The Effectiveness of rTMS in Depressed VA Patients: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for The Effectiveness of rTMS in Depressed VA Patients (NCT01191333), a randomized na study. The primary outcome is The Proportion of Participants Achieving Remission From Depression as Assessed by Hamilton Rating Scale for Depression.

2. Clinical Question

The registry describes a multi-site trial and identifies Major Depressive Disorder as the condition. Its stated purpose was to assess rTMS for people whose depression had not improved enough with medication. The primary outcome is a remission classification based on a rating-scale threshold, rather than a direct comparison of mean depression scores. The secondary outcomes listed include suicidal ideation, depression scores, and mental and physical health measures. Results for those secondary measures are not reported in the registry record.

3. Trial Design

NCT01191333 is recorded as a completed, randomized, triple-masked, parallel trial sponsored by the VA Office of Research and Development. The registry lists enrollment as 164. The recorded study start was 2012-07-02, and primary completion was 2017-02-15. The phase is listed as NA. The record describes the study as multi-site.

The parallel design assigned participants to active rTMS or sham rTMS. The active arm description specifies 20 to 30 sessions, delivered in blocks of 5 by trained medical personnel. The sham arm description specifies the same session range and block structure, also delivered by trained medical personnel. These are the planned arm descriptions; the record does not give participant-level treatment adherence or the number of sessions each participant actually received.

Masking is recorded as triple, but the registry record does not identify which participant, clinician, assessor, or other roles were masked, nor does it describe how masking was maintained. Allocation is recorded as randomized; details of sequence generation, concealment, or randomization procedures are not reported in the registry record. The record also does not state whether treatment delivery or follow-up differed by site.

The primary outcome is listed for the ITT population and is the count of participants achieving remission by HRSD24 at the end of acute treatment, specified as 4-6 weeks. The posted arm counts are 33 in the active group and 31 in the sham group, with analyzed group sizes of 81 and 83 respectively. Details such as the precise analysis population rules, handling of missing primary outcome assessments, and any deviations from the planned design 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

Analysis population for the primary outcome, as defined in the registry: ITT

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 The Proportion of Participants Achieving Remission From Depression as Assessed by Hamilton Rating Scale for Depression, measured over End of acute treatment 4-6 weeks.

The primary endpoint is the proportion of participants achieving remission from depression, assessed with the 24-item Hamilton Rating Scale for Depression, or HRSD24. The registry defines remission as an HRSD24 score <= 10 at the end of the acute treatment phase. The timeframe is recorded as 4-6 weeks. The scale’s total score range is 0 - 76, with higher values representing a worse outcome.

This is a binary endpoint: each participant is classified according to whether the specified threshold is met. The registry reports the number meeting the threshold in each arm, rather than each participant’s score or a group mean. The active-rTMS count was 33 among 81 participants, and the sham-rTMS count was 31 among 83 participants. This endpoint therefore describes the frequency of remission classifications at the specified assessment point; it does not show how much an individual’s score changed or the course of symptoms between assessments.

Using a threshold can make an outcome clinically interpretable as a defined state, while also discarding some detail in the underlying scale scores. Participants close to either side of the threshold are classified differently even if their scores are similar. That general property applies to threshold-based outcomes; the registry does not report additional analyses of continuous HRSD24 scores for the primary endpoint.

7. Results Posted in the Registry

• Active rTMS: 40.7% (33/81) versus 37.3% (31/83) on control; risk difference 3.4 percentage points (95% CI -11.5 to 18.3), risk ratio 1.09 (0.74–1.60); unadjusted two-proportion z-test p = 0.656.

8. Statistical Interpretation

9. Statistical Methods Explained

For the primary endpoint, the registry reports counts of participants meeting a remission threshold in each randomized arm. This is a binary outcome: each assessed participant either meets the HRSD24 criterion of <= 10 or does not. A comparison of proportions summarizes how frequently the outcome occurred in the two groups. The posted counts are 33 among 81 in the active-rTMS arm and 31 among 83 in the sham-rTMS arm.

What does the risk difference express?

The risk difference is the active-arm proportion minus the sham-arm proportion, expressed on the absolute proportion scale. The registry reports an estimate of 0.034. A value of zero corresponds to equal proportions; a positive value means the observed proportion is higher in the active arm, and a negative value means it is higher in the sham arm. The risk difference is often useful for communicating the absolute size of a contrast. The registry reports its confidence interval as -0.115 to 0.183.

