This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.
1. Trial at a Glance
This page covers the registry results for Lifestyle Intervention and Testosterone Replacement in Obese Seniors (NCT02367105), a randomized phase 3 study. The primary outcome is Change in the Physical Performance Test.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT02367105 |
| Phase | Phase 3 |
| Condition | Obesity and Hypogonadism |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Triple |
| Enrollment | 83 |
| Arms in the primary outcome | 2 |
| Lead sponsor | VA Office of Research and Development |
| Results posted | Yes |
2. Clinical Question
Population
The registry describes obese older Veterans with obesity and hypogonadism. The study’s brief summary frames the clinical concern around physical function, frailty, and the possibility that weight-loss therapy could aggravate loss of muscle and bone mass in older adults. Specific eligibility criteria and the age range are not reported in the registry record.
Intervention
Participants were assigned to testosterone replacement together with lifestyle therapy. The lifestyle program combined a behavioral diet intended to induce approximately 10% weight loss with supervised aerobic and exercise training. The registry does not report additional detail about how the program was delivered or the testosterone regimen.
Comparator
The comparison group received placebo together with the same described lifestyle approach: behavioral diet intended to induce approximately 10% weight loss and supervised aerobic and exercise training. The central contrast is therefore the addition of testosterone to lifestyle therapy, rather than lifestyle therapy versus no intervention.
Primary question
The primary outcome was change in the modified physical performance test from baseline to 6 months. The practical statistical question is whether the average change differed between the testosterone-plus-lifestyle group and the placebo-plus-lifestyle group. The posted arm means were 4.9 and 4.6, respectively, and the simple unadjusted recalculation estimates a mean difference of 0.3. The registry’s mixed-model analysis reports a mean difference of -0.3 with p = 0.58. These are different analysis summaries, and the registry does not report a confidence interval for its mixed-model estimate.
The registry describes the rationale as a concern that weight loss in older adults may have consequences for muscle mass, bone mass, and physical function. It presents testosterone as a possible addition to lifestyle therapy, with the aim of preserving function during weight loss. That rationale explains why a functional measure was selected; it does not establish that the intervention achieved those aims. The trial’s posted primary result should be read as an estimate of the between-group difference in the measured performance outcome over the stated follow-up, not as a direct test of every proposed mechanism or longer-term consequence.
3. Trial Design
The registry identifies this as a phase 3, randomized, triple-masked, parallel-group trial. The two groups were testosterone plus lifestyle therapy and placebo plus lifestyle therapy. The registry lists an enrollment of 83. It reports a start date of 2015-02-01, primary completion on 2019-07-31, and a completed status. These administrative details describe the registered study and do not by themselves establish how many participants contributed data to each specific analysis.
The active group received testosterone replacement with behavioral diet and supervised aerobic and exercise training. The placebo group received placebo with the corresponding lifestyle program. The diet was described as intended to induce approximately 10% weight loss. The registry does not report further operational detail about treatment duration, adherence, the amount of contact with staff, or the precise exercise and dietary procedures.
The posted primary outcome is a continuous measure: change in the modified physical performance test between baseline and 6 months. The outcome record gives group means and standard errors for the two arms. A separate sponsor analysis is described as a mixed models analysis of mean difference in final values. The registry does not report the complete model specification, the covariates included, or the exact handling of repeated measurements and missing observations.
The study also lists secondary outcomes covering endurance, functional status, body weight, lean body mass, fat mass, thigh muscle and fat volume, and total hip bone mineral density. The registry lists 45 outcome measures and 47 analyses, while 30 secondary outcomes are posted. Those counts indicate a broad set of outcome reporting, but do not identify the complete analysis plan or establish which results were prespecified as confirmatory. The original sample-size justification and the trial’s own design assumptions are not reported in the registry record.
4. Participant Flow and Accounting
The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.
Before assignment: After obtaining written informed consent, potential participants underwent a comprehensive medical screening procedure, including an exercise stress test. If they were found eligible based on the inclusion/exclusion criteria, they were randomized into one of the two treatment groups.
