Methadone Maintenance for Prisoners: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Methadone Maintenance for Prisoners (NCT00378079), a randomized phase 3 study. The primary outcome is Treatment Retention in the Community.

2. Clinical Question

The clinical question is about treatment retention as measured by time spent in community treatment. The study summary also describes intended assessment of drug abuse, crime, and HIV risk behavior, and the registry lists employment as a secondary outcome. The posted primary result, however, is specifically about days in community treatment. It does not by itself establish what happened to every other outcome named in the study summary.

3. Trial Design

The registry identifies this as a randomized, phase 3, parallel-group trial with no masking. Its status is completed. The listed enrollment is 211. The start is recorded as 2003-09, and primary completion as 2008-01. The sponsor is Friends Research Institute, Inc.

Three strategies are listed: counseling only in prison; counseling only in prison with initiation of methadone in the community; and counseling and methadone maintenance in prison with continuation in the community. The study summary describes the intended comparison as treatment initiated in prison and continued after release versus counseling only or initiation of methadone in the community. Arm descriptions in the registry record are blank, so details beyond the listed intervention names and summary are not reported in the registry record.

For the primary outcome, the posted group counts are 64.0 for counseling only, 69.0 for counseling with community initiation, and 71.0 for prison initiation with continuation. These arm-specific values should be read as reported; they should not be treated as a new accounting of enrollment. The registry record does not report how randomization was generated or concealed, whether assignment was stratified, or how treatment adherence was assessed. Masking is recorded as none, but the record does not specify which study personnel or outcome assessors knew assignment.

The primary completion timeframe is one year post prison release, and the endpoint is measured in days in community treatment. The registry lists employment as a secondary outcome, measured as number of days employed in the past 30 at one year. Although the study summary mentions drug abuse, crime, and HIV risk behavior, the registry record does not provide their results in the posted outcomes. It also does not report a formal statistical analysis plan or the original assumptions used to plan the trial.

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: See above

Overall Study

Reasons for not completing this period:

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

6. Primary Endpoint

The registry lists the primary outcome as Treatment Retention in the Community, measured over one year post prison release.

The primary endpoint is treatment retention in the community, expressed as days in community treatment during one year post prison release. It is a continuous outcome: the registry reports a mean and standard deviation for each strategy. More days indicate a greater measured duration in community treatment, but the endpoint does not directly describe treatment quality, medication adherence, or outcomes beyond the stated timeframe.

Retention is used because it quantifies how long participants remained in community treatment after release. Comparing group means gives a concise measure of average time in treatment, while the standard deviations describe the spread of individual durations around each group mean. In this trial, the mean was 23.1 days for counseling only, 91.3 days for counseling with methadone initiated in the community, and 166.0 days for counseling and methadone maintenance initiated in prison with continuation.

As a general statistical point, a mean can summarize a continuous outcome but may not describe its full distribution. The record does not report medians, distribution plots, or the proportion with no days in treatment. Nor does it report whether the analysis accounted for censoring, loss to follow-up, or any particular distributional feature of days in treatment. Those details are not reported in the registry record, so the posted means should be interpreted as group summaries rather than a complete description of individual treatment histories.

7. Results Posted in the Registry

• 2 Counseling Only in Prison, With Initiation of Methadone Main: mean 91.30 versus 23.10 on control; difference 68.20 (95% CI 29.73 to 106.67), standardized effect d = 0.59; z-test p = <0.001.
• 3 Counseling and Methadone Maintenance in Prison, With Continu: mean 166.00 versus 23.10 on control; difference 142.90 (95% CI 100.31 to 185.49), standardized effect d = 1.09; z-test p = <0.001.

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.

Employment

• 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:
  • 2 Counseling Only in Prison, With Initiation of Methadone Main: mean 10.30 versus 12.00 on control; difference -1.70 (95% CI -5.30 to 1.90), standardized effect d = -0.16; z-test p = 0.355.
  • 3 Counseling and Methadone Maintenance in Prison, With Continu: mean 8.50 versus 12.00 on control; difference -3.50 (95% CI -7.01 to 0.01), standardized effect d = -0.34; z-test p = 0.051.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between 2 Counseling Only in Prison, With Initiation of Methadone Main and the control. The interval gives the range of effects that remain compatible with the data.
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between 3 Counseling and Methadone Maintenance in Prison, With Continu and the control. The interval gives the range of effects that remain compatible with the data.

