Clinical Efficacy of a Toothpaste on Hypersensitivity Reduction: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Clinical Efficacy of a Toothpaste on Hypersensitivity Reduction (NCT01040169), a randomized na study. The primary outcome is Tooth Hypersensitity to Touch Stimuli (Tactile).

2. Clinical Question

The posted results report mean tactile scores of 10.83 for Nupro C and 10.63 for ProClude. The unadjusted comparison calculated from the posted group summaries estimates a mean difference of -0.2 for ProClude relative to Nupro C. Its confidence interval crosses zero, so the summary statistics do not establish a clear difference between the group means. The sponsor’s reported ANCOVA result is a separate analysis and reports a p value of 0.05; its estimated effect and confidence interval are not reported in the registry record.

This question concerns a measured sensitivity response at the specified assessment, not a broader claim about symptoms, daily function, or longer-term outcomes. The registry record describes the trial as randomized, double masked, and parallel, with 79 participants enrolled. It does not report enough detail to establish how the primary analysis handled all participants or whether the analysis adjusted for particular baseline measurements.

3. Trial Design

The registry record describes a randomized, double-masked, parallel trial of two prophylaxis pastes. The record lists 79 participants enrolled. The posted primary outcome results include 35 participants in the Nupro C Prophylaxis Paste arm and 44 in the ProClude Prophylaxis Paste arm. The record marks the trial as completed and gives the primary completion month as 2008-08.

The paste descriptions appear in two places in the record. The arm descriptions identify Nupro C as fluoride free and ProClude as arginine, while the intervention listings use the names Mint Prophy paste - Fluoride free and Arginine/Calcium Carbonate. Both interventions are classified as devices in the record. The record does not explain these naming differences or provide further formulation details, so the arm labels are used when discussing the posted outcome results.

The primary outcome is titled “Tooth Hypersensitity to Touch Stimuli (Tactile)” in the record. It is a continuous measure reported as a mean with standard deviation, assessed at 12 weeks (Final). The recorded measurement is force in grams applied before the participant reports pain. The outcome description says the force is applied using an electronic force-sensing probe and that a lower score indicates higher hypersensitivity.

The registry record names ANCOVA as the sponsor’s analysis method and reports a p value of 0.05 for the two groups. It does not report an adjusted effect estimate or confidence interval for that analysis. Details such as the covariates in the model, the analysis population, and the original sample-size justification are not reported in the registry record. The posted numerical group summaries support a separate unadjusted comparison, but that calculation does not replace the sponsor’s analysis.

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:

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 Tooth Hypersensitity to Touch Stimuli (Tactile), measured over 12 weeks (Final).

The primary endpoint measures tactile tooth hypersensitivity as force applied before a participant reports pain. The record describes measurement with an electronic force-sensing probe, with force applied to a hypersensitive tooth until pain is felt. The resulting value is recorded in grams of force. Although the outcome unit is displayed as “Units on a scale,” its description identifies grams of force as the measurement unit.

The direction of the scale matters for interpretation. A higher force score means that more force was required before pain was reported; according to the record, a lower score indicates higher hypersensitivity. Therefore, a group mean cannot be interpreted without knowing this direction. The posted means are 10.83 for Nupro C and 10.63 for ProClude, so the observed group averages are close on this scale, with the Nupro C mean slightly higher.

A continuous outcome is useful because it preserves the measured force values rather than reducing them to categories. Reporting a mean summarizes the group’s average score, while the standard deviation describes the spread of individual scores around that mean. Neither summary alone describes every participant’s response. The reported standard deviations are 1.89 for Nupro C and 2.11 for ProClude.

The endpoint is specific to tactile response at the final assessment at 12 weeks. The registry record does not establish how well a change on this scale corresponds to a meaningful change in everyday experience, and it does not report a threshold for an important difference. The results should therefore be read as a comparison on the recorded probe measure, rather than as a complete account of participants’ symptoms or experience.

7. Results Posted in the Registry

• ProClude Prophylaxis Paste: mean 10.63 versus 10.83 on control; difference -0.20 (95% CI -1.08 to 0.68), standardized effect d = -0.10; z-test p = 0.657.