Overall Study
| Stage | Placebo + Lifestyle Therapy | Testosterone + Lifestyle Therapy |
|---|---|---|
| STARTED | 41 | 42 |
| COMPLETED | 36 | 34 |
| NOT COMPLETED | 5 | 8 |
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.
| Characteristic | Unit | Placebo + Lifestyle Therapy | Testosterone + Lifestyle Therapy | Total |
|---|---|---|---|---|
| Participants analysed | 41 | 42 | 83 | |
| Age, Continuous | years | 72.2 (SD 3.2) | 73.6 (SD 3.7) | 73.4 (SD 3.5) |
| Sex: Female, Male: Female | Participants | 0 | 0 | 0 |
| Sex: Female, Male: Male | Participants | 41 | 42 | 83 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 8 | 19 | 27 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 32 | 20 | 52 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 1 | 3 | 4 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 1 | 0 | 1 |
| Race (NIH/OMB): Asian | Participants | 0 | 0 | 0 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 0 | 1 | 1 |
| Race (NIH/OMB): Black or African American | Participants | 14 | 20 | 34 |
| Race (NIH/OMB): White | Participants | 22 | 19 | 41 |
| Race (NIH/OMB): More than one race | Participants | 2 | 2 | 4 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 2 | 0 | 2 |
| Region of Enrollment: United States | participants | 41 | 42 | 83 |
| Body mass index | kg/m^2 | 36.9 (SD 4.9) | 37.1 (SD 5.6) | 37.0 (SD 5.2) |
| Total testosterone level | ng/dl | 218 (SD 43) | 210 (SD 63) | 214 (SD 54) |
| Physical Performance Test score | units on a scale | 28.3 (SD 3.1) | 28.5 (SD 2.8) | 28.4 (SD 2.9) |
6. Primary Endpoint
The registry lists the primary outcome as Change in the Physical Performance Test, measured over Baseline and 6 months.
| Element | Registry entry |
|---|---|
| Result type | Mean |
| Measure of spread | Standard Error |
| Unit | units on a scale |
| Endpoint classification | Continuous Endpoint |
The primary endpoint is change in the modified physical performance test from baseline to 6 months. It is a measure of physical function, expressed in units on a scale. The registry describes a test built from seven standardized tasks—walking 50 ft, putting on and removing a coat, picking up a penny, standing up from a chair, lifting a book, climbing one flight of stairs, and performing a progressive Romberg test—plus climbing up and down four flights of stairs and performing a 360-degree turn. The score for each task ranges from 0 to 4, and the maximum total score is 36. Higher scores indicate better physical function.
As a general measurement principle, a performance test can provide a structured way to assess ability to carry out physical tasks rather than relying only on a participant’s overall impression. That makes it relevant to the registry’s stated concern about physical function and frailty in older adults undergoing weight loss. A change score is intended to describe how the measure shifted over the assessment period. The registry reports group means for change, but does not report a threshold for a clinically important change or explain how changes on the scale map to daily independence.
The endpoint therefore addresses a specific functional question over the stated six-month period. It does not by itself measure all aspects of frailty, long-term independence, bone health, muscle preservation, or use of health services. Those broader topics are part of the rationale and outcome list, but cannot be substituted for the primary endpoint.
7. Results Posted in the Registry
- Testosterone + Lifestyle Therapy: mean 4.90 versus 4.60 on control; difference 0.30 (95% CI -0.53 to 1.13), standardized effect d = 0.16; z-test p = 0.480.
Mean difference: Testosterone + Lifestyle Therapy
95% CI: -0.53 to 1.13
Recalculated from the posted summary statistics
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.
| Secondary outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Change in Endurance Capacity | Continuous Endpoint | Mean difference | 1.20 (0.37 to 2.03) | 41 per arm |
| Change in Functional Status | Continuous Endpoint | Mean difference | 0.20 (-0.91 to 1.31) | 2,607 per arm |
| Change in Body Weight | Continuous Endpoint | Mean difference | 0.80 (-0.86 to 2.46) | 367 per arm |
Change in Endurance Capacity
- 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 errors.
- Result:
- Testosterone Plus Lifestyle Therapy: mean 4.00 versus 2.80 on control; difference 1.20 (95% CI 0.37 to 2.03), standardized effect d = 0.62; z-test p = 0.005.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically higher for Testosterone Plus Lifestyle Therapy than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Change in Functional Status
- 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 errors.
