Evaluation of Efficacy of Experimental Gel to Foam Dentifrices in Dental Erosion: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Evaluation of Efficacy of Experimental Gel to Foam Dentifrices in Dental Erosion (NCT01657903), a randomized na study. The primary outcome is Relative Erosion Resistance (RER) of Enamel Specimens Post 4 Hours of Treatment Exposure.

2. Clinical Question

3. Trial Design

This was a randomized, single-masked, crossover study, with an enrollment of 56. It was listed as completed. The registry gives a start date of 2011-11 and a primary completion date of 2012-02. The study compared three sodium fluoride/potassium nitrate toothpaste regimens with a fluoride-free potassium nitrate toothpaste using a modified in-situ model of dental erosion and remineralization.

In a crossover design, participants receive more than one treatment regimen over successive periods. This design can allow comparisons within participants, but interpreting it depends on details such as treatment sequence, period effects, and any washout procedures. Those protocol details are not reported in the registry record. The registry identifies the study as crossover but does not describe the sequence or timing of each treatment period beyond the primary endpoint timeframe.

The primary endpoint was reported as a least-squares mean with standard error. The analysis population was per protocol, and the registry notes that dropout-related differences affected participant counts across analyses. The posted arm summaries list 55, 54, 54, and 56 participants, respectively. These counts should not be treated as a single common crossover sample size for every comparison.

The record reports three sponsor analyses using ANOVA for comparisons between each sodium fluoride/potassium nitrate regimen and the fluoride-free regimen. Other aspects of the statistical plan, including any planned interim analyses, 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

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: Per protocol (PP) population: All randomized subjects who had at least one assessment of efficacy and considered unaffected by major protocol deviations, were included in analysis. Due to drop outs, there was difference in number of participants analyzed.

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

6. Primary Endpoint

The registry lists the primary outcome as Relative Erosion Resistance (RER) of Enamel Specimens Post 4 Hours of Treatment Exposure, measured over Baseline, 4 hours post treatment in each treatment period.

The primary endpoint, relative erosion resistance (RER), describes the response of enamel specimens to sequential erosive challenges. Specimens underwent a dietary erosive challenge, and indentations in the enamel were measured. A subsequent erosion challenge allowed comparison of indentation measurements at baseline, after the first challenge, and after the second challenge. The registry defines percentage RER using those three measurements. Smaller negative RER values indicate better resistance to enamel surface change under the study regimen.

This endpoint is useful for comparing treatments in a controlled in-situ model because it quantifies enamel changes following specified erosive challenges. The measurement is a continuous outcome: it can take a range of values rather than only classifying participants into categories. That makes differences in mean RER a natural summary for comparing regimens.

The outcome is measured on enamel specimens, not as a direct clinical event or a patient-reported outcome. It therefore describes the response of the specimens within the study model. It does not, by itself, establish how the regimens affect dental erosion in everyday use or other clinical outcomes.

The primary timeframe was baseline and four hours after treatment in each treatment period. The registry reports least-squares means and standard errors for the endpoint, and adjusted mean differences with confidence intervals for the sponsor's comparisons.

7. Results Posted in the Registry

• NaF/KNO3 Toothpaste 2: mean -36.53 versus -36.66 on control; difference 0.13 (95% CI -7.73 to 7.99), standardized effect d = 0.01; z-test p = 0.974.
• NaF/KNO3 Toothpaste 3: mean -36.98 versus -36.66 on control; difference -0.32 (95% CI -8.18 to 7.54), standardized effect d = -0.02; z-test p = 0.936.
• No Fluoride/KNO3 Toothpaste: mean -77.82 versus -36.66 on control; difference -41.16 (95% CI -48.95 to -33.37), standardized effect d = -1.97; z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

The registry characterizes the primary outcome as continuous and reports least-squares means with standard errors. A continuous outcome can vary across a scale, so analyses often compare average values between treatment conditions. A least-squares mean is a model-based mean adjusted for terms included in the statistical model. Which terms were included in this study's model, beyond the reported ANOVA method, is not reported in the registry record.

