Exercise and QUality Diet After Leukemia: The EQUAL Study: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Exercise and QUality Diet After Leukemia: The EQUAL Study (NCT02244411), a randomized na study. The primary outcome is Weight Loss.

2. Clinical Question

The EQUAL study asks whether two approaches to weight-loss support differ in their 24-month weight results among adult survivors of childhood acute lymphoblastic leukemia (ALL) who are overweight or obese. The registry describes a randomized, parallel-group comparison: individualized diet and physical activity counseling through a website and email, versus self-directed weight loss supported by general information brochures.

This is a question about the comparison between two forms of support, not a comparison with no information or no weight-loss guidance. Both groups were assigned an approach, and the registry describes the primary analysis as intent-to-treat. The posted group means and unadjusted comparison provide a descriptive view of the outcome; the registry record lists no posted analysis results for the specified adjusted model.

3. Trial Design

The registry identifies EQUAL as a randomized, parallel-group trial with no masking. It lists an enrollment of 358 participants and a completed status. The study began in 2014-09, and its primary completion date is 2025-07-16. Its sponsor is Memorial Sloan Kettering Cancer Center.

Participants were assigned to an intervention group or a control group. The intervention consisted of an individual diet and physical activity counselor through Healthways at Hopkins, with communication primarily by website and email. The counselor was to remain with each participant for 24 months. The control group received general information brochures about healthy living and weight loss, without access to that website or those counselors. The registry's description of the intervention's dietary advice is incomplete, so further details of that advice are not reported in the registry record.

The registry describes additional study activities including questionnaires, a fasting blood draw, height and weight measurement, waist circumference measurement, and blood pressure measurement. These activities do not change the definition of the primary endpoint: weight loss, measured in kilograms, at 24 months.

There were 181 participants in the intervention group and 177 in the control group in the posted outcome results. The registry states that the intended primary analysis would use a linear mixed-effects model with robust standard errors and an unstructured covariance matrix. Its description names time, randomization arm, history of CRT, gender, age, and race, as well as interactions between time and randomization arm. The original design assumptions, including the trial's own sample-size justification, are not reported in the registry record.

4. Participant Flow and Accounting

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

Overall Study

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 Weight Loss, measured over 24 months.

The primary endpoint is weight loss at 24 months, measured in kilograms. It is a continuous measure: participants can have a range of values rather than being classified only as having or not having an event. The registry describes the reported group statistic as a mean with a standard error. The posted results give a mean of -0.36 in the intervention group and 0.18 in the control group.

Weight is relevant to the study's stated purpose because the EQUAL study was designed for adult survivors of childhood ALL who are overweight or obese and aimed to compare two ways of informing participants about weight loss. A continuous endpoint retains information about the amount of weight change rather than reducing the result to a category. The primary time point is 24 months, matching the duration of the counselor relationship described for the intervention group.

The registry says that weight was measured and that the intended model would use weight as the outcome and account for time and randomization arm, among other listed terms. The posted results label the endpoint as weight loss, but the record does not clarify the direction convention used for the group values. For that reason, the numerical means and their comparison can be described without assigning a specific clinical interpretation to the sign. The registry record does not provide a posted estimate from the intended adjusted model.

7. Results Posted in the Registry

• Intervention Group: mean -0.36 versus 0.18 on control; difference -0.54 (95% CI -2.54 to 1.46), standardized effect d = -0.06; z-test p = 0.597.

8. Statistical Interpretation

9. Statistical Methods Explained

The registry describes a randomized, parallel-group study and an intended intent-to-treat analysis. In a randomized study, assignment is used to create comparison groups; an intent-to-treat approach generally analyzes participants according to their assigned group. The registry does not report details about how missing outcomes or departures from assigned support would be handled, so the exact implementation of that approach is not reported in the registry record.

What does the intended model do?

The planned primary analysis is described as a linear mixed-effects model with robust standard errors and an unstructured covariance matrix. The outcome is weight measured over time. The listed model terms include time, randomization arm, history of CRT, gender, age, and race, together with interactions between time and randomization arm. A model of this kind can represent repeated measurements from the same participant while estimating how the outcome changes over time and how those patterns differ between assigned groups.

Repeated measurements on one participant are generally related: a person's measurements tend to be more alike than measurements from unrelated people. A mixed-effects model can account for this within-participant structure. An unstructured covariance specification is a flexible way to represent relationships among repeated measurements, rather than imposing a particular pattern of correlations. The registry does not report the number or timing of measurements included in the model, so those details are not reported in the registry record.