The registry lists employment as a secondary outcome, measured as number of days employed in the past 30 at one year. Its overall pattern differs from the primary treatment-retention pattern: the posted group means do not show progressively higher employment across the strategies, and the estimated contrasts are small relative to their uncertainty. The primary endpoint measures time in community treatment; employment is a separate outcome with a different meaning and measurement window. The two outcomes need not move in the same direction.

Employment is relevant to the broader study context, but it does not directly measure treatment retention. A result on this outcome therefore neither confirms nor negates the primary finding. Nor can the registry record establish whether employment was a prespecified secondary endpoint, whether its analysis was adjusted, or how missing employment information was handled. Those details are not reported in the registry record.

Unadjusted secondary results generally carry less weight than a prespecified primary result because multiple outcomes and comparisons create more opportunities for apparently notable findings to occur by chance. This is a general statistical concern; the record does not report a multiplicity plan that would quantify or control it. The registry lists six outcome measures and no reported analyses, while only the employment secondary result is posted in the outcome information. The record does not explain how the posted secondary outcome relates to any unposted measures.

It is therefore appropriate to treat employment as supplementary context, not as a decisive test of the study's primary question. The available secondary information is too limited to support a broad account of drug use, crime, or HIV risk behavior, despite their appearance in the study summary. Results for those outcomes are not reported in the registry record.

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

• Employment

9. Statistical Interpretation

10. Statistical Methods Explained

These methods explanations describe general statistical ideas and the calculations represented by the posted results. They do not establish which methods were prespecified or used by the trial investigators; those details are not reported in the registry record.

What does a mean difference describe?

For a continuous outcome, a mean is the arithmetic average of observed values in a group. A mean difference compares the average in one group with the average in a reference group. Here the outcome is days in community treatment, and counseling only is the reference. The posted differences are 68.2 days for counseling with methadone initiated in the community and 142.9 days for prison-initiated methadone with continuation. Positive estimates indicate that the compared group had a higher reported mean than the reference group.

A mean difference summarizes the contrast in the original measurement units, which makes it directly interpretable as days. It does not say how many participants individually had longer treatment, nor does it describe the distribution of values. Two groups can have different means while still having substantial overlap among individual observations. The standard deviations in the registry record are large, emphasizing that group averages should not be mistaken for uniform participant experiences.

Why show standard deviations?

A standard deviation describes the spread of observed values around a group mean. It is not the uncertainty in the mean itself. The posted primary standard deviations are 72.5, 144.6, and 166.4 days in the three groups. The wide spread indicates that individual treatment durations varied substantially. A standard deviation is useful context when reading a mean, but it does not reveal whether the data are symmetric, skewed, clustered at zero, or otherwise concentrated. The registry record does not report distributional summaries that would answer those questions.

As a general point, strong skew or many observations at a boundary can make a mean less representative of a typical participant. The record does not report enough detail to determine whether such features were present. Alternative summaries, such as medians or quantiles, are not posted for this endpoint.

What does a confidence interval add?

A confidence interval gives a range of values compatible with the estimate under the statistical procedure used. In repeated use of a method with its assumptions met, intervals at a stated confidence level have a defined long-run coverage interpretation. A 95% interval is not a guarantee that a particular interval contains the true effect, and its endpoints do not represent the full range of individual outcomes. The primary intervals are 29.73 to 106.7 days and 100.3 to 185.5 days. Both lie above zero, the value corresponding to no mean difference.

The width of an interval reflects precision as well as the scale of the outcome and the method used. Wider intervals permit a broader range of effect values; narrower intervals indicate greater precision under the model. The record does not state the method used to construct the comparisons or intervals, so the calculation details cannot be verified from the registry record alone.

How should p-values be read?

A p-value describes how unusual data at least as incompatible with a specified null hypothesis would be if that hypothesis and the statistical model were true. It is not the probability that the null hypothesis is true, and it does not measure the size or importance of a difference. The posted primary unadjusted p-values are <0.001 for both contrasts. They provide evidence against a zero mean difference under the assumptions of the comparison, but they do not resolve concerns about missing observations, analysis choices, or multiple outcome testing.

