Biobehavioral Interventions for HIV-negative, Stimulant Using Men Who Have Sex With Men: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Biobehavioral Interventions for HIV-negative, Stimulant Using Men Who Have Sex With Men (NCT01140880), a randomized phase 2 study. The primary outcome is Time From Exposure to Truvada Initiation.

2. Clinical Question

3. Trial Design

This was a randomized, phase 2, parallel-group study with no masking reported. Enrollment was 170. The registry lists the study as completed, with a start of 2010-05 and primary completion in 2013-03. Friends Research Institute, Inc. is listed as the sponsor. The study title and objectives describe a behavioral intervention intended to address stimulant use and access to PEP following a potential HIV exposure.

The two arms were contingency management and yoked contingency management. In both arms, participants submitted urine samples on Monday, Wednesday, and Friday for 8 weeks, for 24 planned samples. In the contingency-management arm, increasingly valuable incentives were linked to samples without stimulant metabolites. In the yoked condition, incentives were described as independent of stimulant use. The record also lists Truvada as a drug intervention, consistent with the primary outcome concerning its initiation after exposure.

The primary endpoint was reported for 40 participants with evaluable data who initiated Truvada during the study: 26 in contingency management and 14 in yoked contingency management. That endpoint population is not the same as the enrollment count. The secondary abstinence outcome and the adverse-event counts each use 70 participants per arm. These different denominators describe different reported analyses or reporting populations; the registry record does not explain how participants moved between those populations or why the counts differ.

The registry record does not report the original sample-size justification, the detailed randomization procedure, or a statistical analysis plan. It also lists no reported analyses. Accordingly, the posted group summaries and unadjusted comparisons are the basis for describing the quantitative results, rather than evidence of a broader prespecified analysis strategy.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: 40 participants with evaluable data initiated Truvada during the course of the study.

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.

Population: 170 participants enrolled. 30 participants in the Yoked Contingency Management arm were involved in a protocol violation that rendered their data unusable. An additional 14 participants from each arm were either withdrawn, died (n = 1, not study related), or were lost to follow-up. Thus, baseline N = 140 (70/70), and follow-up N = 112 (56/56).

6. Primary Endpoint

The registry lists the primary outcome as Time From Exposure to Truvada Initiation, measured over 6-month follow-up.

The primary endpoint measures the number of hours between exposure to viral inoculum and the start of the Truvada medication regimen. It is reported as a mean with standard deviation at 6-month follow-up. For this measure, a smaller value indicates a shorter interval between the exposure and initiation among participants whose initiation data could be evaluated.

This timing measure addresses one part of the study’s stated PEP objective: whether participants initiate medication promptly following a potential exposure. It does not, on its own, measure whether all randomized participants experienced a potential exposure, whether they initiated PEP, how well they adhered to the regimen, or whether they completed it. Nor does it measure HIV incidence. The registry record describes the primary population as 40 participants who initiated Truvada and had evaluable data. That restriction matters when interpreting the endpoint: it is a comparison of initiation timing among those participants, rather than an all-randomized comparison of the likelihood of starting PEP.

Mean time is useful for conveying the average delay in hours, while the standard deviation describes how spread out individual times were around each arm’s mean. The means were close, and the reported standard deviations indicate appreciable variation among participants. These summaries provide a direct description of timing but do not show the full distribution, such as whether a small number of long delays influenced the mean. Distributional details are not reported in the registry record.

7. Results Posted in the Registry

• Yoked Contingency Management: mean 33.00 versus 32.80 on control; difference 0.20 (95% CI -10.04 to 10.44), standardized effect d = 0.01; z-test p = 0.969.

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.

Abstinence From Stimulant Drug Use (Cocaine, Amphetamine, Methamphetamine)

• 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:
  • Yoked Contingency Management: mean 6.00 versus 8.90 on control; difference -2.90 (95% CI -5.49 to -0.31), standardized effect d = -0.37; z-test p = 0.028.
• Interpretation:
  • The 95% confidence interval excludes no difference, so the mean is statistically lower for Yoked Contingency Management than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

The posted secondary result concerns stimulant-free urinalyses, a measure of stimulant abstinence during the thrice-weekly assessment period. It addresses a behavioral target of the intervention, whereas the primary result concerns the timing of Truvada initiation after a potential exposure. These outcomes sit at different points in the proposed sequence: the intervention targets stimulant use, while PEP initiation is a subsequent prevention behavior. The registry record does not establish that a change in the first outcome caused a change in the second.

