Determination of the ED90 for Epidural Hydromorphone and Morphine for Postoperative Pain Using a Biased-Coin Up-and-Down Sequential Design After Elective Cesarean Delivery

Introduction

Effective management of postoperative pain following cesarean delivery is critical, as inadequate analgesia is associated with several adverse outcomes, including chronic pain, opioid dependence, impaired functional recovery, and a higher incidence of postpartum depression.^1,2 Unlike postoperative analgesia for other surgical procedures, pain control after cesarean delivery must provide sufficient relief while preserving maternal–infant bonding and ensuring breastfeeding safety. A multimodal analgesic regimen is currently considered the standard of care. Such protocols typically incorporate long-acting neuraxial opioids alongside scheduled non-opioid medications, such as acetaminophen and nonsteroidal anti-inflammatory drugs (NSAIDs).³

Combined spinal-epidural anesthesia (CSEA) is widely employed for cesarean delivery, as this technique not only provides the rapid onset of spinal anesthesia but also allows intraoperative adjustment of the anesthetic level or postoperative prolongation of analgesia via epidural supplementation of local anesthetics.⁴ Furthermore, postoperative analgesia via the epidural catheter reduces the use of systemic analgesic drugs and their associated side effects.^5,6 Opioids mediate their analgesic effects by binding to spinal opioid receptors. Owing to their limited systemic absorption, the likelihood of transfer into breast milk and subsequent neonatal absorption is reduced. Moreover, this approach significantly reduces the need for intravenous analgesics during the first 24 hours postoperatively,⁷ positioning it as a recommended option for post-cesarean analgesia.⁸ Nevertheless, epidural opioid administration is associated with potential adverse effects, including delayed respiratory depression, pruritus, and nausea and vomiting.⁹

Currently, hydromorphone and morphine are the primary opioids recommended for epidural analgesia.¹⁰ Hydromorphone is less hydrophilic, resulting in a faster onset and shorter duration of action. Previous research indicates that the first request for supplemental analgesia occurs approximately 13 hours after epidural hydromorphone administration,¹¹ with typical dosing regimens ranging from 0.2 to 0.6 mg.¹² In contrast, morphine, a hydrophilic opioid, has a long-lasting effect; studies have shown that its analgesic effect can persist for up to 20 hours after epidural administration.^11,13 However, evidence suggests that increasing the epidural dose beyond 3.75 mg does not yield a corresponding improvement in analgesic efficacy.¹⁴ Despite this, there remains a knowledge gap regarding the optimal epidural hydromorphone dose, which is less well established than that of morphine.

The primary objective of this study was to determine the 90% effective dose (ED90) of epidural hydromorphone and morphine for patients undergoing post-cesarean analgesia, using a biased-coin up-and-down sequential allocation method.¹⁵ The biased-coin up-and-down sequential design is an efficient and widely recognized method for exploring dose-response relationships and estimating specific quantiles (eg., ED90) with the minimum required sample size. Secondary objectives included comparing postoperative pain scores, total opioid consumption, and the incidence of adverse effects (nausea/vomiting, pruritus, respiratory depression, and neonatal outcomes) between patients receiving epidural hydromorphone and those receiving epidural morphine.

Methods

Ethics

The study population comprised women who underwent cesarean delivery at Sichuan Provincial People’s Hospital between May and December 2024. The study was approved by the Institutional Ethics Committee (approval number: 2024177) and registered with the Chinese Clinical Trial Registry (registration number: ChiCTR2400084510).

Patients

All patients provided written informed consent. Inclusion criteria consisted of full-term primiparous women undergoing cesarean delivery with an American Society of Anesthesiologists (ASA) status of II or III. Exclusion criteria were as follows: contraindications to CSEA, opioid allergy, a history of analgesic abuse, concurrent additional surgery (eg., tubal ligation or myomectomy), intraoperative administration of the long-acting local anesthetic ropivacaine via the epidural route, conversion to general anesthesia, a previous history of cesarean delivery, voluntary withdrawal from the study, or the need for reoperation due to significant postoperative hemorrhage.