8. Statistical Interpretation

9. Statistical Methods Explained

The registry record presents a continuous primary outcome as a mean and standard deviation for each arm. A mean is the arithmetic average of observed scores in a group. A standard deviation describes how dispersed those scores are around the mean. Together, these summaries give a view of the group averages and within-group variability, but they do not show the distribution of individual measurements or reveal whether unusual values affected the mean.

What does the unadjusted comparison estimate?

The recalculated comparison is an unadjusted difference between the two posted means. It takes the ProClude mean relative to the Nupro C mean, giving an estimate of -0.2. With this direction of subtraction, a negative value means that the ProClude group’s posted mean is lower. Since a lower score indicates greater hypersensitivity according to the outcome description, the direction of the estimate should not be reversed when describing the scale. The estimate is a comparison of group averages, not a statement about each participant.

The recalculation uses the group sample sizes and standard deviations as well as their means. It does not adjust for baseline outcome values or other covariates. In general, adjustment can account for measured characteristics included in a model and can produce an estimate different from an unadjusted comparison. Whether such adjustment is appropriate and how it affects the result depend on the planned analysis and the data. The registry record reports ANCOVA for the sponsor’s analysis but does not identify its covariates or provide the adjusted estimate.

What does a confidence interval express?

A confidence interval gives a range of effect estimates that are reasonably compatible with the data and the calculation’s assumptions. It is not a range containing a fixed proportion of individual participant scores, and it does not assign a probability to the true effect after the data have been observed. A wider interval indicates less precision than a narrower interval on the same scale. Here, the recalculated interval crosses zero, meaning that the posted summaries do not rule out no difference in the unadjusted group means. Its span also allows effects in either direction, so the estimate should be treated as uncertain.

Why are the two p values different?

The unadjusted recalculation reports p = 0.657, while the registry record reports p = 0.05 for ANCOVA. A p value describes how surprising data at least as incompatible with a null hypothesis would be under the model assumptions if that null hypothesis were true. It is not the probability that the null hypothesis is true, and it does not measure the magnitude or practical importance of an effect.

Different analysis methods can produce different estimates and p values, particularly when one analysis adjusts for covariates and the other does not. The registry record does not give enough information to determine why the sponsor’s result differs from the recalculation. It does not report the ANCOVA parameter estimate, confidence interval, covariates, or analysis population. The discrepancy is therefore important: the recalculated result is a transparent comparison from the posted summaries, but it is not a reconstruction of the sponsor’s ANCOVA. The sponsor’s own analysis takes precedence when reporting that analysis.

Why does variability matter?

In general, the precision of a mean comparison depends on the amount of variation in the outcome and the number of observations contributing to each group. Greater variability makes it harder to distinguish a group difference from random variation. This is one reason that means should be read alongside standard deviations and confidence intervals, rather than in isolation. The posted standard deviations, 1.89 and 2.11, show that participant scores varied around both group means.

General statistical models may also rely on assumptions about the outcome distribution, independence of observations, and how variability is represented. The registry record does not report diagnostic checks or detailed model assumptions for the sponsor’s ANCOVA. The endpoint is measured on a continuous force scale, but the record does not include distributions or participant-level data that would allow a reader to examine those assumptions independently.

What can be inferred from the analysis?

The unadjusted estimate and interval describe the posted summary data under the recalculation method. The sponsor’s reported p value describes a different analysis for which the effect estimate is not posted. Neither result alone establishes clinical importance. In general, statistical evidence, effect magnitude, precision, and relevance to participants are distinct considerations. The registry record provides the primary measure and the two group summaries, but does not report an important-difference threshold or further outcome context.

The planning calculations associated with the unadjusted effect are prospective illustrations of sample sizes under stated assumptions. They are not evidence that the original trial was designed that way, and they do not represent the probability that this completed trial detected an effect. The registry record does not report the trial’s original sample-size justification or its detailed statistical analysis plan. These distinctions keep the posted result, sponsor analysis, and planning illustration from being treated as interchangeable.

