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Cancer, Lung NA Continuous Endpoint NCT03016403

A Stepped Care Intervention to Reduce Disparities in Mental Health Services Among Cancer Patients and Caregivers: Complete Statistical Analysis

This randomized, parallel-group trial compared a stepped-care behavioral intervention with enhanced usual care for underserved lung and head and neck cancer patients and their caregivers. The primary outcome was patient-reported depression at 6 months; caregiver outcomes and serious adverse events were also recorded.

Trial start: 2017-04-03  ·  Enrollment: 535  ·  Sponsor: University of Colorado, Denver
Scope of this record

This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.

1. Trial at a Glance

This page covers the registry results for A Stepped Care Intervention to Reduce Disparities in Mental Health Services Among Cancer Patients and Caregivers (NCT03016403), a randomized na study. The primary outcome is Symptoms of Depression-Patients.

535
Enrollment
NA
2
Arms
In the primary outcome
-2.10
Mean difference
Patients in Stepped Care Intervention
-3.58–-0.62
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT03016403
PhaseNA
ConditionCancer, Lung, Cancer, Head and Neck
AllocationRandomized
Design modelParallel
MaskingNone (open label)
Enrollment535
Arms in the primary outcome2
Lead sponsorUniversity of Colorado, Denver
Results postedYes

2. Clinical Question

Population

Medically underserved people with lung or head and neck cancer and their caregivers were the intended population. The registry describes underserved patients as low-income, uninsured, or underinsured, and notes that cancer treatment can bring physical and emotional stress. The primary outcome concerns patients. Its analysis population is described as all participants who were randomized, with reported means corresponding to observed values at 6 months. The registry reports overall enrollment of 535, but does not report the full eligibility criteria or the number of caregivers and patients enrolled separately in the summary details.

Intervention

The stepped-care intervention was a behavioral program grounded in evidence-based Cognitive Behavioral Therapy. The described strategies include stress management, relaxation treatment strategies, and coping skills training. The registry says the intervention was adapted to address different levels of symptom severity, including mild, moderate, or severe depression and anxiety symptoms. Further details of how care was stepped or how participants moved between intervention components are not reported in the registry record.

Comparator

The comparator was enhanced usual care. The registry describes supportive mental health care at Denver Health, St. Mary’s, and St. Joseph’s hospitals, including printed materials, support groups, crisis counseling, and specialized care such as psychiatric medication. It also notes that the amount of usual mental health care each patient received varied. The registry does not report a standardized amount of comparator care for each participant.

Primary question

The primary question was whether patient-reported depression scores at 6 months differed between patients assigned to stepped care and patients assigned to enhanced usual care. Scores came from the PROMIS-Cancer Depression form, on which higher values indicate worse depression. The posted arm means were 13.2 for stepped care and 15.3 for enhanced usual care. The unadjusted recalculation estimates a mean difference of -2.1 for stepped care relative to enhanced usual care. The registry also reports a mixed-model analysis; its estimate is expressed in the opposite numerical direction, and the registry does not specify the contrast coding needed to reconcile the signs.

3. Trial Design

The study is listed as a randomized, parallel-group trial of two behavioral interventions: stepped-care intervention and enhanced usual care. Masking is listed as none. The registry reports phase as not applicable. The sponsor is the University of Colorado, Denver, and the trial status is completed. Its recorded start date is 2017-04-03, and its primary completion date is 2020-07-17. Overall enrollment is 535.

The study focused on disparities in mental health services among underserved people with lung or head and neck cancer and their caregivers. The stepped-care approach was intended to address a range of depression and anxiety symptom severity. The registry describes intervention strategies drawn from Cognitive Behavioral Therapy, including stress management, relaxation treatment strategies, and coping skills training. Enhanced usual care included supportive mental health services, but the amount of care varied between patients.

The primary outcome was patient depression at 6 months. Caregiver outcomes included coping, anxiety symptoms, depression symptoms, perceived stress, and caregiving burden. Patient secondary outcomes included health-related quality of life and perceived stress. The registry lists 10 outcome measures and 10 analyses. The summary details describe a primary depression analysis among randomized participants, with observed means at 6 months. The primary arm summaries contain 139 participants in enhanced usual care and 147 in stepped care; the caregiver summaries for the detailed secondary outcomes contain 118 and 131 participants, respectively.