Study Design

Upon arrival in the operating room, patients were monitored with electrocardiography, non-invasive blood pressure, and pulse oximetry, and intravenous access was secured. CSEA was performed at the L3-4 or L2-3 interspace. Following identification of the epidural space, 10 mg of bupivacaine (0.5%, 2 mL) was injected intrathecally. An epidural catheter was then inserted 4 cm cephalad. Ten minutes after completing the puncture, the anesthetic level was assessed. If the level of anesthesia was below T4 as assessed by cold/pinprick, the epidural catheter was aspirated to confirm the absence of blood or cerebrospinal fluid, followed by a test dose of 3 mL of 2% lidocaine administered via the epidural route to exclude the possibilities of total spinal, high spinal, and local anesthetic systemic toxicity. Thereafter, an additional 3–5 mL dose was administered to ensure achievement of a T4 sensory block level. Blood pressure was maintained within 20% of baseline using vasopressors (ephedrine/phenylephrine) and fluid resuscitation. Oxytocin was administered post-delivery as required. For intraoperative pain, intravenous esketamine (10–30 mg) was administered, along with 10 mg of dexamethasone for antiemetic prophylaxis.

Based on existing literature and prior institutional experience, the initial doses for postoperative epidural analgesia were set at 400 µg for hydromorphone and 2 mg for morphine.^14,16 A designated anesthesiologist (Doctor A) determined whether the patient should receive hydromorphone or morphine based on a random number sequence. The dose for each subsequent patient in a given drug group was determined by the outcome of the preceding evaluable patient using a biased-coin rule targeting the ED90 (τ = 0.9). The biased-coin probability was (1 − τ)/τ ≈ 0.11 (ie., 1/9). If the previous patient experienced inadequate analgesia, the next patient received the next higher dose. Conversely, if analgesia was satisfactory in the previous patient, the subsequent dose was determined by a biased-coin toss: the probability of de-escalating to the next lower dose was 1/9, and the probability of maintaining the current dose was 8/9. Inadequate analgesia was defined as VAS scores for movement or rest > 3 points within 12 hours after surgery, or the need for additional hydromorphone via a patient-controlled intravenous analgesia (PCIA) pump. Satisfactory analgesia was defined as VAS scores for both movement and rest ≤ 3 points within 12 hours after cesarean delivery, with no requirement for additional opioid analgesics.¹⁷

The epidural doses for hydromorphone were as follows:

150–200-250-300-350-400-450-500-550-600µg.

The epidural doses for morphine were as follows:

1–1.5-2-2.5-3-3.5–4mg.^18,19

Note: The starting dose for each sequence is in bold.

Following the determination of the drug formulation by the attending anesthesiologist (Doctor A), the study medication was prepared by an anesthetic nurse (Nurse C) according to the protocol. Hydromorphone and morphine for postoperative epidural analgesia were diluted with normal saline to concentrations of 0.01% and 0.1%, respectively. No local anesthetics were added to the solutions, and the syringes were covered with opaque labels to ensure blinding. The prepared solution was administered via the epidural catheter upon completion of uterine suture closure. Postoperative analgesia consisted of scheduled oral extended-release acetaminophen (650 mg every 6 hours for 4 doses) and a hydromorphone PCIA pump (50 µg/mL; 200 µg bolus; 20-minute lockout). Oral oxycodone (5 mg) was available for refractory pain. Patients were continuously monitored on the ward, with granisetron (1 mg IV) available for nausea and naloxone (0.2 mg IV) for respiratory depression (respiratory rate < 8 breaths/min).²⁰ If the patient experienced intolerable pruritus, 0.5 mg of butorphanol could be administered intravenously.

A blinded anesthesiologist (Doctor B) was responsible for collecting all outcome data, which were then reported to Doctor A. Doctor B was unaware of the drugs used for postoperative epidural analgesia. VAS pain scores (0–10, where 0 = no pain and 10 = worst imaginable pain) were documented at rest and during movement (eg., coughing) at 6, 12, and 24 hours postoperatively. The incidence and severity of adverse effects, including nausea, vomiting, pruritus, and respiratory depression, were also recorded. The severity of nausea and pruritus was graded based on patient self reports using a 4 point scale (0 = none, 1 = mild, 2 = moderate, 3 = severe). Additionally, Doctor B collected demographic and clinical data from the hospital information system, including maternal age, body mass index (BMI), gestational age, neonatal weight, Apgar scores, and the total 24 hour consumption of oxycodone, granisetron, butorphanol, and hydromorphone.

Statistical Analysis

Statistical analysis was performed to determine the ED90 using an up-down sequential allocation method with a biased-coin design, which improves the precision of ED90 estimation. The up-down allocation method is characterized by non-independent observations and an unknown data distribution, which precludes the rigorous derivation of theoretical guidelines and complicates sample size calculation. In most simulation scenarios, it was determined that a sample size ranging from 20 to 40 cases would yield stable estimates of the target dose.^21,22 Accordingly, 40 cases per group (80 cases total) were included in the study. The data for hydromorphone and morphine were analyzed separately using isotonic regression with the pooled-adjacent-violators algorithm to derive the modified isotonic estimator for the ED90 dose. A bootstrap method was used to construct 95% confidence intervals (CI) for the ED90 and for the probability of success at the ED90.

