Supporting Parents Program: Intervention for Families in CPS: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Supporting Parents Program: Intervention for Families in CPS (NCT01332851), a randomized na study. The primary outcome is Child Welfare Outcomes: CWS Removal From Birth Parent Home.

2. Clinical Question

3. Trial Design

The registry describes a randomized, single-masked, parallel-group study comparing Promoting First Relationships (PFR) with Resource & Referral. Enrollment is listed as 270. The two named conditions are behavioral interventions, and the registry record lists child abuse and child neglect as the conditions under study. The study status is completed; the recorded start is 2011-01 and primary completion is 2015-06.

PFR is described as a strengths-based, 10 week in-home parenting intervention based on attachment theory. The registry description refers to weekly themes for discussion, an activity, and time for “joining,” including checking in with the parent, listening to concerns, and establishing a supportive relationship. Resource & Referral is described as phone assistance from a specialist who conducts a needs assessment, with a local services resource packet. The descriptions available in the registry record are incomplete at their ends, so additional intervention details are not reported in the registry record.

The registry summary says the study evaluates feasibility and effectiveness of the intervention relative to Resource & Referral, and also refers to evaluating training community social service workers in providing the intervention. The listed arms, however, are PFR and Resource & Referral. Further details about how any provider-training evaluation was incorporated into the randomized design are not reported in the registry record.

Single masking is recorded, but which people were masked is not reported in the registry record. Details of the randomization procedure, allocation concealment, participant flow, adherence, and treatment completion are also not reported in the registry record. These omissions limit what can be concluded about trial conduct from the registry description 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.

Before assignment: 4 participants were not randomized (2 already had the study intervention, 1 refused to sign the HIPAA agreement, and 1 was not located). 19 additional caregivers were enrolled post randomization when the study parent lost custody of their child. They were not "randomized" to a condition, but they were consented to participate and supplied data.

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 Child Welfare Outcomes: CWS Removal From Birth Parent Home, measured over 1 year post intervention.

The primary endpoint is whether a child was removed from the birth parent’s home within one year after the parent completed the intervention. For parents who did not complete it, the endpoint window was anchored to the estimated date when the intervention would have been completed. The registry says outcome status came from official child welfare administrative records.

This is a binary event status for each child over a defined follow-up window, but the primary analysis was not limited to comparing the proportions with a recorded removal. The record says a survival model predicted the hazard of removal. A time-to-event approach uses the timing of an event, along with information about participants whose event time may not be observed within the follow-up period, rather than treating every participant as if their event status were observed at an identical time. The registry does not state how censoring or incomplete follow-up was handled.

Using administrative records gives the endpoint a defined source outside a parent’s report. The result addresses a specific child welfare event over the stated period; it does not directly measure the quality of parenting, family relationships, or all aspects of child development. Those broader domains appear among the secondary outcomes, including parenting stress, child social-emotional development, behavior, emotion regulation, and observed parent-child interaction.

7. Results Posted in the Registry

• Resource & Referral: 13.0% (16/123) versus 5.6% (7/124) on control; risk difference 7.4 percentage points (95% CI 0.2 to 14.6), risk ratio 2.30 (0.98–5.40); unadjusted two-proportion z-test p = 0.046.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is a time-to-event endpoint: removal from the birth parent’s home within one year after the intervention completion date, or the estimated completion date for parents who did not complete. The registry reports a Cox proportional hazards analysis. This method compares event hazards over follow-up, where a hazard is the instantaneous event rate among participants who have not yet experienced the event. A hazard ratio summarizes the relative hazards between groups under the model.

What does the Cox estimate describe?

The reported Cox estimate is 2.50, with a 95% confidence interval from 1.03 to 6.10. Given the group ordering and the direction of the event counts, it is interpreted as the estimated hazard in Resource & Referral relative to PFR. A hazard ratio of 1 would represent equal hazards under the model; values above 1 indicate a higher estimated hazard for the numerator group. This does not mean that the probability of removal is 2.50 times as large at every point, because a hazard ratio is not the same quantity as a risk ratio. The Cox model also relies on a proportional hazards assumption: the relative hazard is treated as stable over follow-up. Whether that assumption was checked, and how it was assessed, is not reported in the registry record.