Because the comparisons are unadjusted, their p-values do not account for a broader family of comparisons unless an adjustment was made elsewhere. The registry record does not report a multiplicity procedure. Therefore, the posted p-values should be understood as results for the individual displayed contrasts rather than as evidence that a family-wide error rate was controlled.

Why can over-dispersion matter?

As a general statistical concept, over-dispersion means that observed variability is greater than a model assumes. If a model understates variability, standard errors can be too small and confidence intervals too narrow, making results appear more precise than they are. For continuous outcomes, the shape of the distribution and the relation between the assumed model and actual variability can matter. The large standard deviations make variability important to consider, but the registry record does not describe an over-dispersion assessment or establish that a particular model assumption was violated.

For this continuous endpoint, the reported standard deviations are part of the descriptive summaries used to characterize spread. They should not be confused with a formal model diagnostic. The registry record does not report residual checks, robust standard errors, transformations, or another method for handling non-normality.

What can be inferred from the posted analysis?

The posted arm summaries and comparisons permit an unadjusted comparison of group means. They do not reveal whether adjustment for baseline factors was planned, whether an intention-to-treat population was used, or how deviations from assigned treatment were handled. The registry record reports zero analyses under its analysis listing, and no reported analyses are listed for the secondary outcome. Accordingly, there is no documented investigator analysis in the record against which to assess the recalculated contrasts.

The observed-effect planning illustrations are separate from evidence about this completed trial. They use the observed differences and stated assumptions to show hypothetical group sizes for future planning. They are not a measure of the probability that the completed trial detected an effect. The trial's original design assumptions, including any planned effect size or formal sample-size justification, are not reported in the registry record.

11. Confidence Intervals and Precision

The primary confidence intervals indicate the range of mean differences compatible with the unadjusted comparisons under their calculation assumptions. For counseling with methadone initiation in the community versus counseling only, the estimate is 68.2 days, with an interval from 29.73 to 106.7 days. For prison-initiated methadone with continuation versus counseling only, the estimate is 142.9 days, with an interval from 100.3 to 185.5 days.

Neither primary interval includes zero. The interval for community initiation still spans a range of possible mean differences, and the interval for prison initiation also spans a range. Thus, the point estimates should not be treated as exact values. The intervals express uncertainty about average differences, not the range of days experienced by individual participants. The large group standard deviations—72.5, 144.6, and 166.4 days—show that participant outcomes varied widely within groups, a distinct issue from the precision of the estimated mean differences.

The employment comparison intervals are less conclusive about the direction of a mean difference: the interval for community initiation is -5.303 to 1.903 days, and the interval for prison initiation extends from -7.012 days to an upper endpoint close to zero. The latter upper endpoint is reported as 0.012, which is more precise than the display precision allowed for this explanatory text; the registry's posted p-value is 0.051. These intervals should be read alongside the means and the outcome's status as secondary, rather than as definitive evidence of a difference or no difference.

Precision depends on the observed spread, group sizes, and the analysis method. The registry provides group counts and standard deviations, but does not report its interval-construction method, missing-data handling, or adjusted estimates. Therefore, the intervals are informative about the posted unadjusted comparisons but do not address every source of uncertainty relevant to the trial.

12. Planning a Similar Trial: Sample Size

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

The planning illustrations give hypothetical participants per arm for 80% power and participants per arm for 90% power. They are not total sample sizes or total event counts. The assumptions listed 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 to the stated fraction of the observed effect. These are planning illustrations based on the observed effects, not the trial's original design assumptions; the original sample-size justification and design assumptions are not reported in the registry record.

The 80% power column describes the number of participants per arm that the planning calculation estimates would be needed to have an 80% chance of detecting the specified effect under those assumptions. The 90% column uses a higher target chance of detection, and therefore generally calls for more participants per arm for the same effect. These are prospective planning quantities, not outcomes measured in this completed trial.

For the primary comparison with community initiation, planning for 100% of the observed effect gives 46 participants per arm for 80% power and 61 for 90% power. Planning for 75% of the observed effect gives 81 and 108; planning for 50% gives 181 and 242. For the comparison with prison initiation and continuation, the corresponding figures are 14 and 18 at 100% of the observed effect, 24 and 32 at 75%, and 53 and 71 at 50%.