The registry record does not report the randomization procedure, allocation ratio as specified in the original protocol, recruitment flow, eligibility details, or the trial’s original sample-size justification. It also does not provide the full intervention manual or a detailed schedule of follow-up assessments. Those omissions limit what can be inferred about implementation and design decisions from the registry summary alone.

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.

Baseline

StagePatients in Enhanced Usual CarePatients in Stepped Care InterventionCaregivers in Enhanced Usual CareCaregivers in Stepped Care Intervention
STARTED139147118131
COMPLETED12312010797
NOT COMPLETED16271134

Reasons for not completing this period:

ReasonPatients in Enhanced Usual CarePatients in Stepped Care InterventionCaregivers in Enhanced Usual CareCaregivers in Stepped Care Intervention
Death5810
Withdrawal by Subject28410
Lost to Follow-up911624

6-week Follow-up

StagePatients in Enhanced Usual CarePatients in Stepped Care InterventionCaregivers in Enhanced Usual CareCaregivers in Stepped Care Intervention
STARTED12312010797
COMPLETED12010710388
NOT COMPLETED31349

Reasons for not completing this period:

ReasonPatients in Enhanced Usual CarePatients in Stepped Care InterventionCaregivers in Enhanced Usual CareCaregivers in Stepped Care Intervention
Death1400
Lost to Follow-up2748
Withdrawal by Subject0201

3-month Follow-up and 6-month Follow-up

StagePatients in Enhanced Usual CarePatients in Stepped Care InterventionCaregivers in Enhanced Usual CareCaregivers in Stepped Care Intervention
STARTED12010710388
COMPLETED108969581
NOT COMPLETED121187

Reasons for not completing this period:

ReasonPatients in Enhanced Usual CarePatients in Stepped Care InterventionCaregivers in Enhanced Usual CareCaregivers in Stepped Care Intervention
Death6400
Lost to Follow-up6786
Withdrawal by Subject0001

Analysis population for the primary outcome, as defined in the registry: Intention to treat population- all participants who were randomized were included in this analysis. The reported means correspond to the observed means at 6 months.

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.

CharacteristicUnitPatients in Enhanced Usual CarePatients in Stepped Care InterventionCaregivers in Enhanced Usual CareCaregivers in Stepped Care InterventionTotal
Participants analysed139147118131535
Age, Customized: Under 18Participants00000
Age, Customized: 18 to 65Participants65696469267
Age, Customized: Above 65Participants74783336221
Age, Customized: Unknown or Not ReportParticipants00212647
Sex: Female, Male: FemaleParticipants54659299310
Sex: Female, Male: MaleParticipants85822632225
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants27342837126
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants1121138994408
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants00101
Race (NIH/OMB): American Indian or Alaska NativeParticipants13138
Race (NIH/OMB): AsianParticipants116513
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants10304
Race (NIH/OMB): Black or African AmericanParticipants693725
Race (NIH/OMB): WhiteParticipants12312299107451
Race (NIH/OMB): More than one raceParticipants21227
Race (NIH/OMB): Unknown or Not ReportedParticipants5114727
Region of Enrollment: United Statesparticipants139147118131286
Language Preference: EnglishParticipants133132111118494
Language Preference: SpanishParticipants61571341
Diagnosis: Head and neck cancerParticipants606000120
Diagnosis: Lung cancerParticipants798700166
Cancer Stage: Stage 0, I, & IIParticipants656700132
Cancer Stage: Stage III & IVParticipants737800151
Cancer Stage: Unknown or Not ReportedParticipants12003
Step at Baseline: Step 1 & 2Participants10611489106415
Step at Baseline: Step 3 & 4Participants33322925119
Step at Baseline: Unknown or Not ReportedParticipants01001

6. Primary Endpoint

The registry lists the primary outcome as Symptoms of Depression-Patients, measured over 6-months.

ElementRegistry entry
Result typeMean
Measure of spreadStandard Deviation
Unitscore on a scale
Endpoint classificationContinuous Endpoint

The primary endpoint was patient-reported depression measured at 6 months with the Patient-Reported Outcomes Measurement Information System-Cancer Form v1.0 Depression measure, consisting of 30 items. It is a continuous score on a scale ranging from 8 to 40. Higher scores indicate worse depression. The registry says raw scores were used in analyses.

