ACTIVE: Advanced Cognitive Training for Independent and Vital Elderly: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for ACTIVE: Advanced Cognitive Training for Independent and Vital Elderly (NCT00298558), a randomized phase 2, phase 3 study. The primary outcome is Changes in Cognitive Abilities of Memory From Baseline to Year 10.

2. Clinical Question

3. Trial Design

ACTIVE was a randomized, parallel-group trial of cognitive training interventions for older adults. The registry lists PHASE2 and PHASE3, single masking, and an enrollment of 2832. The listed conditions are Aging and Healthy. The study status is completed; its recorded start is 1998-03 and primary completion is 2010-12.

Participants were assigned to Memory Training, Reasoning Training, Speed of Processing Training, or Control. The three training programs focused on distinct abilities. Memory training taught mnemonic strategies for remembering lists, sequences, text material, and story details. Reasoning training taught approaches for identifying patterns or sequences in problems. Speed-of-processing training used increasingly complex computer tasks involving visual search and divided attention. Control participants did not complete cognitive training interventions.

The registry’s brief summary says the study tested whether cognitive training could maintain functional independence by improving basic mental abilities, with follow-up assessments through five years. The primary outcome is described separately as change in memory from baseline to year 10, with a timeframe of up to 10 years. These are the registry’s respective descriptions; details explaining the follow-up schedule are not reported in the registry record.

The record also lists secondary aims concerning health-related quality of life, driving function, health service use, health, genetic and cognitive moderators, and estimates of effects in the general population. It lists 9 outcome measures and 18 analyses. Further details of eligibility, the allocation procedure, training dose, adherence, masking procedures, and the trial’s original design assumptions are not reported in the registry record.

4. Participant Flow and Accounting

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

Before assignment: Eligibility and demographics were gathered at telephone screening.Health history, physical status, functional status, mental status, cognitive and function measures were gathered via in-person exams in individual and small-group formats at baseline.Eligible subjects were randomly assigned to one of three interventions or no-contact control group.

Baseline

Intervention

Immediate Post Test

Booster

Analysis population for the primary outcome, as defined in the registry: Of the randomized subjects, 943 subjects who had the memory outcome at year 10 were used.

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: Of 2832 randomized subjects, 30 subjects were randomized inappropriately in violation of the protocol and excluded from the analysis. Therefore, 2802 subjects were used for the baseline analysis.

6. Primary Endpoint

The registry lists the primary outcome as Changes in Cognitive Abilities of Memory From Baseline to Year 10, measured over Up to 10 years.

The primary endpoint is change in the memory outcome from baseline to year 10. The outcome is a summed score based on the Rey Auditory-Verbal Learning Test (AVLT), the Hopkins Verbal Learning Test (HVLT), and the Rivermead Behavioral Paragraph Recall test immediate recall. Its possible range is 0 to 132 units on a scale, with higher values representing better performance. Change is calculated as year 10 minus baseline; therefore, a negative change indicates a decline from baseline.

Combining measures of verbal learning and recall into one outcome gives the trial a way to assess memory performance across several tasks rather than relying on a single test result. The registry record does not explain the rationale for selecting this particular endpoint or the weighting of its component tests beyond describing it as their summation. It reports that 943 randomized subjects with a year-10 memory outcome were used. This endpoint therefore concerns the measured change among that group, rather than a result available for every randomized subject.

7. Results Posted in the Registry

• Memory Training: mean -10.60 versus -9.40 on control; difference -1.20 (95% CI -6.58 to 4.18), standardized effect d = -0.04; z-test p = 0.662.
• Reasoning Training: mean -11.20 versus -9.40 on control; difference -1.80 (95% CI -6.93 to 3.33), standardized effect d = -0.06; z-test p = 0.491.
• Speed of Processing Training: mean -12.70 versus -9.40 on control; difference -3.30 (95% CI -8.37 to 1.77), standardized effect d = -0.12; z-test p = 0.202.

8. Statistical Interpretation

9. Statistical Methods Explained

What does a mean change describe?

The primary outcome is continuous, and its summary measure is the mean. A mean change describes the average difference between the year-10 measurement and baseline within a group. Because the endpoint is defined as year 10 minus baseline, negative group means correspond to average declines on this score. The group means do not describe every individual participant: individual changes can vary around the mean.

The registry also reports a standard deviation for each group. In general, a standard deviation describes the spread of individual observations around a group mean. A larger spread means individual outcomes are more dispersed, while a smaller spread means they are more closely grouped around the mean. Here, the reported standard deviations are 28.3 for Memory Training, 26.3 for Reasoning Training, 25.5 for Speed of Processing Training, and 29.6 for Control. The registry gives no confidence limits alongside these group means.

What is a mean difference?