Smaller effects are harder to distinguish from random variation, so they require more participants under the same assumptions. These values are not observed power. They do not show the probability that the completed trial detected its effect, and they do not demonstrate that the original design was adequate. The planning calculation assumes a two-arm comparison and does not describe the full three-arm design or any multiplicity adjustment.

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 = 68.200; pooled standard deviation σ = 115.678.
2. n = 2 × (1.96 + 0.842)² × 115.678² / 68.200² = 45.2, rounded up to 46 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 <- 68.2                      # observed difference in means
sigma <- 115.678107939612                     # 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(378079)
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 = 46 (80% power), 61 (90% power)
 75% of observed effect: n per arm = 81 (80% power), 108 (90% power)
 50% of observed effect: n per arm = 181 (80% power), 242 (90% power)
power.t.test: 46.1 
Simulated power at n = 46 per arm: 0.794 (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

Multiplicity arises when a study assesses several outcomes, treatment contrasts, time points, or subgroups. The more statistical tests that are considered together, the greater the chance that at least one result appears unusual by chance alone. This general concern is important when interpreting individual unadjusted p-values, especially for secondary outcomes. The registry lists six outcome measures, but does not report a multiplicity strategy, such as a testing hierarchy or adjustment procedure. It is therefore not possible to determine whether the posted p-values were intended to support family-wise claims across outcomes or comparisons.

The registry records zero analyses and lists no reported analyses for employment. This means the registry record does not document an investigator analysis plan or analysis population for the posted outcomes. It does not establish that no analyses were performed outside the registry. Details of the statistical analysis plan, including covariate adjustment, handling of protocol deviations, and whether analyses followed randomized assignment, are not reported in the registry record.

Missing data can affect both the estimate and its precision. If outcome availability differs by group or is related to treatment duration, a comparison based only on observed records may not represent all randomized participants. The registry record does not report the amount or pattern of missing primary or secondary outcome data, reasons for missingness, imputation methods, or sensitivity analyses. Those omissions prevent assessment of how robust the posted means are to missing observations.

The record also does not state the population used for analysis: for example, whether all randomized participants were analyzed in their assigned groups or whether another analysis set was used. It does not report whether participants were excluded after randomization, or how treatment switching and adherence were handled. These are important interpretation details for a randomized trial, but no particular approach should be assumed from the available record.

Finally, the registry does not report interim analyses or stopping rules. Their presence or absence is not reported in the registry record. Without those details, the posted unadjusted comparisons can be described, but their relationship to a prespecified inferential plan remains uncertain.

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 1% reporting threshold.

Most frequent serious adverse event terms

Serious events with the highest arm-level rate: hospitalizations (21.1%), death (8.6%).

The registry reports serious adverse event counts for three groups. The entries list 15 affected among 70 at risk for counseling only, 6 among 70 at risk for counseling with community initiation, and 16 among 71 at risk for prison initiation and continuation. These are the serious-event figures recorded for the groups; the registry does not explain the definitions, ascertainment period, or whether an individual could contribute to more than one event category.

The serious-event terms listed most prominently are hospitalizations, at 21.1%, and Death, at 8.6%. The registry does not provide a death count in the group-specific fields, so no group-specific death comparison can be made from this record. The other-event fields show 0 at risk and 0 affected in each group; their meaning and completeness are not explained.

These entries should be read as descriptive safety reporting, not as a causal comparison. The record does not provide adjusted comparisons, confidence intervals, details about event severity beyond the serious classification, or information about attribution to treatment. The group-specific counts alone do not establish whether the strategies caused, prevented, or changed serious events.

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

The central statistical finding is a difference in reported mean days in community treatment between each methadone strategy and counseling only during one year post prison release. The posted unadjusted estimates are 68.2 days for community initiation and 142.9 days for prison initiation with continuation. Their confidence intervals lie above zero, and the posted p-values are <0.001. The largest observed mean is in the strategy initiated in prison with continuation, but these group averages do not describe every participant's experience.

The result does not establish that the same difference would occur in another population, setting, or treatment program. The study summary concerns male offenders previously, but not currently, heroin-dependent. The registry record does not report detailed participant characteristics or further eligibility information. Generalizing beyond the described group requires evidence not available in the posted result.