A continuous symptom score can retain information about the degree of reported symptoms rather than reducing responses to a simple category. Comparing group means therefore describes the average score in each arm and the average difference between those scores. The standard deviations describe the spread of individual scores around each arm’s mean; they provide context for how variable participants’ reported outcomes were.

Depression was selected as the primary patient outcome in a trial whose stated purpose was to address mental health needs among underserved cancer patients and caregivers. The timing and scale make the endpoint a report of symptoms at the specified follow-up, not a measure of every aspect of mental health care access, treatment use, or long-term course. The registry says the reported means correspond to observed means at 6 months and that all randomized participants were included in the intention-to-treat analysis. It does not explain how missing 6-month measurements were handled or whether any other score transformation was used beyond the statement that raw scores were analyzed.

7. Results Posted in the Registry

Mean difference: Patients in Stepped Care Intervention

-2.10

95% CI: -3.58 to -0.62

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals11.912.913.914.915.916.9Patients in Enhanced Usual Ca… (n=139)Patients in Stepped Care Inte… (n=147)score on a scale (95% CI)
Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Patients in Stepped Care Inte…-3.87-3.04-2.21-1.38-0.540.29mean difference vs control (95% CI)

8. Secondary Efficacy Endpoints

The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.

Secondary outcomeTypeEffect measureEstimate (95% CI)Planning size, 80% power
Change in Coping-CaregiversContinuous EndpointMean difference19.00 (6.30 to 31.70)113 per arm
Symptoms of Anxiety-CaregiversContinuous EndpointMean difference-3.00 (-4.74 to -1.26)86 per arm
Symptoms of Depression-CaregiversContinuous EndpointMean difference-1.80 (-3.38 to -0.22)193 per arm

Change in Coping-Caregivers

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Stepped-Care Intervention-2.544.8212202734mean difference vs control (95% CI)

Symptoms of Anxiety-Caregivers

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Caregivers in Stepped Care In…-5.12-4.02-2.92-1.82-0.720.38mean difference vs control (95% CI)

Symptoms of Depression-Caregivers

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Caregivers in Stepped Care In…-3.65-2.87-2.08-1.30-0.510.27mean difference vs control (95% CI)

The secondary outcomes cover several aspects of patient and caregiver experience, including coping, anxiety, depression, perceived stress, health-related quality of life, and caregiving burden. The registry names seven secondary outcomes. Numerical details in the posted results describe caregiver coping, caregiver anxiety, and caregiver depression. They do not provide detailed numerical comparisons for every named secondary outcome in the registry record for this analysis.

Across the three caregiver outcomes with detailed numerical comparisons, the simple unadjusted recalculations point in a favorable direction for the stepped-care arm according to the relevant score means and their scale descriptions. However, the registry-reported mixed-model analyses do not provide the same degree of statistical evidence for these comparisons: their confidence intervals include zero, and their p-values are 0.21, 0.052, and 0.214. The registry record does not explain the difference between these results and the unadjusted calculations. Different analysis methods and contrast conventions may matter, but the details needed to attribute the differences are not reported.

This pattern does not negate the primary result, which concerns patient depression rather than caregiver outcomes. Nor should secondary outcomes be treated as independent replications of the primary endpoint: they involve different respondents and constructs. They provide broader context about outcomes the trial intended to assess, but their interpretation is less definitive when multiple outcomes are examined and the record does not report a multiplicity adjustment. Unadjusted secondary p-values do not account for the increased chance of at least one apparently notable finding across a set of tests.

The registry lists 10 outcome measures and 10 analyses, but the full statistical plan and the status of each analysis are not detailed in the record. The secondary results should therefore be read as exploratory context rather than as a collection of separate confirmatory conclusions. In particular, a numerical trend in an unadjusted comparison is not sufficient on its own to establish a reliable difference, and the caregiver findings should not be used to infer unreported effects on patient quality of life, perceived stress, or caregiving burden.