- Result:
- Testosterone Plus Lifestyle Therapy: mean 3.10 versus 2.90 on control; difference 0.20 (95% CI -0.91 to 1.31), standardized effect d = 0.08; z-test p = 0.724.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Testosterone Plus Lifestyle Therapy and the control. The interval gives the range of effects that remain compatible with the data.
Change in Body Weight
- 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 errors.
- Result:
- Testosterone Plus Lifestyle Therapy: mean -9.80 versus -10.60 on control; difference 0.80 (95% CI -0.86 to 2.46), standardized effect d = 0.21; z-test p = 0.346.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Testosterone Plus Lifestyle Therapy and the control. The interval gives the range of effects that remain compatible with the data.
The secondary outcomes cover several domains rather than a single narrow construct: endurance capacity, functional status, body weight, body composition, muscle and fat volume in the thigh, and total hip bone mineral density. The registry reports 30 secondary outcomes, alongside a larger list of outcome measures. Only some secondary results are described in detail in the posted outcome data. Collectively, the listed domains provide context for the trial’s rationale, but they do not all measure the same underlying response.
Across the outcomes with detailed figures, the unadjusted recalculation does not present a uniform pattern. Endurance capacity has an interval above zero, whereas the intervals for functional status and body weight include zero. This pattern is not a substitute for the primary result: the primary endpoint remains change in the modified physical performance test. Endurance capacity and functional status are related to physical ability but are distinct measures, and body weight is a separate outcome. The registry’s broader list includes body-composition and bone measures, but the registry entries do not provide detailed estimates for each of those outcomes.
Secondary analyses can help describe whether findings are consistent across related outcomes, but they generally carry less weight when many comparisons are examined and the analysis plan is not fully available. With numerous outcomes, chance alone can produce some nominally notable results. The registry does not report whether a multiplicity adjustment was prespecified or applied, nor does it identify a confirmatory hierarchy for the secondary outcomes. The recalculated secondary p-values are unadjusted and should be read as exploratory rather than as separate definitive tests.
The sponsor’s mixed-model results also differ in sign or magnitude from the simple recalculations for the selected secondary outcomes. The registry record does not provide enough methodological detail to explain those differences. A cautious reading keeps each outcome’s estimate tied to its own method and avoids using a favorable finding in one secondary measure to override the primary endpoint or to imply a general effect across physical function, weight, body composition, or bone outcomes.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Change in Endurance Capacity
- Change in Functional Status
- Change in Body Weight
- Change in Lean Body Mass
- Change in Fat Mass
- Change in Thigh Muscle Volume
- Thigh Fat Volume
- Change in Total Hip Bone Mineral Density
9. Statistical Interpretation
For the primary outcome, the posted mean change was 4.6 in the placebo-plus-lifestyle group and 4.9 in the testosterone-plus-lifestyle group. The simple unadjusted recalculation estimates the active-versus-control mean difference as 0.3, with a 95% confidence interval from -0.531 to 1.132 and an unadjusted p-value of 0.48. This interval includes zero and spans values on either side of zero. Thus, the recalculation does not give a precise estimate that clearly separates the groups on this outcome. It is compatible with a range of possible between-group differences under the assumptions of that calculation.
The registry’s own mixed models analysis reports a mean difference in final values of -0.3 and p = 0.58. Its sign is opposite to the simple recalculated contrast, and its p-value is not the same. The registry does not provide a confidence interval for the mixed-model estimate or enough model detail to reconcile the contrast direction. The reported mixed-model result is the trial’s own analysis; the unadjusted recalculation is a separate summary based on posted arm statistics. They should not be treated as interchangeable estimates.
Selected secondary results show a varied pattern. For endurance capacity, the posted means were 2.8 ml/kg/min in the placebo-plus-lifestyle group and 4.0 ml/kg/min in the testosterone-plus-lifestyle group. The unadjusted recalculated difference was 1.2, with a 95% confidence interval from 0.368 to 2.032 and p = 0.005. The registry’s mixed-model analysis reports -1.2 and p = 0.03. For functional status, the recalculated difference was 0.2, with an interval from -0.909 to 1.309 and p = 0.724; the sponsor analysis reports 0.0 and p = .97. For body weight, the posted means were -10.6 kilograms and -9.8 kilograms, with a recalculated difference of 0.8, an interval from -0.863 to 2.463, and p = 0.346. The sponsor analysis reports -0.7 and p = 0.56.