The overall pattern is not uniform across endpoints. The primary comparison does not show a clear difference in mean initiation time, while the secondary comparison points toward a difference in stimulant-free urinalyses. This distinction is important: a behavioral measure can differ between arms without a corresponding detectable difference in a downstream behavior, particularly when the downstream endpoint is available only for participants who initiated Truvada and had evaluable data.

The secondary comparison is unadjusted. When several outcomes or comparisons are considered, the chance of obtaining at least one apparently noteworthy result can increase unless the analysis plan addresses multiplicity. The registry record lists four outcome measures but reports only one secondary result and no reported analyses. It does not state which outcomes were primary in any analysis hierarchy beyond the posted primary endpoint, whether additional comparisons were conducted, or how multiplicity was handled. The unadjusted secondary result therefore carries less confirmatory weight than a result supported by a prespecified and fully reported analysis plan.

These cautions do not erase the observed secondary pattern; they frame how much weight it can bear. It is a result for a separate measure and a different reported denominator, not a replication of the primary endpoint. The registry record does not provide the detailed results for adherence, PEP completion, or other potential-exposure outcomes. As a result, the secondary abstinence finding cannot fill those evidentiary gaps or establish that the broader prevention objectives were met.

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

• Abstinence From Stimulant Drug Use (Cocaine, Amphetamine, Methamphetamine)

9. Statistical Interpretation

10. Statistical Methods Explained

The primary and secondary outcomes are continuous measures summarized by a mean and standard deviation. In general, a mean represents the arithmetic average of observed values. A standard deviation describes how dispersed individual observations are around that average; it is not the uncertainty in the mean itself. The reported endpoint summaries use these quantities to describe time to Truvada initiation and the number of stimulant-free urinalyses.

What does the mean difference represent?

The comparison is expressed as the mean in the yoked contingency-management arm relative to the mean in the contingency-management arm. For the primary endpoint, the arm means were 33.0 and 32.8 hours, and the posted difference was 0.2 hours. For the secondary endpoint, the respective means were 6.0 and 8.9 stimulant-free urinalyses, and the posted difference was -2.9. The direction depends on the outcome and the stated arm ordering. A positive value for time means the yoked arm’s mean was higher; a negative value for stimulant-free urinalyses means its mean was lower.

In general, a mean difference is easy to interpret in the outcome’s original units, but it compresses the data into a single contrast. It does not show every participant’s result, the shape of the distribution, or whether there are subgroups with different patterns. The registry record does not post participant-level distributions for these outcomes.

How should the confidence interval be read?

In general, a confidence interval describes the uncertainty around an estimated effect under the method used to calculate it. It gives a range of values compatible with the observed data and that method’s assumptions. For the primary difference, the interval extends from -10.04 to 10.44 hours. This range includes zero and values on both sides, so the estimate does not precisely locate the difference. For the secondary difference, the interval extends from -5.486 to -0.314 stimulant-free urinalyses. Its endpoints are both below zero for the stated comparison direction.

A confidence interval is not a guarantee that the true effect lies in the displayed range, nor does it show the probability that one particular value is correct. It is also not a range containing most individual participants’ values; the standard deviations convey a different aspect of the data. The posted interval widths matter alongside the point estimates: the primary interval leaves room for potentially meaningful differences in either direction, while the secondary interval is narrower and lies on one side of zero.

What does an unadjusted p-value say?

In general, a p-value describes how unusual data at least as incompatible with a null hypothesis would be if that hypothesis and the model assumptions were true. It is not the probability that the null hypothesis is true, and it does not quantify clinical importance. The primary unadjusted p-value is 0.969; the secondary unadjusted p-value is 0.028. These values accompany the corresponding estimates and intervals, but they do not replace them. In particular, an unadjusted p-value does not account for the number of outcomes or comparisons unless an adjustment is applied.