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

9. Statistical Interpretation

Clinical Biostats interpretation

At 6 months, the observed mean depression score was 15.3 among patients in enhanced usual care and 13.2 among patients in stepped care. Because higher scores indicate worse depression, the lower observed mean in the stepped-care arm is in the direction of less reported depression. The unadjusted recalculation expresses the stepped-care mean relative to the enhanced-usual-care mean as -2.1, with a 95% confidence interval from -3.584 to -0.616 and an unadjusted p-value of 0.006. The confidence interval and point estimate describe a difference between group means, not the change experienced by every participant.

The registry’s reported mixed-model analysis gives a mean difference of 1.75, a 95% confidence interval from 0.52 to 2.98, and p = 0.006. This has the opposite sign from the recalculation because the results are presented in a different direction or contrast convention; the registry record does not specify enough about the coding to establish the reason. The reported analysis and the unadjusted recalculation should therefore be read with attention to their contrast direction, rather than treating positive and negative signs as directly contradictory. Both estimates are reported as comparisons of the two arms, and both indicate a separation between the group means under their respective conventions.

The observed standard deviations were 7.0 in enhanced usual care and 5.7 in stepped care. These describe variability among participants, not precision of the estimated mean difference. The arm summaries include 139 and 147 patients, respectively. Although the overall trial enrollment was 535, that total should not be substituted for the endpoint-specific group counts when interpreting this comparison.

The registry also reports results for selected caregiver outcomes. Their pattern is not uniformly aligned across analyses: simple unadjusted recalculations and mixed-model estimates differ in statistical evidence for the described secondary comparisons. Those outcomes are secondary, and the record does not report a multiplicity adjustment. They should not displace the primary patient outcome or be treated as independent confirmation without considering the many outcomes tested and the distinct analysis methods.

These results describe group averages in this trial and the uncertainty around those estimates. They do not establish that every patient’s depression changed by the average amount, explain how participants experienced care, or demonstrate the cause of every observed difference. The data do not establish effects beyond the recorded follow-up. They also do not support conclusions about other populations or forms of usual care that were not studied.

10. Statistical Methods Explained

The primary outcome is continuous: it is a score on a scale rather than a count or a yes-or-no event. The posted arm summaries therefore give a mean and standard deviation for each group. The mean indicates the group’s average score, while the standard deviation indicates how dispersed participant scores were around that average. The registry reports observed 6-month means of 15.3 for enhanced usual care and 13.2 for stepped care, with standard deviations of 7.0 and 5.7. Higher scores mean worse depression.

What does the unadjusted mean difference represent?

The recalculated mean difference compares the two observed arm means directly. It is -2.1 when expressed as stepped care minus enhanced usual care. The negative direction corresponds to a lower average depression score in stepped care because the scale assigns worse depression to higher scores. This is a simple, unadjusted comparison based on the posted summary statistics. It does not incorporate participant-level covariates or any model structure that may have been used in the trial’s reported analysis. It should not be mistaken for a fully specified reanalysis of individual records.

A confidence interval for a mean difference describes a range of values compatible with the estimate under the statistical model and its assumptions. Its width reflects uncertainty in the estimate. An interval that does not include zero is conventionally read as evidence of a difference at the corresponding confidence level, while the endpoints also indicate how large or small the difference could plausibly be under that analysis. This general interpretation does not make the interval a probability statement about the true value or about an individual participant.

What did the registry report as its analysis?

The registry reports a Mixed Models Analysis for the primary comparison, with the parameter described as Mean Difference (Final Values). It reports an estimate of 1.75, a 95% confidence interval from 0.52 to 2.98, and p = 0.006. The recalculation based on the arm summaries is unadjusted, whereas the registry identifies its method as a mixed-model analysis. The sign is also reversed between the two presentations. The registry record does not describe the model formula, covariates, repeated-measures structure, correlation assumptions, estimation method, or contrast coding. Without those details, it is not possible to establish precisely why the estimates differ in sign or magnitude. The direction of the arm means is clear from the scale description, but the reported estimate’s positive sign must be interpreted according to the contrast convention used by the registry analysis.

In general, mixed models can account for dependence among repeated measurements or clustered observations when that structure is part of the data and the model. They can also accommodate predictors specified in the model. Those are general properties, not details confirmed for this trial’s analysis. The registry does not say which such features were included, so no claim about adjustment or repeated-measures handling can be made from the method label alone.

How should the p-values be read?