How do risk ratios and odds ratios differ?

The risk ratio compares the outcome proportion in one group with the proportion in the other group. A ratio of 1 represents equal proportions. The reported risk ratio is 1.091, with a confidence interval from 0.744 to 1.6. The odds ratio compares the odds of the outcome between groups rather than comparing the proportions directly. An odds ratio of 1 represents equal odds. The reported odds ratio is 1.153, with a confidence interval from 0.616 to 2.161. Ratios can look different from an absolute difference because they use a different scale; they are alternative descriptions of the same group comparison, not separate outcomes.

What do the confidence intervals convey?

A confidence interval gives a range of values compatible with the data and the method’s assumptions, at the stated confidence level when that level is specified. The registry comparison provides intervals for the risk difference, risk ratio, and odds ratio, but does not state the confidence level in the record. For the risk difference, the interval spans zero; for the ratio measures, the intervals span 1. These are the respective values representing no group contrast. The breadth of an interval conveys precision: a wider interval leaves more uncertainty about the size and direction of the contrast.

How should the p-value be read?

The registry reports an unadjusted p-value of 0.656. In general, a p-value measures how unusual data at least as discrepant as the observed data would be under a specified null model and statistical assumptions. It does not give the probability that the null model is true, the probability that the finding is a false positive, or the size of an effect. The record does not describe the specific test, its implementation, or whether any alternative model was considered.

Why distinguish the outcome scale from its analysis?

The endpoint is classified using the HRSD24 threshold, and the comparison is recorded as a binary count outcome. The scale itself has a range of 0 - 76, with higher scores indicating worse outcomes, but the posted primary result does not present a comparison of mean scores. In general, reducing a scale to a threshold makes the result easier to describe as the proportion meeting a defined criterion, while losing information about the distances between scores and changes within each category.

What is not specified about the analysis?

The registry lists the primary population as ITT, but does not report the detailed population definition, analysis model, missing-data method, covariate adjustment, or test procedure. The number of analyses is recorded as 0. That registry entry does not explain how the displayed comparison was generated. Statistical analysis details beyond the posted comparison are therefore not reported in the registry record. Any interpretation of the estimates should stay with their stated scales and the uncertainty intervals, rather than assuming an unreported adjustment or analysis procedure.

10. Confidence Intervals and Precision

The risk-difference estimate is 0.034, with a confidence interval from -0.115 to 0.183. Because this interval includes zero, the posted data are compatible with no difference in remission proportions as well as differences in either direction. Its range indicates that the estimate is not precise enough to pin down a narrow set of plausible contrasts. The registry does not specify the confidence level for the interval.

The ratio-scale estimates also have intervals spanning their no-contrast value of 1: the risk ratio is 1.091, with an interval from 0.744 to 1.6, and the odds ratio is 1.153, with an interval from 0.616 to 2.161. These intervals show uncertainty in the relative comparison as well as in the absolute comparison. The different numerical ranges arise because the measures are defined on different scales; they should not be compared by their raw magnitudes.

Precision is affected by the amount of information available for the outcome, including the numbers of participants and observed events, and by the variability inherent in the endpoint. In general, more information tends to narrow uncertainty intervals, but the registry does not report a precision target or the design assumptions used for the trial. The posted interval is an expression of uncertainty under the method used for the comparison, whose details are not reported in the registry record.

The point estimate alone should not be treated as a definitive effect. Nor does an interval that crosses a no-difference value demonstrate equivalence. Establishing equivalence would require an explicit equivalence question and a prespecified margin, neither of which is reported in the registry record.

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, not total events. They are illustrations based on the observed effect and are not the trial’s original design assumptions. The listed assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set as the stated fraction of the observed effect. The trial’s own sample-size justification and design assumptions are not reported in the registry record.

The 80% power column gives the illustrative participants per arm for a design with an 80% chance of detecting the specified effect under those assumptions, if that effect and model were correct. The 90% power column gives the corresponding planning number for a 90% chance. These are prospective planning quantities, not a description of what happened in this completed trial. They do not state the probability that the posted result is correct, and they are not observed power.