The registry record lists no reported analyses and does not describe whether the displayed comparisons were prespecified, adjusted, or selected from a larger analysis set. Thus, the p-values are best treated as unadjusted summaries of the posted contrasts. No claim about a prespecified threshold or confirmatory testing strategy can be made from the record.

Why do denominators and analysis populations matter?

The primary comparison includes 26 and 14 participants with evaluable initiation data who initiated Truvada. The secondary comparison includes 70 participants in each arm. Adverse-event reporting also lists 70 at risk in each arm. The overall enrollment was 170. In general, a result applies most directly to the participants whose outcomes contributed to that result. Different denominators can arise for different outcomes, but the reasons must not be assumed. The registry record does not explain the differences in counts, provide a participant flow, or state how missing outcome data were handled.

Because the primary endpoint population is defined by initiation, this comparison is not an intention-to-treat estimate of the effect on the probability of initiating. If initiation is related to participant characteristics or treatment assignment, conditioning on initiation can alter the population represented by the timing comparison. Whether that occurred cannot be determined from the posted information. The record does not report an all-randomized analysis of initiation or details of the analysis population for the other outcomes.

What assumptions underlie the planning illustrations?

The sample-size illustrations use the observed effect and assume a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each row considers a stated fraction of the observed effect. For non-time-to-event outcomes, the displayed values are participants per arm. These calculations are planning illustrations based on the observed estimates, not the original study design. The registry record does not report the original sample-size assumptions or justification.

In general, estimates based on small or restricted analysis populations can be uncertain, and planning calculations based on an observed effect inherit uncertainty from that estimate. The illustrations should therefore be read as conditional planning scenarios rather than predictions of a future trial’s results. They do not change the interpretation of the observed confidence intervals or establish the appropriate design for a new study.

11. Confidence Intervals and Precision

The primary mean difference is 0.2 hours, with a 95% confidence interval from -10.04 to 10.44 hours. The interval includes zero and extends to differences in both directions. This means the posted estimate is not precise enough to identify the direction of a possible arm difference: the data are compatible with a shorter mean time in one arm or a longer mean time in that arm, within the interval’s range. The interval is also wide relative to the small point estimate, so the near-equal means should not be mistaken for a precise demonstration of equivalence.

Precision is affected by both the amount of information and variability in the outcome. The primary analysis used 40 participants, split between groups of 26 and 14, and the standard deviations were 15.1 and 16.1 hours. Unequal group counts can contribute to uncertainty, especially when the smaller group is limited in size. The registry record does not provide a prespecified margin for equivalence or non-inferiority, so the confidence interval cannot be interpreted against such a margin.

The secondary difference has a 95% confidence interval from -5.486 to -0.314 stimulant-free urinalyses. It lies below zero for the comparison of yoked contingency management relative to contingency management. This interval is more directionally constrained than the primary interval, but its interpretation remains subject to the unadjusted status of the comparison, the separate analysis population, and the absence of a reported multiplicity plan. Precision does not resolve those design and analysis questions.

In general, confidence intervals describe uncertainty in an estimated group contrast, whereas standard deviations describe spread among participants. Neither alone establishes practical importance. The registry record does not state what difference in initiation time or abstinence would be considered important, and the primary interval consequently cannot be judged against a recorded clinical threshold.

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 sample-size illustrations are planning calculations based on the observed effect, not the trial’s original design assumptions. The registry record does not report the original sample-size justification. The listed planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each scenario uses the stated fraction of the observed effect. For these non-time-to-event outcomes, the figures are participants per arm, not total events.

The 80% power column gives the estimated participants per arm for a planning scenario designed to have an 80% chance of detecting the specified effect under the calculation assumptions, if that effect and assumptions held. The 90% power column gives the corresponding per-arm planning number for a higher chance of detecting that same specified effect. These are design calculations, not forecasts of the results of a later study. This is not observed power.

Rows that plan for a smaller fraction of the observed effect require more participants per arm. That pattern reflects a general feature of study planning: smaller differences are harder to distinguish from random variation, so more information is needed to detect them with the same planned power. The figures should not be read as recommendations without considering whether the assumed effect is scientifically meaningful, whether equal allocation is appropriate, and whether the calculation model fits the intended study.