What does the sponsor's ANOVA compare?

The sponsor reports ANOVA analyses for three comparisons: each sodium fluoride/potassium nitrate regimen against the fluoride-free potassium nitrate regimen. For each comparison, the registry gives an adjusted mean difference, a 95% confidence interval, and a p-value. ANOVA is a general method for assessing differences in means across groups or conditions. In a crossover study, the suitability and interpretation of an ANOVA depend on how treatment, period, sequence, and participant structure are represented. The registry does not provide enough detail to reconstruct those model terms.

The adjusted mean difference is the estimated contrast between conditions after adjustment for the model terms. The registry's sponsor-reported contrasts are 41.15, 41.28, and 40.83. The posted confidence intervals are all on the positive side of zero, and the corresponding p-values are each < 0.001. The exact contrast coding and sign convention are not described in the registry record, so the estimates should be read alongside the registry's endpoint definition and the sponsor's stated comparison groups.

What does the unadjusted recalculation represent?

The recalculated comparisons use posted arm-level summary statistics to form simple unadjusted comparisons. They are not a reconstruction of the sponsor's adjusted ANOVA. The recalculation uses an approximate pooled standard deviation, and the record flags a discrepancy between the recalculated and sponsor-reported results. The sponsor's own analysis takes precedence. In particular, the posted arm summaries and a simple independent comparison do not reproduce all features of a crossover analysis.

For the three unadjusted comparisons, the registry lists mean differences of 0.13, -0.32, and -41.16, with p-values of 0.974, 0.936, and <0.001. Their confidence intervals also differ from the adjusted intervals reported by the sponsor. These unadjusted results are best treated as a separate descriptive check on the posted summary statistics, rather than as the trial's primary inferential analysis.

Why do standard errors and standard deviations differ?

A standard error describes uncertainty in an estimated mean, whereas a standard deviation describes variation among observations. The primary arm summaries give standard errors of 2.824, 2.848, 2.847, and 2.799. The recalculations use an approximate pooled standard deviation. A standard error is not itself a measure of participant-to-participant or specimen-to-specimen variability, and the crossover structure may require information about within-participant correlations to reproduce a model-based comparison. Those correlation details are not reported in the registry record.

General statistical point: in repeated-measure or crossover data, observations from the same participant are often related. Accounting for that relationship can affect standard errors and confidence intervals. A simple comparison that treats treatment groups as independent may not reflect that structure. This is one reason to distinguish the sponsor's adjusted analysis from unadjusted recalculations based only on posted summaries.

What do the confidence intervals and p-values contribute?

A confidence interval gives a range of values compatible with the data and the statistical model at the stated confidence level. It communicates both the estimated contrast and its precision. A p-value assesses how compatible the observed data are with a specified null hypothesis under model assumptions; it is not the probability that the null hypothesis is true, nor a measure of clinical importance. The sponsor reports 95% confidence intervals, while the recalculated results are separate unadjusted estimates.

General statistical point: statistical significance does not answer whether a difference matters clinically or generalizes beyond the study setting. Here, the endpoint concerns enamel specimens in a modified in-situ model, and the registry does not report a clinical threshold for an important RER difference.

What is not available for reproducing the analysis?

The registry does not report the full statistical analysis plan, model terms, treatment sequence, period effects, within-participant covariance structure, or procedures for missing observations. It also does not report the original sample-size justification or planned multiplicity procedure. Without these details, the reported ANOVA can be described but not independently reconstructed from the registry record. The available information supports reading the posted estimates in their stated context, while keeping those limitations in view.

10. Confidence Intervals and Precision

The sponsor's three adjusted mean differences are reported with 95% confidence intervals. For the comparisons against the fluoride-free regimen, the intervals are 34.42 to 47.89, 34.51 to 48.06, and 34.06 to 47.61. Each interval lies above zero, consistent with the sponsor's reported p-values of < 0.001 under the stated analysis. The intervals also show the range of adjusted differences compatible with the data and model, rather than pinpointing one exact value.