How does the recalculation differ?

The registry posts event counts of 7 among 124 in PFR and 16 among 123 in Resource & Referral. The recalculated risk difference is 0.074, with a 95% confidence interval from 0.002 to 0.146 and an unadjusted p-value of 0.046. This is an unadjusted comparison of the observed proportions, using the posted counts and denominators. It does not incorporate event timing in the way the Cox model does. The recalculation is therefore a useful descriptive cross-check, not a replacement for the sponsor’s time-to-event analysis. The sponsor’s own analysis takes precedence when describing the trial’s reported primary analysis.

A risk difference expresses the absolute difference between the observed group risks; the posted estimate is in proportion units. Its confidence interval expresses uncertainty about that difference under the recalculation method. Because the estimate and interval are close to zero at the lower end, the data are compatible with a small absolute difference as well as a larger one within the stated interval. The interval does not account for uncertainty from unreported design or analysis decisions.

What does a confidence interval convey?

A confidence interval is a range of values that reflects the statistical uncertainty around an estimate under the model and method used. It is not a guarantee that the true effect lies inside the particular interval, and it does not include every possible source of uncertainty, such as bias from incomplete outcome data or departures from model assumptions. The reported Cox interval ranges from 1.03 to 6.10, which indicates substantial uncertainty about the size of the relative hazard even though the interval excludes 1.

The corresponding reported p-value is =.043. A p-value describes how incompatible the observed data are with a specified null model, assuming the model and its assumptions hold. It is not the probability that the null hypothesis is true, nor does it measure the probability that a finding is due to chance. The p-value does not measure clinical importance or establish that the estimated effect is precise.

Why consider the event counts alongside the model?

The event counts offer an accessible account of how many participants experienced the endpoint in each group, while the model result addresses the time-to-event comparison. These summaries complement one another but are not interchangeable. For example, counts and denominators do not retain the timing information used by a survival model. The registry does not give event times, censoring details, or a fuller survival curve description, so the primary analysis cannot be independently reconstructed from the posted summary alone.

There are also limits to what can be inferred from the registry’s method label. The record identifies regression, Cox proportional hazards, and a superiority analysis, but it does not describe covariate adjustment, handling of missing data, checks of proportional hazards, or the specific analysis population. Those elements are not reported in the registry record and should not be assumed.

For binary event data, variation can be substantial when event counts are limited. General statistical explanation: a small number of events can make estimates sensitive to the particular observations, and uncertainty intervals can remain wide even when a point estimate appears clear. In this trial, the posted counts and the wide Cox interval make the uncertainty about effect size important to retain when interpreting the result.

10. Confidence Intervals and Precision

The principal estimate is a Cox hazard ratio of 2.50, with a 95% confidence interval from 1.03 to 6.10. The interval is wide relative to the point estimate: values near the lower limit imply a modest difference in hazards, while values nearer the upper limit imply a substantially larger difference. The data therefore do not pin down the magnitude closely. The lower limit is only just above 1, so the interval also indicates that the result is sensitive to uncertainty around the null value.

The reported p-value is =.043. It is consistent with the confidence interval’s exclusion of 1, but neither value should be interpreted as a measure of the effect’s practical importance. The estimate is a relative hazard, not an absolute probability. The registry does not report a confidence interval for each group’s event probability, and no such interval should be inferred from the posted model result.

The unadjusted recalculation reports a risk difference of 0.074, with a confidence interval from 0.002 to 0.146. This interval also spans a range of possible absolute differences, from close to zero to a larger difference. The recalculation’s p-value is 0.046. Since this result is based on group counts and denominators rather than event timing, it is not the same estimand as the Cox hazard ratio.