The interaction between time and randomization arm allows the time pattern to differ by group. In general, an interaction means that the association of one model term with the outcome can depend on another term. Here, it permits the modeled outcome trajectory to vary between the assigned groups over time. The registry does not provide the model coefficients, the fitted group trajectories, or the adjusted comparison at 24 months.

Why use robust standard errors?

Standard errors quantify uncertainty in estimated model quantities. Robust standard errors use a method intended to make uncertainty estimates less dependent on some assumptions about the variability of the observations. They do not change the basic need to define the outcome, model, and analysis population clearly. The registry names robust standard errors but does not give further implementation details, such as the specific estimator or any small-sample adjustment.

General statistical context: over-dispersion occurs when observed variability is greater than a model's assumed variability. If variability is not represented well, standard errors and tests can be misleading. Robust methods can offer some protection against certain variance-model errors, but they are not a substitute for a suitable model or adequate reporting. The registry's mention of robust standard errors does not establish which particular departures from assumptions were assessed.

How do the posted summaries differ from the planned analysis?

The posted results give group means and standard errors, along with an unadjusted mean difference and confidence interval. That comparison uses the posted summary statistics rather than the listed mixed-effects model. The intended model includes repeated time measurements and adjustment terms; a simple summary comparison does not reflect those model terms. Consequently, the unadjusted contrast is useful for describing the posted group summaries, but it is not an estimate identified as coming from the trial's planned adjusted model.

The registry describes the endpoint as weight loss at 24 months and says the planned analysis would model weight as a function of time and randomization arm, among other terms. However, it does not state the exact contrast extracted from the model, the model's link between fitted measurements and the 24-month endpoint, or how its estimate would be reported. Those details are not reported in the registry record.

What does a confidence interval contribute?

A confidence interval is a range of values generated by a statistical procedure to convey uncertainty about an estimate. In general, its endpoints depend on the estimate and its estimated uncertainty. It should not be read as a guarantee that the true value lies within the interval, nor does it show the range of individual participant outcomes. The posted unadjusted interval extends from -2.543 to 1.463. Because it includes zero, the posted data do not rule out a zero mean difference under the calculation used.

The unadjusted p-value of 0.597 summarizes how incompatible the observed comparison is with a specified no-difference hypothesis under the statistical calculation used. A p-value does not measure the probability that the hypothesis is true, the probability that chance alone caused the results, or the practical importance of a difference. It also does not resolve the distinction between the unadjusted calculation and the planned adjusted model.

What is not documented?

The registry lists one primary outcome measure and no posted analyses. It does not report the model's final estimates, details of missing-data handling, a multiplicity strategy, interim analyses, or the original sample-size justification. It also does not report a protocol-based statistical analysis plan in the information summarized by the registry record. These omissions mean that the statistical plan can only be described to the extent that the registry's outcome description states it; unreported choices should not be inferred.

10. Confidence Intervals and Precision

The posted unadjusted mean difference is -0.54, with a confidence interval from -2.543 to 1.463. The interval crosses zero and includes values in both numerical directions. That span indicates that the point estimate should not be treated as a highly precise description of the group contrast. The interval is for the unadjusted mean difference, not for the adjusted mixed-effects model described in the registry.

A confidence interval expresses uncertainty about an estimated quantity under the method used to calculate it. In general, an interval is not a range containing most individual participants' outcomes. It also does not guarantee that the true value is within its endpoints. Rather, it gives a range of estimates compatible with the posted data and the calculation's assumptions. The registry does not report confidence intervals for the separate group means.

The group standard errors are 0.78 for the intervention mean and 0.66 for the control mean. They describe uncertainty in those estimated means, rather than variability among individual participants. The group sizes in the posted results are 181 and 177, respectively. The record does not report individual-level outcome distributions or an adjusted-model confidence interval, so the precision of the intended adjusted comparison cannot be assessed from the posted results.

The unadjusted p-value is 0.597. It should be interpreted alongside the estimate and interval rather than as a stand-alone verdict. The interval is especially useful for seeing that the posted comparison leaves room for a range of possible mean differences, including zero. This uncertainty limits the strength of conclusions about the magnitude and direction of the contrast.

11. Planning a Similar Trial: Sample Size

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

The planning figures are participants per arm, not total events. They are illustrative calculations based on the observed effect, not the trial's own original design assumptions. The planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set to the stated fraction of the observed effect.

For planning for 100% of the observed effect, the calculation gives 5,050 participants per arm for 80% power and 6,760 participants per arm for 90% power. For planning for 75% of the observed effect, it gives 8,977 participants per arm for 80% power and 12,018 participants per arm for 90% power. For planning for 50% of the observed effect, it gives 20,198 participants per arm for 80% power and 27,039 participants per arm for 90% power.