10. Confidence Intervals and Precision

The unadjusted recalculated mean difference is -0.2, with a confidence interval from -1.084 to an upper bound of 0.684 in the calculation. The interval crosses zero, so the posted summaries are compatible with no unadjusted mean difference as well as with differences in either direction. The interval is not concentrated entirely on one side of zero.

The width of an interval reflects uncertainty in the estimate under the analysis assumptions. In general, more precise estimates have narrower intervals, while less precise estimates have wider intervals. Here the interval covers values below and above zero. This means that the point estimate alone should not be read as a definitive separation between the groups. The observed means are close, but the interval also cautions against treating the point estimate as the only plausible value.

This interval belongs to the unadjusted recalculation, not the sponsor’s ANCOVA. The sponsor analysis has a reported p value of 0.05, but its effect estimate and confidence interval are not reported in the registry record. The recalculated interval therefore cannot be used to describe the precision of the adjusted result, and the sponsor’s p value cannot be used to infer an unreported confidence interval.

Precision is also not the same as clinical importance. The registry record does not give a threshold for a meaningful difference on the force scale, nor does it explain how a change in probe-measured force relates to participants’ experience. Without such context, the interval can be interpreted statistically but not classified as clinically important or unimportant. The result is best read as an uncertain estimate on the specified tactile measure, rather than as proof of equivalence or of a meaningful difference.

11. Planning a Similar Trial: Sample Size

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

The sample-size table and curve are planning illustrations based on the observed unadjusted effect, not the trial’s original design calculations. The figures are participants per arm, not total events. The stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The planning effect is set to the listed fraction of the observed effect.

The 80% power column shows the number of participants per arm that the planning calculation estimates would be needed to have an 80% chance of detecting the specified effect under those assumptions. The 90% power column uses a higher probability of detection and therefore calls for more participants per arm for the same effect. These are planning quantities, not results observed in the completed trial. This is not observed power.

The table considers planning for 100%, 75%, and 50% of the observed effect. As the effect to be detected becomes smaller, it becomes harder to distinguish it from random variation, so the required number of participants per arm rises. The table displays this pattern across both power targets. The plotted curve gives a visual view of how the planning requirement changes with the assumed effect size; it should be read using the same assumptions as the table.

These calculations inherit the uncertainty of the observed effect used to construct them. They are not a sample-size recommendation for another study and do not establish the design rationale for this trial. The registry record does not report the original sample-size justification, the trial’s intended target effect, or its original power calculation. The planning figures should therefore be kept separate from the trial’s actual enrollment and from the sponsor’s ANCOVA result.

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 = -0.200; pooled standard deviation σ = 2.016.
2. n = 2 × (1.96 + 0.842)² × 2.016² / -0.200² = 1,594.7, rounded up to 1,595 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 <- -0.199999999999999                      # observed difference in means
sigma <- 2.01581957809437                     # 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(1040169)
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 = 1,595 (80% power), 2,135 (90% power)
 75% of observed effect: n per arm = 2,836 (80% power), 3,796 (90% power)
 50% of observed effect: n per arm = 6,379 (80% power), 8,540 (90% power)
power.t.test: 1595.7 
Simulated power at n = 1,595 per arm: 0.802 (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 record reports that the sponsor compared the two groups using ANCOVA and gives a p value of 0.05. It does not report an adjusted mean difference, confidence interval, model covariates, or further detail that would allow the analysis to be reproduced. The sponsor result must therefore be described on its own terms: as the reported p value from an ANCOVA, without an effect-size estimate or precision interval in the record.

The separate recalculation uses the posted arm means, standard deviations, and sample sizes to estimate an unadjusted mean difference of -0.2, with p = 0.657. It is not an ANCOVA and does not reproduce the sponsor’s analysis. Adjustment can change an estimate or its uncertainty, but the registry record does not report enough information to determine why the results differ in this case.

Because the record flags a discrepancy, the sponsor’s own analysis takes precedence when stating the sponsor’s result. That precedence does not make the missing adjusted estimate available, nor does it make the unadjusted calculation equivalent to the sponsor analysis. Readers should keep the reported ANCOVA p value distinct from the recalculated unadjusted comparison and avoid treating either as a complete account of the other.

