysis, while the posted estimates still allow a careful account of what was measured and how uncertain the comparisons are.

18. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.

The primary outcome was assessed at baseline and Week 8, but the registry does not provide individual participant results, distributions, or additional follow-up estimates. Arm-level means and SEs cannot reveal the full pattern of participant changes or how results vary across assessable teeth. The registry does not report the clinical importance of a score difference or a threshold for interpreting a change as meaningful.

The analysis description is incomplete. Although the sponsor reports ANCOVA, the covariates and model specification are not reported. The recalculations rely on summary data and an approximate pooled spread, so they cannot replace an analysis of participant-level data. The two sponsor-reported contrasts and the recalculated contrasts are not all identical, especially for Test Product 2.

The registry does not report the original sample-size rationale, the handling of missing data, or a multiplicity plan. The Intent-to-Treat population definition requires a post-baseline assessment, and the record does not detail participants who lacked one or how missing observations affected the analyses. It also does not report assessor reliability or details of masking implementation.

The study involved 123 enrolled participants across four arms, with outcome counts of 30 or 31 per arm. Such counts offer limited information about uncommon events, and the registry provides only summary adverse-event counts rather than further event descriptions. The study’s 8-week treatment period does not provide longer-term outcome information. These limitations constrain the precision and scope of conclusions that can be drawn from the registry results.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: A Study to Investigate the Stain and Plaque Removal Capability of Two Experimental Potassium Nitrate Dentifrices — NCT03267511.
• Registry record last updated 2019-01-08; status last verified 2019-01.
• Results first posted 2019-01-08.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

22. Record Summary

NCT03267511 is a completed randomized, double-masked, parallel-group Phase 2 study of four potassium nitrate dentifrices in healthy subjects with a propensity for extrinsic dental stain. The study enrolled 123 participants and assessed change from baseline in Overall MLSI at Week 8 after twice-daily brushing.

All four arm-level mean changes were negative. The sponsor reported ANCOVA comparisons of Test Product 1 with Reference Product 1 and Test Product 2 with Reference Product 2; both 95% confidence intervals included zero. Unadjusted recalculations from summary statistics use different contrasts for some arms and are approximate.

The registry records zero serious adverse events and zero deaths in each arm. Details of the original sample-size justification, multiplicity, missing-data methods, and full ANCOVA specification are not reported in the registry record.