In general, power is the chance that a study will detect an effect of a specified size under the assumed design and statistical procedure. The 80% column gives the calculated participants per arm for an assumed design with 80% power; the 90% column gives the corresponding number for 90% power. Higher planned power requires more participants under the listed assumptions. The calculations also illustrate that smaller effects need more participants to detect than larger effects. These figures are not observed power.

The original trial's sample-size justification and design assumptions are not reported in the registry record. The planning figures therefore should not be taken as the target used to design or conduct EQUAL, or as an assessment of whether its enrollment was adequate for the intended analysis.

12. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = -0.540; pooled standard deviation σ = 9.685.
2. n = 2 × (1.96 + 0.842)² × 9.685² / -0.540² = 5,049.4, rounded up to 5,050 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 <- -0.54                      # observed difference in means
sigma <- 9.68484905011924                     # 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(2244411)
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 = 5,050 (80% power), 6,760 (90% power)
 75% of observed effect: n per arm = 8,977 (80% power), 12,018 (90% power)
 50% of observed effect: n per arm = 20,198 (80% power), 27,039 (90% power)
power.t.test: 5050.3 
Simulated power at n = 5,050 per arm: 0.802 (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.

13. Multiplicity, Missing Data and Analysis Populations

The registry lists one primary outcome measure, weight loss, and no posted secondary outcome measures. It also lists no posted analyses. The number of listed primary measures alone does not establish how many statistical tests were planned or performed, because a model can include several terms and contrasts. The registry record does not report a multiplicity strategy, such as whether or how testing across outcomes, time points, or model contrasts was addressed.

Multiplicity is the issue that arises when multiple statistical questions are assessed. In general, the more tests considered, the greater the chance that at least one result may appear unusual by chance if each test is interpreted separately. A prespecified approach can clarify which results are primary and how any additional tests are handled. For EQUAL, the available registry information does not report such an approach or the number of analyses actually performed.

The primary outcome description says that the intended analysis would be intent-to-treat. In general, intent-to-treat analysis retains participants in their assigned groups for analysis, regardless of whether they fully followed the assigned intervention. The registry does not provide details about how that principle was implemented, which participants contributed to the analysis, or how missing measurements were handled. Those details are not reported in the registry record.

Missing-data handling matters because participants may lack measurements at some time points, and different methods for handling missing outcomes can rely on different assumptions. The registry describes a mixed-effects model but does not specify the missing-data assumptions, methods for imputation, sensitivity analyses, or the amount of missing outcome data. It is therefore not possible to assess the consequences of missingness from the posted record alone.

The registry also does not report interim analyses, stopping rules, or adjustments for interim looks. No conclusion about whether these were planned or conducted can be drawn from their absence in the posted record. The information supports describing the stated endpoint and model, but not reconstructing an unreported analysis plan or making assumptions about the multiplicity or missing-data procedures.

14. Safety Results

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

Deaths

Other (non-serious) adverse events

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

Most frequent serious adverse event terms

Serious events with the highest arm-level rate: death nos (0.6%).

The serious adverse event figures list 0 affected participants among 181 at risk in the intervention group and 1 among 177 at risk in the control group. The control group entry is identified as Death NOS, with a reported value of 0.6%. The registry lists 0 deaths in the intervention group and 1 in the control group. It lists no other adverse events in either group.

These are descriptive counts in the registry record. They do not establish that assignment caused or prevented an event, and they do not by themselves provide a reliable comparison of safety between groups. With only one serious event listed, the figures contain limited information about the frequency of uncommon outcomes. The record does not report further clinical details about the event or provide an analysis comparing adverse-event risks.

“Death NOS” is the registry's reported serious-event term; the record does not give further details in the information. The adverse-event entries should be read separately from the weight outcome. They do not determine the interpretation of the primary endpoint or the uncertainty around its mean difference.

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

The posted results show mean weight-loss values of -0.36 in the intervention group and 0.18 in the control group at 24 months. The unadjusted mean difference, intervention minus control, is -0.54. Its confidence interval, -2.543 to 1.463, includes zero, and the unadjusted p-value is 0.597. Together, these figures describe a numerical difference whose direction and magnitude remain uncertain in the unadjusted comparison.

The result does not establish that one approach is better or worse. It does not prove that there is no difference, either: an interval that includes zero can also include nonzero differences. The estimate is based on the posted group summaries and is not the adjusted result from the linear mixed-effects model described by the registry. That adjusted result is not reported in the registry record.