14. Multiplicity, Missing Data and Analysis Populations

The registry record lists two outcome measures and two analyses, but it posts no secondary outcome results. The primary endpoint is identifiable as the tactile response at the final assessment at 12 weeks. The record does not explain the full relationship between the listed analyses and outcomes, or provide a statistical analysis plan detailing which comparisons were primary, secondary, or exploratory.

Multiplicity arises when several outcomes, time points, or statistical comparisons are examined. In general, making more comparisons can increase the chance of at least one apparently unusual result arising by chance. Methods such as prespecifying a primary comparison or adjusting for multiple testing can address this issue, but the registry record does not report whether any multiplicity strategy was planned or used. No adjustment should be assumed from the listed p value alone.

The record does not report how missing outcome measurements were handled, how many participants lacked the primary endpoint, or whether the analysis used all randomized participants. The arm counts shown with the results do not establish the analysis population or explain whether any enrolled participants were excluded. It also does not report imputation, sensitivity analyses, or reasons for missing measurements. The effect of missing data on the result therefore cannot be assessed from the registry record.

Details of the sponsor’s ANCOVA are also limited. The covariates, model specification, handling of baseline measurements, and analysis population are not reported in the registry record. These details matter because the adjusted estimate and its uncertainty depend on the model and the data included. The record does not provide participant-level data or model diagnostics for independent evaluation.

These reporting gaps do not establish that the analysis was inappropriate; they limit what can be verified from the record. The posted primary summaries and recalculation are interpretable as an unadjusted comparison, while the sponsor’s reported ANCOVA p value cannot be fully evaluated without its estimate, uncertainty, and analysis details.

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 0% reporting threshold.

The serious adverse event figures show 0 affected participants among 35 at risk in the Nupro C Prophylaxis Paste group and 0 among 44 at risk in the ProClude Prophylaxis Paste group. The record also lists 0 participants with other adverse events among 35 at risk in Nupro C and 0 among 44 at risk in ProClude. These are the counts posted in the registry record for the groups shown.

A zero count in the posted results means that no affected participants are listed for that category in the record; it does not establish that an event was impossible or that risk was absent. The record does not provide further detail about the adverse-event collection process, observation duration for safety, severity definitions, or whether the counts reflect all participants who received an intervention.

Deaths are shown as null rather than as a numeric count. That means the death figure is not reported in the registry record; it should not be interpreted as a report of zero deaths. The record lists no serious adverse-event terms, but this does not provide a detailed safety profile beyond the posted counts. These data describe what is recorded and do not support broader conclusions about comparative safety.

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

The posted results describe average tactile scores at the final assessment at 12 weeks. Nupro C has a mean of 10.83 and ProClude has a mean of 10.63. On the scale described in the record, a higher value corresponds to more force before pain is reported and a lower value to greater hypersensitivity. The difference between the means is summarized by an unadjusted estimate of -0.2 for ProClude relative to Nupro C.

The recalculated confidence interval crosses zero, and the recalculated p value is 0.657. This means the summary-data comparison does not establish a clear unadjusted difference between the group means. It does not prove that the pastes have identical effects, that the groups are equivalent, or that any possible difference is unimportant. The record gives no equivalence margin or threshold for a meaningful difference on the force scale.

The registry record separately reports an ANCOVA p value of 0.05. Because it does not post the adjusted effect estimate or confidence interval, the size and precision of the sponsor’s adjusted result cannot be described from the record. The unadjusted recalculation is not a substitute for that analysis. With the discrepancy flagged, the sponsor’s own analysis takes precedence as the sponsor-reported result, while the recalculation remains a separate analysis of the posted summaries.

The outcome is a probe-based tactile measurement, not a complete measure of the participants’ overall experience. The record does not report additional context such as an important-difference threshold, other symptom outcomes, or secondary outcome results. It also does not provide enough information to assess missing data or the analysis population. The result should therefore be confined to the posted comparison on this endpoint, rather than extended to claims about broader benefit, lack of benefit, or clinical importance.

