Effects of Foot Strengthening on the Incidence of Injuries in Long Distance Runners: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Effects of Foot Strengthening on the Incidence of Injuries in Long Distance Runners (NCT02306148), a randomized na study. The primary outcome is Number of Participants With Running Related Lower Limb Injuries.

2. Clinical Question

3. Trial Design

The registry record describes a randomized, single-masked, parallel-group trial. Participants were assigned to foot and ankle strengthening or a control condition. The identity of the party or parties who were masked is not reported in the registry record, so the masking description does not establish whether participants, outcome assessors, or other trial personnel were unaware of group assignment.

Enrollment was 118. The record lists 61 participants in the control group and 57 in the strengthening group for the primary outcome. The intervention combined physiotherapist-led training over 2 months with home exercise under training software supervision. Both groups were instructed to continue running as usual; the control group practiced a 15 seconds isometric lower-limb stretching protocol.

The primary outcome concerned diagnosed running-related lower-limb injuries in recreational runners within 12 months of the study. Its timeframe is listed as 1 year. Secondary outcomes include time to the first injury, toes and hallux muscle strength, foot muscle volume, foot health and functionality, running kinematics, ground reaction forces, and foot inversion and eversion during running. The registry record indicates nine secondary outcomes as posted, although detailed numerical summaries are available for only some of these outcomes in the record.

The trial is marked completed. The study start is recorded as 2015-04 and primary completion as 2019-03-01. The registry record does not report the original design’s sample-size assumptions, eligibility details, recruitment setting, or the identity of the masked party. It also does not report whether participants were analyzed according to their assigned groups or how missing outcome data were handled.

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 Number of Participants With Running Related Lower Limb Injuries, measured over 1 year.

The primary endpoint counts participants diagnosed with a running-related lower-limb injury within 12 months of the study. Each participant contributes to the endpoint as having or not having an injury; the measure is not the total number of injuries. This distinction matters because a participant with multiple injuries is still counted as one participant for this endpoint.

In the control group, 20 of 61 participants were recorded with an injury; in the strengthening group, 8 of 57 were recorded with an injury. The endpoint therefore gives a group-level summary of whether participants experienced at least one qualifying injury during the stated period. It is directly aligned with the trial’s stated objective of investigating running-related injury prevalence.

A binary endpoint can be summarized as the proportion with an event in each group and as a difference between those proportions. The reported risk difference compares the strengthening group with the control group, so a negative estimate indicates a lower observed proportion in the strengthening group. This is a description of the posted group results, not by itself proof that the intervention caused the difference. The registry record does not give further detail on injury ascertainment, diagnostic criteria, or the analysis population used for this endpoint.

7. Results Posted in the Registry

• Foot and Ankle Strengthening: 14.0% (8/57) versus 32.8% (20/61) on control; risk difference -18.8 percentage points (95% CI -33.6 to -3.9), risk ratio 0.43 (0.21–0.89); unadjusted two-proportion z-test p = 0.017.

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.

Time to the First Injury

• 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:
  • Foot and Ankle Strengthening: mean 7.63 versus 10.15 on control; difference -2.52 (95% CI -3.47 to -1.57), standardized effect d = -0.95; z-test p = <0.001.
• Interpretation:
  • The 95% confidence interval excludes no difference, so the mean is statistically lower for Foot and Ankle Strengthening than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

Toes and Hallux Muscle Strength

• 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:
  • Foot and Ankle Strengthening: mean 27.31 versus 25.61 on control; difference 1.70 (95% CI -1.35 to 4.75), standardized effect d = 0.20; z-test p = 0.275.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Foot and Ankle Strengthening and the control. The interval gives the range of effects that remain compatible with the data.

Foot and Ankle Running Kinematics

• 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:
  • Foot and Ankle Strengthening: mean 0.17 versus 2.88 on control; difference -2.71 (95% CI -4.94 to -0.48), standardized effect d = -0.44; z-test p = 0.017.
• Interpretation:
  • The 95% confidence interval excludes no difference, so the mean is statistically lower for Foot and Ankle Strengthening than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

The secondary outcomes span several kinds of measurement: time to the first injury, muscle strength, foot muscle volume, foot health and functionality, and running mechanics. The registry record indicates nine secondary outcomes as posted, but only some have detailed numerical summaries in the record. Results for outcomes without a numerical summary are not reported in the registry record.

