Efficacy of Betalactam Antibiotics in Prolonged Infusion Compared to Intermittent in Pediatric Patients With Sepsis: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Efficacy of Betalactam Antibiotics in Prolonged Infusion Compared to Intermittent in Pediatric Patients With Sepsis (NCT03019965), a randomized na study. The primary outcome is Number of Participants With Clinical Response.

2. Clinical Question

The registry describes the study as evaluating efficacy and safety. The primary endpoint is a clinical response, while the listed secondary outcome concerns adverse events. The reported comparison combines the listed antibiotics within each infusion strategy; separate clinical-response results for each antibiotic are not reported in the registry record. The evidence therefore addresses the overall comparison as posted, rather than establishing separate estimates for each drug or regimen.

3. Trial Design

The registry describes a randomized, parallel-group trial with no masking. It lists an enrollment of 426 and a completed status. The recorded study start was 2017-02-01, and primary completion was 2019-12-30. The sponsor is Coordinación de Investigación en Salud, Mexico. The registry title refers to two pediatric third-level care hospitals.

One group received intermittent infusion, and the other received prolonged infusion. The intermittent group included piperacillin/tazobactam, imipenem, and meropenem; the prolonged group included continuous piperacillin/tazobactam, extended imipenem, and extended meropenem. The registry describes dosing and infusion schedules for these regimens. It does not report the allocation sequence method, allocation concealment, or the rule used to select an antibiotic for an individual participant.

The primary outcome was the number of participants with clinical response. The registry defines response in terms of resolution of infection-related signs and symptoms; failure includes insufficient improvement, death, or an indeterminate outcome when evaluation was not possible. The timeframe is described as 14 days after antibiotic cessation, up to an average of 28 days or discharge if discharge occurred before 14 days after cessation.

The posted primary outcome counts are 178 of 201 in the intermittent group and 169 of 202 in the prolonged-infusion group. The registry also lists adverse events as a secondary outcome. Although the design is randomized, the posted record does not describe the randomization procedures in detail, the analysis population, or whether the primary comparison was adjusted for any variables. Those details 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: the pre-specified intent was to only compare "Intermittent" and "Prolonged" Arm/Groups with the grouping of betalactam antibiotics (imipenem, meropenem and piperacillin/tazobactam)

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: The efficacy of the maneuver was evaluated by frequency of clinical response and calculation of the absolute risk reduction and the number needed to treat.

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 Number of Participants With Clinical Response, measured over Number of participants with clinical response at 14 days after antibiotic cessation, up to an average of 28 days or the day of your discharge if this occurred before 14 days after antibiotic cessation..

The primary endpoint counts participants with a clinical response. The registry defines resolution as disappearance of all signs and symptoms related to the infection. It defines failure as insufficient lessening of signs and symptoms to qualify as improvement, and includes death or an indeterminate outcome when evaluation was not possible for any reason. The endpoint is therefore a participant-level binary outcome: each participant is classified as having a response or not having one.

The timeframe is stated as assessment at 14 days after antibiotic cessation, up to an average of 28 days or discharge if discharge occurred before 14 days after antibiotic cessation. This timing anchors the outcome to the end of antibiotic treatment rather than solely to study entry. The exact procedures for assessing symptoms, determining resolution, and handling assessments after early discharge are not reported in the registry record.

A clinical response endpoint can summarize whether the intended clinical state was reached, rather than measuring only a laboratory value or treatment process. The registry says efficacy was evaluated by response frequency and calculation of absolute risk reduction and number needed to treat. Those measures describe differences in event frequency between groups; they do not, by themselves, establish why a difference occurred. The record does not provide a separate endpoint result for each antibiotic, so the posted primary comparison concerns the combined infusion groups.

7. Results Posted in the Registry

• Prolonged Infusion. Continuous Piperacillin/Tazobactam, Extended Imipenem, Extended Meropenem: 83.7% (169/202) versus 88.6% (178/201) on control; risk difference -4.9 percentage points (95% CI -11.6 to 1.8), risk ratio 0.94 (0.87–1.02); unadjusted two-proportion z-test p = 0.156.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is binary: a participant either met the registry definition of clinical response or did not. For a binary outcome, a risk ratio compares the response frequency in one group with the response frequency in the other. A value of 1 represents equal frequencies on the relative scale. Values below or above 1 indicate lower or higher response frequency in the numerator group, respectively. The sponsor reports a risk ratio of 0.95 for prolonged infusion compared with intermittent infusion.

What does the confidence interval add?

A confidence interval describes the uncertainty around an estimate under the statistical model used. The sponsor's 95% confidence interval for the risk ratio is 0.87 to 1.02. Because the interval includes 1, it includes no relative difference. It also includes values below and above 1, so the result does not sharply determine the direction of the relative association. A confidence interval is not a guarantee that the true effect lies in the interval, and it does not incorporate uncertainties that were not represented in the analysis, such as problems with outcome measurement or missing data.