Confidence intervals describe sampling uncertainty under the analysis assumptions. They do not account for unreported features such as missing outcome data, departures from model assumptions, or choices among multiple outcomes. The registry does not report enough detail to assess those sources of uncertainty. The appropriate reading is therefore that the posted analyses suggest a difference in the specified outcome, while the size of that difference remains imprecise.

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 illustrations based on the observed effect, not the original trial design. For this time-to-event outcome, the figures represent the total number of events required, rather than participants per arm. The 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 at the stated fraction of the observed effect. The trial’s own original sample-size assumptions are not reported in the registry record.

The 80% power column gives the illustrated event total for a design with an 80% chance of detecting the specified effect under the planning assumptions, if that effect and assumptions were correct. The 90% power column gives the corresponding event total for a design targeting 90% power. These are prospective planning concepts, not measurements of how likely this completed trial was to detect its result.

For 100% of the observed effect, the illustration gives 244 total events for 80% power and 326 for 90% power. For 75% of the observed effect, it gives 396 total events for 80% power and 529 for 90% power. For 50% of the observed effect, it gives 801 total events for 80% power and 1,072 for 90% power. Smaller effects require more events to detect under otherwise unchanged assumptions, which is why the figures increase as the target effect becomes a smaller fraction of the observed effect.

These planning values are not observed power. Observed power is not a useful substitute for interpreting the effect estimate and its confidence interval after a study is completed. The figures also should not be read as the number enrolled in this trial: they describe event totals for hypothetical planning scenarios, whereas the registry lists enrollment of 270.

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, p₀ and p₁ are the control and treatment proportions, and p̄ is their average.

Worked calculation for this trial

1. Control proportion p₀ = 0.056; treatment proportion p₁ = 0.130; average p̄ = 0.093.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.4113 = 0.8061.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.4080 = 0.3433.
4. n = (0.8061 + 0.3433)² / (0.0736)² = 243.7, rounded up to 244 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
p0 <- 0.0564516129032258                          # control proportion
p1 <- 0.130081300813008                          # treatment proportion
n_per_arm <- function(power, frac = 1) {
  q1 <- p0 + (p1 - p0) * frac               # smaller effect = fraction of the observed difference
  pbar <- (p0 + q1) / 2
  z_b <- qnorm(power)
  ceiling(round((z_a * sqrt(2 * pbar * (1 - pbar)) + z_b * sqrt(p0 * (1 - p0) + q1 * (1 - q1)))^2 / (q1 - p0)^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 (unrounded n per arm)
cat("power.prop.test:", round(power.prop.test(p1 = p0, p2 = p1, power = 0.80)$n, 1), "\n")

# Simulation: how often does the z-test reject at the 80%-power sample size?
set.seed(1332851)
n    <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z  <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))

Output from running the code

100% of observed effect: n per arm = 244 (80% power), 326 (90% power)
 75% of observed effect: n per arm = 396 (80% power), 529 (90% power)
 50% of observed effect: n per arm = 801 (80% power), 1,072 (90% power)
power.prop.test: 243.7 
Simulated power at n = 244 per arm: 0.811 (20000 replicates)

The simulation draws many pairs of event counts at the planned sample size and counts how often the two-proportion z-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’s reported primary result is the sponsor’s Cox proportional hazards analysis: hazard ratio 2.50, 95% confidence interval 1.03 to 6.10, and p =.043. This time-to-event analysis is the result to use when describing the trial’s stated primary analysis. The direction, with a higher estimated hazard in Resource & Referral relative to PFR, agrees with the posted counts: 16 events among 123 in Resource & Referral and 7 among 124 in PFR.

The recalculated comparison of the posted counts gives a risk difference of 0.074, with a confidence interval from 0.002 to 0.146 and an unadjusted p-value of 0.046. It is a simple, unadjusted comparison of proportions. It does not account for event timing as the Cox model does, so differences between the estimates or p-values need not indicate an error.