The result also does not settle the study summary's broader questions about drug abuse, crime, and HIV risk behavior. Those outcomes are not reported in the registry record in the information available for interpretation. Employment is listed as a secondary outcome, but it is a distinct measure and does not substitute for those other outcomes. The posted primary result addresses treatment duration, not overall health, safety, or social outcomes.

Because the posted comparisons are unadjusted and the registry does not report the analysis population, missing-data approach, multiplicity plan, or prespecified statistical methods, the estimates should be interpreted with those limitations in mind. Confidence intervals and p-values quantify uncertainty under statistical assumptions; they do not correct for undisclosed analysis choices or incomplete outcome information.

In short, the posted data indicate higher group-average treatment duration in the two methadone strategies relative to counseling only. They do not by themselves prove a mechanism, establish effects on outcomes not reported, or provide medical advice. The interpretation is confined to the defined endpoint, recorded timeframe, and statistical information in the registry record.

17. Why This Trial Matters Statistically

This trial is statistically informative because it compares three randomized strategies while measuring the primary outcome in days, a scale that communicates the average contrast directly. The structure permits two comparisons against a shared counseling-only reference group: methadone initiation in the community and initiation in prison with continuation. The posted means and confidence intervals give both the direction and uncertainty of these contrasts.

The result also illustrates why a difference in means should be read alongside variation. The reported standard deviations are substantial, so group averages do not imply that individual treatment durations were similar. Confidence intervals describe uncertainty in average differences, whereas standard deviations describe spread among observed values. Keeping those quantities distinct prevents an average contrast from being mistaken for a prediction about an individual.

The trial also raises common questions in registry-based interpretation: how multiple comparisons are handled, whether an analysis plan is available, and how missing observations are treated. The registry record does not report these details or any formal analyses. Those gaps do not erase the posted summaries, but they limit the strength of claims that can be drawn from them.

Finally, the employment outcome shows why a study's primary and secondary endpoints should be interpreted separately. A result for treatment retention does not determine the result for employment or for other outcomes named in a study summary. Clear endpoint-specific interpretation is essential when a trial addresses a broader social and behavioral context than its posted primary measure alone.

18. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.

Several trial-specific limitations follow from the information available in the registry record. The population is described broadly as male offenders previously, but not currently, heroin-dependent, but detailed baseline characteristics and eligibility criteria are not reported. This limits assessment of how closely the enrolled group represents other populations of interest.

The registry reports no masking and gives blank arm descriptions. Although the intervention names and study summary clarify the broad strategies, further implementation details, treatment adherence information, and the identity of outcome assessors are not reported. The record also does not explain how community treatment days were collected or verified.

The primary outcome has large standard deviations, and no medians, quantiles, or distributional information are posted. The means therefore provide only a partial view of treatment duration. The registry record does not report how participants with missing outcome information were handled, whether any censoring occurred, or whether the analysis accounted for it.

Most importantly for statistical interpretation, no reported analyses are listed. The record does not provide a statistical analysis plan, analysis population, covariate-adjusted results, multiplicity procedure, interim analysis information, or original sample-size assumptions. The comparisons discussed are unadjusted re-calculations from posted summary statistics, not a substitute for a documented trial analysis.

The safety information is also limited: group-specific serious-event figures are posted without details about event ascertainment, attribution, overlap, or comparison methods. Results for drug abuse, crime, and HIV risk behavior are not reported in the registry record, despite being named in the study summary. These gaps restrict assessment of the broader study aims.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Methadone Maintenance for Prisoners — NCT00378079.
• Registry record last updated 2014-04-03; status last verified 2014-04.
• Results first posted 2014-04-03.
• 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 3 parallel-group trial with no masking and enrollment of 211. The trial compares counseling only, counseling with methadone initiation in the community, and counseling with methadone maintenance initiated in prison and continued after release. The primary outcome is mean days in community treatment during one year post prison release.

Posted primary means are 23.1 days, 91.3 days, and 166.0 days, respectively. Compared with counseling only, the unadjusted mean differences are 68.2 days and 142.9 days; both posted p-values are <0.001. Employment is listed as a secondary outcome. The registry record does not report formal analyses, a multiplicity plan, missing-data methods, or the original design assumptions.