A p-value measures how incompatible the observed data are with a specified null hypothesis under the model and assumptions used. It is not the probability that the null hypothesis is true, nor does it describe the size or practical importance of the difference. The unadjusted recalculation reports p = 0.006, and the registry reports p = 0.006 for its mixed-model analysis. The two p-values arise from analyses that are not described as identical. The registry does not report a complete statistical analysis plan that would clarify which result was designated as the confirmatory test or how testing across outcomes was addressed.

Statistical significance does not determine whether a difference is important to patients, whether the intervention was delivered consistently, or whether findings apply outside this study. Interpretation should consider the scale, the estimated difference, the confidence interval, the analysis population, and limitations in the record, rather than a p-value alone.

Why can over-dispersion matter?

Over-dispersion is a general concern in analyses of counts or event data when the observed variation exceeds what a chosen probability model expects. It can make standard errors too small if ignored. The primary endpoint is a continuous score summarized by means and standard deviations, not a count outcome, so over-dispersion is not the central issue for this comparison. More generally, analysis assumptions should match the outcome type and data structure. The registry does not provide enough detail to assess the assumptions of the mixed model used for the primary result.

The registry describes the primary analysis population as all participants who were randomized, and says the displayed means correspond to observed means at 6 months. Those statements identify the intended population and the source of the arm means, but they do not explain the handling of participants without observed 6-month outcomes. The missing-data method, if any, is not reported in the registry record. The record also does not specify whether the analysis used every randomized participant’s available data, imputation, likelihood-based handling, or another approach.

11. Confidence Intervals and Precision

The unadjusted primary estimate is a mean difference of -2.1 points for stepped care relative to enhanced usual care. Its reported 95% confidence interval is -3.584 to -0.616. This interval conveys uncertainty around the estimated difference: the point estimate is not known without error, and values across the interval are compatible with the recalculation under its assumptions. The interval does not include zero, while its width shows that the size of the difference is not pinned down to a single value.

The registry’s mixed-model analysis reports a 95% confidence interval from 0.52 to 2.98 around its estimate of 1.75. That interval also does not include zero. Its sign is opposite the unadjusted estimate because the reported analysis uses a different presentation direction or contrast convention; the record does not state which. The two intervals come from different analyses and should not be combined or treated as interchangeable. The registry does not provide enough model details to assess why their widths differ.

Confidence intervals address statistical precision, not all forms of uncertainty. They do not capture limitations from incomplete outcome data, potential departures from model assumptions, measurement issues, or limits to generalizability. Nor do they show the distribution of individual participant responses. The standard deviations of 7.0 and 5.7 describe score variability in the two arms, whereas the confidence interval describes uncertainty in the estimated group contrast. These quantities answer different questions.

The observed means are based on 139 patients in enhanced usual care and 147 in stepped care. The registry says the primary analysis included all randomized participants and that the reported means are observed 6-month means, but does not detail missing-data handling. Accordingly, the interval should be interpreted as precision under the analysis used, not as a guarantee that all relevant sources of uncertainty have been addressed.

12. Planning a Similar Trial: Sample Size

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

Effect to detectParticipants per arm, 80% powerParticipants per arm, 90% power
100% of the observed effect145194
75% of the observed effect257344
50% of the observed effect577773
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect1002005001,0002,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, two-sample comparison of means with the pooled standard deviation. Calculated for the comparison: Patients in Stepped Care Intervention.

The sample-size illustrations use participants per arm, not total events. Each row describes planning for a stated fraction of the observed effect, with separate figures for 80% and 90% power. The 80% column gives the number of participants per arm that the illustration estimates would be needed to have an 80% chance of detecting the specified effect, under its assumptions, if that effect were the true one. The 90% column expresses the same idea for a higher chance of detection. Greater power generally requires more participants, all else equal.

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 the stated fraction of the observed effect. For the primary comparison, planning for 100% of the observed effect corresponds to 145 participants per arm for 80% power and 194 participants per arm for 90% power. Planning for 75% of the observed effect corresponds to 257 and 344 participants per arm. Planning for 50% of the observed effect corresponds to 577 and 773 participants per arm. Smaller effects need more participants because they are harder to distinguish from random variation.