Across the detailed summaries, the directions and precision are not uniform. The posted mean for time to the first injury is lower in the strengthening group, while the posted mean differences for strength and running kinematics differ in direction and have differing uncertainty. The binary primary outcome and the time-to-first-injury summary also describe different aspects of injury occurrence. Without the time-to-event analysis population and methods, the summaries cannot be combined into a single account of injury timing and incidence.

Secondary outcomes can help describe possible changes in function or movement alongside the primary injury endpoint, but they do not replace it. Their relationship to the primary result is descriptive: the record does not report mediation analyses that would establish whether a change in strength or mechanics explains the primary outcome. Nor does it report a plan assigning confirmatory status to particular secondary outcomes.

Unadjusted secondary comparisons carry less weight when many outcomes are examined because the chance of at least one apparently notable result can increase with the number of comparisons. This is a general statistical concern, not a claim about what occurred in this trial. The registry record does not report multiplicity adjustment, a hierarchy of outcomes, or an analysis plan that would clarify which secondary findings were confirmatory. These results are therefore best treated as descriptive and hypothesis-generating rather than as independent confirmation of the primary comparison.

Secondary outcomes registered for this trial, for reference (only those above were recalculated):

• Time to the First Injury
• Toes and Hallux Muscle Strength
• Foot Muscles Hypertrophy (Volume)
• Foot Health and Functionality
• Foot and Ankle Running Kinematics
• Ground Reaction Forces During Running
• Foot Inversion During Running
• Foot Eversion During Running

9. Statistical Interpretation

10. Statistical Methods Explained

The primary endpoint is binary: a participant either had a diagnosed running-related lower-limb injury within the stated period or did not. The posted counts can be expressed as group proportions, and the primary comparison is a risk difference. A risk difference subtracts the control-group proportion from the intervention-group proportion. Negative values mean the observed proportion was lower in the intervention group; positive values mean it was higher. This sign convention describes direction, not cause.

The registry comparison reports a risk difference of -0.188 and a 95% confidence interval from -0.336 to -0.039. A confidence interval is a range of values compatible with the data under the assumptions of the calculation. In general, it conveys uncertainty about an estimated quantity; it does not mean there is a 95% probability that this particular interval contains the true value. The interval is based on an unadjusted recalculation from the posted group summaries, not a reported adjusted sponsor model. The record marks no discrepancy for this comparison.

The unadjusted p-value for the primary comparison is 0.017. In general, a p-value describes how unusual data at least as incompatible with a specified null hypothesis would be if that null hypothesis and the test assumptions were true. It is not the probability that the null hypothesis is true, nor does it measure the size or clinical importance of an effect. The registry record does not report a formal primary analysis, so this p-value should be interpreted as an unadjusted summary rather than attributed to a prespecified model.

Risk ratios and odds ratios provide alternative summaries for binary outcomes. The posted risk ratio is 0.428, with a confidence interval from 0.205 to 0.894; the posted odds ratio is 0.335, with a confidence interval from 0.134 to 0.839. These measures use different scales from the risk difference. A risk ratio compares group proportions as a ratio, while an odds ratio compares odds. For an outcome that is not rare, an odds ratio should not be read as though it were a risk ratio. None of these relative measures removes the limitations of an unadjusted comparison or supplies details about the trial’s analysis plan.

Secondary continuous outcomes are reported as group means and standard deviations, with mean differences and confidence intervals. A mean difference is the intervention-group mean minus the control-group mean. A negative difference means the posted mean is lower in the intervention group; a positive difference means it is higher. A standard deviation describes the spread of individual observations around a group mean. It is not the uncertainty of the mean itself. The registry record does not describe the statistical tests, any covariate adjustments, or how the continuous outcomes were distributed.

For time to the first injury, the record posts means and standard deviations and an unadjusted mean difference, but it does not describe a time-to-event analysis. General time-to-event methods account for when events occur and can accommodate participants whose event time is not observed during follow-up through censoring. The registry record does not report censoring, a survival model, or the number of events used in such an analysis. The posted mean summaries alone should not be interpreted as a full time-to-event analysis.