The recalculated comparisons subtract the control mean change from the mean change in each training group. A negative mean difference means the training group’s observed mean change is lower than control’s under this comparison. For example, the memory comparison is -1.2, while the reasoning comparison is -1.8 and the speed-of-processing comparison is -3.3. These are unadjusted comparisons calculated from the posted group summaries, not the trial’s own mixed-model estimates.

In general, an unadjusted comparison does not account for covariates or features of repeated measurements beyond what is reflected in the summary data used for the calculation. The registry record’s original analysis plan and details of any adjustment for covariates are not reported in the registry record. The recalculated estimates should consequently be understood as simple comparisons of the posted group means, not as a reconstruction of the full trial analysis.

What does a confidence interval convey?

In general, a confidence interval expresses the uncertainty around an estimated effect under the assumptions of the statistical method used. A narrower interval indicates greater precision for the estimate; a wider interval indicates less precision. An interval that includes zero is compatible with no difference, but it can also include nonzero differences in either direction. It does not demonstrate that the groups are equivalent, nor does it show the probability that the true effect lies inside the interval.

The recalculated mean-difference intervals are 95% intervals. The sponsor’s posted mixed-model results use 99% intervals and report effect sizes rather than mean differences. Confidence intervals at different levels and estimates on different scales should not be treated as interchangeable. The registry’s detailed mixed-model specification is not reported in the registry record.

Why can the analyses differ?

The trial’s reported analyses use mixed models. In general, mixed models can be used to analyze data with repeated measurements or other related observations, while accounting for dependence among observations through the model structure. The registry record does not report enough detail to identify the exact model terms, covariance structure, handling of missing measurements, or adjustment variables. It would not be appropriate to infer those choices from the label alone.

The recalculated estimates instead use the posted means, standard deviations, and group sizes to produce simple, unadjusted pairwise comparisons. Their confidence intervals describe uncertainty under that calculation, not the full uncertainty model used in the sponsor’s mixed-model analysis. The sponsor’s effect-size estimates may also use a scale or standardization not described in the registry record, so their numerical values cannot be read as the same unit as the raw mean differences.

Why does over-dispersion matter in general?

For a continuous outcome, the spread of observations affects the precision of a group comparison: more variation generally makes an estimated difference less precise when other features remain unchanged. In general, over-dispersion means that observed variability exceeds what a statistical model assumes. If variability is underestimated, uncertainty can be understated; if it is accounted for appropriately, standard errors and intervals reflect the greater spread. The posted summaries include group standard deviations, but the registry record does not report whether over-dispersion was assessed or relevant to the sponsor’s model.

The reported p-values are another way of expressing how compatible the data are with a specified null hypothesis under the analysis assumptions. They do not measure the size or practical importance of an effect, and they are not the probability that the null hypothesis is true. The registry gives p-values for the mixed-model results, while the recalculations give unadjusted p-values. The registry does not report whether or how these tests were adjusted for multiple comparisons.

10. Confidence Intervals and Precision

The recalculated 95% confidence intervals for the mean differences are wide enough to include zero and values on either side. For Memory Training versus Control, the estimated difference is -1.2, with an interval from -6.576 to 4.176. For Reasoning Training versus Control, it is -1.8, with an interval from -6.928 to 3.328. For Speed of Processing Training versus Control, it is -3.3, with an interval from -8.365 to 1.765. Each estimate is therefore uncertain in direction as well as magnitude.

The sponsor’s mixed-model results also have 99% confidence intervals that include zero: 0.06 from -0.14 to 0.27 for Memory Training; -0.11 from -0.31 to 0.10 for Reasoning Training; and -0.05 from -0.25 to 0.15 for Speed of Processing Training. These intervals are for effect sizes, not the unadjusted raw mean differences. They should be interpreted on the effect-size scale used by the sponsor analysis, whose detailed definition is not reported in the registry record.

In general, a confidence interval shows a range of estimates compatible with the observed data under the analysis assumptions; it does not identify a single certain value. The group standard deviations are substantial relative to the observed mean changes, and the numbers included for the year-10 outcome are smaller than the overall randomized enrollment. These features are relevant to precision, but the registry record does not report a formal explanation of the precision achieved or the original sample-size justification.

The intervals do not establish equivalence or rule out differences that may matter. The registry record does not report a prespecified equivalence margin or a clinically important difference for this score. The appropriate reading is that the posted estimates have considerable uncertainty about the direction and size of between-group differences.

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 estimates describe participants per arm for 80% power and participants per arm for 90% power. They are planning illustrations based on the observed effect, not the trial’s original design assumptions. The stated 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 these continuous-outcome calculations, the figures are participants per arm, not total events.

The 80% power column indicates the illustrative number of participants per arm for a design with an 80% chance of detecting the specified effect if that effect is real, under the listed assumptions. The 90% column gives the corresponding planning target for a 90% chance. These are design calculations, not descriptions of what occurred in ACTIVE. This is not observed power.