These are planning illustrations based on the observed effect, not the trial’s original design assumptions. The original sample-size justification and planning assumptions are not reported in the registry record. The illustrations are not observed power and do not describe the probability that the trial’s result is correct. They also do not establish that the enrolled sample was adequate for every primary or secondary outcome. Their purpose is to show how required group size changes under the stated assumptions when the target effect is varied.

13. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z1−α/2 = 1.960) and the desired power (z1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n = 2 (z1−α/2 + z1−β)2 σ2 / Δ2

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 = -2.100; pooled standard deviation σ = 6.365.
  2. n = 2 × (1.96 + 0.842)2 × 6.3652 / -2.1002 = 144.2, rounded up to 145 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 <- -2.1                      # observed difference in means
sigma <- 6.36494028163127                     # 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(3016403)
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 = 145 (80% power), 194 (90% power)
 75% of observed effect: n per arm = 257 (80% power), 344 (90% power)
 50% of observed effect: n per arm = 577 (80% power), 773 (90% power)
power.t.test: 145.2 
Simulated power at n = 145 per arm: 0.801 (20000 replicates)

The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

14. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
Mixed Models AnalysisMean Difference (Final Values) 1.750.52 to 2.980.006

The registry reports the sponsor’s primary analysis as a Mixed Models Analysis of final values, with a mean difference of 1.75, a 95% confidence interval from 0.52 to 2.98, and p = 0.006. The unadjusted recalculation from the posted arm means gives a mean difference of -2.1 when the contrast is stepped care minus enhanced usual care, with an unadjusted p-value of 0.006. The arm means themselves are 13.2 for stepped care and 15.3 for enhanced usual care.

The opposite signs indicate that the results are not written using the same contrast direction, or that the model’s contrast coding differs from the direct subtraction used in the recalculation. The registry record does not specify the coding, so the exact reason cannot be confirmed. The analysis methods are also not identical: one is the registry-reported mixed-model result, while the recalculation is a simple unadjusted comparison of posted summary statistics. Differences in estimates and uncertainty can arise when analyses use different methods, but the record does not state which model features produced this particular result.

The registry reports no discrepancy flag. The sponsor’s result should be read as the result of the analysis it reports, while the recalculation is useful as a transparent comparison of the posted arm summaries. The sign should not be interpreted without noting the contrast direction and the scale’s meaning. The record does not provide enough detail to reconstruct the sponsor’s model or reconcile the estimates beyond these observations.

15. Multiplicity, Missing Data and Analysis Populations

The registry lists 10 outcome measures and 10 analyses, including the primary patient depression outcome and secondary outcomes for patients and caregivers. Testing several outcomes creates a multiplicity issue: even when no underlying differences exist, examining many results can increase the chance that one or more appear notable by chance. This is a general statistical concern, not evidence that any particular reported result is false.

The registry record does not report whether the trial used a family-wise error adjustment, a false-discovery procedure, a prespecified testing hierarchy, or another strategy to address multiplicity. It also does not give a complete statistical analysis plan that identifies which outcomes and contrasts were intended to be confirmatory. Accordingly, the secondary p-values should be treated as unadjusted unless the registry explicitly identifies otherwise. They do not carry the same evidential weight as a prespecified primary analysis when the handling of multiple testing is unknown.

The primary outcome is explicitly identified as patient depression at 6 months, and the registry describes an intention-to-treat population consisting of all randomized participants. It further says the displayed means are observed means at 6 months. However, the record does not report the number of participants with missing primary outcome data, reasons for missingness, or the statistical method used to handle missing measurements. It is therefore not possible to determine from these registry entries whether the analysis retained all randomized participants through a model-based approach, used a complete-case subset, imputed outcomes, or relied on another method.

In general, missing-data methods rely on assumptions about why measurements are unavailable and how unobserved values relate to observed information. Those assumptions can affect estimates and precision. The available description does not permit assessment of whether the assumptions were plausible in this trial or whether sensitivity analyses were conducted. The registry also does not report interim analyses or stopping rules, and no such procedures should be inferred from the completed status or the posted results.