Data were analyzed with SPSS (version 22.0) and are presented as mean ± standard deviation (SD), median (interquartile range [IQR]), or n (%). Group comparisons were made using independent samples t tests (for normally distributed continuous data), Mann–Whitney U-tests (for non normally distributed continuous data), chi square tests, or Fisher’s exact tests (for categorical data), as appropriate. Fisher’s exact test was specifically used for the following complications: nausea, vomiting, and pruritus. All tests were two tailed, with a significance level of P < 0.05. An exploratory analysis was performed for dose levels that were administered to at least 10 patients.

Results

Between May and September 2024, 104 patients were enrolled in the study. In the hydromorphone group (n = 50), five participants voluntarily withdrew and five were excluded due to nonadherence to the acetaminophen regimen. Similarly, in the morphine group (n = 54), nine withdrew and five were excluded for the same reason. Consequently, 40 patients per group were included in the final analysis (Figure 1). No participant developed respiratory depression or excessive sedation on the ward. There were no significant differences between the two groups in baseline patient characteristics or in newborn Apgar scores (Table 1).

Table 1 Baseline Characteristics in Patients Who Received Hydromorphone or Morphine

Figure 1 The flow chart for the study.

Figures 2 and 3 present the results of the biased-coin up-and-down dose allocation. Isotonic regression analysis yielded an ED90 of 500 µg (95% CI, 495.00–532.50 µg) for epidural hydromorphone and an ED90 of 3 mg (95% CI, 2.97–3.21 mg) for epidural morphine. Effective analgesia was achieved in 19/21 (90.5%) patients receiving 500 µg of epidural hydromorphone and in 20/22 (90.9%) patients receiving 3 mg of epidural morphine. No statistically significant differences were observed between the hydromorphone (500 µg) and morphine (3 mg) groups with respect to VAS scores at 6, 12, and 24 hours, the incidence of nausea, vomiting, and pruritus, or hydromorphone consumption (Table 2).

Table 2 Comparison of VAS Scores, Number of Adverse Events, and Postoperative Hydromorphone Consumption Between the Hydromorphone 500 µg and Morphine 3 mg Groups

Figure 2 The up-down sequences of administered doses of epidural hydromorphone.

Figure 3 The up-down sequences of administered doses of epidural morphine.

A comparative analysis of adverse effects between the 400 µg and 450 µg hydromorphone groups, or between the 2 mg and 2.5 mg morphine groups, was not feasible owing to insufficient sample sizes. Therefore, the analysis focused on the hydromorphone groups receiving 500 µg and 550 µg and the morphine groups receiving 3 mg and 3.5 mg. Postoperative outcomes, including VAS pain scores at 6, 12, and 24 hours, the incidence of nausea and vomiting, the incidence of pruritus, and total hydromorphone consumption from the PCIA pump, were compared. No statistically significant differences were observed in any of these outcome measures between the higher dose groups (Tables 3 and 4). Additionally, no patients in this study received postoperative oxycodone, granisetron, or butorphanol.

Table 3 Comparison of VAS Scores, Number of Adverse Events and Postoperative Hydromorphone Consumption Between the 3 mg and 3.5 mg Groups of Morphine

Table 4 Comparison of VAS Scores, Number of Adverse Events and Postoperative Hydromorphone Consumption Between the 500 µg and 550 µg Groups of Hydromorphone

The incidences of nausea, vomiting, and pruritus within the first 24 postoperative hours are summarized in Table 5. Over the 24-hour period, the hydromorphone group showed a lower overall incidence of pruritus compared with the morphine group (27.5% vs 40.0%), while the incidence of nausea and vomiting was similar in the two groups (25% vs 22.5%). During the first 6 hours after surgery, the numbers of patients with pruritus and with nausea/vomiting were higher in the hydromorphone group than in the morphine group. Over time, the numbers of patients with pruritus and with nausea/vomiting in the hydromorphone group gradually decreased. In contrast, the number of patients with nausea/vomiting in the morphine group gradually decreased, whereas the number of patients with pruritus remained stable.