The rows consider planning for 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect. The figures are 3,248 and 4,347 participants per arm for 100% of the observed effect; 5,751 and 7,699 for 75% of the observed effect; and 12,888 and 17,252 for 50% of the observed effect, for 80% and 90% power respectively. Smaller effects require more participants to detect under the same planning assumptions. These illustrations use the observed effect as a starting point, so they should not be interpreted as evidence that the original trial was designed around that effect.

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

Worked calculation for this trial

1. Control proportion p₀ = 0.373; treatment proportion p₁ = 0.407; average p̄ = 0.390.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6899 = 1.3522.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.6895 = 0.5803.
4. n = (1.3522 + 0.5803)² / (0.0339)² = 3,247.2, rounded up to 3,248 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 <- 0.373493975903614                          # control proportion
p1 <- 0.407407407407407                          # 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(1191333)
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 = 3,248 (80% power), 4,347 (90% power)
 75% of observed effect: n per arm = 5,751 (80% power), 7,699 (90% power)
 50% of observed effect: n per arm = 12,888 (80% power), 17,252 (90% power)
power.prop.test: 3247.2 
Simulated power at n = 3,248 per arm: 0.796 (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.

13. Multiplicity, Missing Data and Analysis Populations

The registry lists 5 secondary outcomes: suicidal ideation measured by the Beck Scale for Suicide Ideation, depression measured by the Beck Depression Inventory, mental and physical component scores from the VR-36, and depression measured by the Montgomery Asberg Depression Rating Scale. Results for those secondary outcomes are not reported in the registry record. The record lists 6 outcome measures and 0 analyses.

When several outcomes or comparisons are tested, the chance of obtaining at least one apparently notable result can increase. Statistical approaches to multiplicity can address that issue, but the registry record does not report whether any adjustment was planned or applied. It also does not identify a hierarchy among the secondary outcomes or say whether they were intended to support confirmatory or exploratory conclusions. The primary comparison is labeled unadjusted, and no adjusted primary result is posted.

The primary population is identified as ITT. The record does not provide a detailed definition of how participants were included in that population, how the analysis handled participants without an outcome assessment, or whether all randomized participants contributed to the endpoint. Missing-data methods, imputation procedures, sensitivity analyses, and reasons for missing assessments are not reported in the registry record. The listed arm sizes for the primary comparison are 81 and 83, but the record does not explain any distinction between these analysis sizes and the overall enrollment entry.

Without those details, it is not possible to assess how missing outcomes or multiple testing may have influenced the posted results. This does not establish that either issue altered the result; it means that the relevant procedures are not described in the registry record. The posted primary estimate and its uncertainty can be described, while broader claims about analysis robustness cannot be evaluated from the information recorded.

14. 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 serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: acoustic stimulation tests abnormal (6.0%), suicidal ideation (4.9%), alcohol poisoning (2.5%), hypoacusis (2.5%), depression (2.4%).

The registry reports serious adverse events for each arm using the number at risk and the number affected. In the active-rTMS arm, 22 of 81 participants were recorded as affected by a serious adverse event; in the sham-rTMS arm, 18 of 83 were affected. The recorded death count is 0 in each arm. These are counts, not a comparison adjusted for follow-up time or participant characteristics.

The registry also lists the most frequent serious-event terms and percentages: Acoustic stimulation tests abnormal, 6.0%; Suicidal ideation, 4.9%; Alcohol poisoning, 2.5%; Hypoacusis, 2.5%; Depression, 2.4%; and Suicide attempt, 1.2%. The record does not provide arm-specific counts for these terms in the information posted here, nor does it explain the denominator or coding details behind each percentage. They should not be treated as rates attributable to a particular arm.

In addition to serious events, other adverse events were recorded as affecting 71 of 81 in the active arm and 69 of 83 in the sham arm. The registry does not provide further event-level detail in this summary. These safety counts describe what the record reports; without definitions, timing, exposure information, and additional analysis details, they do not establish whether an event was caused by an intervention or how the groups compare statistically.

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

The posted result estimates the difference between active rTMS and sham rTMS in the proportion classified as in remission by the HRSD24 threshold at the end of acute treatment. The active arm had 33 participants meeting the threshold among 81, and the sham arm had 31 among 83. The reported risk difference is 0.034, with a confidence interval from -0.115 to 0.183 and an unadjusted p-value of 0.656.