What does the p-value test?

The registry reports a chi-squared analysis with p = 0.156. In general, a p-value describes how unusual data at least as incompatible with a specified null hypothesis would be if that hypothesis and the model assumptions were true. It is not the probability that the null hypothesis is true, nor a measure of clinical importance. The registry identifies the analysis type as superiority. The reported p-value does not provide evidence meeting a conventional 0.05 significance threshold, but that alone does not establish equivalence or rule out effects that the interval still permits.

Why can the risk difference be useful?

The risk difference expresses the absolute difference in event frequency between groups, whereas the risk ratio expresses a relative comparison. Absolute differences can help readers understand the scale of a contrast in the study population. The registry says that absolute risk reduction and number needed to treat were used in evaluating efficacy. The analysis includes an unadjusted recalculation from the posted summaries, but the sponsor's reported risk-ratio analysis is the reported inferential result. No additional interpretation should be attached to a recalculation beyond what its unadjusted basis supports.

Why might over-dispersion matter?

General statistical explanation: over-dispersion occurs when observed variability is greater than a model expects. It is especially relevant to count outcomes or clustered observations, because a model that assumes too little variability can produce uncertainty estimates that are too narrow. The primary endpoint is reported as a count of participants with a binary response, and the sponsor used a chi-squared method. The registry does not report an over-dispersion assessment or a model-based adjustment for clustering, so whether either issue was evaluated is not reported in the registry record.

What does randomization establish, and what remains unknown?

General statistical explanation: random assignment is intended to make groups comparable, on average, with respect to both measured and unmeasured baseline factors. That benefit depends on how assignment was implemented and on how participants were retained and analyzed. The registry labels allocation randomized, but the sequence generation and concealment procedures are not reported in the registry record. Masking is listed as none. The record does not describe blinding of outcome assessors, the analysis population, or handling of protocol deviations. These omissions limit assessment of how the design was carried through into the reported result.

The posted result is for the pooled prolonged-infusion and intermittent-infusion groups. The registry does not report separate tests or estimates for the three antibiotics, nor does it describe adjustment for multiple comparisons. The single reported primary comparison should therefore be read as the overall comparison presented in the record, not as evidence about each drug separately. The statistical methods and findings for unreported analyses cannot be inferred from the posted result.

10. Confidence Intervals and Precision

The sponsor-reported risk ratio is 0.95, and its 95% confidence interval ranges from 0.87 to 1.02. The interval is the main summary of statistical precision for the reported relative comparison: it shows that the estimate is uncertain enough to include the value 1, which represents equal response frequency on the risk-ratio scale. It also extends to values below and above 1, so the posted result does not establish a single direction of relative difference.

The p-value is 0.156. It is consistent with the confidence interval's inclusion of no relative difference, but neither statistic proves that the groups are equivalent. Demonstrating equivalence or non-inferiority would require a prespecified margin and an analysis designed for that question; such a margin and analysis are not reported in the registry record.

Precision depends in part on the number of participants and the number of outcome events, but also on the analysis method and study design. The primary outcome counts are 178 of 201 in the intermittent group and 169 of 202 in the prolonged group. The registry lists an enrollment of 426, while the posted primary outcome denominators sum to fewer participants than that enrollment. The reasons for the difference are not reported in the registry record, so it is not possible to determine from the record whether this reflects exclusions, missing outcome data, or another reporting feature.

The confidence interval reflects uncertainty under the reported analysis, not every possible source of uncertainty. It does not quantify potential effects of open-label conduct, outcome assessment, antibiotic selection, or unreported missing-data decisions. Separate confidence intervals by antibiotic are not reported, and the combined estimate should not be interpreted as demonstrating that precision was the same for each regimen.

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 sample-size figures are planning illustrations based on the observed effect, not the trial's original design assumptions. For this binary-outcome comparison, the figures are participants per arm, not total events. The listed 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 80% power column means the number of participants per arm estimated to provide an 80% chance of detecting the specified effect under those planning assumptions, if that effect and the assumptions were correct. The 90% power column gives the corresponding planning number for a 90% chance. These are hypothetical design calculations, not evidence about the probability that the trial's result is correct. This is not observed power.

The rows consider planning for 100%, 75%, and 50% of the observed effect. Smaller effects require more participants to detect under the same assumptions, so the participant counts increase as the target effect becomes smaller. The illustrations do not show what the original trial planned or establish that the trial was adequately powered for its original question. The trial's own sample-size justification, original effect assumption, and design power are not reported in the registry record.

