Supplementary material C — Exploratory Literature Search – The inherent bias in studies reporting outcomes using total opioid burden metrics: a simulation study

C.1 Introduction

Given the mathematical proof and the results of the simulation, an exploratory search of the literature was performed to establish a formal systematic literature search protocol. The intention of the literature search is to understand to what extent does the current literature describe TOB methodology and if it was possible to estimate the bias in published works. To formally calculate the bias the error in the conversion value is needed which requires the knowledge of the biological ground truth. As this is not possible, a range of different conversion values, each with their own unknown error was used to as a proxy for a range of conversion value errors.

C.2 Methods

A informal search of literature to understand the use of opioid equivalence metrics in peri-operative and surgical studies published in 2025 was performed. A search of the PUBMED database was performed on 7th July 2026 using the following search string.

PUBMED search term

((((((“opioid equivalent” OR “oral morphine equivalence” OR “oral morphine equivalent” OR “oral morphine equivalents” OR “OME” OR “morphine milligram equivalents” OR “morphine milligram equivalence” OR “MME” OR “morphine equivalent daily dose” OR “MEDD”) AND (“perioperative” OR “peri-operative” OR “postoperative” OR “post-operative” OR “surgical” OR “surgery” OR “post-surgical” OR “postsurgical”))) AND (“2025/01/01”[Date - Publication] : “2025/12/31”[Date - Publication]))) AND (“clinical trial”[Filter] OR “clinical trial” OR “controlled clinical trial” OR “randomized controlled trial” OR “interventional” OR “intervention study” OR “clinical trials as topic”[MeSH Terms] OR “cohort studies”[MeSH Terms] OR “cohort” OR “prospective” OR “retrospective” OR “case-control” OR “comparative study” OR “evaluation study”))

Primary and full text screening was carried out using the inclusion criteria detailed in Table C.1 by one author.

Table C.1: Litrature extraction proforma

Criteria	Include	Exclude
Population	All patient groups undergoing a surgical procedure	Patients not undergoing surgical procedures. Non-human studies
Concept	Studies using a total opioid burden metric as a primary or secondary outcome (Such as oral morphine equivalence (OME), milligram morphine equivalence (MME) or opioid equivalence)	Outcomes not including opioid totals
Context	Patients undergoing surgical procedures	Palliative care studies or Pharmacology studies
Other	Any studies comparing a control against and intervention or two interventions.

Papers where ordered randomly within the Covidence platform and data was extracted from a random subset by a single author as presented by the platform¹. Primary Data extraction was performed using a drop down selection proforma including study design, methodology and reporting of total opioid metrics. Free text notes were collected to aid secondary data collection.

For each paper where group average doses of each opioid were described, these were extracted. If only median values were provided, an estimated mean was calculated using Wan’s 2014 approximation (\(\hat{d_i} = \frac{Q_1 + M + Q_3}{3}\) ) to preserve the linearity with in the arithmetic mean². Where opioid routes where not provided then IV was assumed and where conversion values were not provided, the Nielsen set was used³.

The group mean of total opioid burden reported by the paper was extracted. Then using the mean doses and the conversion values provided, the group mean was calculated independently. Following this, all possible group means were calculated by applying each of the possible values provided in Table 1 of Neilsens Conversion set (summarised in Table C.2), as the range of plausible conversion values an author may use³.

Table C.2

Medication	Conversion values
morphine	2
fentanyl	100, 150, 200, 300
oxycodone	3
tramadol	0.1, 0.2, 0.25
hydromorphone	15, 20
hydrocodone	1, 1.33

C.3 Results

C.3.1 Reporting of opioid burden metrics

480 studies were identified in the rapid literature search, a sample of 83 that fit the eligibility had data extracted. The majority of studies were cohort studies and most common intervention was anaesthetic interventions (Figure C.1).

Figure C.1: **Study design and intervention types in included literature** - Bar charts summarising the study design and intervention type of studies included in the rapid literature review. Left panel shows count by study design; right panel shows count by intervention type.

With regards to the opioid conversion sets used, 24 (29%) cited another source, whilst 3 (4%) included the conversion values within the paper. 56 (67%) papers did not include any citation or description of the opioid conversion sets used. 8 (10%) papers described the proportions of different opioids between intervention groups (Figure C.2). Of these 8 papers, 3 provided count data only and not mean/median dose for each opioid within treatment groups.

Figure C.2: **Opioid conversion set reporting and within-group proportion documentation** - Heatmap showing the count of studies by opioid conversion set type and whether opioid proportions within groups were reported. Cell counts are displayed as text labels.

C.3.2 Impact of varying conversion values on studies

Table C.3 details the 5 studies where opioid proportions could be recovered. Of note, only Baran cited a opioid conversion set⁴, all other authors did not describe which value sets were used. Two studies were randomised controlled trials (RCT), whilst the remainder were retrospective cohort studies. With regards to the interventions analysed, in this subset, all were concerning analgesia either during or after the surgical procedure and were classed as anesthesia interventions.

Table C.3: Summary table of litrature articles that presented breakdown by opioid groups.