These secondary summaries should be interpreted in the context of the primary outcome and the broad set of outcomes recorded. They do not change what the primary estimate says about the measured physical performance test. Nor do nominal p-values alone establish a consistent or definitive pattern across outcomes. The registry does not report whether adjustments for multiple comparisons were used, so the secondary p-values are best treated as exploratory evidence rather than as a set of independent confirmatory tests.
Overall, the posted data show a small estimated difference in the primary arm means, but the recalculated interval is wide enough to include both negative and positive differences. The registry’s mixed-model analysis also reports a non-small p-value, but without an interval its precision is harder to assess. These results describe uncertainty in this trial’s measured outcomes; they do not establish the presence or absence of an effect in other populations, at other follow-up times, or on outcomes not measured in the posted results.
10. Statistical Methods Explained
Continuous outcomes are often summarized by a mean for each group. A mean is the arithmetic average of the recorded values for the outcome under analysis. In this trial, the posted primary endpoint is a continuous change measure, and the registry gives a mean and standard error for each group. The standard error describes the sampling uncertainty of an estimated mean; it is not the spread of individual participants’ scores. As a general statistical distinction, a standard deviation describes variability among observations, whereas a standard error describes uncertainty in an estimate of the mean.
What does a mean difference represent?
A mean difference compares the average outcome in one group with the average in another. The recalculated primary contrast is 0.3 for testosterone plus lifestyle therapy versus placebo plus lifestyle therapy, based on the posted means of 4.9 and 4.6. The direction depends on which group is subtracted from which. A positive value in the recalculation means the active-group mean is higher under that stated contrast; it does not, by itself, indicate that the difference is important or precise. The registry’s sponsor analysis reports a different sign convention or estimate, and the record does not explain the relationship between those values.
What does the confidence interval add?
A confidence interval gives a range of values compatible with the data under the method’s assumptions. In general, a wider interval indicates less precision, while a narrower interval indicates more precision. The recalculated primary interval runs from -0.531 to 1.132. Because it includes zero, the posted summary statistics do not pin down the direction of the difference. The interval also communicates more than a threshold-based p-value: it gives a range of plausible effect estimates on the outcome’s scale. It does not mean that the true value has a specified probability of lying within this particular interval.
The recalculated intervals and p-values are unadjusted, simple comparisons derived from the posted summary statistics. They are not the sponsor’s mixed-model estimates. The registry identifies the sponsor method as mixed models analysis of mean difference in final values, but the complete model formula, covariates, covariance structure, and missing-data assumptions are not reported in the registry record. A mixed model can use information across repeated measurements and account for correlations among observations, depending on its specification. Without the specification, it is not possible to assess exactly how it did so in this study.
Why can analyses differ?
Different analysis methods can produce different estimates and p-values even when they concern the same outcome and groups. They may use different time points, adjustment variables, assumptions about repeated observations, or participant records. The registry’s primary recalculation compares posted group summaries, whereas the sponsor’s stated method is a mixed model using final values. The record does not report enough detail to identify which methodological choices account for the differences, so any explanation beyond that would be speculative. The sponsor analysis should be read as the trial’s reported analysis, with the simple recalculation serving as a transparent, unadjusted comparison of the posted summaries.
The p-value is a measure of how surprising data at least as inconsistent with a specified null model would be, assuming that model and its assumptions. It is not the probability that the null hypothesis is true, and it does not measure the size or clinical importance of a difference. The recalculated primary p-value is 0.48, while the sponsor reports 0.58. Neither figure supplies the missing interval around the sponsor’s estimate. A p-value should therefore be interpreted alongside the estimate, interval, outcome scale, and analysis method rather than as a stand-alone verdict.
Why does multiplicity matter?
The registry contains a broad collection of outcomes and analyses. When many outcomes or comparisons are examined, some may appear notable by chance even if no underlying difference exists. As a general statistical principle, multiplicity procedures can control the chance of false-positive findings across a defined family of tests, but they can also affect precision and power. The registry does not report whether such a procedure was planned or used, how tests were grouped, or which secondary analyses were intended to be confirmatory. The listed secondary p-values should therefore be understood as unadjusted in the recalculations and should not be treated as a collection of independent confirmations.