All three sponsor estimates are similar in scale, and their confidence intervals overlap. Overlap is not a formal test that the three active regimens are equivalent or identical. The registry does not report sponsor-adjusted head-to-head contrasts among the three sodium fluoride/potassium nitrate regimens, so their relative differences cannot be assessed from these sponsor comparisons alone.

The simple unadjusted recalculations have different estimates and intervals. For the comparison with NaF/KNO3 Toothpaste 2, the interval is -7.731 to 7.991; for NaF/KNO3 Toothpaste 3, it is -8.18 to 7.54; for the fluoride-free regimen, it is -48.95 to -33.37. These intervals belong to the unadjusted recalculation, not the sponsor's adjusted ANOVA. Because the record flags a discrepancy, the sponsor's analysis takes precedence.

Precision depends on the analysis model and the data structure. The registry identifies a crossover design, but the participant-level information and model details needed to verify standard errors are not reported in the registry record. The confidence intervals quantify uncertainty under the analyses that generated them; they do not resolve questions about missing data, model assumptions, or clinical relevance.

11. Planning a Similar Trial: Sample Size

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

The planning figures are participants per arm for these continuous-outcome comparisons. They are not total event counts. The registry's planning illustration assumes a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. It uses the observed effect as its starting point and considers detecting 100%, 75%, or 50% of that observed effect. These are planning assumptions for the illustration; the trial's original design assumptions are not reported in the registry record.

The 80% power column gives the estimated participants per arm for a design intended to have an 80% chance of detecting the specified effect under the planning assumptions, if that effect is truly present. The 90% power column makes the same kind of illustration for a 90% chance. A higher target power generally requires more participants for a given effect. Likewise, planning to detect a smaller effect requires more participants than planning to detect a larger effect.

The figures vary sharply by comparison because they are tied to the observed effect for that comparison. For example, planning for 100% of the observed effect in the comparison with NaF/KNO3 Toothpaste 2 gives 407,134 participants per arm for 80% power and 545,037 for 90% power. For the comparison with the fluoride-free regimen, the corresponding figures are 5 and 6. These are illustrations based on the posted effects and assumptions, not recommendations for a future study.

This is not observed power. The figures do not describe the probability that the completed trial detected an effect, and they are not the sample size used in the trial. They are prospective calculations under simplified assumptions; the crossover structure and original design rationale are not reflected in a way that can be verified from the registry record.

12. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = 0.130; pooled standard deviation σ = 20.936.
2. n = 2 × (1.96 + 0.842)² × 20.936² / 0.130² = 407,133.5, rounded up to 407,134 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 <- 0.129999999999995                      # observed difference in means
sigma <- 20.9359634167362                     # 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(1657903)
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 = 407,134 (80% power), 545,037 (90% power)
 75% of observed effect: n per arm = 723,793 (80% power), 968,954 (90% power)
 50% of observed effect: n per arm = 1,628,535 (80% power), 2,180,146 (90% power)
power.t.test: 407134.5 
Simulated power at n = 407,134 per arm: 0.801 (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 three sponsor analyses using ANOVA and adjusted mean differences. Each compares one sodium fluoride/potassium nitrate regimen with the fluoride-free potassium nitrate regimen. The sponsor estimates are 41.15, 41.28, and 40.83, with 95% confidence intervals of 34.42 to 47.89, 34.51 to 48.06, and 34.06 to 47.61. Each reported p-value is < 0.001.

The recalculated comparisons are simple unadjusted re-calculations from posted summary statistics. They do not reproduce the sponsor's adjusted analyses: their estimates and confidence intervals differ. The record explicitly flags a discrepancy, so the sponsor's own analysis takes precedence. The recalculations should not be used to replace or reinterpret the sponsor's ANOVA results.

This distinction matters because the study is identified as a crossover trial, while the recalculations use summary-statistic comparisons and do not reconstruct the participant-level model. The registry does not report enough information about model terms or within-participant relationships to independently verify the sponsor's results. Thus, the appropriate reading is to report the sponsor's adjusted findings as the trial's posted inferential analyses and treat the unadjusted recalculations as a separate, limited check.