The rows use the full observed effect and smaller fractions of it. As the target effect becomes smaller, the required participants per arm increase. For example, the Memory Training comparison lists 9,128 participants per arm for 80% power at 100% of the observed effect and 36,509 when planning for 50% of that effect. The corresponding 90% figures are 12,219 and 48,875. The same pattern appears for the other comparisons.

These calculations depend on the estimated effect and variability from the posted data, so they should not be mistaken for a protocol-based sample-size justification. The trial’s own original design assumptions and sample-size rationale are not reported in the registry record. The planning values are illustrations of how changing a target effect and power level affects a hypothetical two-arm design.

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 = -1.200; pooled standard deviation σ = 28.935.
2. n = 2 × (1.96 + 0.842)² × 28.935² / -1.200² = 9,127.1, rounded up to 9,128 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 <- -1.2                      # observed difference in means
sigma <- 28.9353832615775                     # 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(298558)
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 = 9,128 (80% power), 12,219 (90% power)
 75% of observed effect: n per arm = 16,226 (80% power), 21,722 (90% power)
 50% of observed effect: n per arm = 36,509 (80% power), 48,875 (90% power)
power.t.test: 9128.1 
Simulated power at n = 9,128 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. Analyses Reported by the Sponsor

The registry reports the sponsor’s analysis as mixed models, with effect-size estimates, 99% confidence intervals, and p-values. The unadjusted recalculations are separate comparisons of posted means using group sizes and standard deviations. They estimate raw mean differences and use 95% confidence intervals and unadjusted p-values. Since the methods, estimates, and interval levels differ, their numerical results should not be expected to match exactly.

The sponsor’s results are 0.06 for Memory Training, -0.11 for Reasoning Training, and -0.05 for Speed of Processing Training. Their respective 99% intervals are -0.14 to 0.27, -0.31 to 0.10, and -0.25 to 0.15. The recalculated mean differences are -1.2, -1.8, and -3.3, respectively, each with an interval including zero. These are not directly comparable values because the sponsor reports effect sizes and the recalculations report mean differences in the outcome’s units.

No discrepancy is flagged between the posted results and recalculations. The sponsor’s mixed-model analysis remains the trial’s own reported analysis; the recalculations offer a simple, unadjusted view based on summary statistics. The registry record does not provide enough model detail to reproduce or fully audit the sponsor’s analysis.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists 9 outcome measures, 18 analyses, and 3 secondary outcome descriptions. The primary outcome is the change in memory from baseline to year 10. The secondary outcomes concern health-related quality of life, driving function, health service use, moderators related to health, genetics, and cognition, and estimation of effects in the general population. These multiple outcomes and comparisons create the possibility of multiple statistical tests.

When many hypotheses are tested, the chance of at least one apparently unusual result can increase if each test is interpreted without accounting for the broader set of tests. In general, multiplicity procedures can adjust the interpretation or testing threshold across a family of comparisons. Whether the trial prespecified a multiplicity strategy, which tests were considered a family, and whether the reported p-values were adjusted are not reported in the registry record. The recalculated p-values are explicitly unadjusted.

The primary outcome population is described as 943 randomized subjects who had the memory outcome at year 10. The overall randomized enrollment is 2832. The record does not describe the amount or pattern of missing year-10 outcome data, reasons for missingness, imputation methods, or sensitivity analyses. It also does not state whether the year-10 analysis follows an intention-to-treat principle or another analysis-population definition. The observed outcome subset should not be assumed to represent all randomized participants without additional information.

The brief study summary describes follow-up assessments through five years, while the primary outcome is described as a change through year 10. The registry record does not explain the relationship between these follow-up descriptions, nor does it detail the schedule or completeness of the later assessments. The model’s handling of repeated measurements and missing data is also not reported in the registry record. These omissions limit assessment of how missingness and repeated observations may affect the estimates.

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.

The registry reports serious adverse event figures of 0 affected participants for Memory Training, Reasoning Training, Speed of Processing Training, and Control. The corresponding numbers at risk are 711, 705, 712, and 704. The record also reports 0 affected participants for other adverse events in each group, using those same group-specific numbers at risk.

These are the posted counts, not evidence that no adverse events occurred outside the registry’s reporting definitions or collection period. The registry does not list serious adverse event terms, and death counts are not reported in the registry record. The record does not provide further detail about event definitions, observation periods, ascertainment, severity, or the relationship of any event to the intervention.

The adverse-event groups and the primary-outcome analysis population are reported separately. The safety counts should not be used to infer how many participants contributed to the year-10 memory analysis. These figures are descriptive registry entries and do not, by themselves, establish comparative safety.