There are several other aspects of the analysis that cannot be resolved from the record. The analysis populations, exclusions after randomization, outcome-specific denominators, handling of missing observations, and missing-data sensitivity analyses are not reported. These details matter because a group summary can depend on which participants contributed data and on how absent measurements were treated. The arm counts attached to posted outcomes provide context for those summaries, but do not fully describe the underlying analysis population or all data-processing decisions.
The study’s original sample-size justification, planned effect, and original design assumptions are not reported. The separate planning illustrations use the observed recalculated effect and stated planning assumptions; they are not evidence about the trial’s original design. General power calculations concern the probability of detecting a specified effect under stated assumptions. They do not change the uncertainty in the observed estimates and should not be used to reinterpret a non-small p-value as proof of no effect.
11. Confidence Intervals and Precision
For the primary endpoint, the recalculated mean difference is 0.3, and its 95% confidence interval extends from -0.531 to 1.132. The interval crosses zero, so the posted summary statistics are compatible with differences in either direction. Its width also indicates that the point estimate should not be read as a highly precise measure of the between-group contrast. The interval expresses uncertainty in the estimated mean difference; it does not describe the range of individual participants’ changes.
The arm-level standard errors for the primary outcome are 0.3 in each group. These quantify uncertainty around the group means, not individual variability. The confidence interval for the recalculated contrast is derived from the posted summaries and is not the interval from the sponsor’s mixed model. The registry does not report a confidence interval for the sponsor estimate of -0.3. Consequently, the registry’s p-value of 0.58 does not supply the same information about plausible effect sizes that an interval would provide.
Intervals for the selected secondary outcomes also vary. The recalculated endurance-capacity interval, from 0.368 to 2.032, lies above zero, while the intervals for functional status, from -0.909 to 1.309, and body weight, from -0.863 to 2.463, include zero. These recalculations are unadjusted, and the corresponding sponsor analyses do not include confidence intervals in the registry record. The intervals should be considered in light of the full set of outcomes and the unreported multiplicity approach.
As a general principle, precision depends on the amount and variability of information used in an estimate, as well as the analysis method. A confidence interval does not establish clinical importance: that requires context about the outcome scale and meaningful change, which the registry does not provide. The interval is also conditional on the calculation’s assumptions. Here the recalculated intervals are simple, unadjusted comparisons, so they are not a substitute for the trial’s model-based analysis or its unreported model-based uncertainty.
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.
| Effect to detect | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 652 | 873 |
| 75% of the observed effect | 1,159 | 1,551 |
| 50% of the observed effect | 2,607 | 3,489 |
The planning illustrations express the number of participants per arm for 80% power and the number of participants per arm for 90% power. They are not total event counts because these outcomes are continuous, not time-to-event outcomes. The assumptions stated for the illustrations are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each illustration considers an effect equal to a stated fraction of the observed effect. For example, rows describe planning for 100%, 75%, or 50% of the observed effect.
The 80% power column means the illustrated number of participants per arm under which the calculation would have an 80% probability of detecting the specified effect, if the assumptions used in the calculation hold. The 90% power column describes the corresponding planning target for a 90% probability. These are planning targets, not guarantees: actual performance depends on whether the assumptions and effect size are appropriate. Smaller effects require more participants to detect under the same general assumptions, which is why the illustrations increase as the target moves from the full observed effect to a smaller fraction.
For the primary outcome, the planning estimates are 652 participants per arm for 80% power and 873 for 90% power when planning for 100% of the observed effect. For 75% of the observed effect, the figures are 1,159 and 1,551; for 50%, they are 2,607 and 3,489. The calculations are based on the observed recalculated effect, not the trial’s original design justification. The original design assumptions and sample-size rationale are not reported in the registry record. These figures are not observed power; they are hypothetical planning illustrations under the stated assumptions.
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 z1−α/2 = 1.960) and the desired power (z1−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
- Observed difference Δ = 0.300; pooled standard deviation σ = 1.933.