14. Multiplicity, Missing Data and Analysis Populations

The registry reports three sponsor comparisons of sodium fluoride/potassium nitrate regimens against the fluoride-free regimen. It does not report a multiplicity adjustment or a planned procedure for controlling the chance of false-positive findings across multiple comparisons. Whether the sponsor's reported p-values were adjusted for multiplicity is not reported in the registry record.

General statistical point: when several hypotheses are tested, the chance of at least one apparently significant result can increase if each test is interpreted independently. A prespecified multiplicity strategy can address that issue. Without the registry's analysis plan, it is not possible to determine whether or how multiplicity was handled in this study. The reported p-values should therefore be interpreted as posted, without assuming an adjustment that is not documented.

The primary analysis population is described as per protocol: randomized participants with at least one efficacy assessment and no major protocol deviations considered to affect eligibility for that analysis. The registry states that dropouts caused differences in the numbers analyzed. The arm summaries list different participant counts. The exact number of observations contributing to each adjusted comparison and the reasons for each exclusion are not reported in the registry record.

The registry does not describe the methods used to handle missing outcome data, nor does it report sensitivity analyses for missingness. It also does not provide enough information to assess whether missingness may have been related to treatment or outcome. These gaps matter because analysis restricted to a per-protocol population can differ from an analysis of all randomized participants.

The crossover design raises additional analysis questions about treatment sequence, period effects, carryover, and within-participant correlation. The registry identifies the design but does not report how those features were handled in the sponsor's ANOVA. Planned interim analyses and the original sample-size justification are also not reported in the registry record. These are limitations in what can be independently assessed, not evidence that any particular procedure was or was not used.

15. Safety Results

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

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 1% reporting threshold.

Most frequent non-serious adverse event terms

The registry's serious adverse event figures are zero reported events in each of the four treatment groups. The listed numbers at risk are 55, 55, 54, and 56, respectively. The record does not list serious adverse event terms. Death counts are not reported in the registry record.

These figures describe what was posted for the study groups; they do not establish that no serious events occurred outside the reported record or that the regimens have no safety risks. The registry also gives other adverse event counts of 2, 0, 1, and 2 across the four groups, with the same group-specific numbers at risk. The record does not provide further detail about the nature or severity of those other events in the information.

The trial is a crossover study, and the safety group counts should be read in light of that design. The registry does not give additional detail about exposure duration or participant-level event attribution by treatment period. These counts are descriptive safety reporting and do not establish comparative safety.

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

The posted results concern relative erosion resistance of enamel specimens in a modified in-situ erosion and remineralization model. The registry reports adjusted comparisons of three sodium fluoride/potassium nitrate toothpaste regimens with a fluoride-free potassium nitrate regimen. Those sponsor analyses have adjusted mean differences of 41.15, 41.28, and 40.83, with 95% confidence intervals entirely above zero and p-values of < 0.001.

These results describe the endpoint under the study conditions and the sponsor's analysis. The registry defines smaller negative RER values as indicating better treatment-regimen resistance in the model. The reported adjusted contrasts are presented as estimates for specified comparison groups, but the registry does not state the contrast sign convention in detail. Interpretation should therefore retain the stated groups, endpoint definition, and reported estimates rather than extending the results to unmeasured outcomes.

The findings do not establish a clinical effect on dental erosion in routine use. The endpoint is based on enamel specimens after erosive challenges, rather than a clinical outcome measured over longer-term dental care. The registry does not report a threshold for a clinically meaningful difference in RER. Statistical significance alone does not show that an effect is important to patients.

The record also does not report sponsor-adjusted head-to-head comparisons among the three sodium fluoride/potassium nitrate regimens. The comparisons against the fluoride-free regimen therefore do not establish how the three sodium fluoride/potassium nitrate regimens rank against one another. Further, the registry provides limited detail about missing data, crossover model terms, and multiplicity handling, which restricts independent assessment of the analysis.