The comparison is between individualized counselor support with website and email communication, and self-directed weight loss supported by general brochures. It is not a comparison with no support or no information. The result also applies to the study's stated population of adult survivors of childhood leukemia; the study summary specifies survivors of childhood ALL who are overweight or obese. The registry record does not provide sufficient additional participant detail to define how broadly the findings might apply beyond that population.

Group means do not reveal the distribution of individual outcomes, differences in engagement with the assigned approaches, or the experience of participants who did not contribute measurements. The registry record does not report those details. The posted figures should therefore be interpreted as a summary of group averages and uncertainty, not as a description of what happened to every participant.

Finally, statistical uncertainty is distinct from clinical importance. The registry does not define a threshold for a clinically meaningful difference in weight loss. Without such a threshold and without the adjusted model result, the posted statistics do not determine whether the estimated contrast would be meaningful to participants. They describe the available unadjusted comparison, with uncertainty, rather than a treatment recommendation.

16. Why This Trial Matters Statistically

This trial raises a useful statistical question about how to compare a supported behavioral program with self-directed information in a randomized study. The two groups received different forms of support, and the primary outcome was continuous weight loss at 24 months. That setup makes both the group averages and the uncertainty around their contrast important: a point estimate alone cannot show how precisely the groups differ.

The registry's intended analysis is more complex than a single comparison of means. It describes repeated weight measurements analyzed over time, with adjustment for listed participant characteristics and an interaction between time and randomization arm. Such a plan can address trajectories as well as group assignment, but the registry does not post the fitted results. Comparing that intended model with the posted unadjusted summary is therefore an important distinction when interpreting the evidence.

The confidence interval around the unadjusted difference includes zero and spans values on either side. That illustrates why a result should be read through its estimate and precision rather than reduced to a single p-value. It also shows why a nonsignificant-looking comparison should not be treated as proof of equivalence or proof of no effect.

The planning illustration offers another statistical lesson: the number of participants required depends strongly on the effect size assumed for planning. The calculations are explicitly based on the observed effect and are not the trial's original design rationale. Keeping planning scenarios separate from the enrollment and the trial's own design is essential to avoid reading a retrospective illustration as evidence about the original plan.

Finally, the registry's limited reporting on missing data, multiplicity, and the actual adjusted analysis makes transparency consequential. Clear reporting of the model result and its assumptions would allow readers to evaluate the primary question more directly, while the posted summary still permits a careful description of the unadjusted group means and their uncertainty.

17. Limitations

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

The registry record contains an incomplete intervention description: the dietary advice for the intervention group ends after “low-”. Additional details of the dietary program are not reported in the registry record. The control description identifies general brochures on healthy living and weight loss, but the record does not provide further detail about their contents or how participants used them.

The posted primary outcome results consist of group means and standard errors and an unadjusted comparison. Although the registry describes a linear mixed-effects model for an intent-to-treat analysis, no analyses are posted, and the adjusted model estimate is not reported in the registry record. The distinction matters because the intended model includes time and other terms that are not represented in the unadjusted summary comparison.

The registry does not report the number or schedule of weight measurements, outcome completeness, missing-data handling, or sensitivity analyses. It also does not report adherence to the assigned approaches, participation in counseling, or access and use of the website. These omissions prevent assessment of how fully each approach was received and how missing observations may have affected the analysis.

Further limitations in the posted information include no reported multiplicity strategy, interim analyses, or original sample-size justification. The record also does not define a threshold for a clinically meaningful difference in weight loss. Its safety entries provide sparse event counts without additional event details or a comparative analysis.

These are limitations of what is reported in the registry record; they do not establish that a particular procedure was not used or that a particular issue affected the results. They mark questions that cannot be answered from the posted information.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Exercise and QUality Diet After Leukemia: The EQUAL Study — NCT02244411.
• Registry record last updated 2026-07-24; status last verified 2025-07.
• Results first posted 2026-07-24.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

21. Record Summary

The EQUAL study (NCT02244411) is a completed, randomized, parallel-group study sponsored by Memorial Sloan Kettering Cancer Center. The registry lists an enrollment of 358 and no masking. It compares individualized diet and physical activity counseling through Healthways at Hopkins with self-directed weight loss supported by general brochures.

The primary outcome is weight loss in kilograms at 24 months. Posted group means are -0.36 for the intervention group and 0.18 for the control group. The unadjusted mean difference is -0.54, with a confidence interval from -2.543 to 1.463 and an unadjusted p-value of 0.597. The adjusted model described in the registry is not reported in the posted analyses.

The registry lists one primary outcome measure and no posted analyses. Further details about missing data, multiplicity, and the original sample-size justification are not reported in the registry record.