Table 5 Details of Postoperative Nausea, Vomiting, and Pruritus Within 24 hours in Patients Receiving Epidural Hydromorphone and Morphine

Discussion

In this study, we employed a biased-coin up-and-down sequential allocation method to determine the ED90 of epidural hydromorphone or morphine for post-cesarean analgesia, which yielded estimated values of 500 µg for hydromorphone and 3 mg for morphine. Furthermore, comparisons of adverse effects across different dosage levels and of total rescue opioid consumption revealed no statistically significant differences between the hydromorphone and morphine groups.

Liu et al used a modified Dixon up-and-down method and found that the ED90 of epidural hydromorphone was 1105 µg, which is significantly different from the findings of the present study.²³ Their study selected an initial epidural dose of 750 μg based on the empirical ratio that the epidural dose is approximately ten times the intrathecal dose;¹⁷ additionally, ropivacaine was co-administered for postoperative analgesia, and no analysis of adverse effects was performed. In contrast, our study adopted a commonly used clinical dose (400 µg) as the starting dose and demonstrated that 500 µg of epidural hydromorphone provided adequate analgesia for 90% of patients when combined with postoperative multimodal analgesia (oral acetaminophen). We also found that the incidence of postoperative pruritus and nausea/vomiting was 28.6% and 25%, respectively. Overall, the discrepancy in the estimated ED90 values between the two studies may be attributable to differences in the initial doses selected and the multimodal analgesia regimens employed. In a study by Yang et al assessing the efficacy of different doses of epidural hydromorphone (200, 400, and 600 µg) for post-cesarean analgesia, 600 µg hydromorphone combined with ropivacaine was reported to provide satisfactory analgesia, albeit with a significantly higher incidence of pruritus compared to lower doses. Similarly, a study on post-vaginal delivery analgesia showed that 500 µg epidural hydromorphone provided effective pain control.²⁴ Collectively, these findings suggest that a moderate dose of 500 µg epidural hydromorphone, when combined with non-opioid analgesics, can achieve a favorable balance between analgesic efficacy and safety. Similarly, the derived ED90 of 3 mg for epidural morphine is consistent with effective doses in prior post-cesarean studies and with recommendations from the European Society of Regional Anaesthesia and Pain Therapy,^25,26 which endorses epidural morphine doses of 2 to 3 mg as an alternative to intrathecal opioids for cesarean delivery analgesia.

From a safety perspective, no episodes of respiratory depression were observed, which is consistent with the established safety profile of standard epidural opioid doses in this setting.^13,27 Furthermore, our findings indicated that among patients receiving hydromorphone, the incidences of pruritus and nausea were most pronounced within the first 6 hours postoperatively and decreased significantly over time, although no statistically significant correlation with dosage was identified. In the morphine group, the incidence of pruritus within the initial 6 hours was lower than that in the hydromorphone group; however, new cases emerged during the subsequent 12- and 24-hour intervals. This delayed presentation may be attributed to morphine’s slower onset and longer duration of action compared with hydromorphone.²⁸ Although the severity of nausea, vomiting, and pruritus was higher in the morphine group, there were no statistically significant differences in the incidence of these adverse effects between the two groups. Similarly, a study by Marroquin et al found no significant differences in the incidence of nausea and vomiting, or in the use of antiemetic and antipruritic medications, between patients receiving 600 µg of epidural hydromorphone and 3 mg of epidural morphine, although that study did not standardize the use of antiemetics.¹¹ Most studies suggest that opioid-induced pruritus was a dose-dependent adverse effect.²⁹ However, Palmer et al suggested that the threshold dose of epidural morphine for inducing pruritus is relatively low (below 1.25 mg), and that the incidence and severity of pruritus and nausea/vomiting may be independent of the epidural morphine dose.³⁰ Nevertheless, the number of parturients in each dose group in that study was only 12, which may have resulted in insufficient statistical power.

This study has several limitations. First, although the up-and-down sequential allocation method can estimate the dose effective for a specific percentage of patients, it cannot guarantee that this dose is appropriate for all patients. Therefore, in clinical practice, the administered dose should be individualized according to each patient’s specific conditions. Second, despite the fact that pain assessments were conducted by the same anesthesiologist for all patients, the resulting pain scores are inherently subjective. Third, as this was a single center study that included only healthy women undergoing elective cesarean delivery, the obtained ED90 value may not be directly generalizable to patients undergoing emergency cesarean delivery or to those with severe comorbidities, such as preeclampsia or morbid obesity.

Conclusion

In conclusion, using a biased-coin up-and-down sequential design, we estimated the ED90 for post-cesarean analgesia to be 500 µg for epidural hydromorphone and 3 mg for epidural morphine. No statistically significant differences in adverse effects were observed between the two drugs at their respective ED90 doses.