The registry marks no discrepancy between the sponsor’s analysis and the recalculation. Even so, the quantities have different interpretations: the Cox result describes a relative hazard, while the recalculation describes an absolute difference in observed risks. The recalculation is supplementary and does not supersede the sponsor’s own analysis.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists 14 outcome measures, 10 analyses, and 11 posted secondary outcomes. The secondary outcomes cover parenting stress, child social-emotional development, child behavior problems, emotion regulation, engagement or exploration, atypical affective communication, and observed parent-child interaction. The registry does not report a multiplicity adjustment, a hierarchy for testing outcomes, or a prespecified strategy for selecting among analyses. Without those details, the collection of outcome findings should not be treated as though each were an isolated confirmatory test.

Multiplicity matters because conducting many statistical tests can raise the chance that at least one result appears notable even when there is no underlying effect for that outcome. General statistical explanation: prespecifying a primary endpoint and limiting confirmatory claims can help control this issue, while exploratory outcomes can still be informative but require cautious interpretation. The registry identifies a primary outcome and reports a primary analysis, but details of a formal testing hierarchy are not reported in the registry record.

Missing-data handling is not reported in the registry record. The primary outcome is described as coming from official administrative records, but the record does not state whether records were complete for all participants or how unavailable outcome information was handled. It also does not report the number of participants included in each analysis or reasons for any exclusions.

The analysis population is not reported in the registry record. It is not stated whether the primary analysis followed an intention-to-treat approach, included only participants with complete outcome information, or used another population definition. Randomization is recorded, but the registry does not provide enough information to assess how departures from assigned intervention, incomplete intervention participation, or loss to follow-up were handled statistically.

The Cox model is identified, but covariate adjustment and model diagnostics are not described. The handling of censoring, the proportional hazards assumption, and any sensitivity analyses are not reported in the registry record. These gaps do not negate the posted result, but they constrain independent assessment of the model and the robustness of the conclusion.

15. 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 non-serious adverse event terms

The registry lists zero serious adverse events among 124 participants in PFR and zero among 123 participants in Resource & Referral. It also lists zero deaths in each group. These are reported counts for the groups at risk, not a detailed account of the kinds of events monitored or how events were collected.

Other adverse events are listed for 36 participants in PFR and 42 in Resource & Referral, with group sizes of 124 and 123. The registry does not provide terms describing those other events in the information recorded. No serious adverse event terms are listed. The absence of listed serious events should be read as a report of the recorded counts, not as proof that no safety concerns of any kind could occur.

The record does not describe the safety-monitoring process, event definitions, attribution procedures, or follow-up duration for adverse events. Without those details, the counts cannot establish whether the groups differed in event severity, timing, or cause. These figures describe what the registry reports and should not be used as medical guidance.

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

The posted result concerns one specific outcome: removal from the birth parent’s home within one year after intervention completion, measured using official child welfare administrative records. The reported Cox model estimates a higher hazard in Resource & Referral relative to PFR, with a hazard ratio of 2.50 and a 95% confidence interval from 1.03 to 6.10. The event counts point in the same direction, with 7 events in PFR and 16 in Resource & Referral.

The estimates do not establish the exact size of a difference. The confidence interval is wide, and its lower bound is close to the null value of 1. The unadjusted risk-difference recalculation likewise spans from a value close to zero to a larger absolute difference. The data therefore support a cautious description of the observed contrast, not a claim that its magnitude is known precisely.

The result does not show that PFR changes every aspect of family functioning or child development. The registry lists secondary measures in those broader areas, but the primary endpoint is removal from the birth parent’s home. Nor does the result identify why the event counts differed. A statistical association between assigned groups and the endpoint does not, by itself, establish a mechanism.

The registry does not report important analysis details, including the analysis population, missing-data procedures, censoring handling, or checks of the Cox model assumptions. It also does not report a multiplicity plan for the wider set of outcomes and analyses. Those omissions limit how fully readers can evaluate the result and its robustness.