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

The posted primary outcome means indicate that memory scores declined from baseline on average in all four groups, because the endpoint defines change as year 10 minus baseline and negative values indicate decline. The observed group mean changes range from -9.4 in Control to -12.7 in Speed of Processing Training. The recalculated comparisons estimate mean differences of -1.2 for Memory Training, -1.8 for Reasoning Training, and -3.3 for Speed of Processing Training relative to Control. Their confidence intervals include zero and extend in both directions.

The sponsor’s mixed-model effect-size estimates are also accompanied by 99% intervals that include zero. The registry results therefore do not give precise evidence about the direction or magnitude of the differences between each training group and control. They do not prove that the groups are equivalent, and they do not show that any difference is impossible. No equivalence margin or threshold for a meaningful difference is reported in the registry record.

The primary outcome was available for 943 randomized subjects at year 10, while the full randomized enrollment was 2832. The posted year-10 results consequently describe the analyzed participants and cannot be assumed to represent all randomized participants without information about missing outcomes and the analysis population. The registry does not report those details.

These statistical findings address a measured memory score, not every aspect of cognitive function or functional independence. Although the study’s brief summary frames the broader purpose as maintaining functional independence, the registry entries do not establish what the results mean for daily functioning or other outcomes. The results should be read as estimates with uncertainty for the specific memory measure, rather than as a general conclusion about cognitive training or individual care.

17. Why This Trial Matters Statistically

ACTIVE illustrates several recurring challenges in the analysis of long-term clinical studies. A trial can randomize a substantial overall group yet have a smaller set of participants with the specific long-term outcome used for a comparison. Here, the registry reports enrollment of 2832 and says that the year-10 memory outcome was analyzed among 943 randomized subjects who had that measurement. Understanding who contributes to a long-term endpoint is essential for interpreting what the estimates represent.

The trial also compares distinct interventions against a control while tracking several outcomes and analyses. When multiple comparisons are available, readers need to know whether the analysis plan identified a primary comparison and how multiplicity was handled. Those details are not reported in the registry record. This matters because unadjusted results from several tests should not be interpreted in isolation as if only one hypothesis had been examined.

The record provides both mixed-model results and enough summary statistics for simple unadjusted mean comparisons. Considering the two approaches illustrates why the estimate’s scale and model matter: sponsor effect sizes and recalculated mean differences are not interchangeable. Confidence intervals are useful because they communicate the uncertainty and range of compatible effects, rather than reducing interpretation to whether a p-value crosses a threshold.

Finally, planning calculations based on observed effects can help show how assumptions about a target effect relate to participant requirements, but they are not a substitute for a documented original design rationale. The record’s missing details on sample-size planning, missing data, and model specification limit how completely the analysis can be assessed.

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.

The year-10 primary outcome is reported for 943 randomized subjects who had the measure, compared with overall randomized enrollment of 2832. The registry record does not describe missing outcomes, reasons for loss of measurement, or how the analyzed group relates to all randomized participants. This limits interpretation of the year-10 estimates as effects for the full randomized population.

Important analytical details are not reported in the registry record, including the original sample-size justification, the mixed-model specification, covariate adjustment, handling of missing observations, and whether the analysis used an intention-to-treat population. The record also does not describe a multiplicity strategy despite listing 9 outcome measures and 18 analyses. The posted unadjusted recalculations do not address those unknown design and analysis choices.

The registry summary describes follow-up through five years, while the primary memory endpoint has a timeframe of up to 10 years. The record does not explain that difference or describe the schedule and completeness of the year-10 follow-up. The primary endpoint is a composite summed from three verbal-memory measures, but the rationale for the endpoint construction is not stated beyond its component tests and possible range.

The posted means and standard deviations are descriptive summaries; they do not show individual outcome distributions or changes over time. The registry’s effect-size definition and detailed mixed-model output are not reported, limiting direct comparison with raw mean differences. These limitations concern what can be established from the registry record and do not, on their own, demonstrate that the analyses were inappropriate.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: ACTIVE: Advanced Cognitive Training for Independent and Vital Elderly — NCT00298558.
• Registry record last updated 2014-04-16; status last verified 2014-01.
• Results first posted 2014-02-24.
• 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.

22. Record Summary

NCT00298558, ACTIVE: Advanced Cognitive Training for Independent and Vital Elderly, is recorded as a completed randomized, single-masked, parallel-group study with enrollment of 2832. It compared memory, reasoning, and speed-of-processing cognitive training with a control group that did not receive cognitive training.

The primary outcome is change in a summed memory score from baseline to year 10, with negative changes indicating decline. The record reports group means and standard deviations for participants with year-10 outcome data, along with sponsor mixed-model results and unadjusted recalculated comparisons. The reported intervals for both approaches include zero, while the estimates remain uncertain in size and direction.

The record does not report key details about missing data, the original sample-size rationale, multiplicity, or the full mixed-model specification. The statistical results therefore describe the posted analyses and their precision, with limits on how completely the underlying methods can be assessed.