The primary observed mean difference is small relative to the uncertainty around it, so its planning illustrations are especially sensitive to the effect used in the calculation. The secondary outcome has a different estimate and scale, so its planning values are not interchangeable with those for the primary outcome. Each set of figures belongs to its own outcome and observed effect.

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, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = 0.200; pooled standard deviation σ = 15.449.
2. n = 2 × (1.96 + 0.842)² × 15.449² / 0.200² = 93,670.0, rounded up to 93,670 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 <- 0.200000000000003                      # observed difference in means
sigma <- 15.4493910627742                     # 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(1140880)
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 = 93,670 (80% power), 125,398 (90% power)
 75% of observed effect: n per arm = 166,525 (80% power), 222,929 (90% power)
 50% of observed effect: n per arm = 374,680 (80% power), 501,591 (90% power)
power.t.test: 93670.9 
Simulated power at n = 93,670 per arm: 0.800 (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. Multiplicity, Missing Data and Analysis Populations

The registry record lists four outcome measures and identifies time from exposure to Truvada initiation as the primary outcome. One secondary outcome is posted: abstinence from stimulant drug use, measured as stimulant-free urinalyses. The record lists no reported analyses. It does not describe a hierarchy for testing outcomes, a correction for multiple comparisons, or another multiplicity strategy. The posted p-values are therefore unadjusted, and the secondary result should be interpreted with that limitation in mind.

Multiplicity matters because testing several outcomes can increase the chance that at least one result appears unusual even when there is no true effect on any outcome. In general, methods for addressing this issue depend on the planned questions and analysis structure. Since the registry record does not report those details, it is not possible to determine whether the displayed secondary test was part of a prespecified confirmatory family, an exploratory analysis, or one of multiple analyses.

Missing-data handling is also not reported in the registry record. The primary result includes 40 participants with evaluable data who initiated Truvada, while the secondary and adverse-event summaries each list 70 participants per arm. Enrollment was 170. The record does not provide a flow of participants, reasons for unavailable outcomes, rules for defining evaluable data, or an imputation or sensitivity-analysis approach. These omissions limit assessment of whether the analyzed participants represent the randomized groups.

The record does not state whether the primary analysis followed an intention-to-treat principle, whether additional populations were defined, or how protocol deviations were handled. It also does not report interim analyses or stopping rules. These aspects of the statistical plan are not reported in the registry record and should not be inferred from the posted summary statistics.

15. Safety Results

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

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 0% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: suicidal ideation/exacerbated depression (1.4%), death (1.4%).

The adverse-event summaries list 70 participants at risk in each arm. One participant in each arm is listed as having a serious adverse event. Other adverse events are listed for 8 participants in contingency management and 0 in yoked contingency management. These are counts of affected participants in the registry summary, not a complete description of event timing, severity beyond the serious classification, or causal relationship to an intervention.

The serious-event term list includes suicidal ideation/exacerbated depression (1.4%) and death (1.4%). The record does not identify the arm associated with each term in that list. Death counts by group are not reported in the registry record. The listed percentages should be read as registry-reported values, not as estimates adjusted for exposure time or differences in follow-up.

Safety counts do not show whether events were judged related to the study condition, whether participants experienced more than one event, or when events occurred. Those details are not reported in the registry record. The adverse-event denominators also differ from the primary endpoint denominators, so they should not be conflated with the analysis of Truvada initiation timing.

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

The posted results describe a comparison of two behavioral conditions in a study of stimulant-using men who have sex with men. For the primary endpoint, the reported group means for time to Truvada initiation are close, and the confidence interval for the mean difference includes zero while extending across values in both directions. The result is uncertain rather than a precise estimate of no difference. It does not establish equivalence between the conditions.

The primary outcome applies to the 40 participants who initiated Truvada and had evaluable timing data. It does not answer whether assignment to one condition changed the likelihood that all randomized participants initiated PEP. The registry’s stated objectives also include adherence and completion, but detailed results for those objectives are not reported in the registry record. No conclusion about those outcomes follows from the timing comparison alone.

The secondary outcome measures stimulant-free urinalyses, not PEP behavior. Its posted estimate favors a higher mean count in contingency management, but the comparison is unadjusted and relates to a separate outcome and analysis population. It cannot establish that abstinence changes caused differences in PEP initiation, nor can it demonstrate an effect on HIV incidence. The registry record does not report HIV infection results as an outcome in the posted analyses.