The record identifies the primary analysis as a mixed-model analysis of final values, but does not provide model specifications, covariates, or analysis diagnostics. The summary’s statement that all randomized participants were included identifies the intended analysis population, but does not by itself resolve questions about missing observations or the exact estimation procedure. These gaps warrant caution in interpreting both the primary estimate’s analytic basis and the secondary comparisons.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Patients in Enhanced Usual Care131399.4%
Patients in Stepped Care Intervention1914712.9%
Caregivers in Enhanced Usual Care11180.8%
Caregivers in Stepped Care Intervention01310.0%
Participants with at least one serious adverse event
Serious adverse events by armPatients in Enhanced Usual Ca…9.4%Patients in Stepped Care Inte…12.9%Caregivers in Enhanced Usual …0.8%Caregivers in Stepped Care In…0.0%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
Patients in Enhanced Usual Care13 of 139
Patients in Stepped Care Intervention18 of 147
Caregivers in Enhanced Usual Care1 of 118
Caregivers in Stepped Care Intervention0 of 131

Other (non-serious) adverse events

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

ArmParticipants affected of at risk
Patients in Enhanced Usual Care0 of 139
Patients in Stepped Care Intervention0 of 147
Caregivers in Enhanced Usual Care0 of 118
Caregivers in Stepped Care Intervention0 of 131

Most frequent serious adverse event terms

Event termOrgan systemPatients in Enhanced Usual CarePatients in Stepped Care InterventionCaregivers in Enhanced Usual CareCaregivers in Stepped Care Intervention
DeathGeneral disorders13 of 13918 of 1471 of 1180 of 131
Respiratory failure with hypoxiaRespiratory, thoracic and mediastinal disorders0 of 1391 of 1470 of 1180 of 131

Serious events with the highest arm-level rate: death (12.2%), respiratory failure with hypoxia (0.7%).

Do not overextend the safety comparison. Serious-adverse-event counts are safety observations, not efficacy outcomes, and should not be combined with the primary result into a single benefit-risk number.

Serious adverse event figures are reported separately for patients and caregivers in each arm. Among patients in enhanced usual care, 13 of 139 were reported as affected by a serious adverse event; among patients in stepped care, 19 of 147 were affected. For caregivers, the corresponding figures were 1 of 118 in enhanced usual care and 0 of 131 in stepped care. The registry reports zero other adverse events in each of these groups. These are counts of participants affected as recorded, not a comparison adjusted for follow-up time or other characteristics.

The adverse-event information also lists death as a serious event term at 12.2% and respiratory failure with hypoxia at 0.7%. Deaths are separately reported as 13 among patients in enhanced usual care, 18 among patients in stepped care, 1 among caregivers in enhanced usual care, and 0 among caregivers in stepped care. These counts should be read as registry entries, not as evidence that an intervention caused an event. The registry entries do not provide event timing, relatedness assessments, causes for each death, or exposure-adjusted comparisons.

The group counts alone cannot establish whether risks differed, because the registry summary does not supply the details needed to interpret duration of observation or participant-level event histories. They are safety reporting figures, not a causal estimate of treatment-related harm.

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

The primary result describes a difference in average patient-reported depression scores at 6 months between participants assigned to stepped care and those assigned to enhanced usual care. The observed mean score was lower in the stepped-care arm, and the scale defines higher scores as worse depression. The unadjusted recalculation estimates the difference as -2.1 points, while the registry’s mixed-model result reports a positive estimate under a contrast direction that is not specified in the record. Both presentations indicate a difference between group averages, but their signs must be interpreted with the contrast convention in mind.

This result does not mean that every patient in stepped care reported fewer symptoms, or that each person’s score changed by the estimated group difference. Group means can conceal variation in individual experiences, including people whose scores differ from the average. The standard deviations indicate that scores varied within both arms. The estimate also does not tell whether any observed difference was meaningful to participants; the registry entries do not provide a threshold for interpreting the clinical importance of a score difference.

The result does not establish the mechanism behind any difference, the amount or consistency of intervention received, or whether mental health service access changed. Enhanced usual care itself included a variable amount of supportive care. The available summary does not show how treatment adherence, referrals, or actual service use related to depression scores.

Nor does the result settle effects for caregivers or for every other patient outcome. Secondary results concern distinct measures and should be read with caution, particularly because the record does not report a multiplicity strategy and because the sponsor-reported and unadjusted analyses are not identical. The findings also do not establish outcomes beyond the recorded 6-month assessment or generalize automatically to populations and care settings not described in the trial.