The curve should be read as a visual representation of the same planning relationship: the required participants per arm depend on the target effect size and desired power. It is not an observed outcome curve and does not change the assumptions underlying the listed calculations.

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 = 0.886; treatment proportion p₁ = 0.837; average p̄ = 0.861.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.4891 = 0.9586.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.4879 = 0.4106.
4. n = (0.9586 + 0.4106)² / (-0.0489)² = 782.8, rounded up to 783 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 <- 0.885572139303483                          # control proportion
p1 <- 0.836633663366337                          # 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(3019965)
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 = 783 (80% power), 1,048 (90% power)
 75% of observed effect: n per arm = 1,341 (80% power), 1,795 (90% power)
 50% of observed effect: n per arm = 2,900 (80% power), 3,881 (90% power)
power.prop.test: 782.8 
Simulated power at n = 783 per arm: 0.803 (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 reports the sponsor's primary analysis as a chi-squared comparison of risk ratios: 0.95, with a 95% confidence interval from 0.87 to 1.02 and p = 0.156. The unadjusted recalculation uses the posted participant counts and is a separate check based on summary data, not a replacement for the sponsor's analysis. No discrepancy is flagged between the sponsor result and the recalculation.

The sponsor's analysis is the result to prioritize when describing the trial's reported inferential finding. The recalculation can help readers see how an unadjusted comparison relates to the posted counts, but it cannot reproduce any analysis details that are not reported, such as participant-level adjustments or handling of missing outcomes. The registry does not report such adjustments for the primary analysis.

Both estimates concern the combined prolonged-infusion group compared with the combined intermittent-infusion group. Neither establishes a separate result for piperacillin/tazobactam, imipenem, or meropenem. The reported result should be interpreted with its confidence interval and the limitations of the registry description, rather than as a definitive statement of equivalence or of the effect of every individual regimen.

14. Multiplicity, Missing Data and Analysis Populations

The registry reports one primary outcome, clinical response, and lists adverse events as a secondary outcome. It also reports a primary chi-squared analysis. Whether additional outcomes, subgroups, or alternative analyses were tested but not posted is not reported in the registry record. A complete multiplicity plan, including any hierarchy or adjustment for multiple comparisons, is not reported in the registry record.

Multiplicity matters because conducting many statistical tests can increase the chance of obtaining at least one apparently notable result by chance. General statistical explanation: a prespecified primary outcome and analysis help clarify which result is intended to carry the main confirmatory interpretation. The registry identifies the primary outcome and reports a superiority analysis, but details of a broader prespecified statistical analysis plan are not reported in the registry record. No adjustment for multiple testing is described in the posted analysis.

The primary outcome counts include 201 participants in the intermittent group and 202 in the prolonged-infusion group, whereas the registry lists total enrollment of 426. Reasons for the difference are not reported in the registry record. The record does not state how missing primary outcomes were handled, whether all randomized participants were included in the analysis, or whether any participants were excluded after randomization. It also does not report an intention-to-treat or per-protocol analysis population.

The clinical-response definition includes an indeterminate outcome when evaluation was not possible, but the number of participants classified as indeterminate is not reported separately. The registry does not describe imputation, sensitivity analyses for missing outcomes, or the timing and completeness of outcome assessment. These omissions prevent assessment of whether missingness or analysis exclusions could affect the estimated comparison.

The record labels allocation randomized, but the randomization sequence method and concealment procedures are not reported. Masking is listed as none; whether outcome assessors were masked is not reported in the registry record. These design and analysis details are relevant to interpretation, especially for a clinical endpoint requiring assessment of signs and symptoms.

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 1.49% reporting threshold.

Most frequent non-serious adverse event terms

The posted serious adverse-event counts show 0 participants affected among 201 at risk in the intermittent group and 0 among 202 at risk in the prolonged-infusion group. For other adverse events, the counts are 1 of 201 and 3 of 202, respectively. The registry separately lists 17 deaths in the intermittent group and 19 in the prolonged-infusion group.

These are counts, not estimates of a causal effect. The record does not report the definitions used for serious and other adverse events, the observation period for these counts, event severity details, or whether events were considered related to treatment. It also does not describe how deaths relate to the adverse-event counts, so they should not be assumed to be included in, or separate from, those categories.

Zero recorded serious adverse events in both groups does not establish that serious events cannot occur, and the small number of other adverse events does not support a precise comparative safety estimate. The registry lists adverse events as a secondary outcome, but a formal statistical comparison of these counts is not reported. Read the figures as the adverse-event information posted for the enrolled groups, with the stated reporting limitations.

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

The posted data show the number of participants recorded as having a clinical response in each combined infusion group: 178 of 201 with intermittent infusion and 169 of 202 with prolonged infusion. The sponsor's reported relative comparison is a risk ratio of 0.95, with a 95% confidence interval from 0.87 to 1.02 and p = 0.156. The interval includes no relative difference, and the result does not meet a conventional 0.05 significance threshold.