The unadjusted recalculations differ from the sponsor's adjusted results, and the record flags a discrepancy. The sponsor's own analysis takes precedence. The recalculations should be viewed as limited summary-statistic checks, not as an alternative primary analysis or grounds for claims beyond the posted adjusted findings.

17. Why This Trial Matters Statistically

This trial illustrates why the design and analysis must be read together. A crossover design allows participants to receive multiple regimens, but treatment observations from the same participant may be related. A model that accounts for that structure can produce different estimates and uncertainty than a simple comparison of arm-level summaries. The registry identifies the crossover design and reports sponsor ANOVA analyses, but does not provide the model details needed to reproduce them.

It also demonstrates why adjusted and unadjusted estimates should not be conflated. The sponsor's comparisons are adjusted mean differences, while the recalculations are simple unadjusted estimates from posted summary statistics. Their disagreement is flagged in the record, and the sponsor's own analysis takes precedence. Reporting that distinction avoids treating a simplified recalculation as if it were the trial's planned analysis.

The endpoint itself is statistically informative but bounded in scope. RER quantifies specimen response to erosive challenges, allowing continuous comparisons within a controlled in-situ model. It does not directly answer questions about clinical outcomes or real-world use. Statistical interpretation must keep the measurement scale and model context in view.

Finally, the registry provides evidence of between-regimen differences in the posted adjusted comparisons but limited information about multiplicity, missing-data handling, and the crossover model. Those reporting gaps affect how fully an outside reader can audit assumptions and precision. They do not erase the posted results, but they define the limits of what can be concluded from the registry record alone.

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 main endpoint is measured on enamel specimens in a modified in-situ model. The registry does not report a clinical threshold for an important RER difference, and the outcome is not itself a direct measure of longer-term clinical dental outcomes. Generalizing the specimen-based comparisons beyond this model requires evidence not reported in the registry record.

The study is identified as crossover, but the registry does not describe treatment sequence, period effects, washout procedures, or how the sponsor's ANOVA handled within-participant dependence. These details are important for understanding the analysis and assessing whether the model reflects the design. The registry also does not provide participant-level data needed to reproduce the adjusted estimates.

The primary analysis used a per-protocol population, and the registry notes that dropout led to differences in the numbers analyzed. The exact missing-data procedures, reasons for participant exclusion, and sensitivity analyses are not reported in the registry record. The original sample-size rationale and any planned interim analyses are also not reported.

Multiplicity handling is not described despite three sponsor comparisons against the fluoride-free regimen. In addition, no sponsor-adjusted head-to-head comparisons among the three sodium fluoride/potassium nitrate regimens are posted. The discrepancy between the sponsor's adjusted results and the simple unadjusted recalculations further underscores that only the sponsor analysis should be treated as the trial's posted inferential result.

Safety reporting is limited in the registry record. Serious adverse event counts are listed as zero for each group, but event terms are not listed and death counts are not reported. These limitations constrain interpretation of the safety information and the broader scope of the findings.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Evaluation of Efficacy of Experimental Gel to Foam Dentifrices in Dental Erosion — NCT01657903.
• Registry record last updated 2015-01-26; status last verified 2014-07.
• Results first posted 2015-01-26.
• 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

This randomized, single-masked crossover study enrolled 56 participants and evaluated three sodium fluoride/potassium nitrate toothpaste regimens against a fluoride-free potassium nitrate regimen. The primary endpoint was relative erosion resistance of enamel specimens after treatment exposure in a modified in-situ erosion and remineralization model.

The sponsor reported three adjusted ANOVA comparisons, each with a 95% confidence interval above zero and p < 0.001. Simple unadjusted recalculations differ, and the sponsor's own analysis takes precedence. The registry reports zero serious adverse events in each group, while death counts are not reported in the registry record.

Interpretation is limited by the specimen-based endpoint and by missing registry detail on crossover model terms, missing-data handling, multiplicity, and the original sample-size rationale.