General concerns about over-dispersion apply when count data vary more than an assumed model expects. That issue can affect standard errors and confidence intervals in count models. The primary endpoint is specifically described as the number of participants with an event, not a count of repeated injuries per participant. The registry record does not report a count model or an over-dispersion assessment, so those methods cannot be attributed to this trial.

Random allocation can, in general, help make groups comparable on average, but it does not guarantee that every trial group is balanced or that missing data and post-randomization differences are harmless. The registry record does not report baseline characteristics, allocation concealment, adherence, or analysis populations. It is therefore not possible to assess those features from the posted outcome summaries.

11. Confidence Intervals and Precision

The primary risk difference is -0.188, with a 95% confidence interval from -0.336 to -0.039. The estimate is negative, and the interval’s endpoints are also negative. The interval nevertheless covers a range of possible magnitudes, so the point estimate should not be treated as exact. A confidence interval describes sampling uncertainty under the calculation’s assumptions; it does not account for every potential source of bias or uncertainty in trial conduct.

The registry also posts a risk ratio of 0.428, with a confidence interval from 0.205 to 0.894, and an odds ratio of 0.335, with a confidence interval from 0.134 to 0.839. These relative measures likewise have intervals that do not include their null value of 1. The three measures express the comparison on different scales and should not be treated as interchangeable. The primary risk difference is often easier to relate to a change in observed group proportions, while the relative measures describe ratios.

For the posted secondary outcomes, the mean difference in toes and hallux muscle strength is 1.7, with a confidence interval from -1.352 to 4.752. The mean difference in foot and ankle running kinematics is -2.71, with a confidence interval from -4.942 to -0.478. The intervals have different relationships to zero, but the registry’s lack of reported analysis plans and multiplicity handling limits how strongly these exploratory comparisons should be interpreted. The record does not report confidence intervals for all listed secondary outcomes.

Precision is not the same as importance. The registry record does not specify a clinically important threshold for the injury outcome or the secondary measures. Confidence intervals also cannot establish that the observed differences would recur in another group of runners. Their interpretation depends on the accuracy of outcome measurement, the analysis assumptions, and the completeness of follow-up, details that are not reported in the registry record.

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.

The planning figures are illustrations based on the observed effect, not the trial’s original design assumptions. The registry record’s planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The scenarios consider detecting 100%, 75%, or 50% of the observed effect. Smaller effects require more participants per arm for the same target power.

For these non-time-to-event outcomes, the figures are participants per arm. The sample-size convention in the registry record says that time-to-event planning figures, if present, are total events; the other figures are participants per arm. The 80% power column gives the planning count per arm associated with an 80% chance of detecting the specified effect under the stated assumptions, if that effect and those assumptions were true. The 90% power column gives the corresponding planning count for a higher target chance of detection. For example, the primary outcome’s 100% of the observed effect scenario lists 79 participants per arm for 80% power and 106 participants per arm for 90% power. The figures are planning illustrations and are not observed power.

The scenarios are not evidence that the effect used for planning is the true effect, and the trial’s own sample-size justification is not reported in the registry record. Planning from an observed effect can be particularly uncertain because that estimate comes from the same trial and may not represent the effect in a future study. The figures should be read as conditional illustrations, not as a verdict on whether the completed trial was adequately sized.

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 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, p₀ and p₁ are the control and treatment proportions, and p̄ is their average.

Worked calculation for this trial

1. Control proportion p₀ = 0.328; treatment proportion p₁ = 0.140; average p̄ = 0.234.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.5988 = 1.1737.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.5840 = 0.4915.
4. n = (1.1737 + 0.4915)² / (-0.1875)² = 78.9, rounded up to 79 participants per arm for 80% power.