Those figures describe the observed comparison and its uncertainty. The confidence interval includes zero, so the posted estimate does not distinguish clearly between no difference and differences in either direction. It also does not establish that the interventions are equivalent, because the registry does not report an equivalence design or margin. The p-value should not be interpreted as the probability that either treatment is effective or ineffective.

The result applies to the specified remission threshold and assessment timeframe. It does not give a complete account of changes in HRSD24 scores, the duration of any remission, later outcomes, or outcomes on the listed secondary measures. The record does not report secondary results or longer-term findings in the data summarized for this comparison.

The registry describes a population with Major Depressive Disorder whose medication treatment had not helped or had not helped enough, but it does not provide the detailed eligibility criteria needed to define the limits of generalizability. The posted findings should therefore be understood as a comparison within the trial record’s stated population and outcome framework, not as a conclusion about every person with depression or every use of rTMS. They do not substitute for a broader assessment of clinical context, other evidence, or individual circumstances.

16. Why This Trial Matters Statistically

This trial illustrates several issues that arise when a clinical outcome is converted into a binary endpoint. The HRSD24 has a total score range of 0 - 76, but the primary analysis classifies participants according to whether their score is <= 10. That creates an interpretable remission category, while leaving out information about how scores are distributed within the remission and non-remission groups. Statistical readers need to keep the threshold definition distinct from the underlying scale.

The result also shows why an effect estimate should be read with its confidence interval. The risk difference is 0.034, while its interval extends from -0.115 to 0.183. The observed estimate alone gives an incomplete account; the interval indicates that the data do not tightly determine the size or direction of the group contrast. A p-value of 0.656 is not a substitute for that information and does not quantify clinical importance.

Reporting several effect measures can aid interpretation when their scales are made clear. The risk difference describes an absolute contrast, while the risk ratio and odds ratio describe relative contrasts. The registry reports all three, and all three intervals include their respective no-contrast values. Reading them together emphasizes the uncertainty without treating each metric as an independent result.

The record also highlights the importance of transparent analysis reporting. It identifies an ITT population and lists secondary outcomes, but does not provide detailed missing-data procedures, multiplicity handling, or the specific statistical test. Those omissions limit what can be evaluated about robustness and the interpretation of multiple outcomes. A clear distinction between posted estimates and unreported methods is therefore essential when assessing clinical-trial results.

17. 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 registry record does not report the detailed inclusion and exclusion criteria, baseline characteristics, or participant flow. Although enrollment is listed as 164 and the primary comparison gives arm sizes of 81 and 83, the record does not explain the relationship between enrollment and those endpoint analysis sizes. It also does not report how many participants completed treatment, the number of sessions actually received, or reasons for discontinuation.

Important design and analysis details are not reported in the registry record. These include the randomization sequence and concealment procedures, the roles covered by triple masking, the statistical test or model used for the primary comparison, and the handling of missing endpoint data. The record does not state the confidence level for the reported intervals or provide a detailed definition of the ITT analysis population. Consequently, the posted comparison cannot be independently assessed against a fully described analysis plan from this record alone.

The registry does not report the trial’s original sample-size justification, its planned effect size, or whether interim analyses were conducted. It also does not provide results for the secondary outcomes listed, despite listing 5 secondary measures. Follow-up beyond the acute-treatment endpoint is not described in the posted primary result. The serious-adverse-event summary does not provide event timing or arm-specific details for the named serious-event terms.

These are limits of the registry information available for interpreting this comparison. They do not establish that procedures were absent or that unreported information would change the result; those details are simply not reported in the registry record.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: The Effectiveness of rTMS in Depressed VA Patients — NCT01191333.
• Registry record last updated 2018-03-09; status last verified 2018-02.
• Results first posted 2018-02-07.
• 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.

21. Record Summary

NCT01191333, titled “The Effectiveness of rTMS in Depressed VA Patients,” is recorded as a completed, randomized, triple-masked, parallel, multi-site trial sponsored by the VA Office of Research and Development. Enrollment is listed as 164. The active-rTMS and sham-rTMS arms were described as 20 to 30 treatment sessions in blocks of 5.

The primary endpoint was remission by HRSD24 score <= 10 at the end of acute treatment, recorded as 4-6 weeks. The posted counts were 33 of 81 for active rTMS and 31 of 83 for sham rTMS. The risk difference was 0.034, with a confidence interval from -0.115 to 0.183 and an unadjusted p-value of 0.656. The registry record does not report results for the listed secondary outcomes.