Authors	Title	Study design	Population	Control group	Intervention group	Opioid conversion set included
Baran 2025	Optimizing Analgesia After Minimally Invasive Cardiac Surgery: A Randomized Non-Inferiority Trial Comparing Interpectoral Plane Block Plus Serratus Anterior Plane Block to Erector Spinae Plane Block.	RCT	Patients aged 18–75 years scheduled for their first minimally invasive cardiac surgery with ASA score I-III	Erector spinae plane block (ESPB)	ESPB plus Serratus anetrior plane block	Cited
Fedorka 2025¹	Liposomal Bupivacaine + Bupivacaine Versus Bupivacaine Interscalene Nerve Block Effect on Pain After Rotator Cuff Repair: A Randomized Control Trial.	RCT	Adults undergoing arthroscopic rotator cuff repair with a planned interscalene nerve block	Bupivicaine	Liposomal bupivicaine	Not described
Carter 2025²	Inpatient Multimodal Pain Regimens Do Not Impact Hospital Length of Stay or Long-term Postoperative Opioid Use Following 1 and 2-Level Lumbar Fusion.	Cohort study	Patients aged18 or older who had undergone either a posterior lumbardecompression and fusion (PLDF) or transforaminallumbar interbody fusion (TLIF) from 2018 to 2019	Opioid only postop analgesia	Multimodal postop analgesia	Not described
Hall 2025³	Ketamine as part of multi-modal analgesia may reduce opioid requirements following cardiac surgery: a retrospective observational cohort study.	Cohort study	Adult patients admitted for elective cardiac surgery	Standard postoperative analgesia	Postoperative analgeia with ketamine	Not described
¹ Median values provided, converted to means
² Paper divided into Tramadol OME and non-tramadol OME, Only other opioid, beside tramadol in the multi-modal group was oxycodone. Assumes IV for conversion value of oxycodone. Outcome extracted for total in-hospital OME.
³ Outcomes for Dose in PACU and total in hospital

Table C.4 provides three sets of results for the studies detailed. The first is the study reported outcomes, this is the mean total opioid burden for the control and intervention groups. From this an observed difference is calculated with a percentage change from the control. The second column set is the de-novo calculation, by using the mean dose of each opioid within each group and conversion set provided (or Neilsens if not) to attempt to calculate the control and intervention group means. From these de-novo estimates a second difference of the treatment group was calculated.

Finally, regardless of the conversion sets used, the de-novo calculation was repeated across the possible grid values of the Neilsen conversion set. The minimum and maximum possible differences were then extracted.

Table C.4: Table of reported outcomes and de-novo calalculated outcomes.

Authors	Study reported outcome			De Novo calculated outcome			Range of estimates
Authors	Control group	Intervention group	Difference	Control group	Intervention group	Difference	Lower bound	Upper bound
Baran 2025	178.0	208.8	30.8mg (17.3%)	182.1	205.1	22.9mg (12.6%)	22.9mg (12.2%)	68.8mg (12.7%)
Fedorka 2025	43.7	39.4	-4.4mg (-10.0%)	87.5	78.7	-8.7mg (-10.0%)	-13.1mg (-10.0%)	-13.1mg (-10.0%)
Carter 2025	315.0	209.0	-106mg (-33.7%)	314.5	209.0	-105.5mg (-33.5%)	-119.8mg (-40.2%)	-98.4mg (-30.5%)
Gold 2025 (PACU)	164.6	111.5	-53.1mg (-32.3%)	36.8	29.5	-7.3mg (-19.8%)	-10mg (-22.6%)	-4.6mg (-15.5%)
Gold 2025 (Hospital)	107.8	56.0	-51.9mg (-48.1%)	218.8	110.9	-107.9mg (-49.3%)	-114.3mg (-50.4%)	-101.9mg (-48.3%)
Hall 2025	118.9	90.1	-28.8mg (-24.2%)	149.1	66.7	-82.4mg (-55.3%)	-82.6mg (-55.4%)	-81.5mg (-53.3%)

This table highlights the difficulty in re-calculating the total opioid burdens that the authors have produced. This is likely due to a number of assumptions as details in the methods such as estimating mean values from medians and assuming medication routes. Only one study, Fedorka 2025, showed no sensitivity to the conversion value set used⁵. This is because, in the RCT only oxycodone was used in the post-operative period, as so whilst the group estimates may vary, the treatment effect percentage is fixed at 10%.

Figure C.3 demonstrates the reported difference in opioid burden (red cross) compared to the de-novo calculated difference (green cross). When the the grid search of the possible combinations of the values used by Neilsen was performed, the minimum and maximum values are demonstrated by the orange whiskers.

Figure C.3: Forest style plot illustrating the percentage change in opioid use associated with an intervention. Blue cross denote the study reported outcome. Orange diamond and error bar denote the the primary point estimate and range using different conversion values.

C.4 Discussion

There were some key learning points from the preliminary data collection that was integrated into the protocol as presented in Supplementary material D.

Search strategy - A single database was used for speed and ease, this was expanded to include 2 further databases sources.

Screening - A single reviewer with no verification was performed for speed and ease, a formal screening strategy was defined in the protocol. The inclusion criteria was narrowed to only include interventional study, this was due to a number of non-comparative observational trials being included in the primary data extraction. The full text screening stage was integrated into the primary data extraction in the proforma.

Data extraction - The primary and secondary data collection proformas were formalised in the protocol. For each field a descriptor was included to further define the value to be entered. The primary data collection proforma was focused to remove data points that were deemed no longer required.

Analysis plan - The analysis plan was formalised and analysis script defined.