Statistical Concerns Regarding the Sample Size Justification in a Randomized Comparison of DPE and Standard Epidural PIEB Intervals for Labor Analgesia [Letter]

Dear editor

We read with great interest the recent article by Yang et al comparing the optimal programmed intermittent epidural bolus (PIEB) intervals between dural puncture epidural (DPE) and standard epidural techniques for labor analgesia.1 We commend the authors for their rigorous randomized double-blinded design and thoughtful refinement of the “effective analgesia” definition to better reflect clinical practice. However, we wish to raise several methodological considerations that may help readers interpret the findings more accurately.

First, the sample size justification warrants careful scrutiny. The authors stated that “enrolling a minimum of 32 participants in each group would yield a power greater than 90% to detect a 5-minute difference in EI90 values between groups”, assuming α=0.05. This statement invokes the conventional two-sample mean test framework. However, the BCUD design used in this study is specifically designed to estimate a target quantile within a single group using sequential allocation and isotonic regression;2,3 it does not inherently support a between-group hypothesis test for two independent means.2 Because each participant’s PIEB interval depends on the preceding participant’s response, the data are not independent of the draws from a common distribution. The only valid between-group quantity is the comparison of the two group-specific quantile estimates. However, the authors did not perform any formal between-group statistical tests on the primary outcome; no P-value or 95% confidence interval for the difference in EI90 between the two groups was reported in the study. Thus, the stated power calculation employs a framework that is conceptually misaligned with the BCUD design and does not correspond to any actual inferential analysis conducted. We would respectfully suggest that the authors clarify the actual model and variance assumptions underlying this calculation or reframe it as a precision-based sample size justification for estimating each group’s EI90 separately.

Second, the final isotonic regression estimates yielded 95% confidence intervals of 35.0–52.3 min for the DPE group and 33.0–49.7 min for the standard group. The widths of these intervals (17.3 and 16.7 min) are more than three times the purported 5-minute detectable difference. In BCUD designs, estimation precision is a central design consideration, and such wide intervals suggest only modest precision for point estimates. Furthermore, this study used a 10-minute step size for PIEB interval adjustments. While isotonic regression can produce interpolated estimates that are not multiples of the step size, a design with a 10-minute resolution inherently constrains the precision available for detecting a 5-minute difference. Notably, the observed between-group difference in EI90 was 4.5 min —essentially the same magnitude as the 5-minute difference the study was purportedly powered to detect, yet no formal test was performed. Indeed, the reported intervals are visibly asymmetric (for the DPE group, 41.7 minutes lies 6.7 minutes above the lower bound but 10.6 minutes below the upper bound), departing from the symmetric normal approximation framework implicit in the stated power calculation. If the two intervals were combined under the independence assumption, the 95% CI for the between-group difference would span roughly −7.5 to 16.5 min, covering clinically meaningful effects in both directions.

Third, while overlapping 95% confidence intervals suggest no statistically significant difference, they do not establish equivalence or the absence of a clinically meaningful effect.2 The authors concluded that “the DPE technique did not exert a clinically meaningful effect”, implying a claim of equivalence; however, no formal non-inferiority or equivalence test with a prespecified margin was performed. We note that the authors themselves acknowledge in the Discussion that the BCUD-derived sample size is “suited for estimating EI90” but “precludes inferential analysis of secondary outcomes”. While this acknowledgment specifically addresses secondary outcomes, it sits uneasily with both the claim of >90% power for a between-group EI90 difference and a conclusion asserting the absence of a clinically meaningful effect without any formal between-group tests. Therefore, we respectfully suggest that the conclusion be framed as “no statistically significant difference was detected between the two groups” rather than “no clinically meaningful effect”, unless an equivalence test with a predefined margin is performed.

For future studies comparing BCUD-estimated parameters between groups, we would encourage post-hoc bootstrap resampling to evaluate the precision of between-group differences. Additionally, centered isotonic regression (CIR),4 implemented in the R package cir,5 reduces bias relative to classical isotonic regression and may offer a more reliable framework for comparisons.

We fully agree that DPE does not appear to substantially alter the optimal PIEB interval and thank the authors for their valuable contribution to obstetric anesthesia. We hope that these considerations will assist in interpreting the findings and guide future research.

Disclosure

The authors declare no conflicts of interest in this communication.