This does not prove that the infusion strategies are equivalent, nor does it establish that one strategy is better. The confidence interval remains compatible with a range of relative effects, and the registry does not report an equivalence or non-inferiority margin. The p-value alone cannot determine the size or importance of an effect.

The result is pooled across three antibiotics in each group. It therefore does not establish the response comparison for any individual drug, and the registry does not provide antibiotic-specific estimates. It also does not report how antibiotic selection was made. The posted inference concerns the combined strategies as defined by the record.

The trial is described as randomized and open-label, but details of allocation procedures, outcome-assessor masking, missing-data handling, and analysis populations are not reported. The difference between total enrollment and the primary outcome denominators is not explained. These gaps limit how fully the result can be assessed.

The safety counts are descriptive and lack details about event definitions, timing, and attribution. They should not be interpreted as proving that a strategy caused or prevented an adverse event. Overall, the registry provides a comparison with uncertainty, not a definitive conclusion about clinical equivalence, individual antibiotics, or safety beyond the posted counts.

17. Why This Trial Matters Statistically

This trial raises a statistical question that is common in comparative clinical research: how should a pooled estimate be interpreted when each study strategy contains more than one drug regimen? The posted result combines piperacillin/tazobactam, imipenem, and meropenem within each infusion group. The overall risk ratio summarizes that combined comparison, but it does not reveal whether effects differ by antibiotic. Because separate results and the rule for choosing an antibiotic are not reported, readers should avoid treating the pooled estimate as a drug-by-drug finding.

The confidence interval also matters as much as the point estimate. A risk ratio of 0.95 may look close to 1, but the interval from 0.87 to 1.02 includes values both below and above 1. This illustrates why a non-significant result is not the same as evidence of equivalence. Precision and the range of effects compatible with the analysis are central to interpretation.

The record provides a sample-size planning illustration based on the observed effect, but the original design assumptions are not reported. This makes it important to distinguish a retrospective planning calculation from the trial's own sample-size justification. Such illustrations can show how smaller target effects require larger planned samples, but they cannot recover the rationale used when the trial was designed.

Finally, the clinical response and adverse-event results are only as interpretable as their definitions, assessment, and analysis. The record gives a response definition and counts, but does not describe missing-data handling, outcome-assessor masking, or the analysis population. These reporting details are not peripheral: they determine how confidently the statistical comparison can be connected to the trial's design and conduct.

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 primary outcome denominators are 201 and 202, while the registry lists enrollment of 426. The reason for this difference is not reported in the registry record. The record does not say whether participants were excluded from the primary analysis, had missing outcomes, or were handled in another way.

The outcome is pooled across three antibiotics in each group. Antibiotic-specific response counts and estimates are not reported, and the method for selecting the antibiotic is not reported. This limits interpretation of the combined comparison and does not permit conclusions about any one drug regimen.

The registry labels allocation as randomized and masking as none, but does not report the random sequence generation, concealment, or whether assessors of clinical response were masked. The method used to assess response and the handling of early discharge are also not described in detail. These features matter because the endpoint depends on assessing signs and symptoms.

The record does not report the primary analysis population, missing-data methods, protocol deviations, or sensitivity analyses. It also does not report an original sample-size justification, the trial's planned effect assumption, or a full statistical analysis plan. Multiplicity handling is not described. These omissions make it difficult to evaluate the intended analysis and the robustness of the posted estimate.

Safety reporting is limited to counts of participants affected and deaths. Definitions, observation periods, event attribution, and the relationship between death counts and adverse-event categories are not reported. No formal comparative safety analysis is posted. These limitations apply to the interpretation of the registry results and do not establish that unreported analyses or procedures were or were not performed.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Efficacy of Betalactam Antibiotics in Prolonged Infusion Compared to Intermittent in Pediatric Patients With Sepsis — NCT03019965.
• Registry record last updated 2021-08-05; status last verified 2021-07.
• Results first posted 2021-08-05.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

22. Record Summary

The registry describes a completed, randomized, parallel-group trial with no masking, an enrollment of 426, and a study population of children with sepsis. It compares prolonged infusion of piperacillin/tazobactam, imipenem, or meropenem with intermittent infusion of those antibiotics. The primary outcome is clinical response assessed after antibiotic cessation.

The posted primary counts are 178 of 201 in the intermittent group and 169 of 202 in the prolonged-infusion group. The sponsor reports a risk ratio of 0.95, a 95% confidence interval of 0.87 to 1.02, and p = 0.156. Adverse-event counts and deaths are also listed. The registry record does not report several design and analysis details, including missing-data handling, the analysis population, and the original sample-size justification.