- n = 2 × (1.96 + 0.842)2 × 1.9332 / 0.3002 = 651.6, rounded up to 652 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 <- 0.300000000000001 # observed difference in means
sigma <- 1.93275853524323 # 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(2367105)
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 = 652 (80% power), 873 (90% power)
75% of observed effect: n per arm = 1,159 (80% power), 1,551 (90% power)
50% of observed effect: n per arm = 2,607 (80% power), 3,489 (90% power)
power.t.test: 652.5
Simulated power at n = 652 per arm: 0.798 (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.
14. Analyses Reported by the Sponsor
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| Mixed Models Analysis | Mean Difference (Final Values) -0.3 | not reported | 0.580 |
The registry reports the sponsor’s primary analysis as a mixed models analysis of mean difference in final values. It gives an estimate of -0.3 and p = 0.58, but does not report a confidence interval or the details needed to reconstruct the model. The recalculation instead uses the posted group means and standard errors to make a simple unadjusted comparison. It estimates a difference of 0.3, with a 95% confidence interval from -0.531 to 1.132 and p = 0.48.
The direction of the two estimates differs, and their p-values are not identical. The registry does not state why, so it is not possible to attribute the difference to a particular model feature or coding convention. The same distinction appears in the selected secondary summaries: the sponsor reports -1.2 for endurance capacity, 0.0 for functional status, and -0.7 for body weight, while the recalculated contrasts are 1.2, 0.2, and 0.8, respectively. These different values should be reported as separate analyses, not combined or averaged.
The sponsor’s mixed-model analysis is the trial’s reported analysis. The recalculation is a secondary, transparent comparison from posted summary statistics and does not replace the sponsor method. Because the registry record lacks model details and model-based intervals, the recalculated interval should not be represented as the uncertainty interval for the sponsor estimate. Nor can the registry record establish which technical choices account for the differing values.
15. Multiplicity, Missing Data and Analysis Populations
The registry lists a broad set of outcome measures and analyses, including 45 outcome measures, 47 analyses, and 30 posted secondary outcomes. When many hypotheses are tested, the chance of at least one apparently notable result can increase even if no true effects exist. As a general statistical concept, multiplicity refers to this problem and to methods that may adjust inference across a defined family of tests. The registry does not report whether multiplicity was addressed, which outcomes were grouped together for any adjustment, or which outcomes were designated as confirmatory.
Accordingly, the recalculated p-values for secondary outcomes are unadjusted. They indicate the results of the individual comparisons under their respective assumptions, but do not account for the number of outcomes or analyses. Their evidential weight is therefore limited, particularly when considered alongside the many listed outcomes. The primary outcome is the clearest focus for the principal question, while secondary findings can be used to describe patterns and generate further questions rather than to make a set of independent claims.
The registry record does not report the analysis populations, post-randomization exclusions, participant flow for each endpoint, missing-data amounts, or sensitivity analyses for missing observations. It also does not describe how missing values were handled in the sponsor’s mixed models. These omissions matter because the analyzed data may depend on which participants have usable measurements and on the assumptions used for missing outcomes. The outcome-level arm counts are reported, but they do not answer every question about eligibility for analysis or missingness.
The protocol’s original sample-size justification, the prespecified target effect, interim analysis plans, and detailed statistical analysis plan are not reported in the registry record. This means the posted results do not establish whether every reported analysis followed a prespecified procedure, or how any potential deviations were handled. The known planning assumptions for the separate sample-size illustrations should not be mistaken for the trial’s original design assumptions.
16. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Placebo + Lifestyle Therapy | 1 | 41 | 2.4% |
| Testosterone + Lifestyle Therapy | 1 | 42 | 2.4% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Placebo + Lifestyle Therapy | 0 of 41 |
| Testosterone + Lifestyle Therapy | 0 of 42 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 5% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Placebo + Lifestyle Therapy | 12 of 41 |
| Testosterone + Lifestyle Therapy | 6 of 42 |
Most frequent serious adverse event terms
| Event term | Organ system | Placebo + Lifestyle Therapy | Testosterone + Lifestyle Therapy |
|---|---|---|---|
| Congestive heart failure | Cardiac disorders | 1 of 41 | 1 of 42 |
| Cellulitis | Skin and subcutaneous tissue disorders | 1 of 41 | 1 of 42 |
| Cardiac arrest | Cardiac disorders | 1 of 41 | 0 of 42 |
| Pulmonary embolism | Respiratory, thoracic and mediastinal disorders | 0 of 41 | 1 of 42 |
| Bleeding peptic ulcer | Gastrointestinal disorders | 1 of 41 | 0 of 42 |
| Duodenitis | Gastrointestinal disorders | 0 of 41 | 1 of 42 |
| Acute kidney injury | Renal and urinary disorders | 1 of 41 | 0 of 42 |
| Ankle fracture | Musculoskeletal and connective tissue disorders | 0 of 41 | 1 of 42 |
| Idiopathic thrombocytopenia | Blood and lymphatic system disorders | 0 of 41 | 1 of 42 |
| Hyperosmolar hyperglycemic state | Endocrine disorders | 0 of 41 | 1 of 42 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Placebo + Lifestyle Therapy | Testosterone + Lifestyle Therapy |
|---|---|---|---|
| hypoglycemia, asymptomatic and symptomatic | Metabolism and nutrition disorders | 4 of 41 | 4 of 42 |
| Elevated PSA | Neoplasms benign, malignant and unspecified (incl cysts and polyps) | 4 of 41 | 1 of 42 |
| Dizziness/orthostasis | Vascular disorders | 4 of 41 | 1 of 42 |
Serious events with the highest arm-level rate: congestive heart failure (2.4%), cardiac arrest (2.4%), bleeding peptic ulcer (2.4%), cellulitis (2.4%), acute kidney injury (2.4%).
The registry reports serious adverse events for the placebo-plus-lifestyle group and the testosterone-plus-lifestyle group. The serious-event risk sets are 41 and 42, and 1 participant in each group is reported as affected. The registry reports 0 deaths in each group. These counts describe the posted serious-adverse-event summary; they do not show the timing, duration, severity beyond the serious classification, or relationship of an event to treatment.
For other adverse events, the registry reports 12 affected in the placebo-plus-lifestyle group and 6 in the testosterone-plus-lifestyle group, with risk sets of 41 and 42. The record lists congestive heart failure, cardiac arrest, bleeding peptic ulcer, cellulitis, acute kidney injury, and pulmonary embolism among the serious terms, each shown as 2.4%. The record does not provide enough detail to determine event timing or whether the listed terms occurred in the same or different participants. The terms should not be summed or interpreted as a count of unique people.
These are descriptive safety figures from the registry record. They do not establish that a treatment caused or prevented an event, and the counts alone do not provide a complete comparison of safety. Follow-up duration by event, exposure, adjudication procedures, and the relationship assessment are not reported in the registry record. The figures therefore belong alongside, rather than in place of, the trial’s outcome estimates and the limits of its safety reporting.
17. What the Result Does, and Does Not, Mean
The primary result describes the difference in average change on a specific performance test over 6 months among participants in the two randomized groups. The simple recalculation estimates a difference of 0.3, but its confidence interval extends from -0.531 to 1.132. That uncertainty means the posted summary statistics do not precisely establish the direction or size of the between-group difference. The sponsor’s mixed-model result is -0.3 with p = 0.58; it too does not provide a model-based confidence interval in the registry record.
This finding should not be translated into a claim that testosterone plus lifestyle therapy does or does not work. A non-small p-value is not proof that there is no difference, and a point estimate alone is not evidence that a difference is important. The registry does not report a threshold for clinically meaningful change on the physical performance test. It also does not report the information needed to judge how closely the endpoint reflects broader outcomes such as independence, frailty, or health-service use.
The result applies to the registered comparison and the posted follow-up period. It does not establish outcomes beyond 6 months or determine what would happen under different lifestyle programs, treatment regimens, or populations. The trial description concerns obese older Veterans with obesity and hypogonadism; the registry does not report detailed eligibility criteria sufficient to characterize generalizability more precisely.
Secondary outcomes add context but do not convert the primary result into a broader conclusion. Endurance, functional status, body weight, body composition, and bone measures are distinct outcomes. The available detailed secondary estimates vary, and the registry does not report a multiplicity approach. Safety counts are also descriptive and do not establish causation. The most defensible interpretation is therefore bounded: these are uncertain estimates from a randomized comparison, with a non-small primary p-value, selected secondary findings, and incomplete reporting of model details, missing data, and analysis plans.