Statistical evidence about a group difference is not medical advice and is not a recommendation about care. It is a description of what the registry reports and how uncertain the estimate is under the analysis used. The missing details on the original analysis plan, missing-data handling, and model specification limit stronger conclusions about robustness.

18. Why This Trial Matters Statistically

This trial raises an important statistical question about evaluating a behavioral program in a setting where the comparator is not an inert or uniform condition. Enhanced usual care included supportive mental health services, and the amount received varied. The comparison is therefore between an organized stepped-care intervention and a setting in which participants could receive different forms and amounts of usual support. That context matters when interpreting an average contrast: it represents the trial’s comparison as implemented, not a comparison with no mental health care.

The trial also includes both patients and caregivers, while its primary endpoint is specific to patients. Separating patient and caregiver outcomes helps keep the estimand clear: the primary estimate is about patient-reported depression, not a combined score for everyone involved in care. The caregiver outcomes expand the scope of assessment, but involve distinct constructs and analysis populations. Their findings require separate interpretation rather than being blended into the primary result.

Statistically, the record illustrates why an effect estimate, uncertainty interval, scale direction, and analysis method should be read together. The simple recalculation and the registry’s mixed-model result use different presentations and yield estimates with opposite signs. The posted arm means and the scale direction help orient the direct comparison, while the lack of model and contrast details prevents a full reconstruction of the registry analysis. This is a meaningful reporting limitation, not a reason to ignore either result.

The range of outcomes also highlights the importance of prespecification and multiplicity control. The registry records many outcomes, but does not report how multiple testing was handled. The distinction between a designated primary endpoint and secondary outcomes helps readers avoid treating every nominally notable comparison as equally persuasive. The absent design assumptions and missing-data details further show how registry summaries can communicate results while leaving important questions about analytic robustness unresolved.

19. Limitations

The registry summary leaves several trial-specific uncertainties. Although overall enrollment is 535, the registry entries do not describe participant flow from screening through randomization and follow-up, or explain how the endpoint-specific analysis counts relate to the overall enrollment. The primary outcome analysis is described as intention to treat, but observed means are reported at 6 months and the method for handling missing outcomes is not reported in the registry record. This makes it difficult to assess the effect of incomplete follow-up on the estimates.

The primary registry analysis is labeled a Mixed Models Analysis of final values, but the model specification is not reported. Covariates, repeated-measure structure, contrast coding, estimation details, and diagnostics are not described. The reported estimate has the opposite sign from the straightforward stepped-care-minus-enhanced-usual-care recalculation, and the record does not identify the coding convention. Although the arm means and scale direction clarify which arm had the lower observed score, the numerical difference between the two analyses cannot be fully explained from the available information.

The registry does not report the original sample-size justification or the assumptions used to plan enrollment. The planning illustrations based on the observed effect do not establish how the trial was designed or what its intended detectable effect was. It also does not report an analysis plan for multiplicity, interim monitoring, or stopping rules. These details should not be inferred.

Enhanced usual care varied in the amount of mental health support received, according to the registry description. That variability is part of the comparator condition and may complicate interpretation of what the contrast represents. Further detail on actual service use, intervention delivery, and participant adherence is not available in the registry record. The registry summary also does not provide enough information to assess generalizability beyond the underserved lung and head and neck cancer patients and caregivers it describes.

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23. Record Summary

NCT03016403 is a completed randomized, parallel-group behavioral trial sponsored by the University of Colorado, Denver. It compared a stepped-care intervention with enhanced usual care for underserved lung and head and neck cancer patients and their caregivers. The overall enrollment was 535, masking was listed as none, and phase was listed as not applicable.

The primary endpoint was patient-reported depression at 6 months using the PROMIS-Cancer Depression measure. The observed mean was 13.2 in stepped care and 15.3 in enhanced usual care. The registry reports a mixed-model mean difference of 1.75, with a 95% confidence interval from 0.52 to 2.98 and p = 0.006; the unadjusted recalculation is expressed in the opposite direction. Caregiver outcomes and adverse events were also recorded.

The registry does not report the original sample-size justification, detailed model specification, multiplicity approach, or missing-data method. Those omissions constrain interpretation beyond the posted estimates and the trial’s described comparison.

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