The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
p0 <- 0.327868852459016                          # control proportion
p1 <- 0.140350877192982                          # treatment proportion
n_per_arm <- function(power, frac = 1) {
  q1 <- p0 + (p1 - p0) * frac               # smaller effect = fraction of the observed difference
  pbar <- (p0 + q1) / 2
  z_b <- qnorm(power)
  ceiling(round((z_a * sqrt(2 * pbar * (1 - pbar)) + z_b * sqrt(p0 * (1 - p0) + q1 * (1 - q1)))^2 / (q1 - p0)^2, 6))
}
for (f in c(1, 0.75, 0.5))
  cat(sprintf("%3.0f%% of observed effect: n per arm = %s (80%% power), %s (90%% power)\n", 100 * f,
              format(n_per_arm(0.80, f), big.mark = ","), format(n_per_arm(0.90, f), big.mark = ",")))

# Check against R's built-in function (unrounded n per arm)
cat("power.prop.test:", round(power.prop.test(p1 = p0, p2 = p1, power = 0.80)$n, 1), "\n")

# Simulation: how often does the z-test reject at the 80%-power sample size?
set.seed(2306148)
n    <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z  <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))

Output from running the code

100% of observed effect: n per arm = 79 (80% power), 106 (90% power)
 75% of observed effect: n per arm = 151 (80% power), 202 (90% power)
 50% of observed effect: n per arm = 360 (80% power), 481 (90% power)
power.prop.test: 78.9 
Simulated power at n = 79 per arm: 0.813 (20000 replicates)

The simulation draws many pairs of event counts at the planned sample size and counts how often the two-proportion z-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

14. Multiplicity, Missing Data and Analysis Populations

The registry record lists multiple secondary outcomes in addition to the primary injury endpoint. When several outcomes are tested, interpreting each p-value in isolation can overstate the strength of evidence. In general, multiplicity procedures can control the chance of false-positive findings across a defined family of tests, or a prespecified hierarchy can distinguish primary from secondary comparisons. The registry record does not report a multiplicity adjustment, a testing hierarchy, or a statistical analysis plan explaining how multiple outcomes were handled.

The record also lists no reported analyses. This means the statistical methods used by the investigators, including any adjustment for baseline variables or repeated measurements, are not reported in the registry record. The comparison estimates and p-values posted for the outcomes are unadjusted recalculations from summary statistics and should not be mistaken for a complete report of the investigators’ analyses.

Missing-data methods and analysis populations are also not reported in the registry record. The outcome counts give group-specific denominators, but the record does not explain whether these denominators include every randomized participant, how missing injury status was handled, or whether participants were analyzed by assigned group. It does not report withdrawals, losses to follow-up, adherence, or reasons for missing data. These details matter because incomplete follow-up can affect an injury outcome over a year, and different analysis populations can produce different estimates.

Other protocol and conduct details are not reported in the registry record, including the original sample-size justification, allocation concealment, the identity of the masked party, and whether interim analyses were conducted. None should be inferred from the randomized, single-masked, parallel-group description. These reporting gaps limit evaluation of prespecification, risk of bias, and the extent to which the posted comparisons represent the trial’s intended analyses.

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.

The registry reports zero serious adverse events in the control group and zero in the foot and ankle strengthening group. It also reports zero other adverse events in each group and zero deaths in each group. The listed at-risk groups are 61 for control and 57 for strengthening. No serious adverse event terms are listed.

These are the adverse-event figures posted in the registry record. They indicate that no events in these categories were recorded in the posted results; they do not establish that no adverse events occurred outside the record or that the intervention has no risks. The record does not provide definitions for serious or other adverse events, collection procedures, event attribution rules, or additional narrative safety information. Zero counts should therefore be read as reported counts, not as a complete assessment of safety.

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

The primary result describes fewer participants with a recorded running-related lower-limb injury in the strengthening group than in the control group. The estimated risk difference is -0.188, with a 95% confidence interval from -0.336 to -0.039. This is evidence of a group difference in the posted summaries, with uncertainty represented by the interval. It does not by itself show that strengthening caused the difference.

The trial was randomized, which is relevant to causal interpretation in general, but the registry record does not report enough information to evaluate all aspects of conduct and analysis. Allocation concealment, analysis populations, adherence, missing-data handling, and a formal analysis plan are not reported. The posted comparison is unadjusted, and the record lists no reported analyses. These limitations mean the outcome summaries cannot answer every question about how robust the comparison is.

The result also does not establish how the observed difference would apply to other runners, settings, or training approaches. Eligibility details and participant characteristics are not reported in the registry record. The record does not provide a threshold for a clinically important difference, so statistical evidence of a difference should not be equated with evidence that the difference is important to runners.