18. Why This Trial Matters Statistically
This trial is statistically notable because it asks a focused comparative question within a design that holds the lifestyle program in common across groups. Both arms received a diet and supervised exercise program, while the assigned drug differed. That design makes the added contribution of testosterone the central contrast, subject to the trial’s implementation and analysis details. It also means the comparison is not a test of lifestyle therapy against no lifestyle therapy.
The primary endpoint is a continuous functional measure with a defined task-based scoring system. Such outcomes can reveal differences in average performance that may not be apparent from a single event count. At the same time, statistical interpretation requires attention to the scale, measurement variability, and the uncertainty around the group contrast. The recalculated confidence interval is therefore important: it shows that the posted summary estimates leave considerable uncertainty about the direction and size of the difference.
The distinction between the sponsor’s mixed-model analysis and the unadjusted recalculation is also instructive. Both refer to the same broad outcome comparison, but they use different summaries and report different estimates. The registry does not include enough model detail to explain the divergence. This illustrates why the analysis method and its reporting matter alongside the outcome estimate, and why a recalculation from summary statistics should not be mistaken for a reconstruction of the trial’s full analysis.
Finally, the registry lists a broad range of secondary outcomes and analyses. That breadth can help characterize multiple dimensions of physical health, but it also makes prespecification and multiplicity important. Those details, as well as missing-data procedures and original design assumptions, are not reported. The case therefore highlights a general principle: a useful trial interpretation depends not only on point estimates and p-values, but also on precision, analysis transparency, outcome hierarchy, and the limits of the available record.
19. 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 trial-specific reporting gaps limit interpretation. The registry describes the study as randomized and triple-masked, but does not report the sequence-generation procedure, allocation concealment, masking procedures by role, or an assessment of whether masking was maintained. These details cannot be inferred from the design labels alone.
The registry does not report complete eligibility criteria or the age range, so the population cannot be characterized more specifically than the description of obese older Veterans with obesity and hypogonadism. It also does not provide detailed information on testosterone dose or schedule, adherence, treatment duration, or implementation of the lifestyle program. The dietary target and supervised exercise components are described, but further delivery details are absent.
The primary outcome is well described in terms of its tasks and scoring direction, but the record does not state a clinically important difference threshold. It also does not provide the sponsor model’s confidence interval or full specification. The reported sponsor estimates and simple recalculations differ, and the registry does not explain the sign or magnitude differences. No conclusion about their cause can be drawn from the posted details.
Analysis populations, missing-data amounts and handling, post-randomization exclusions, and sensitivity analyses are not reported. The multiplicity plan and status of secondary outcomes as confirmatory or exploratory are also not reported. The original sample-size rationale and interim analysis plan are absent. Finally, safety reporting is limited to summary counts and listed terms; event timing and treatment relationship are not reported. These limitations are specific to what the registry record reports and do not determine whether unreported information exists elsewhere.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Lifestyle Intervention and Testosterone Replacement in Obese Seniors — NCT02367105.
- Registry record last updated 2022-07-26; status last verified 2022-01.
- Results first posted 2020-08-31.
- 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.
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23. Record Summary
The registry record describes a completed phase 3 randomized, triple-masked, parallel-group study of testosterone plus lifestyle therapy versus placebo plus lifestyle therapy in obese older Veterans with obesity and hypogonadism. Enrollment is listed as 83. The primary outcome was six-month change in a modified physical performance test, where higher scores indicate better physical function.
The posted primary arm means were 4.6 for placebo plus lifestyle therapy and 4.9 for testosterone plus lifestyle therapy. The unadjusted recalculation estimates a mean difference of 0.3, with a 95% confidence interval from -0.531 to 1.132 and p = 0.48. The sponsor’s mixed-model analysis reports -0.3 and p = 0.58; a confidence interval and full model details are not reported.
Selected secondary results vary, and their recalculated p-values are unadjusted. The registry lists multiple outcome measures, but does not report a multiplicity plan, full missing-data methods, or the original sample-size justification. Safety counts are descriptive. The estimates should be interpreted with these reporting limits in view.