The study compares two conditions in the registry: a relationship-based in-home intervention and Resource & Referral assistance. The result should be understood within that comparison, the stated follow-up period, and the information available in the registry record. It is not a general conclusion about all parenting programs, child welfare services, or families.

17. Why This Trial Matters Statistically

This trial illustrates why endpoint definition and analysis method matter in clinical and social-service research. The primary outcome is not simply a rating or a one-time assessment: it is a child welfare event occurring over follow-up. The registry identifies a Cox proportional hazards model, which uses the time-to-event framework rather than relying only on the number of events in each group.

The posted results also show why absolute and relative summaries answer different questions. The hazard ratio of 2.50 describes a relative event hazard under the Cox model. The recalculated risk difference of 0.074 describes an unadjusted absolute difference in observed proportions. Readers benefit from seeing how those quantities relate in direction while retaining their distinct meanings.

Precision is central to interpretation. The Cox confidence interval, from 1.03 to 6.10, allows a broad range of effect sizes, even though the reported interval excludes 1. The lower boundary is close to the null, so the p-value alone would not communicate the uncertainty about magnitude. Reporting the estimate together with its interval gives a fuller account of what the data support.

The record also offers a useful example of the limits of registry reporting. It identifies randomization, masking status, intervention arms, the endpoint, and the primary model, but does not report several details needed to assess missing data, model assumptions, analysis populations, and multiplicity. Statistical interpretation should distinguish documented results from unreported design and analysis decisions.

Finally, the planning illustrations make clear that required event totals depend on the effect size a future study aims to detect and the target power. Smaller target effects require more events under the stated assumptions. Such illustrations help with design thinking, but they are not retrospective evidence that the completed study had a particular probability of detecting an effect.

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 registry description leaves several trial-specific uncertainties. It records single masking but does not identify who was masked. Details of the randomization process and allocation concealment are not reported in the registry record. The intervention descriptions are incomplete, and additional details about delivery, adherence, and fidelity are not reported.

Although the registry summary refers to evaluating training community social service workers, the listed arms are PFR and Resource & Referral. How provider training related to the randomized comparison is not reported in the registry record. It is therefore not possible to characterize a separate training contrast from the listed arm information.

The primary analysis is identified as Cox regression, but details needed to assess it are not reported: covariate adjustment, censoring rules, checks of proportional hazards, and sensitivity analyses. The registry also does not describe missing-data procedures or define the analysis population. As a result, the posted estimate cannot be fully reconstructed or independently evaluated from the summary information.

The record lists 14 outcome measures, 10 analyses, and 11 posted secondary outcomes, but does not report a multiplicity strategy or testing hierarchy. The number of participants contributing to each secondary outcome and how missing observations were handled are also not reported. This limits interpretation of secondary findings and their comparability.

Finally, the primary endpoint is limited to removal from the birth parent’s home within the specified one-year window. The registry does not provide event timing details, a complete account of follow-up, or information sufficient to assess generalizability beyond the enrolled families and the two listed conditions. These limitations are specific to what is documented in the registry record; they do not establish that unreported procedures were absent.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Supporting Parents Program: Intervention for Families in CPS — NCT01332851.
• Registry record last updated 2018-06-07; status last verified 2018-05.
• Results first posted 2018-06-07.
• 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

NCT01332851 is a completed randomized, single-masked, parallel-group study of Promoting First Relationships and Resource & Referral. The registry lists enrollment of 270, child abuse and child neglect as conditions, and a start date of 2011-01 with primary completion in 2015-06.

The primary endpoint was removal from the birth parent’s home within one year after intervention completion, using official child welfare administrative records. The reported Cox estimate was 2.50, with a 95% confidence interval from 1.03 to 6.10 and p =.043. The posted event counts were 7 among 124 in PFR and 16 among 123 in Resource & Referral.

The registry does not report several details needed for fuller appraisal, including the analysis population, missing-data handling, censoring procedures, model checks, and multiplicity plan. The result should be interpreted as an outcome-specific estimate with substantial uncertainty about its magnitude.