The safety record lists no affected participants in the posted serious or other adverse-event counts for either arm, while deaths are not reported. These entries are limited to the information recorded and cannot establish that there was no risk. Overall, the data permit a description of group means and the sponsor’s reported analysis, but leave important questions about effect magnitude, precision, analysis details, and clinical relevance unresolved.

17. Why This Trial Matters Statistically

This trial illustrates why the size and precision of an estimated effect matter alongside a p value. The posted means are close, and the unadjusted mean difference is -0.2. Its confidence interval crosses zero, while the sponsor’s ANCOVA p value is reported as 0.05. These results come from different analyses and cannot be treated as interchangeable. A p value alone does not show the magnitude of a difference or how precisely that difference has been estimated.

The record also highlights the value of complete reporting. An adjusted estimate and confidence interval would allow readers to understand the sponsor’s ANCOVA in the outcome’s measurement units. Reporting the model details, analysis population, missing-data handling, and any multiplicity strategy would further support evaluation. Their absence does not show that these procedures were not used; it means they are not reported in the registry record.

The primary endpoint provides a direct, quantitative measurement of force before pain is felt, and its direction is explicitly described. That direction is essential: lower scores correspond to greater hypersensitivity. Clear outcome definitions help prevent a numerical difference from being described in the wrong direction. At the same time, a measurement’s numerical scale does not by itself show whether a difference matters to participants.

Finally, the sample-size illustrations show the general planning consequence of targeting smaller effects: more participants per arm are needed under the stated assumptions. They are not evidence about the trial’s original design rationale. Read together, the endpoint, group summaries, sponsor result, and reporting gaps make this record useful for distinguishing what a trial result says from what remains uncertain.

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 result is reported as group means and standard deviations without participant-level data or a distribution plot in the registry record. These summaries cannot show whether the measurements were skewed, whether outliers influenced the means, or how responses varied across participants. They also do not describe change from baseline.

The intervention names are not fully consistent across the record. The arm descriptions call the products Nupro C Prophylaxis Paste and ProClude Prophylaxis Paste, while the intervention listings use Mint Prophy paste - Fluoride free and Arginine/Calcium Carbonate. The arm descriptions identify the former as fluoride free and the latter as arginine, but the registry record does not explain the naming differences or provide further formulation details.

The sponsor’s ANCOVA is reported without its effect estimate, confidence interval, covariates, or analysis population. This prevents independent interpretation of the size and precision of the adjusted effect. The unadjusted recalculation is based only on the posted summaries and cannot resolve the discrepancy.

The registry record does not report the original sample-size justification, analysis plan, missing-data procedures, multiplicity strategy, or number of missing primary outcome measurements. It also does not report a threshold for a clinically meaningful change on the tactile force measure. The record lists two outcome measures and two analyses but posts no secondary outcome results.

Safety reporting is similarly limited to the displayed counts. The record gives no further context about adverse-event collection or follow-up, and the death fields are not reported as numeric counts. These limitations restrict interpretation to the posted outcomes and do not establish that unreported procedures or data were absent.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Clinical Efficacy of a Toothpaste on Hypersensitivity Reduction — NCT01040169.
• Registry record last updated 2013-12-10; status last verified 2013-11.
• Results first posted 2009-12-29.
• 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 completed randomized, double-masked, parallel trial enrolled 79 participants and compared Nupro C Prophylaxis Paste with ProClude Prophylaxis Paste. The primary outcome was tactile tooth hypersensitivity measured by force before pain was reported, at 12 weeks (Final).

The posted means were 10.83 for Nupro C and 10.63 for ProClude. The unadjusted recalculation estimates a mean difference of -0.2, with a confidence interval crossing zero and p = 0.657. The sponsor’s reported ANCOVA p value is 0.05, but its adjusted estimate and confidence interval are not reported in the registry record. Given the flagged discrepancy, the sponsor’s own analysis takes precedence as the sponsor-reported result.

The record lists zero affected participants in the posted serious and other adverse-event counts for both groups; deaths are not reported. Original design assumptions, analysis details, missing-data handling, and secondary outcome results are not reported in the registry record.