In general, an observed group difference is an estimate subject to sampling variability and the assumptions of its analysis. The confidence intervals express uncertainty about the group contrasts, while the reported means and standard deviations describe the observed summaries. Neither a p-value nor a planning calculation supplies missing information about the analysis population, missing data, outcome distributions, or prespecification.

The findings are best understood as registry-posted estimates for specific outcomes in specific reported populations. They do not establish that either condition works or fails overall, and they do not support medical advice. Broader conclusions would require the full protocol and analysis details, complete outcome reporting, and consideration of how participants without evaluable outcomes were handled.

17. Why This Trial Matters Statistically

This trial is statistically informative because it places a behavioral intervention and a biomedical prevention behavior in the same research question. The intervention was designed to target stimulant use, while the primary endpoint focused on how quickly Truvada was started after a potential exposure. Separating these measures helps avoid treating a behavioral outcome as though it were itself a PEP outcome.

The reported results illustrate why endpoint-specific interpretation matters. The primary analysis is based on participants who initiated Truvada and had evaluable timing data, whereas the secondary abstinence analysis uses a larger reported group in each arm. The denominators affect what each estimate describes. Without a participant flow and explicit missing-data methods, it is difficult to assess how the analyzed groups relate to all randomized participants.

The trial also highlights the distinction between a point estimate and its precision. Similar observed means do not establish that two conditions are equivalent, particularly when the interval around the contrast remains compatible with differences in either direction. Conversely, an unadjusted secondary result should not be treated as a definitive answer to a broader study question when the record does not document a multiplicity plan.

Finally, the planning illustrations show how strongly sample-size requirements depend on the effect chosen for detection. Calculations based on the observed effect are useful for understanding planning scenarios, but they do not replace the original design rationale or establish what a future study should target. The original sample-size justification and statistical plan are not reported in the registry record. This makes the study a useful example of why complete outcome, analysis, and design reporting is essential to judging evidence.

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.

A central limitation is the restricted primary analysis population: the endpoint includes 40 participants who initiated Truvada and had evaluable data, rather than all enrolled participants. Since the outcome is defined only among initiators in this analysis, the comparison does not directly estimate the effect of assignment on the probability of initiation. The registry record does not explain why other enrolled participants are absent from this endpoint analysis or how their outcomes were handled.

Several reported denominators differ. The primary groups contain 26 and 14 participants, while the secondary and adverse-event summaries list 70 per arm. The record does not provide a participant flow or clarify the reasons for these differences. This makes it difficult to evaluate selection into the endpoint populations or compare the results across outcomes.

The registry record does not report the original sample-size justification, statistical analysis plan, multiplicity approach, missing-data methods, or detailed analysis populations. It also does not provide the reported analyses for the other stated objectives, including adherence and PEP completion. These gaps limit assessment of prespecification and of the broader prevention questions.

The primary estimate has substantial uncertainty, and no equivalence margin or threshold for an important difference is reported. The secondary comparison is unadjusted, and the registry does not describe how it fits into the full set of planned outcomes or analyses. Finally, the posted summaries do not show individual-level distributions or event timing. These limitations do not invalidate the reported estimates, but they constrain how broadly or confidently they can be interpreted.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Biobehavioral Interventions for HIV-negative, Stimulant Using Men Who Have Sex With Men — NCT01140880.
• Registry record last updated 2025-03-17; status last verified 2025-03.
• Results first posted 2014-07-02.
• 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 phase 2 parallel-group study with 170 enrolled participants and no masking reported. The study compared contingency management with yoked contingency management among stimulant-using men who have sex with men. Its primary outcome was mean time from exposure to Truvada initiation at 6-month follow-up.

Among 40 participants with evaluable data who initiated Truvada, the mean times were 32.8 hours and 33.0 hours. The posted mean difference was 0.2 hours, with a 95% confidence interval from -10.04 to 10.44 hours and an unadjusted p-value of 0.969. The secondary abstinence outcome was reported for 70 participants per arm; its comparison was unadjusted. The registry record does not report the original sample-size justification, a statistical plan, missing-data methods, or detailed analyses for the other stated objectives.