The secondary outcomes do not establish a mechanism for the primary finding. The registry does not report analyses linking changes in foot strength, function, or running mechanics to injury outcomes. The time-to-first-injury summary is not accompanied by information about its analysis population or time-to-event methods, and its direction does not align simply with the primary count result. The available summaries should therefore be interpreted as separate outcome descriptions, not as a coherent causal pathway.

Overall, the posted data characterize an observed difference within this completed trial. They do not establish a guaranteed effect, rule out reporting or analysis limitations, or support medical advice for individual runners.

17. Why This Trial Matters Statistically

This trial illustrates why a clinical result should be read through more than its p-value. The primary risk difference describes an absolute contrast in the observed proportions, while the confidence interval communicates uncertainty about its magnitude. The risk ratio and odds ratio express the comparison on relative scales. Each measure answers a related but distinct descriptive question, and none should be detached from its assumptions or treated as proof of causation.

The record also demonstrates why endpoint definitions matter. The primary outcome counts participants with at least one qualifying injury, whereas time to the first injury concerns timing. Those outcomes are related but not interchangeable. The registry’s posted time-to-injury means lack the details needed to assess them as a time-to-event analysis, making it important not to force the secondary summary into an explanation of the primary result.

Planning illustrations based on observed effects require particular care. They can show how assumed effect size and target power affect planning counts, but they do not reveal the original design rationale or the power actually achieved. The trial’s original sample-size assumptions are not reported in the registry record. This distinction prevents retrospective planning figures from being mistaken for properties of the completed trial.

Finally, the record is a reminder that interpretation depends on transparency about analysis populations, missing data, multiplicity, and outcome ascertainment. Those details are not reported, and their absence limits conclusions beyond the posted summaries. A statistically careful reading distinguishes the numerical pattern from claims about clinical importance, mechanism, or generalizability.

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.

Several limitations specific to this trial arise from incomplete registry reporting. The primary injury endpoint is described as diagnosed running-related lower-limb injuries within 12 months, but the diagnostic criteria, assessment process, and handling of recurrent injuries are not reported in the registry record. It is therefore not possible to assess how consistently injuries were identified or whether ascertainment could have differed between groups.

The intervention included physiotherapist training, home exercise, and software supervision, while the control involved isometric stretching. The record does not report adherence, the amount of training completed, software use, or whether participants received comparable contact and monitoring. The extent to which the assigned programs were followed cannot be evaluated from the posted summaries.

The record does not report baseline characteristics, eligibility details, allocation concealment, withdrawals, or missing outcome data. It also does not specify the analysis population or confirm whether all randomized participants were included in the reported comparisons. These omissions limit assessment of comparability, attrition, and the relationship between enrollment and outcome denominators.

The secondary results require additional caution because the analysis plan and multiplicity handling are not reported. The time-to-first-injury means are not accompanied by information about censoring, the analysis population, or a time-to-event method. The registry record also does not provide detailed numerical results for every listed secondary outcome. Finally, the original sample-size justification and clinically important thresholds are not reported, limiting assessment of design intent and practical importance.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Effects of Foot Strengthening on the Incidence of Injuries in Long Distance Runners — NCT02306148.
• Registry record last updated 2024-05-28; status last verified 2023-12.
• Results first posted 2024-05-28.
• 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

The registry record describes a completed randomized, single-masked, parallel-group trial of foot and ankle strengthening versus a control stretching protocol in long-distance runners. Enrollment was 118. The primary endpoint was the number of participants with diagnosed running-related lower-limb injuries within 12 months.

The posted primary counts were 20 of 61 in the control group and 8 of 57 in the strengthening group. The unadjusted risk difference was -0.188, with a 95% confidence interval from -0.336 to -0.039 and an unadjusted p-value of 0.017. The registry record also contains secondary outcome summaries and reports zero serious adverse events, zero other adverse events, and zero deaths in each group.

Formal reported analyses, the trial’s original sample-size assumptions, multiplicity handling, missing-data methods, and analysis populations are not reported in the registry record. The posted comparisons should be interpreted as summaries of the recorded outcomes, with these reporting limitations in mind.